Daily Papers

Beyond minimizing a single training loss, many deep learning estimation pipelines rely on an auxiliary objective to quantify and encourage desirable properties of the model (e.g. performance on another dataset, robustness, agreement with a prior). Although the simplest approach to incorporating an auxiliary loss is to sum it with the training loss as a regularizer, recent works have shown that one can improve performance by blending the gradients beyond a simple sum; this is known as gradient surgery. We cast the problem as a constrained minimization problem where the auxiliary objective is minimized among the set of minimizers of the training loss. To solve this bilevel problem, we follow a parameter update direction that combines the training loss gradient and the orthogonal projection of the auxiliary gradient to the training gradient. In a setting where gradients come from mini-batches, we explain how, using a moving average of the training loss gradients, we can carefully maintain this critical orthogonality property. We demonstrate that our method, Bloop, can lead to much better performances on NLP and vision experiments than other gradient surgery methods without EMA.

Learning a policy with great generalization to unseen environments remains challenging but critical in visual reinforcement learning. Despite the success of augmentation combination in the supervised learning generalization, naively applying it to visual RL algorithms may damage the training efficiency, suffering from serve performance degradation. In this paper, we first conduct qualitative analysis and illuminate the main causes: (i) high-variance gradient magnitudes and (ii) gradient conflicts existed in various augmentation methods. To alleviate these issues, we propose a general policy gradient optimization framework, named Conflict-aware Gradient Agreement Augmentation (CG2A), and better integrate augmentation combination into visual RL algorithms to address the generalization bias. In particular, CG2A develops a Gradient Agreement Solver to adaptively balance the varying gradient magnitudes, and introduces a Soft Gradient Surgery strategy to alleviate the gradient conflicts. Extensive experiments demonstrate that CG2A significantly improves the generalization performance and sample efficiency of visual RL algorithms.

Current text-to-image diffusion models have achieved groundbreaking results in image generation tasks. However, the unavoidable inclusion of sensitive information during pre-training introduces significant risks such as copyright infringement and privacy violations in the generated images. Machine Unlearning (MU) provides a effective way to the sensitive concepts captured by the model, has been shown to be a promising approach to addressing these issues. Nonetheless, existing MU methods for concept erasure encounter two primary bottlenecks: 1) generalization issues, where concept erasure is effective only for the data within the unlearn set, and prompts outside the unlearn set often still result in the generation of sensitive concepts; and 2) utility drop, where erasing target concepts significantly degrades the model's performance. To this end, this paper first proposes a concept domain correction framework for unlearning concepts in diffusion models. By aligning the output domains of sensitive concepts and anchor concepts through adversarial training, we enhance the generalizability of the unlearning results. Secondly, we devise a concept-preserving scheme based on gradient surgery. This approach alleviates the parts of the unlearning gradient that contradict the relearning gradient, ensuring that the process of unlearning minimally disrupts the model's performance. Finally, extensive experiments validate the effectiveness of our model, demonstrating our method's capability to address the challenges of concept unlearning in diffusion models while preserving model utility.

Boosting the task accuracy of tiny neural networks (TNNs) has become a fundamental challenge for enabling the deployments of TNNs on edge devices which are constrained by strict limitations in terms of memory, computation, bandwidth, and power supply. To this end, we propose a framework called NetDistiller to boost the achievable accuracy of TNNs by treating them as sub-networks of a weight-sharing teacher constructed by expanding the number of channels of the TNN. Specifically, the target TNN model is jointly trained with the weight-sharing teacher model via (1) gradient surgery to tackle the gradient conflicts between them and (2) uncertainty-aware distillation to mitigate the overfitting of the teacher model. Extensive experiments across diverse tasks validate NetDistiller's effectiveness in boosting TNNs' achievable accuracy over state-of-the-art methods. Our code is available at https://github.com/GATECH-EIC/NetDistiller.

Large Language Models (LLMs) have demonstrated great potential as generalist assistants, showcasing powerful task understanding and problem-solving capabilities. To deploy LLMs as AI assistants, it is crucial that these models exhibit desirable behavioral traits, such as non-toxicity and resilience against jailbreak attempts. Current methods for detoxification or preventing jailbreaking usually involve Supervised Fine-Tuning (SFT) or Reinforcement Learning from Human Feedback (RLHF), which requires finetuning billions of parameters through gradient descent with substantial computation cost. Furthermore, models modified through SFT and RLHF may deviate from the pretrained models, potentially leading to a degradation in foundational LLM capabilities. In this paper, we observe that surprisingly, directly editing a small subset of parameters can effectively modulate specific behaviors of LLMs, such as detoxification and resistance to jailbreaking. Specifically, for a behavior that we aim to avoid, we employ a linear classifier, which we term the behavior probe, to classify binary behavior labels within the hidden state space of the LLM. Using this probe, we introduce an algorithm to identify a critical subset of LLM parameters that significantly influence this targeted behavior. Then we directly edit these selected parameters by shifting them towards the behavior probe. Such a direct parameter editing method necessitates only inference-level computational resources. Experiments demonstrate that in the representative detoxification task, our approach achieves reductions of up to 90.0\% in toxicity on the RealToxicityPrompts dataset and 49.2\% on ToxiGen, while maintaining the LLM's general capabilities in areas such as common sense, question answering, and mathematics. Our code is available at https://github.com/lucywang720/model-surgery.

Dynamic reconstruction of deformable tissues in endoscopic video is a key technology for robot-assisted surgery. Recent reconstruction methods based on neural radiance fields (NeRFs) have achieved remarkable results in the reconstruction of surgical scenes. However, based on implicit representation, NeRFs struggle to capture the intricate details of objects in the scene and cannot achieve real-time rendering. In addition, restricted single view perception and occluded instruments also propose special challenges in surgical scene reconstruction. To address these issues, we develop SurgicalGaussian, a deformable 3D Gaussian Splatting method to model dynamic surgical scenes. Our approach models the spatio-temporal features of soft tissues at each time stamp via a forward-mapping deformation MLP and regularization to constrain local 3D Gaussians to comply with consistent movement. With the depth initialization strategy and tool mask-guided training, our method can remove surgical instruments and reconstruct high-fidelity surgical scenes. Through experiments on various surgical videos, our network outperforms existing method on many aspects, including rendering quality, rendering speed and GPU usage. The project page can be found at https://surgicalgaussian.github.io.

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the algorithmic perspective, that is, the algorithms of GR that efficiently improve the performance. In this study, we first reveal that a specific finite-difference computation, composed of both gradient ascent and descent steps, reduces the computational cost of GR. Next, we show that the finite-difference computation also works better in the sense of generalization performance. We theoretically analyze a solvable model, a diagonal linear network, and clarify that GR has a desirable implicit bias to so-called rich regime and finite-difference computation strengthens this bias. Furthermore, finite-difference GR is closely related to some other algorithms based on iterative ascent and descent steps for exploring flat minima. In particular, we reveal that the flooding method can perform finite-difference GR in an implicit way. Thus, this work broadens our understanding of GR for both practice and theory.

The skeleton of a digital image is a compact representation of its topology, geometry, and scale. It has utility in many computer vision applications, such as image description, segmentation, and registration. However, skeletonization has only seen limited use in contemporary deep learning solutions. Most existing skeletonization algorithms are not differentiable, making it impossible to integrate them with gradient-based optimization. Compatible algorithms based on morphological operations and neural networks have been proposed, but their results often deviate from the geometry and topology of the true medial axis. This work introduces the first three-dimensional skeletonization algorithm that is both compatible with gradient-based optimization and preserves an object's topology. Our method is exclusively based on matrix additions and multiplications, convolutional operations, basic non-linear functions, and sampling from a uniform probability distribution, allowing it to be easily implemented in any major deep learning library. In benchmarking experiments, we prove the advantages of our skeletonization algorithm compared to non-differentiable, morphological, and neural-network-based baselines. Finally, we demonstrate the utility of our algorithm by integrating it with two medical image processing applications that use gradient-based optimization: deep-learning-based blood vessel segmentation, and multimodal registration of the mandible in computed tomography and magnetic resonance images.

Gradient-based optimization has been critical to the success of machine learning, updating a single set of parameters to minimize a single loss. A growing number of applications rely on a generalization of this, where we have a bilevel or nested optimization of which subsets of parameters update on different objectives nested inside each other. We focus on motivating examples of hyperparameter optimization and generative adversarial networks. However, naively applying classical methods often fails when we look at solving these nested problems on a large scale. In this thesis, we build tools for nested optimization that scale to deep learning setups.

Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to numerically implement the proximal step. The most challenging step, in this setup, is to evaluate functions involving density explicitly, such as entropy, in terms of samples. This paper builds on the recent works with a slight but crucial difference: we propose to utilize a variational formulation of the objective function formulated as maximization over a parametric class of functions. Theoretically, the proposed variational formulation allows the construction of gradient flows directly for empirical distributions with a well-defined and meaningful objective function. Computationally, this approach replaces the computationally expensive step in existing methods, to handle objective functions involving density, with inner loop updates that only require a small batch of samples and scale well with the dimension. The performance and scalability of the proposed method are illustrated with the aid of several numerical experiments involving high-dimensional synthetic and real datasets.

Advancing towards generalist agents necessitates the concurrent processing of multiple tasks using a unified model, thereby underscoring the growing significance of simultaneous model training on multiple downstream tasks. A common issue in multi-task learning is the occurrence of gradient conflict, which leads to potential competition among different tasks during joint training. This competition often results in improvements in one task at the expense of deterioration in another. Although several optimization methods have been developed to address this issue by manipulating task gradients for better task balancing, they cannot decrease the incidence of gradient conflict. In this paper, we systematically investigate the occurrence of gradient conflict across different methods and propose a strategy to reduce such conflicts through sparse training (ST), wherein only a portion of the model's parameters are updated during training while keeping the rest unchanged. Our extensive experiments demonstrate that ST effectively mitigates conflicting gradients and leads to superior performance. Furthermore, ST can be easily integrated with gradient manipulation techniques, thus enhancing their effectiveness.

In Federated Learning (FL) and many other distributed training frameworks, collaborators can hold their private data locally and only share the network weights trained with the local data after multiple iterations. Gradient inversion is a family of privacy attacks that recovers data from its generated gradients. Seemingly, FL can provide a degree of protection against gradient inversion attacks on weight updates, since the gradient of a single step is concealed by the accumulation of gradients over multiple local iterations. In this work, we propose a principled way to extend gradient inversion attacks to weight updates in FL, thereby better exposing weaknesses in the presumed privacy protection inherent in FL. In particular, we propose a surrogate model method based on the characteristic of two-dimensional gradient flow and low-rank property of local updates. Our method largely boosts the ability of gradient inversion attacks on weight updates containing many iterations and achieves state-of-the-art (SOTA) performance. Additionally, our method runs up to 100times faster than the SOTA baseline in the common FL scenario. Our work re-evaluates and highlights the privacy risk of sharing network weights. Our code is available at https://github.com/JunyiZhu-AI/surrogate_model_extension.

The widespread use of vector graphics creates a significant demand for vectorization methods. While recent learning-based techniques have shown their capability to create vector images of clear topology, filling these primitives with gradients remains a challenge. In this paper, we propose a segmentation-guided vectorization framework to convert raster images into concise vector graphics with radial gradient fills. With the guidance of an embedded gradient-aware segmentation subroutine, our approach progressively appends gradient-filled B\'ezier paths to the output, where primitive parameters are initiated with our newly designed initialization technique and are optimized to minimize our novel loss function. We build our method on a differentiable renderer with traditional segmentation algorithms to develop it as a model-free tool for raster-to-vector conversion. It is tested on various inputs to demonstrate its feasibility, independent of datasets, to synthesize vector graphics with improved visual quality and layer-wise topology compared to prior work.

The field of computer vision applied to videos of minimally invasive surgery is ever-growing. Workflow recognition pertains to the automated recognition of various aspects of a surgery: including which surgical steps are performed; and which surgical instruments are used. This information can later be used to assist clinicians when learning the surgery; during live surgery; and when writing operation notes. The Pituitary Vision (PitVis) 2023 Challenge tasks the community to step and instrument recognition in videos of endoscopic pituitary surgery. This is a unique task when compared to other minimally invasive surgeries due to the smaller working space, which limits and distorts vision; and higher frequency of instrument and step switching, which requires more precise model predictions. Participants were provided with 25-videos, with results presented at the MICCAI-2023 conference as part of the Endoscopic Vision 2023 Challenge in Vancouver, Canada, on 08-Oct-2023. There were 18-submissions from 9-teams across 6-countries, using a variety of deep learning models. A commonality between the top performing models was incorporating spatio-temporal and multi-task methods, with greater than 50% and 10% macro-F1-score improvement over purely spacial single-task models in step and instrument recognition respectively. The PitVis-2023 Challenge therefore demonstrates state-of-the-art computer vision models in minimally invasive surgery are transferable to a new dataset, with surgery specific techniques used to enhance performance, progressing the field further. Benchmark results are provided in the paper, and the dataset is publicly available at: https://doi.org/10.5522/04/26531686.

In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation in the presence of stragglers. In this paper, we consider the distributed computation of a sequence of gradients {g(1),g(2),ldots,g(J)}, where processing of each gradient g(t) starts in round-t and finishes by round-(t+T). Here Tgeq 0 denotes a delay parameter. For the GC scheme, coding is only across computing nodes and this results in a solution where T=0. On the other hand, having T>0 allows for designing schemes which exploit the temporal dimension as well. In this work, we propose two schemes that demonstrate improved performance compared to GC. Our first scheme combines GC with selective repetition of previously unfinished tasks and achieves improved straggler mitigation. In our second scheme, which constitutes our main contribution, we apply GC to a subset of the tasks and repetition for the remainder of the tasks. We then multiplex these two classes of tasks across workers and rounds in an adaptive manner, based on past straggler patterns. Using theoretical analysis, we demonstrate that our second scheme achieves significant reduction in the computational load. In our experiments, we study a practical setting of concurrently training multiple neural networks over an AWS Lambda cluster involving 256 worker nodes, where our framework naturally applies. We demonstrate that the latter scheme can yield a 16\% improvement in runtime over the baseline GC scheme, in the presence of naturally occurring, non-simulated stragglers.

Data diversity and volume are crucial to the success of training deep learning models, while in the medical imaging field, the difficulty and cost of data collection and annotation are especially huge. Specifically in robotic surgery, data scarcity and imbalance have heavily affected the model accuracy and limited the design and deployment of deep learning-based surgical applications such as surgical instrument segmentation. Considering this, we rethink the surgical instrument segmentation task and propose a one-to-many data generation solution that gets rid of the complicated and expensive process of data collection and annotation from robotic surgery. In our method, we only utilize a single surgical background tissue image and a few open-source instrument images as the seed images and apply multiple augmentations and blending techniques to synthesize amounts of image variations. In addition, we also introduce the chained augmentation mixing during training to further enhance the data diversities. The proposed approach is evaluated on the real datasets of the EndoVis-2018 and EndoVis-2017 surgical scene segmentation. Our empirical analysis suggests that without the high cost of data collection and annotation, we can achieve decent surgical instrument segmentation performance. Moreover, we also observe that our method can deal with novel instrument prediction in the deployment domain. We hope our inspiring results will encourage researchers to emphasize data-centric methods to overcome demanding deep learning limitations besides data shortage, such as class imbalance, domain adaptation, and incremental learning. Our code is available at https://github.com/lofrienger/Single_SurgicalScene_For_Segmentation.

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

Disease progression simulation is a crucial area of research that has significant implications for clinical diagnosis, prognosis, and treatment. One major challenge in this field is the lack of continuous medical imaging monitoring of individual patients over time. To address this issue, we develop a novel framework termed Progressive Image Editing (PIE) that enables controlled manipulation of disease-related image features, facilitating precise and realistic disease progression simulation. Specifically, we leverage recent advancements in text-to-image generative models to simulate disease progression accurately and personalize it for each patient. We theoretically analyze the iterative refining process in our framework as a gradient descent with an exponentially decayed learning rate. To validate our framework, we conduct experiments in three medical imaging domains. Our results demonstrate the superiority of PIE over existing methods such as Stable Diffusion Walk and Style-Based Manifold Extrapolation based on CLIP score (Realism) and Disease Classification Confidence (Alignment). Our user study collected feedback from 35 veteran physicians to assess the generated progressions. Remarkably, 76.2% of the feedback agrees with the fidelity of the generated progressions. To our best knowledge, PIE is the first of its kind to generate disease progression images meeting real-world standards. It is a promising tool for medical research and clinical practice, potentially allowing healthcare providers to model disease trajectories over time, predict future treatment responses, and improve patient outcomes.

In this paper, by introducing Generalized Bernstein condition, we propose the first Obig(sqrt{p}{nepsilon}big) high probability excess population risk bound for differentially private algorithms under the assumptions G-Lipschitz, L-smooth, and Polyak-{\L}ojasiewicz condition, based on gradient perturbation method. If we replace the properties G-Lipschitz and L-smooth by alpha-H{\"o}lder smoothness (which can be used in non-smooth setting), the high probability bound comes to Obig(n^{-alpha{1+2alpha}}big) w.r.t n, which cannot achieve Oleft(1/nright) when alphain(0,1]. To solve this problem, we propose a variant of gradient perturbation method, max{1,g-Normalized Gradient Perturbation} (m-NGP). We further show that by normalization, the high probability excess population risk bound under assumptions alpha-H{\"o}lder smooth and Polyak-{\L}ojasiewicz condition can achieve Obig(sqrt{p}{nepsilon}big), which is the first Oleft(1/nright) high probability excess population risk bound w.r.t n for differentially private algorithms under non-smooth conditions. Moreover, we evaluate the performance of the new proposed algorithm m-NGP, the experimental results show that m-NGP improves the performance of the differentially private model over real datasets. It demonstrates that m-NGP improves the utility bound and the accuracy of the DP model on real datasets simultaneously.

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is delta-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a delta-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

We propose Pulsar, an efficient sphere-based differentiable renderer that is orders of magnitude faster than competing techniques, modular, and easy-to-use due to its tight integration with PyTorch. Differentiable rendering is the foundation for modern neural rendering approaches, since it enables end-to-end training of 3D scene representations from image observations. However, gradient-based optimization of neural mesh, voxel, or function representations suffers from multiple challenges, i.e., topological inconsistencies, high memory footprints, or slow rendering speeds. To alleviate these problems, Pulsar employs: 1) a sphere-based scene representation, 2) an efficient differentiable rendering engine, and 3) neural shading. Pulsar executes orders of magnitude faster than existing techniques and allows real-time rendering and optimization of representations with millions of spheres. Using spheres for the scene representation, unprecedented speed is obtained while avoiding topology problems. Pulsar is fully differentiable and thus enables a plethora of applications, ranging from 3D reconstruction to general neural rendering.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

How to ensure fairness is an important topic in federated learning (FL). Recent studies have investigated how to reward clients based on their contribution (collaboration fairness), and how to achieve uniformity of performance across clients (performance fairness). Despite achieving progress on either one, we argue that it is critical to consider them together, in order to engage and motivate more diverse clients joining FL to derive a high-quality global model. In this work, we propose a novel method to optimize both types of fairness simultaneously. Specifically, we propose to estimate client contribution in gradient and data space. In gradient space, we monitor the gradient direction differences of each client with respect to others. And in data space, we measure the prediction error on client data using an auxiliary model. Based on this contribution estimation, we propose a FL method, federated training via contribution estimation (FedCE), i.e., using estimation as global model aggregation weights. We have theoretically analyzed our method and empirically evaluated it on two real-world medical datasets. The effectiveness of our approach has been validated with significant performance improvements, better collaboration fairness, better performance fairness, and comprehensive analytical studies.

Recent advances in robot-assisted surgery have resulted in progressively more precise, efficient, and minimally invasive procedures, sparking a new era of robotic surgical intervention. This enables doctors, in collaborative interaction with robots, to perform traditional or minimally invasive surgeries with improved outcomes through smaller incisions. Recent efforts are working toward making robotic surgery more autonomous which has the potential to reduce variability of surgical outcomes and reduce complication rates. Deep reinforcement learning methodologies offer scalable solutions for surgical automation, but their effectiveness relies on extensive data acquisition due to the absence of prior knowledge in successfully accomplishing tasks. Due to the intensive nature of simulated data collection, previous works have focused on making existing algorithms more efficient. In this work, we focus on making the simulator more efficient, making training data much more accessible than previously possible. We introduce Surgical Gym, an open-source high performance platform for surgical robot learning where both the physics simulation and reinforcement learning occur directly on the GPU. We demonstrate between 100-5000x faster training times compared with previous surgical learning platforms. The code is available at: https://github.com/SamuelSchmidgall/SurgicalGym.

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value c >0. It is widely used for example for stabilizing the training of deep learning models (Goodfellow et al., 2016), or for enforcing differential privacy (Abadi et al., 2016). Despite popularity and simplicity of the clipping mechanism, its convergence guarantees often require specific values of c and strong noise assumptions. In this paper, we give convergence guarantees that show precise dependence on arbitrary clipping thresholds c and show that our guarantees are tight with both deterministic and stochastic gradients. In particular, we show that (i) for deterministic gradient descent, the clipping threshold only affects the higher-order terms of convergence, (ii) in the stochastic setting convergence to the true optimum cannot be guaranteed under the standard noise assumption, even under arbitrary small step-sizes. We give matching upper and lower bounds for convergence of the gradient norm when running clipped SGD, and illustrate these results with experiments.

Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are sub-optimal. Instead, these problems have been shown to satisfy certain generalized-smooth conditions, which have not been well understood in the existing literature. In this paper, we propose a notion of alpha-symmetric generalized-smoothness that extends the existing notions and covers many important functions such as high-order polynomials and exponential functions. We study the fundamental properties and establish descent lemmas for the functions in this class. Then, to solve such a large class of nonconvex problems, we design a special deterministic normalized gradient descent algorithm that achieves the optimal iteration complexity O(epsilon^{-2}), and also prove that the popular SPIDER variance reduction algorithm achieves the optimal sample complexity O(epsilon^{-3}) in the stochastic setting. Our results show that solving generalized-smooth nonconvex problems is as efficient as solving smooth nonconvex problems.

As deep learning models gain attraction in medical data, ensuring transparent and trustworthy decision-making is essential. In skin cancer diagnosis, while advancements in lesion detection and classification have improved accuracy, the black-box nature of these methods poses challenges in understanding their decision processes, leading to trust issues among physicians. This study leverages the CLIP (Contrastive Language-Image Pretraining) model, trained on different skin lesion datasets, to capture meaningful relationships between visual features and diagnostic criteria terms. To further enhance transparency, we propose a method called MedGrad E-CLIP, which builds on gradient-based E-CLIP by incorporating a weighted entropy mechanism designed for complex medical imaging like skin lesions. This approach highlights critical image regions linked to specific diagnostic descriptions. The developed integrated pipeline not only classifies skin lesions by matching corresponding descriptions but also adds an essential layer of explainability developed especially for medical data. By visually explaining how different features in an image relates to diagnostic criteria, this approach demonstrates the potential of advanced vision-language models in medical image analysis, ultimately improving transparency, robustness, and trust in AI-driven diagnostic systems.

Intra-fraction motion in radiotherapy is commonly modeled using deformable image registration (DIR). However, existing methods often struggle to balance speed and accuracy, limiting their applicability in clinical scenarios. This study introduces a novel approach that harnesses Neural Graphics Primitives (NGP) to optimize the displacement vector field (DVF). Our method leverages learned primitives, processed as splats, and interpolates within space using a shallow neural network. Uniquely, it enables self-supervised optimization at an ultra-fast speed, negating the need for pre-training on extensive datasets and allowing seamless adaptation to new cases. We validated this approach on the 4D-CT lung dataset DIR-lab, achieving a target registration error (TRE) of 1.15\pm1.15 mm within a remarkable time of 1.77 seconds. Notably, our method also addresses the sliding boundary problem, a common challenge in conventional DIR methods.

Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge quickly for large linear inverse problems. For example, the conjugate gradient method (CG), one of the most popular Krylov subspace methods, is based on the idea of minimizing the residual error in the Krylov subspace. However, with the recent advancement of high-performance diffusion solvers for inverse problems, it is not clear how classical wisdom can be synergistically combined with modern diffusion models. In this study, we propose a novel and efficient diffusion sampling strategy that synergistically combines the diffusion sampling and Krylov subspace methods. Specifically, we prove that if the tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG initialized with the denoised data ensures the data consistency update to remain in the tangent space. This negates the need to compute the manifold-constrained gradient (MCG), leading to a more efficient diffusion sampling method. Our method is applicable regardless of the parametrization and setting (i.e., VE, VP). Notably, we achieve state-of-the-art reconstruction quality on challenging real-world medical inverse imaging problems, including multi-coil MRI reconstruction and 3D CT reconstruction. Moreover, our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method. Code is available at https://github.com/HJ-harry/DDS

This work proposes aesthetic gradients, a method to personalize a CLIP-conditioned diffusion model by guiding the generative process towards custom aesthetics defined by the user from a set of images. The approach is validated with qualitative and quantitative experiments, using the recent stable diffusion model and several aesthetically-filtered datasets. Code is released at https://github.com/vicgalle/stable-diffusion-aesthetic-gradients

Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which a function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and a lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms other optimizers. Also, we show that diffGrad performs uniformly well for training CNN using different activation functions. The source code is made publicly available at https://github.com/shivram1987/diffGrad.

Foundation models have revolutionized computer vision by achieving vastly superior performance across diverse tasks through large-scale pretraining on extensive datasets. However, their application in surgical computer vision has been limited. This study addresses this gap by introducing SurgeNetXL, a novel surgical foundation model that sets a new benchmark in surgical computer vision. Trained on the largest reported surgical dataset to date, comprising over 4.7 million video frames, SurgeNetXL achieves consistent top-tier performance across six datasets spanning four surgical procedures and three tasks, including semantic segmentation, phase recognition, and critical view of safety (CVS) classification. Compared with the best-performing surgical foundation models, SurgeNetXL shows mean improvements of 2.4, 9.0, and 12.6 percent for semantic segmentation, phase recognition, and CVS classification, respectively. Additionally, SurgeNetXL outperforms the best-performing ImageNet-based variants by 14.4, 4.0, and 1.6 percent in the respective tasks. In addition to advancing model performance, this study provides key insights into scaling pretraining datasets, extending training durations, and optimizing model architectures specifically for surgical computer vision. These findings pave the way for improved generalizability and robustness in data-scarce scenarios, offering a comprehensive framework for future research in this domain. All models and a subset of the SurgeNetXL dataset, including over 2 million video frames, are publicly available at: https://github.com/TimJaspers0801/SurgeNet.

Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial warm restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple warm restart technique for stochastic gradient descent to improve its anytime performance when training deep neural networks. We empirically study its performance on the CIFAR-10 and CIFAR-100 datasets, where we demonstrate new state-of-the-art results at 3.14% and 16.21%, respectively. We also demonstrate its advantages on a dataset of EEG recordings and on a downsampled version of the ImageNet dataset. Our source code is available at https://github.com/loshchil/SGDR

Nesterov's accelerated gradient (AG) is a popular technique to optimize objective functions comprising two components: a convex loss and a penalty function. While AG methods perform well for convex penalties, such as the LASSO, convergence issues may arise when it is applied to nonconvex penalties, such as SCAD. A recent proposal generalizes Nesterov's AG method to the nonconvex setting. The proposed algorithm requires specification of several hyperparameters for its practical application. Aside from some general conditions, there is no explicit rule for selecting the hyperparameters, and how different selection can affect convergence of the algorithm. In this article, we propose a hyperparameter setting based on the complexity upper bound to accelerate convergence, and consider the application of this nonconvex AG algorithm to high-dimensional linear and logistic sparse learning problems. We further establish the rate of convergence and present a simple and useful bound to characterize our proposed optimal damping sequence. Simulation studies show that convergence can be made, on average, considerably faster than that of the conventional proximal gradient algorithm. Our experiments also show that the proposed method generally outperforms the current state-of-the-art methods in terms of signal recovery.

Medical image registration is a critical task that estimates the spatial correspondence between pairs of images. However, current traditional and deep-learning-based methods rely on similarity measures to generate a deforming field, which often results in disproportionate volume changes in dissimilar regions, especially in tumor regions. These changes can significantly alter the tumor size and underlying anatomy, which limits the practical use of image registration in clinical diagnosis. To address this issue, we have formulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizing image similarity in other normal regions. Our proposed strategy involves a two-stage process. In the first stage, we use similarity-based registration to identify potential tumor regions by their volume change, generating a soft tumor mask accordingly. In the second stage, we propose a volume-preserving registration with a novel adaptive volume-preserving loss that penalizes the change in size adaptively based on the masks calculated from the previous stage. Our approach balances image similarity and volume preservation in different regions, i.e., normal and tumor regions, by using soft tumor masks to adjust the imposition of volume-preserving loss on each one. This ensures that the tumor volume is preserved during the registration process. We have evaluated our strategy on various datasets and network architectures, demonstrating that our method successfully preserves the tumor volume while achieving comparable registration results with state-of-the-art methods. Our codes is available at: https://dddraxxx.github.io/Volume-Preserving-Registration/.

In this work, we develop an open-source surgical simulation environment that includes a realistic model obtained by MRI-scanning a physical phantom, for the purpose of training and evaluating a Learning from Demonstration (LfD) algorithm for autonomous suturing. The LfD algorithm utilizes Dynamic Movement Primitives (DMP) and Locally Weighted Regression (LWR), but focuses on the needle trajectory, rather than the instruments, to obtain better generality with respect to needle grasps. We conduct a user study to collect multiple suturing demonstrations and perform a comprehensive analysis of the ability of the LfD algorithm to generalize from a demonstration at one location in one phantom to different locations in the same phantom and to a different phantom. Our results indicate good generalization, on the order of 91.5%, when learning from more experienced subjects, indicating the need to integrate skill assessment in the future.

In this paper, we propose a general deep learning training framework XGrad which introduces weight prediction into the popular gradient-based optimizers to boost their convergence and generalization when training the deep neural network (DNN) models. In particular, ahead of each mini-batch training, the future weights are predicted according to the update rule of the used optimizer and are then applied to both the forward pass and backward propagation. In this way, during the whole training period, the optimizer always utilizes the gradients w.r.t. the future weights to update the DNN parameters, making the gradient-based optimizer achieve better convergence and generalization compared to the original optimizer without weight prediction. XGrad is rather straightforward to implement yet pretty effective in boosting the convergence of gradient-based optimizers and the accuracy of DNN models. Empirical results concerning the most three popular gradient-based optimizers including SGD with momentum, Adam, and AdamW demonstrate the effectiveness of our proposal. The experimental results validate that XGrad can attain higher model accuracy than the original optimizers when training the DNN models. The code of XGrad will be available at: https://github.com/guanleics/XGrad.

Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning fields. The validity of existing works heavily rely on either a restrictive Lower- Level Strong Convexity (LLSC) condition or on solving a series of approximation subproblems with high accuracy or both. In this work, by averaging the upper and lower level objectives, we propose a single loop Bi-level Averaged Method of Multipliers (sl-BAMM) for BLO that is simple yet efficient for large-scale BLO and gets rid of the limited LLSC restriction. We further provide non-asymptotic convergence analysis of sl-BAMM towards KKT stationary points, and the comparative advantage of our analysis lies in the absence of strong gradient boundedness assumption, which is always required by others. Thus our theory safely captures a wider variety of applications in deep learning, especially where the upper-level objective is quadratic w.r.t. the lower-level variable. Experimental results demonstrate the superiority of our method.

Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised learning can be accelerated by leveraging the fact that gradients lie in a low-dimensional and slowly-changing subspace. In this paper, we conduct a thorough evaluation of this phenomenon for two popular deep policy gradient methods on various simulated benchmark tasks. Our results demonstrate the existence of such gradient subspaces despite the continuously changing data distribution inherent to reinforcement learning. These findings reveal promising directions for future work on more efficient reinforcement learning, e.g., through improving parameter-space exploration or enabling second-order optimization.

Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of the class score function with respect to the input image. This gradient can be interpreted as a sensitivity map, and there are several techniques that elaborate on this basic idea. This paper makes two contributions: it introduces SmoothGrad, a simple method that can help visually sharpen gradient-based sensitivity maps, and it discusses lessons in the visualization of these maps. We publish the code for our experiments and a website with our results.

Sparse training is emerging as a promising avenue for reducing the computational cost of training neural networks. Several recent studies have proposed pruning methods using learnable thresholds to efficiently explore the non-uniform distribution of sparsity inherent within the models. In this paper, we propose Gradient Annealing (GA), where gradients of masked weights are scaled down in a non-linear manner. GA provides an elegant trade-off between sparsity and accuracy without the need for additional sparsity-inducing regularization. We integrated GA with the latest learnable pruning methods to create an automated sparse training algorithm called AutoSparse, which achieves better accuracy and/or training/inference FLOPS reduction than existing learnable pruning methods for sparse ResNet50 and MobileNetV1 on ImageNet-1K: AutoSparse achieves (2x, 7x) reduction in (training,inference) FLOPS for ResNet50 on ImageNet at 80% sparsity. Finally, AutoSparse outperforms sparse-to-sparse SotA method MEST (uniform sparsity) for 80% sparse ResNet50 with similar accuracy, where MEST uses 12% more training FLOPS and 50% more inference FLOPS.

Federated optimization, an emerging paradigm which finds wide real-world applications such as federated learning, enables multiple clients (e.g., edge devices) to collaboratively optimize a global function. The clients do not share their local datasets and typically only share their local gradients. However, the gradient information is not available in many applications of federated optimization, which hence gives rise to the paradigm of federated zeroth-order optimization (ZOO). Existing federated ZOO algorithms suffer from the limitations of query and communication inefficiency, which can be attributed to (a) their reliance on a substantial number of function queries for gradient estimation and (b) the significant disparity between their realized local updates and the intended global updates. To this end, we (a) introduce trajectory-informed gradient surrogates which is able to use the history of function queries during optimization for accurate and query-efficient gradient estimation, and (b) develop the technique of adaptive gradient correction using these gradient surrogates to mitigate the aforementioned disparity. Based on these, we propose the federated zeroth-order optimization using trajectory-informed surrogate gradients (FZooS) algorithm for query- and communication-efficient federated ZOO. Our FZooS achieves theoretical improvements over the existing approaches, which is supported by our real-world experiments such as federated black-box adversarial attack and federated non-differentiable metric optimization.

Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve gradient descent through a highly non-convex loss landscape, causing the optimization process to be unstable and slow. We introduce a method that learns a loss landscape where gradient descent is efficient, bringing massive improvement and acceleration to the inversion process. We demonstrate this advantage on a number of methods for both generative and discriminative tasks, including GAN inversion, adversarial defense, and 3D human pose reconstruction.

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal transport-based differentiable Sinkhorn sorting algorithms to making classic sorting networks differentiable. One problem of current differentiable sorting methods is that they are non-monotonic. To address this issue, we propose a novel relaxation of conditional swap operations that guarantees monotonicity in differentiable sorting networks. We introduce a family of sigmoid functions and prove that they produce differentiable sorting networks that are monotonic. Monotonicity ensures that the gradients always have the correct sign, which is an advantage in gradient-based optimization. We demonstrate that monotonic differentiable sorting networks improve upon previous differentiable sorting methods.

We introduce Reverse Derivative Ascent: a categorical analogue of gradient based methods for machine learning. Our algorithm is defined at the level of so-called reverse differential categories. It can be used to learn the parameters of models which are expressed as morphisms of such categories. Our motivating example is boolean circuits: we show how our algorithm can be applied to such circuits by using the theory of reverse differential categories. Note our methodology allows us to learn the parameters of boolean circuits directly, in contrast to existing binarised neural network approaches. Moreover, we demonstrate its empirical value by giving experimental results on benchmark machine learning datasets.

The blooming of social media and face recognition (FR) systems has increased people's concern about privacy and security. A new type of adversarial privacy cloak (class-universal) can be applied to all the images of regular users, to prevent malicious FR systems from acquiring their identity information. In this work, we discover the optimization dilemma in the existing methods -- the local optima problem in large-batch optimization and the gradient information elimination problem in small-batch optimization. To solve these problems, we propose Gradient Accumulation (GA) to aggregate multiple small-batch gradients into a one-step iterative gradient to enhance the gradient stability and reduce the usage of quantization operations. Experiments show that our proposed method achieves high performance on the Privacy-Commons dataset against black-box face recognition models.

This paper investigates the distinctions between gradient methods applied to non-differentiable functions (NGDMs) and classical gradient descents (GDs) designed for differentiable functions. First, we demonstrate significant differences in the convergence properties of NGDMs compared to GDs, challenging the applicability of the extensive neural network convergence literature based on L-smoothness to non-smooth neural networks. Next, we demonstrate the paradoxical nature of NGDM solutions for L_{1}-regularized problems, showing that increasing the regularization penalty leads to an increase in the L_{1} norm of optimal solutions in NGDMs. Consequently, we show that widely adopted L_{1} penalization-based techniques for network pruning do not yield expected results. Finally, we explore the Edge of Stability phenomenon, indicating its inapplicability even to Lipschitz continuous convex differentiable functions, leaving its relevance to non-convex non-differentiable neural networks inconclusive. Our analysis exposes misguided interpretations of NGDMs in widely referenced papers and texts due to an overreliance on strong smoothness assumptions, emphasizing the necessity for a nuanced understanding of foundational assumptions in the analysis of these systems.

This paper presents a new approach and algorithm for solving a class of constrained Bi-Level Optimization (BLO) problems in which the lower-level problem involves constraints coupling both upper-level and lower-level variables. Such problems have recently gained significant attention due to their broad applicability in machine learning. However, conventional gradient-based methods unavoidably rely on computationally intensive calculations related to the Hessian matrix. To address this challenge, we begin by devising a smooth proximal Lagrangian value function to handle the constrained lower-level problem. Utilizing this construct, we introduce a single-level reformulation for constrained BLOs that transforms the original BLO problem into an equivalent optimization problem with smooth constraints. Enabled by this reformulation, we develop a Hessian-free gradient-based algorithm-termed proximal Lagrangian Value function-based Hessian-free Bi-level Algorithm (LV-HBA)-that is straightforward to implement in a single loop manner. Consequently, LV-HBA is especially well-suited for machine learning applications. Furthermore, we offer non-asymptotic convergence analysis for LV-HBA, eliminating the need for traditional strong convexity assumptions for the lower-level problem while also being capable of accommodating non-singleton scenarios. Empirical results substantiate the algorithm's superior practical performance.

We consider a class of structured fractional minimization problems, in which the numerator part of the objective is the sum of a differentiable convex function and a convex non-smooth function, while the denominator part is a convex or concave function. This problem is difficult to solve since it is non-convex. By exploiting the structure of the problem, we propose two Coordinate Descent (CD) methods for solving this problem. The proposed methods iteratively solve a one-dimensional subproblem globally, and they are guaranteed to converge to coordinate-wise stationary points. In the case of a convex denominator, under a weak locally bounded non-convexity condition, we prove that the optimality of coordinate-wise stationary point is stronger than that of the standard critical point and directional point. Under additional suitable conditions, CD methods converge Q-linearly to coordinate-wise stationary points. In the case of a concave denominator, we show that any critical point is a global minimum, and CD methods converge to the global minimum with a sublinear convergence rate. We demonstrate the applicability of the proposed methods to some machine learning and signal processing models. Our experiments on real-world data have shown that our method significantly and consistently outperforms existing methods in terms of accuracy.

We describe a method to parse a complex, cluttered indoor scene into primitives which offer a parsimonious abstraction of scene structure. Our primitives are simple convexes. Our method uses a learned regression procedure to parse a scene into a fixed number of convexes from RGBD input, and can optionally accept segmentations to improve the decomposition. The result is then polished with a descent method which adjusts the convexes to produce a very good fit, and greedily removes superfluous primitives. Because the entire scene is parsed, we can evaluate using traditional depth, normal, and segmentation error metrics. Our evaluation procedure demonstrates that the error from our primitive representation is comparable to that of predicting depth from a single image.

In this paper, we propose a novel text promptable surgical instrument segmentation approach to overcome challenges associated with diversity and differentiation of surgical instruments in minimally invasive surgeries. We redefine the task as text promptable, thereby enabling a more nuanced comprehension of surgical instruments and adaptability to new instrument types. Inspired by recent advancements in vision-language models, we leverage pretrained image and text encoders as our model backbone and design a text promptable mask decoder consisting of attention- and convolution-based prompting schemes for surgical instrument segmentation prediction. Our model leverages multiple text prompts for each surgical instrument through a new mixture of prompts mechanism, resulting in enhanced segmentation performance. Additionally, we introduce a hard instrument area reinforcement module to improve image feature comprehension and segmentation precision. Extensive experiments on EndoVis2017 and EndoVis2018 datasets demonstrate our model's superior performance and promising generalization capability. To our knowledge, this is the first implementation of a promptable approach to surgical instrument segmentation, offering significant potential for practical application in the field of robotic-assisted surgery.

Patient data from real-world clinical practice often suffers from data scarcity and long-tail imbalances, leading to biased outcomes or algorithmic unfairness. This study addresses these challenges by generating lesion-containing image-segmentation pairs from lesion-free images. Previous efforts in medical imaging synthesis have struggled with separating lesion information from background, resulting in low-quality backgrounds and limited control over the synthetic output. Inspired by diffusion-based image inpainting, we propose LeFusion, a lesion-focused diffusion model. By redesigning the diffusion learning objectives to focus on lesion areas, we simplify the learning process and improve control over the output while preserving high-fidelity backgrounds by integrating forward-diffused background contexts into the reverse diffusion process. Additionally, we tackle two major challenges in lesion texture synthesis: 1) multi-peak and 2) multi-class lesions. We introduce two effective strategies: histogram-based texture control and multi-channel decomposition, enabling the controlled generation of high-quality lesions in difficult scenarios. Furthermore, we incorporate lesion mask diffusion, allowing control over lesion size, location, and boundary, thus increasing lesion diversity. Validated on 3D cardiac lesion MRI and lung nodule CT datasets, LeFusion-generated data significantly improves the performance of state-of-the-art segmentation models, including nnUNet and SwinUNETR. Code and model are available at https://github.com/M3DV/LeFusion.

The backpropagation algorithm has long been the canonical training method for neural networks. Modern paradigms are implicitly optimized for it, and numerous guidelines exist to ensure its proper use. Recently, synthetic gradients methods -where the error gradient is only roughly approximated - have garnered interest. These methods not only better portray how biological brains are learning, but also open new computational possibilities, such as updating layers asynchronously. Even so, they have failed to scale past simple tasks like MNIST or CIFAR-10. This is in part due to a lack of standards, leading to ill-suited models and practices forbidding such methods from performing to the best of their abilities. In this work, we focus on direct feedback alignment and present a set of best practices justified by observations of the alignment angles. We characterize a bottleneck effect that prevents alignment in narrow layers, and hypothesize it may explain why feedback alignment methods have yet to scale to large convolutional networks.

Reconstructing deformable tissues from endoscopic videos is essential in many downstream surgical applications. However, existing methods suffer from slow rendering speed, greatly limiting their practical use. In this paper, we introduce EndoGaussian, a real-time endoscopic scene reconstruction framework built on 3D Gaussian Splatting (3DGS). By integrating the efficient Gaussian representation and highly-optimized rendering engine, our framework significantly boosts the rendering speed to a real-time level. To adapt 3DGS for endoscopic scenes, we propose two strategies, Holistic Gaussian Initialization (HGI) and Spatio-temporal Gaussian Tracking (SGT), to handle the non-trivial Gaussian initialization and tissue deformation problems, respectively. In HGI, we leverage recent depth estimation models to predict depth maps of input binocular/monocular image sequences, based on which pixels are re-projected and combined for holistic initialization. In SPT, we propose to model surface dynamics using a deformation field, which is composed of an efficient encoding voxel and a lightweight deformation decoder, allowing for Gaussian tracking with minor training and rendering burden. Experiments on public datasets demonstrate our efficacy against prior SOTAs in many aspects, including better rendering speed (195 FPS real-time, 100times gain), better rendering quality (37.848 PSNR), and less training overhead (within 2 min/scene), showing significant promise for intraoperative surgery applications. Code is available at: https://yifliu3.github.io/EndoGaussian/.

This paper introduces a network for volumetric segmentation that learns from sparsely annotated volumetric images. We outline two attractive use cases of this method: (1) In a semi-automated setup, the user annotates some slices in the volume to be segmented. The network learns from these sparse annotations and provides a dense 3D segmentation. (2) In a fully-automated setup, we assume that a representative, sparsely annotated training set exists. Trained on this data set, the network densely segments new volumetric images. The proposed network extends the previous u-net architecture from Ronneberger et al. by replacing all 2D operations with their 3D counterparts. The implementation performs on-the-fly elastic deformations for efficient data augmentation during training. It is trained end-to-end from scratch, i.e., no pre-trained network is required. We test the performance of the proposed method on a complex, highly variable 3D structure, the Xenopus kidney, and achieve good results for both use cases.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

In 2015 we began a sub-challenge at the EndoVis workshop at MICCAI in Munich using endoscope images of ex-vivo tissue with automatically generated annotations from robot forward kinematics and instrument CAD models. However, the limited background variation and simple motion rendered the dataset uninformative in learning about which techniques would be suitable for segmentation in real surgery. In 2017, at the same workshop in Quebec we introduced the robotic instrument segmentation dataset with 10 teams participating in the challenge to perform binary, articulating parts and type segmentation of da Vinci instruments. This challenge included realistic instrument motion and more complex porcine tissue as background and was widely addressed with modifications on U-Nets and other popular CNN architectures. In 2018 we added to the complexity by introducing a set of anatomical objects and medical devices to the segmented classes. To avoid over-complicating the challenge, we continued with porcine data which is dramatically simpler than human tissue due to the lack of fatty tissue occluding many organs.

This paper reports Deep LOGISMOS approach to 3D tumor segmentation by incorporating boundary information derived from deep contextual learning to LOGISMOS - layered optimal graph image segmentation of multiple objects and surfaces. Accurate and reliable tumor segmentation is essential to tumor growth analysis and treatment selection. A fully convolutional network (FCN), UNet, is first trained using three adjacent 2D patches centered at the tumor, providing contextual UNet segmentation and probability map for each 2D patch. The UNet segmentation is then refined by Gaussian Mixture Model (GMM) and morphological operations. The refined UNet segmentation is used to provide the initial shape boundary to build a segmentation graph. The cost for each node of the graph is determined by the UNet probability maps. Finally, a max-flow algorithm is employed to find the globally optimal solution thus obtaining the final segmentation. For evaluation, we applied the method to pancreatic tumor segmentation on a dataset of 51 CT scans, among which 30 scans were used for training and 21 for testing. With Deep LOGISMOS, DICE Similarity Coefficient (DSC) and Relative Volume Difference (RVD) reached 83.2+-7.8% and 18.6+-17.4% respectively, both are significantly improved (p<0.05) compared with contextual UNet and/or LOGISMOS alone.

Self-supervised learning (SSL) has potential for effective representation learning in medical imaging, but the choice of data augmentation is critical and domain-specific. It remains uncertain if general augmentation policies suit surgical applications. In this work, we automate the search for suitable augmentation policies through a new method called Dimensionality Driven Augmentation Search (DDA). DDA leverages the local dimensionality of deep representations as a proxy target, and differentiably searches for suitable data augmentation policies in contrastive learning. We demonstrate the effectiveness and efficiency of DDA in navigating a large search space and successfully identifying an appropriate data augmentation policy for laparoscopic surgery. We systematically evaluate DDA across three laparoscopic image classification and segmentation tasks, where it significantly improves over existing baselines. Furthermore, DDA's optimised set of augmentations provides insight into domain-specific dependencies when applying contrastive learning in medical applications. For example, while hue is an effective augmentation for natural images, it is not advantageous for laparoscopic images.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of L-smooth and mu-strongly convex functions distributed over a given network of size n. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous, leading to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix chi_1 and the maximal resistance chi_2leq chi_1 of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires O(nfrac{L{mu}}log(1{epsilon})) local gradients and only O(nchi_1chi_2frac{L{mu}}log(1{epsilon})) communications to reach a precision epsilon, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. We also propose a SDP relaxation to find the optimal gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights. Our source code is released on a public repository.

The gradients of convex functions are expressive models of non-trivial vector fields. For example, Brenier's theorem yields that the optimal transport map between any two measures on Euclidean space under the squared distance is realized as a convex gradient, which is a key insight used in recent generative flow models. In this paper, we study how to model convex gradients by integrating a Jacobian-vector product parameterized by a neural network, which we call the Input Convex Gradient Network (ICGN). We theoretically study ICGNs and compare them to taking the gradient of an Input-Convex Neural Network (ICNN), empirically demonstrating that a single layer ICGN can fit a toy example better than a single layer ICNN. Lastly, we explore extensions to deeper networks and connections to constructions from Riemannian geometry.

We show how to transform a non-differentiable rasterizer into a differentiable one with minimal engineering efforts and no external dependencies (no Pytorch/Tensorflow). We rely on Stochastic Gradient Estimation, a technique that consists of rasterizing after randomly perturbing the scene's parameters such that their gradient can be stochastically estimated and descended. This method is simple and robust but does not scale in dimensionality (number of scene parameters). Our insight is that the number of parameters contributing to a given rasterized pixel is bounded. Estimating and averaging gradients on a per-pixel basis hence bounds the dimensionality of the underlying optimization problem and makes the method scalable. Furthermore, it is simple to track per-pixel contributing parameters by rasterizing ID- and UV-buffers, which are trivial additions to a rasterization engine if not already available. With these minor modifications, we obtain an in-engine optimizer for 3D assets with millions of geometry and texture parameters.

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve mgg 1 lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its variance is more intricate due to the hierarchical sampling of blocks and data and the unique challenge of estimating hyper-gradient. We aim to achieve three nice properties for our algorithm: (a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling I blocks and sampling B samples for each sampled block per-iteration; (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator. However, it is non-trivial to achieve all of these by observing that existing works only achieve one or two of these properties. To address the involved challenges for achieving (a, b, c), we propose two stochastic algorithms by using advanced blockwise variance-reduction techniques for tracking the Hessian matrices (for low-dimensional problems) or the Hessian-vector products (for high-dimensional problems), and prove an iteration complexity of O(mepsilon^{-3I(I<m)}{II} + mepsilon^{-3}{IB}) for finding an epsilon-stationary point under appropriate conditions. We also conduct experiments to verify the effectiveness of the proposed algorithms comparing with existing MBBO algorithms.

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.

Over the past decade, computer vision applications in minimally invasive surgery have rapidly increased. Despite this growth, the impact of surgical computer vision remains limited compared to other medical fields like pathology and radiology, primarily due to the scarcity of representative annotated data. Whereas transfer learning from large annotated datasets such as ImageNet has been conventionally the norm to achieve high-performing models, recent advancements in self-supervised learning (SSL) have demonstrated superior performance. In medical image analysis, in-domain SSL pretraining has already been shown to outperform ImageNet-based initialization. Although unlabeled data in the field of surgical computer vision is abundant, the diversity within this data is limited. This study investigates the role of dataset diversity in SSL for surgical computer vision, comparing procedure-specific datasets against a more heterogeneous general surgical dataset across three different downstream surgical applications. The obtained results show that using solely procedure-specific data can lead to substantial improvements of 13.8%, 9.5%, and 36.8% compared to ImageNet pretraining. However, extending this data with more heterogeneous surgical data further increases performance by an additional 5.0%, 5.2%, and 2.5%, suggesting that increasing diversity within SSL data is beneficial for model performance. The code and pretrained model weights are made publicly available at https://github.com/TimJaspers0801/SurgeNet.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

Self-tuning algorithms that adapt the learning process online encourage more effective and robust learning. Among all the methods available, meta-gradients have emerged as a promising approach. They leverage the differentiability of the learning rule with respect to some hyper-parameters to adapt them in an online fashion. Although meta-gradients can be accumulated over multiple learning steps to avoid myopic updates, this is rarely used in practice. In this work, we demonstrate that whilst multi-step meta-gradients do provide a better learning signal in expectation, this comes at the cost of a significant increase in variance, hindering performance. In the light of this analysis, we introduce a novel method mixing multiple inner steps that enjoys a more accurate and robust meta-gradient signal, essentially trading off bias and variance in meta-gradient estimation. When applied to the Snake game, the mixing meta-gradient algorithm can cut the variance by a factor of 3 while achieving similar or higher performance.

We show that in a variety of large-scale deep learning scenarios the gradient dynamically converges to a very small subspace after a short period of training. The subspace is spanned by a few top eigenvectors of the Hessian (equal to the number of classes in the dataset), and is mostly preserved over long periods of training. A simple argument then suggests that gradient descent may happen mostly in this subspace. We give an example of this effect in a solvable model of classification, and we comment on possible implications for optimization and learning.

Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep learning systems). In this setting, the optimal O(1/t) convergence rate for solving smooth monotone variational inequalities is achieved by the Extra-Gradient (EG) algorithm and its variants. Aiming to alleviate the cost of an extra gradient step per iteration (which can become quite substantial in deep learning applications), several algorithms have been proposed as surrogates to Extra-Gradient with a single oracle call per iteration. In this paper, we develop a synthetic view of such algorithms, and we complement the existing literature by showing that they retain a O(1/t) ergodic convergence rate in smooth, deterministic problems. Subsequently, beyond the monotone deterministic case, we also show that the last iterate of single-call, stochastic extra-gradient methods still enjoys a O(1/t) local convergence rate to solutions of non-monotone variational inequalities that satisfy a second-order sufficient condition.

The conjugate gradient method is a crucial first-order optimization method that generally converges faster than the steepest descent method, and its computational cost is much lower than that of second-order methods. However, while various types of conjugate gradient methods have been studied in Euclidean spaces and on Riemannian manifolds, there is little study for those in distributed scenarios. This paper proposes a decentralized Riemannian conjugate gradient descent (DRCGD) method that aims at minimizing a global function over the Stiefel manifold. The optimization problem is distributed among a network of agents, where each agent is associated with a local function, and the communication between agents occurs over an undirected connected graph. Since the Stiefel manifold is a non-convex set, a global function is represented as a finite sum of possibly non-convex (but smooth) local functions. The proposed method is free from expensive Riemannian geometric operations such as retractions, exponential maps, and vector transports, thereby reducing the computational complexity required by each agent. To the best of our knowledge, DRCGD is the first decentralized Riemannian conjugate gradient algorithm to achieve global convergence over the Stiefel manifold.

Automatic and consistent meningioma segmentation in T1-weighted MRI volumes and corresponding volumetric assessment is of use for diagnosis, treatment planning, and tumor growth evaluation. In this paper, we optimized the segmentation and processing speed performances using a large number of both surgically treated meningiomas and untreated meningiomas followed at the outpatient clinic. We studied two different 3D neural network architectures: (i) a simple encoder-decoder similar to a 3D U-Net, and (ii) a lightweight multi-scale architecture (PLS-Net). In addition, we studied the impact of different training schemes. For the validation studies, we used 698 T1-weighted MR volumes from St. Olav University Hospital, Trondheim, Norway. The models were evaluated in terms of detection accuracy, segmentation accuracy and training/inference speed. While both architectures reached a similar Dice score of 70% on average, the PLS-Net was more accurate with an F1-score of up to 88%. The highest accuracy was achieved for the largest meningiomas. Speed-wise, the PLS-Net architecture tended to converge in about 50 hours while 130 hours were necessary for U-Net. Inference with PLS-Net takes less than a second on GPU and about 15 seconds on CPU. Overall, with the use of mixed precision training, it was possible to train competitive segmentation models in a relatively short amount of time using the lightweight PLS-Net architecture. In the future, the focus should be brought toward the segmentation of small meningiomas (less than 2ml) to improve clinical relevance for automatic and early diagnosis as well as speed of growth estimates.

In recent years, the landscape of computer-assisted interventions and post-operative surgical video analysis has been dramatically reshaped by deep-learning techniques, resulting in significant advancements in surgeons' skills, operation room management, and overall surgical outcomes. However, the progression of deep-learning-powered surgical technologies is profoundly reliant on large-scale datasets and annotations. Particularly, surgical scene understanding and phase recognition stand as pivotal pillars within the realm of computer-assisted surgery and post-operative assessment of cataract surgery videos. In this context, we present the largest cataract surgery video dataset that addresses diverse requisites for constructing computerized surgical workflow analysis and detecting post-operative irregularities in cataract surgery. We validate the quality of annotations by benchmarking the performance of several state-of-the-art neural network architectures for phase recognition and surgical scene segmentation. Besides, we initiate the research on domain adaptation for instrument segmentation in cataract surgery by evaluating cross-domain instrument segmentation performance in cataract surgery videos. The dataset and annotations will be publicly available upon acceptance of the paper.

3D Morphable Models (3DMMs) provide promising 3D face reconstructions in various applications. However, existing methods struggle to reconstruct faces with extreme expressions due to deficiencies in supervisory signals, such as sparse or inaccurate landmarks. Segmentation information contains effective geometric contexts for face reconstruction. Certain attempts intuitively depend on differentiable renderers to compare the rendered silhouettes of reconstruction with segmentation, which is prone to issues like local optima and gradient instability. In this paper, we fully utilize the facial part segmentation geometry by introducing Part Re-projection Distance Loss (PRDL). Specifically, PRDL transforms facial part segmentation into 2D points and re-projects the reconstruction onto the image plane. Subsequently, by introducing grid anchors and computing different statistical distances from these anchors to the point sets, PRDL establishes geometry descriptors to optimize the distribution of the point sets for face reconstruction. PRDL exhibits a clear gradient compared to the renderer-based methods and presents state-of-the-art reconstruction performance in extensive quantitative and qualitative experiments. Our project is available at https://github.com/wang-zidu/3DDFA-V3 .

We present AI-SARAH, a practical variant of SARAH. As a variant of SARAH, this algorithm employs the stochastic recursive gradient yet adjusts step-size based on local geometry. AI-SARAH implicitly computes step-size and efficiently estimates local Lipschitz smoothness of stochastic functions. It is fully adaptive, tune-free, straightforward to implement, and computationally efficient. We provide technical insight and intuitive illustrations on its design and convergence. We conduct extensive empirical analysis and demonstrate its strong performance compared with its classical counterparts and other state-of-the-art first-order methods in solving convex machine learning problems.

Fully quantized training (FQT) accelerates the training of deep neural networks by quantizing the activations, weights, and gradients into lower precision. To explore the ultimate limit of FQT (the lowest achievable precision), we make a first attempt to 1-bit FQT. We provide a theoretical analysis of FQT based on Adam and SGD, revealing that the gradient variance influences the convergence of FQT. Building on these theoretical results, we introduce an Activation Gradient Pruning (AGP) strategy. The strategy leverages the heterogeneity of gradients by pruning less informative gradients and enhancing the numerical precision of remaining gradients to mitigate gradient variance. Additionally, we propose Sample Channel joint Quantization (SCQ), which utilizes different quantization strategies in the computation of weight gradients and activation gradients to ensure that the method is friendly to low-bitwidth hardware. Finally, we present a framework to deploy our algorithm. For fine-tuning VGGNet-16 and ResNet-18 on multiple datasets, our algorithm achieves an average accuracy improvement of approximately 6%, compared to per-sample quantization. Moreover, our training speedup can reach a maximum of 5.13x compared to full precision training.

High-resolution 3D object generation remains a challenging task primarily due to the limited availability of comprehensive annotated training data. Recent advancements have aimed to overcome this constraint by harnessing image generative models, pretrained on extensive curated web datasets, using knowledge transfer techniques like Score Distillation Sampling (SDS). Efficiently addressing the requirements of high-resolution rendering often necessitates the adoption of latent representation-based models, such as the Latent Diffusion Model (LDM). In this framework, a significant challenge arises: To compute gradients for individual image pixels, it is necessary to backpropagate gradients from the designated latent space through the frozen components of the image model, such as the VAE encoder used within LDM. However, this gradient propagation pathway has never been optimized, remaining uncontrolled during training. We find that the unregulated gradients adversely affect the 3D model's capacity in acquiring texture-related information from the image generative model, leading to poor quality appearance synthesis. To address this overarching challenge, we propose an innovative operation termed Pixel-wise Gradient Clipping (PGC) designed for seamless integration into existing 3D generative models, thereby enhancing their synthesis quality. Specifically, we control the magnitude of stochastic gradients by clipping the pixel-wise gradients efficiently, while preserving crucial texture-related gradient directions. Despite this simplicity and minimal extra cost, extensive experiments demonstrate the efficacy of our PGC in enhancing the performance of existing 3D generative models for high-resolution object rendering.

This paper introduces a novel one-stage end-to-end detector specifically designed to detect small lesions in medical images. Precise localization of small lesions presents challenges due to their appearance and the diverse contextual backgrounds in which they are found. To address this, our approach introduces a new type of pixel-based anchor that dynamically moves towards the targeted lesion for detection. We refer to this new architecture as GravityNet, and the novel anchors as gravity points since they appear to be "attracted" by the lesions. We conducted experiments on two well-established medical problems involving small lesions to evaluate the performance of the proposed approach: microcalcifications detection in digital mammograms and microaneurysms detection in digital fundus images. Our method demonstrates promising results in effectively detecting small lesions in these medical imaging tasks.

In this study, we investigate the DIstribution Correction Estimation (DICE) methods, an important line of work in offline reinforcement learning (RL) and imitation learning (IL). DICE-based methods impose state-action-level behavior constraint, which is an ideal choice for offline learning. However, they typically perform much worse than current state-of-the-art (SOTA) methods that solely use action-level behavior constraint. After revisiting DICE-based methods, we find there exist two gradient terms when learning the value function using true-gradient update: forward gradient (taken on the current state) and backward gradient (taken on the next state). Using forward gradient bears a large similarity to many offline RL methods, and thus can be regarded as applying action-level constraint. However, directly adding the backward gradient may degenerate or cancel out its effect if these two gradients have conflicting directions. To resolve this issue, we propose a simple yet effective modification that projects the backward gradient onto the normal plane of the forward gradient, resulting in an orthogonal-gradient update, a new learning rule for DICE-based methods. We conduct thorough theoretical analyses and find that the projected backward gradient brings state-level behavior regularization, which reveals the mystery of DICE-based methods: the value learning objective does try to impose state-action-level constraint, but needs to be used in a corrected way. Through toy examples and extensive experiments on complex offline RL and IL tasks, we demonstrate that DICE-based methods using orthogonal-gradient updates (O-DICE) achieve SOTA performance and great robustness.

Gradient descent optimization algorithms, while increasingly popular, are often used as black-box optimizers, as practical explanations of their strengths and weaknesses are hard to come by. This article aims to provide the reader with intuitions with regard to the behaviour of different algorithms that will allow her to put them to use. In the course of this overview, we look at different variants of gradient descent, summarize challenges, introduce the most common optimization algorithms, review architectures in a parallel and distributed setting, and investigate additional strategies for optimizing gradient descent.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made important advances in the study of the optimization problem for overparametrized low-rank matrix approximation, much emphasis has been placed on discriminative settings and the square loss. In contrast, our model considers another interesting type of loss and connects with the generative setting. We characterize the critical points and minimizers of the Bures-Wasserstein distance over the space of rank-bounded matrices. For low-rank matrices the Hessian of this loss can theoretically blow up, which creates challenges to analyze convergence of optimizaton methods. We establish convergence results for gradient flow using a smooth perturbative version of the loss and convergence results for finite step size gradient descent under certain assumptions on the initial weights.

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects including contact and can be seamlessly incorporated into inference, control and co-design systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of control tasks for soft robots, including problems with nearly 3,000 decision variables.

We consider the training of the first layer of vision models and notice the clear relationship between pixel values and gradient update magnitudes: the gradients arriving at the weights of a first layer are by definition directly proportional to (normalized) input pixel values. Thus, an image with low contrast has a smaller impact on learning than an image with higher contrast, and a very bright or very dark image has a stronger impact on the weights than an image with moderate brightness. In this work, we propose performing gradient descent on the embeddings produced by the first layer of the model. However, switching to discrete inputs with an embedding layer is not a reasonable option for vision models. Thus, we propose the conceptual procedure of (i) a gradient descent step on first layer activations to construct an activation proposal, and (ii) finding the optimal weights of the first layer, i.e., those weights which minimize the squared distance to the activation proposal. We provide a closed form solution of the procedure and adjust it for robust stochastic training while computing everything efficiently. Empirically, we find that TrAct (Training Activations) speeds up training by factors between 1.25x and 4x while requiring only a small computational overhead. We demonstrate the utility of TrAct with different optimizers for a range of different vision models including convolutional and transformer architectures.

Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & Yarats, 2018). This work is an additional step in this direction. In particular, we exploit the ubiquitous clustering structure of rich datasets used in deep learning to design a family of scalable variance reduced optimization procedures by combining existing optimizers (e.g., SGD+Momentum, Quasi Hyperbolic Momentum, Implicit Gradient Transport) with a multi-momentum strategy (Yuan et al., 2019). Our proposal leads to faster convergence than vanilla methods on standard benchmark datasets (e.g., CIFAR and ImageNet). It is robust to label noise and amenable to distributed optimization. We provide a parallel implementation in JAX.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

This is a handbook of simple proofs of the convergence of gradient and stochastic gradient descent type methods. We consider functions that are Lipschitz, smooth, convex, strongly convex, and/or Polyak-{\L}ojasiewicz functions. Our focus is on ``good proofs'' that are also simple. Each section can be consulted separately. We start with proofs of gradient descent, then on stochastic variants, including minibatching and momentum. Then move on to nonsmooth problems with the subgradient method, the proximal gradient descent and their stochastic variants. Our focus is on global convergence rates and complexity rates. Some slightly less common proofs found here include that of SGD (Stochastic gradient descent) with a proximal step, with momentum, and with mini-batching without replacement.

Deep artificial neural networks (DNNs) are typically trained via gradient-based learning algorithms, namely backpropagation. Evolution strategies (ES) can rival backprop-based algorithms such as Q-learning and policy gradients on challenging deep reinforcement learning (RL) problems. However, ES can be considered a gradient-based algorithm because it performs stochastic gradient descent via an operation similar to a finite-difference approximation of the gradient. That raises the question of whether non-gradient-based evolutionary algorithms can work at DNN scales. Here we demonstrate they can: we evolve the weights of a DNN with a simple, gradient-free, population-based genetic algorithm (GA) and it performs well on hard deep RL problems, including Atari and humanoid locomotion. The Deep GA successfully evolves networks with over four million free parameters, the largest neural networks ever evolved with a traditional evolutionary algorithm. These results (1) expand our sense of the scale at which GAs can operate, (2) suggest intriguingly that in some cases following the gradient is not the best choice for optimizing performance, and (3) make immediately available the multitude of neuroevolution techniques that improve performance. We demonstrate the latter by showing that combining DNNs with novelty search, which encourages exploration on tasks with deceptive or sparse reward functions, can solve a high-dimensional problem on which reward-maximizing algorithms (e.g.\ DQN, A3C, ES, and the GA) fail. Additionally, the Deep GA is faster than ES, A3C, and DQN (it can train Atari in {raise.17ex\scriptstyle\sim}4 hours on one desktop or {raise.17ex\scriptstyle\sim}1 hour distributed on 720 cores), and enables a state-of-the-art, up to 10,000-fold compact encoding technique.

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

While backpropagation (BP) is the mainstream approach for gradient computation in neural network training, its heavy reliance on the chain rule of differentiation constrains the designing flexibility of network architecture and training pipelines. We avoid the recursive computation in BP and develop a unified likelihood ratio (ULR) method for gradient estimation with just one forward propagation. Not only can ULR be extended to train a wide variety of neural network architectures, but the computation flow in BP can also be rearranged by ULR for better device adaptation. Moreover, we propose several variance reduction techniques to further accelerate the training process. Our experiments offer numerical results across diverse aspects, including various neural network training scenarios, computation flow rearrangement, and fine-tuning of pre-trained models. All findings demonstrate that ULR effectively enhances the flexibility of neural network training by permitting localized module training without compromising the global objective and significantly boosts the network robustness.

In recent years, various powerful policy gradient algorithms have been proposed in deep reinforcement learning. While all these algorithms build on the Policy Gradient Theorem, the specific design choices differ significantly across algorithms. We provide a holistic overview of on-policy policy gradient algorithms to facilitate the understanding of both their theoretical foundations and their practical implementations. In this overview, we include a detailed proof of the continuous version of the Policy Gradient Theorem, convergence results and a comprehensive discussion of practical algorithms. We compare the most prominent algorithms on continuous control environments and provide insights on the benefits of regularization. All code is available at https://github.com/Matt00n/PolicyGradientsJax.

There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training data, learning under privacy constraints, or even heavy-tailed noise due to the dynamics of the algorithm itself. Here we study SGD with robust gradient estimators based on estimating the median. We first consider computing the median gradient across samples, and show that the resulting method can converge even under heavy-tailed, state-dependent noise. We then derive iterative methods based on the stochastic proximal point method for computing the geometric median and generalizations thereof. Finally we propose an algorithm estimating the median gradient across iterations, and find that several well known methods - in particular different forms of clipping - are particular cases of this framework.

In the radiation therapy of nasopharyngeal carcinoma (NPC), clinicians typically delineate the gross tumor volume (GTV) using non-contrast planning computed tomography to ensure accurate radiation dose delivery. However, the low contrast between tumors and adjacent normal tissues necessitates that radiation oncologists manually delineate the tumors, often relying on diagnostic MRI for guidance. % In this study, we propose a novel approach to directly segment NPC gross tumors on non-contrast planning CT images, circumventing potential registration errors when aligning MRI or MRI-derived tumor masks to planning CT. To address the low contrast issues between tumors and adjacent normal structures in planning CT, we introduce a 3D Semantic Asymmetry Tumor segmentation (SATs) method. Specifically, we posit that a healthy nasopharyngeal region is characteristically bilaterally symmetric, whereas the emergence of nasopharyngeal carcinoma disrupts this symmetry. Then, we propose a Siamese contrastive learning segmentation framework that minimizes the voxel-wise distance between original and flipped areas without tumor and encourages a larger distance between original and flipped areas with tumor. Thus, our approach enhances the sensitivity of features to semantic asymmetries. % Extensive experiments demonstrate that the proposed SATs achieves the leading NPC GTV segmentation performance in both internal and external testing, e.g., with at least 2\% absolute Dice score improvement and 12\% average distance error reduction when compared to other state-of-the-art methods in the external testing.

Organ at risk (OAR) segmentation is a critical process in radiotherapy treatment planning such as head and neck tumors. Nevertheless, in clinical practice, radiation oncologists predominantly perform OAR segmentations manually on CT scans. This manual process is highly time-consuming and expensive, limiting the number of patients who can receive timely radiotherapy. Additionally, CT scans offer lower soft-tissue contrast compared to MRI. Despite MRI providing superior soft-tissue visualization, its time-consuming nature makes it infeasible for real-time treatment planning. To address these challenges, we propose a method called SegReg, which utilizes Elastic Symmetric Normalization for registering MRI to perform OAR segmentation. SegReg outperforms the CT-only baseline by 16.78% in mDSC and 18.77% in mIoU, showing that it effectively combines the geometric accuracy of CT with the superior soft-tissue contrast of MRI, making accurate automated OAR segmentation for clinical practice become possible. See project website https://steve-zeyu-zhang.github.io/SegReg

This study addresses the challenge of accurately segmenting 3D Gaussian Splatting from 2D masks. Conventional methods often rely on iterative gradient descent to assign each Gaussian a unique label, leading to lengthy optimization and sub-optimal solutions. Instead, we propose a straightforward yet globally optimal solver for 3D-GS segmentation. The core insight of our method is that, with a reconstructed 3D-GS scene, the rendering of the 2D masks is essentially a linear function with respect to the labels of each Gaussian. As such, the optimal label assignment can be solved via linear programming in closed form. This solution capitalizes on the alpha blending characteristic of the splatting process for single step optimization. By incorporating the background bias in our objective function, our method shows superior robustness in 3D segmentation against noises. Remarkably, our optimization completes within 30 seconds, about 50times faster than the best existing methods. Extensive experiments demonstrate the efficiency and robustness of our method in segmenting various scenes, and its superior performance in downstream tasks such as object removal and inpainting. Demos and code will be available at https://github.com/florinshen/FlashSplat.

Anatomical segmentation is a fundamental task in medical image computing, generally tackled with fully convolutional neural networks which produce dense segmentation masks. These models are often trained with loss functions such as cross-entropy or Dice, which assume pixels to be independent of each other, thus ignoring topological errors and anatomical inconsistencies. We address this limitation by moving from pixel-level to graph representations, which allow to naturally incorporate anatomical constraints by construction. To this end, we introduce HybridGNet, an encoder-decoder neural architecture that leverages standard convolutions for image feature encoding and graph convolutional neural networks (GCNNs) to decode plausible representations of anatomical structures. We also propose a novel image-to-graph skip connection layer which allows localized features to flow from standard convolutional blocks to GCNN blocks, and show that it improves segmentation accuracy. The proposed architecture is extensively evaluated in a variety of domain shift and image occlusion scenarios, and audited considering different types of demographic domain shift. Our comprehensive experimental setup compares HybridGNet with other landmark and pixel-based models for anatomical segmentation in chest x-ray images, and shows that it produces anatomically plausible results in challenging scenarios where other models tend to fail.

Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL). Renowned for its convergence guarantees and stability compared to other RL algorithms, its practical application is often hindered by sensitivity to hyper-parameters, particularly the step-size. In this paper, we introduce the integration of the Polyak step-size in RL, which automatically adjusts the step-size without prior knowledge. To adapt this method to RL settings, we address several issues, including unknown f* in the Polyak step-size. Additionally, we showcase the performance of the Polyak step-size in RL through experiments, demonstrating faster convergence and the attainment of more stable policies.

Differential private optimization for nonconvex smooth objective is considered. In the previous work, the best known utility bound is widetilde O(d/(nvarepsilon_DP)) in terms of the squared full gradient norm, which is achieved by Differential Private Gradient Descent (DP-GD) as an instance, where n is the sample size, d is the problem dimensionality and varepsilon_DP is the differential privacy parameter. To improve the best known utility bound, we propose a new differential private optimization framework called DIFF2 (DIFFerential private optimization via gradient DIFFerences) that constructs a differential private global gradient estimator with possibly quite small variance based on communicated gradient differences rather than gradients themselves. It is shown that DIFF2 with a gradient descent subroutine achieves the utility of widetilde O(d^{2/3}/(nvarepsilon_DP)^{4/3}), which can be significantly better than the previous one in terms of the dependence on the sample size n. To the best of our knowledge, this is the first fundamental result to improve the standard utility widetilde O(d/(nvarepsilon_DP)) for nonconvex objectives. Additionally, a more computational and communication efficient subroutine is combined with DIFF2 and its theoretical analysis is also given. Numerical experiments are conducted to validate the superiority of DIFF2 framework.

We introduce DIFFTACTILE, a physics-based differentiable tactile simulation system designed to enhance robotic manipulation with dense and physically accurate tactile feedback. In contrast to prior tactile simulators which primarily focus on manipulating rigid bodies and often rely on simplified approximations to model stress and deformations of materials in contact, DIFFTACTILE emphasizes physics-based contact modeling with high fidelity, supporting simulations of diverse contact modes and interactions with objects possessing a wide range of material properties. Our system incorporates several key components, including a Finite Element Method (FEM)-based soft body model for simulating the sensing elastomer, a multi-material simulator for modeling diverse object types (such as elastic, elastoplastic, cables) under manipulation, a penalty-based contact model for handling contact dynamics. The differentiable nature of our system facilitates gradient-based optimization for both 1) refining physical properties in simulation using real-world data, hence narrowing the sim-to-real gap and 2) efficient learning of tactile-assisted grasping and contact-rich manipulation skills. Additionally, we introduce a method to infer the optical response of our tactile sensor to contact using an efficient pixel-based neural module. We anticipate that DIFFTACTILE will serve as a useful platform for studying contact-rich manipulations, leveraging the benefits of dense tactile feedback and differentiable physics. Code and supplementary materials are available at the project website https://difftactile.github.io/.

We present As-Plausible-as-Possible (APAP) mesh deformation technique that leverages 2D diffusion priors to preserve the plausibility of a mesh under user-controlled deformation. Our framework uses per-face Jacobians to represent mesh deformations, where mesh vertex coordinates are computed via a differentiable Poisson Solve. The deformed mesh is rendered, and the resulting 2D image is used in the Score Distillation Sampling (SDS) process, which enables extracting meaningful plausibility priors from a pretrained 2D diffusion model. To better preserve the identity of the edited mesh, we fine-tune our 2D diffusion model with LoRA. Gradients extracted by SDS and a user-prescribed handle displacement are then backpropagated to the per-face Jacobians, and we use iterative gradient descent to compute the final deformation that balances between the user edit and the output plausibility. We evaluate our method with 2D and 3D meshes and demonstrate qualitative and quantitative improvements when using plausibility priors over geometry-preservation or distortion-minimization priors used by previous techniques. Our project page is at: https://as-plausible-aspossible.github.io/

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

As lung cancer evolves, the presence of enlarged and potentially malignant lymph nodes must be assessed to properly estimate disease progression and select the best treatment strategy. Following the clinical guidelines, estimation of short-axis diameter and mediastinum station are paramount for correct diagnosis. A method for accurate and automatic segmentation is hence decisive for quantitatively describing lymph nodes. In this study, the use of 3D convolutional neural networks, either through slab-wise schemes or the leveraging of downsampled entire volumes, is investigated. Furthermore, the potential impact from simple ensemble strategies is considered. As lymph nodes have similar attenuation values to nearby anatomical structures, we suggest using the knowledge of other organs as prior information to guide the segmentation task. To assess the segmentation and instance detection performances, a 5-fold cross-validation strategy was followed over a dataset of 120 contrast-enhanced CT volumes. For the 1178 lymph nodes with a short-axis diameter geq10 mm, our best performing approach reached a patient-wise recall of 92%, a false positive per patient ratio of 5, and a segmentation overlap of 80.5%. The method performs similarly well across all stations. Fusing a slab-wise and a full volume approach within an ensemble scheme generated the best performances. The anatomical priors guiding strategy is promising, yet a larger set than four organs appears needed to generate an optimal benefit. A larger dataset is also mandatory, given the wide range of expressions a lymph node can exhibit (i.e., shape, location, and attenuation), and contrast uptake variations.

Extent of resection after surgery is one of the main prognostic factors for patients diagnosed with glioblastoma. To achieve this, accurate segmentation and classification of residual tumor from post-operative MR images is essential. The current standard method for estimating it is subject to high inter- and intra-rater variability, and an automated method for segmentation of residual tumor in early post-operative MRI could lead to a more accurate estimation of extent of resection. In this study, two state-of-the-art neural network architectures for pre-operative segmentation were trained for the task. The models were extensively validated on a multicenter dataset with nearly 1000 patients, from 12 hospitals in Europe and the United States. The best performance achieved was a 61\% Dice score, and the best classification performance was about 80\% balanced accuracy, with a demonstrated ability to generalize across hospitals. In addition, the segmentation performance of the best models was on par with human expert raters. The predicted segmentations can be used to accurately classify the patients into those with residual tumor, and those with gross total resection.

We propose efficient Langevin Monte Carlo algorithms for sampling distributions with nonsmooth convex composite potentials, which is the sum of a continuously differentiable function and a possibly nonsmooth function. We devise such algorithms leveraging recent advances in convex analysis and optimization methods involving Bregman divergences, namely the Bregman--Moreau envelopes and the Bregman proximity operators, and in the Langevin Monte Carlo algorithms reminiscent of mirror descent. The proposed algorithms extend existing Langevin Monte Carlo algorithms in two aspects -- the ability to sample nonsmooth distributions with mirror descent-like algorithms, and the use of the more general Bregman--Moreau envelope in place of the Moreau envelope as a smooth approximation of the nonsmooth part of the potential. A particular case of the proposed scheme is reminiscent of the Bregman proximal gradient algorithm. The efficiency of the proposed methodology is illustrated with various sampling tasks at which existing Langevin Monte Carlo methods are known to perform poorly.

This paper extends the classic theory of convex optimization to the minimization of functions that are equal to the negated logarithm of what we term as a sum-log-concave function, i.e., a sum of log-concave functions. In particular, we show that such functions are in general not convex but still satisfy generalized convexity inequalities. These inequalities unveil the key importance of a certain vector that we call the cross-gradient and that is, in general, distinct from the usual gradient. Thus, we propose the Cross Gradient Descent (XGD) algorithm moving in the opposite direction of the cross-gradient and derive a convergence analysis. As an application of our sum-log-concave framework, we introduce the so-called checkered regression method relying on a sum-log-concave function. This classifier extends (multiclass) logistic regression to non-linearly separable problems since it is capable of tessellating the feature space by using any given number of hyperplanes, creating a checkerboard-like pattern of decision regions.

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives.

Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection of variational objectives and gradient estimators, which are implemented monolithically (and without formal correctness arguments) in PPL backends. In this paper, we propose a more modular approach to supporting variational inference in PPLs, based on compositional program transformation. In our approach, variational objectives are expressed as programs, that may employ first-class constructs for computing densities of and expected values under user-defined models and variational families. We then transform these programs systematically into unbiased gradient estimators for optimizing the objectives they define. Our design enables modular reasoning about many interacting concerns, including automatic differentiation, density accumulation, tracing, and the application of unbiased gradient estimation strategies. Additionally, relative to existing support for VI in PPLs, our design increases expressiveness along three axes: (1) it supports an open-ended set of user-defined variational objectives, rather than a fixed menu of options; (2) it supports a combinatorial space of gradient estimation strategies, many not automated by today's PPLs; and (3) it supports a broader class of models and variational families, because it supports constructs for approximate marginalization and normalization (previously introduced only for Monte Carlo inference). We implement our approach in an extension to the Gen probabilistic programming system (genjax.vi, implemented in JAX), and evaluate on several deep generative modeling tasks, showing minimal performance overhead vs. hand-coded implementations and performance competitive with well-established open-source PPLs.

We tackle the problem of image inpainting in the remote sensing domain. Remote sensing images possess high resolution and geographical variations, that render the conventional inpainting methods less effective. This further entails the requirement of models with high complexity to sufficiently capture the spectral, spatial and textural nuances within an image, emerging from its high spatial variability. To this end, we propose a novel inpainting method that individually focuses on each aspect of an image such as edges, colour and texture using a task specific GAN. Moreover, each individual GAN also incorporates the attention mechanism that explicitly extracts the spectral and spatial features. To ensure consistent gradient flow, the model uses residual learning paradigm, thus simultaneously working with high and low level features. We evaluate our model, alongwith previous state of the art models, on the two well known remote sensing datasets, Open Cities AI and Earth on Canvas, and achieve competitive performance.

While deep learning models have become the predominant method for medical image segmentation, they are typically not capable of generalizing to unseen segmentation tasks involving new anatomies, image modalities, or labels. Given a new segmentation task, researchers generally have to train or fine-tune models, which is time-consuming and poses a substantial barrier for clinical researchers, who often lack the resources and expertise to train neural networks. We present UniverSeg, a method for solving unseen medical segmentation tasks without additional training. Given a query image and example set of image-label pairs that define a new segmentation task, UniverSeg employs a new Cross-Block mechanism to produce accurate segmentation maps without the need for additional training. To achieve generalization to new tasks, we have gathered and standardized a collection of 53 open-access medical segmentation datasets with over 22,000 scans, which we refer to as MegaMedical. We used this collection to train UniverSeg on a diverse set of anatomies and imaging modalities. We demonstrate that UniverSeg substantially outperforms several related methods on unseen tasks, and thoroughly analyze and draw insights about important aspects of the proposed system. The UniverSeg source code and model weights are freely available at https://universeg.csail.mit.edu

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex objectives on these domains, utilizing the principles of Sinkhorn matrix scaling and mirror descent. The proposed algorithm is robust to noise, and can be used in an online setting. We provide theoretical guarantees for convex objectives and experimental results showcasing it effectiveness on both synthetic and real-world data.

Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-specific progressions is essential for effective therapies. Current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. This "one size fits all" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. We present the GliODIL framework, which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging, leveraging a Fisher-Kolmogorov type physics model to describe tumor growth. This is achieved through the newly introduced method of Optimizing the Discrete Loss (ODIL), where both data and physics-based constraints are softly assimilated into the solution. Our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. By blending data-driven techniques with physics-based constraints, GliODIL enhances recurrence prediction in radiotherapy planning, challenging traditional uniform margins and strict adherence to the Fisher-Kolmogorov partial differential equation (PDE) model, which is adapted for complex cases.

Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a mathcal{O}(varepsilon^{-2.5}) sample complexity of this method for finding a global varepsilon-optimal policy. Improving over the previously known mathcal{O}(varepsilon^{-3}) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to mathcal{mathcal{O} }(varepsilon^{-2}) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.

Diffusion models have recently gained recognition for generating diverse and high-quality content, especially in the domain of image synthesis. These models excel not only in creating fixed-size images but also in producing panoramic images. However, existing methods often struggle with spatial layout consistency when producing high-resolution panoramas, due to the lack of guidance of the global image layout. In this paper, we introduce the Multi-Scale Diffusion (MSD) framework, a plug-and-play module that extends the existing panoramic image generation framework to multiple resolution levels. By utilizing gradient descent techniques, our method effectively incorporates structural information from low-resolution images into high-resolution outputs. A comprehensive evaluation of the proposed method was conducted, comparing it with the prior works in qualitative and quantitative dimensions. The evaluation results demonstrate that our method significantly outperforms others in generating coherent high-resolution panoramas.

We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings: they either assume some knowledge of the problem parameters, impose strong global Lipschitz conditions, or fail to give bounds that hold with high probability. We provide a comprehensive analysis of this basic method without any of these limitations, in both the convex and non-convex (smooth) cases, that additionally supports a general ``affine variance'' noise model and provides sharp rates of convergence in both the low-noise and high-noise~regimes.

We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and leverages its underlying structure making the gradients sequentially predictable. By exploiting the predictability and ideas from optimistic online learning, the proposed algorithm can accelerate the convergence and increase sample efficiency. After establishing a tighter upper bound under some convexity conditions on the regret, we offer a complimentary view of our algorithm which generalizes the offline and stochastic version of nonconvex optimization. In the nonconvex case, we establish a non-asymptotic convergence bound independently of the initialization. We illustrate the practical speedup on several deep learning models via numerical experiments.

Deep multitask networks, in which one neural network produces multiple predictive outputs, can offer better speed and performance than their single-task counterparts but are challenging to train properly. We present a gradient normalization (GradNorm) algorithm that automatically balances training in deep multitask models by dynamically tuning gradient magnitudes. We show that for various network architectures, for both regression and classification tasks, and on both synthetic and real datasets, GradNorm improves accuracy and reduces overfitting across multiple tasks when compared to single-task networks, static baselines, and other adaptive multitask loss balancing techniques. GradNorm also matches or surpasses the performance of exhaustive grid search methods, despite only involving a single asymmetry hyperparameter alpha. Thus, what was once a tedious search process that incurred exponentially more compute for each task added can now be accomplished within a few training runs, irrespective of the number of tasks. Ultimately, we will demonstrate that gradient manipulation affords us great control over the training dynamics of multitask networks and may be one of the keys to unlocking the potential of multitask learning.

Contrastive learning has been applied successfully to learn vector representations of text. Previous research demonstrated that learning high-quality representations benefits from batch-wise contrastive loss with a large number of negatives. In practice, the technique of in-batch negative is used, where for each example in a batch, other batch examples' positives will be taken as its negatives, avoiding encoding extra negatives. This, however, still conditions each example's loss on all batch examples and requires fitting the entire large batch into GPU memory. This paper introduces a gradient caching technique that decouples backpropagation between contrastive loss and the encoder, removing encoder backward pass data dependency along the batch dimension. As a result, gradients can be computed for one subset of the batch at a time, leading to almost constant memory usage.

There are two widely known issues with properly training Recurrent Neural Networks, the vanishing and the exploding gradient problems detailed in Bengio et al. (1994). In this paper we attempt to improve the understanding of the underlying issues by exploring these problems from an analytical, a geometric and a dynamical systems perspective. Our analysis is used to justify a simple yet effective solution. We propose a gradient norm clipping strategy to deal with exploding gradients and a soft constraint for the vanishing gradients problem. We validate empirically our hypothesis and proposed solutions in the experimental section.

We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm drives a natural stationarity measure to zero at the rate O(k^{-1/4}). As a consequence, we obtain the first complexity guarantees for the stochastic proximal point, proximal subgradient, and regularized Gauss-Newton methods for minimizing compositions of convex functions with smooth maps. The guiding principle, underlying the complexity guarantees, is that all algorithms under consideration can be interpreted as approximate descent methods on an implicit smoothing of the problem, given by the Moreau envelope. Specializing to classical circumstances, we obtain the long-sought convergence rate of the stochastic projected gradient method, without batching, for minimizing a smooth function on a closed convex set.

Many optimization problems are inherently multi-objective. To address them, we formalize Jacobian descent (JD), a direct generalization of gradient descent for vector-valued functions. Each step of this algorithm relies on a Jacobian matrix consisting of one gradient per objective. The aggregator, responsible for reducing this matrix into an update vector, characterizes JD. While the multi-task learning literature already contains a variety of aggregators, they often lack some natural properties. In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient. We propose a new aggregator specifically designed to satisfy this. Emphasizing conflict between objectives, we then highlight direct applications for our methods. Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective. On simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. The performance of our aggregator in those experiments also corroborates our theoretical findings. Lastly, as speed is the main limitation of JD, we provide a path towards a more efficient implementation.

Deep neural networks are vulnerable to universal adversarial perturbation (UAP), an instance-agnostic perturbation capable of fooling the target model for most samples. Compared to instance-specific adversarial examples, UAP is more challenging as it needs to generalize across various samples and models. In this paper, we examine the serious dilemma of UAP generation methods from a generalization perspective -- the gradient vanishing problem using small-batch stochastic gradient optimization and the local optima problem using large-batch optimization. To address these problems, we propose a simple and effective method called Stochastic Gradient Aggregation (SGA), which alleviates the gradient vanishing and escapes from poor local optima at the same time. Specifically, SGA employs the small-batch training to perform multiple iterations of inner pre-search. Then, all the inner gradients are aggregated as a one-step gradient estimation to enhance the gradient stability and reduce quantization errors. Extensive experiments on the standard ImageNet dataset demonstrate that our method significantly enhances the generalization ability of UAP and outperforms other state-of-the-art methods. The code is available at https://github.com/liuxuannan/Stochastic-Gradient-Aggregation.

Federated Learning (FL) has recently emerged as a promising distributed machine learning framework to preserve clients' privacy, by allowing multiple clients to upload the gradients calculated from their local data to a central server. Recent studies find that the exchanged gradients also take the risk of privacy leakage, e.g., an attacker can invert the shared gradients and recover sensitive data against an FL system by leveraging pre-trained generative adversarial networks (GAN) as prior knowledge. However, performing gradient inversion attacks in the latent space of the GAN model limits their expression ability and generalizability. To tackle these challenges, we propose Gradient Inversion over Feature Domains (GIFD), which disassembles the GAN model and searches the feature domains of the intermediate layers. Instead of optimizing only over the initial latent code, we progressively change the optimized layer, from the initial latent space to intermediate layers closer to the output images. In addition, we design a regularizer to avoid unreal image generation by adding a small {l_1} ball constraint to the searching range. We also extend GIFD to the out-of-distribution (OOD) setting, which weakens the assumption that the training sets of GANs and FL tasks obey the same data distribution. Extensive experiments demonstrate that our method can achieve pixel-level reconstruction and is superior to the existing methods. Notably, GIFD also shows great generalizability under different defense strategy settings and batch sizes.

The recently introduced Segment Anything Model (SAM) combines a clever architecture and large quantities of training data to obtain remarkable image segmentation capabilities. However, it fails to reproduce such results for Out-Of-Distribution (OOD) domains such as medical images. Moreover, while SAM is conditioned on either a mask or a set of points, it may be desirable to have a fully automatic solution. In this work, we replace SAM's conditioning with an encoder that operates on the same input image. By adding this encoder and without further fine-tuning SAM, we obtain state-of-the-art results on multiple medical images and video benchmarks. This new encoder is trained via gradients provided by a frozen SAM. For inspecting the knowledge within it, and providing a lightweight segmentation solution, we also learn to decode it into a mask by a shallow deconvolution network.

Ridge Rider (RR) is an algorithm for finding diverse solutions to optimization problems by following eigenvectors of the Hessian ("ridges"). RR is designed for conservative gradient systems (i.e., settings involving a single loss function), where it branches at saddles - easy-to-find bifurcation points. We generalize this idea to non-conservative, multi-agent gradient systems by proposing a method - denoted Generalized Ridge Rider (GRR) - for finding arbitrary bifurcation points. We give theoretical motivation for our method by leveraging machinery from the field of dynamical systems. We construct novel toy problems where we can visualize new phenomena while giving insight into high-dimensional problems of interest. Finally, we empirically evaluate our method by finding diverse solutions in the iterated prisoners' dilemma and relevant machine learning problems including generative adversarial networks.

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the stepsize. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the stepsize but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

We introduce Gradient Descent with Adaptive Momentum Scaling (Grams), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning. Unlike traditional optimizers that directly integrate momentum into updates, Grams separates the update direction, derived from current gradients, from momentum, which is used solely for adaptive magnitude scaling. This approach enables Grams to achieve improved loss descent compared to state-of-the-art cautious and momentum-based optimizers. We establish a global convergence guarantee for Grams and validate its effectiveness through extensive empirical evaluations. The results demonstrate Grams' superior performance, including faster convergence and better generalization, compared to widely-used optimizers such as Adam, Lion, and their cautious variants. Our results highlight Grams' potential as a transformative approach for efficient optimization in large-scale machine learning.

Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian settings. However, some of the most popular of these optimization tools - namely Adam , Adagrad and the more recent Amsgrad - remain to be generalized to Riemannian manifolds. We discuss the difficulty of generalizing such adaptive schemes to the most agnostic Riemannian setting, and then provide algorithms and convergence proofs for geodesically convex objectives in the particular case of a product of Riemannian manifolds, in which adaptivity is implemented across manifolds in the cartesian product. Our generalization is tight in the sense that choosing the Euclidean space as Riemannian manifold yields the same algorithms and regret bounds as those that were already known for the standard algorithms. Experimentally, we show faster convergence and to a lower train loss value for Riemannian adaptive methods over their corresponding baselines on the realistic task of embedding the WordNet taxonomy in the Poincare ball.

Surgical video segmentation is a critical task in computer-assisted surgery and is vital for enhancing surgical quality and patient outcomes. Recently, the Segment Anything Model 2 (SAM2) framework has shown superior advancements in image and video segmentation. However, SAM2 struggles with efficiency due to the high computational demands of processing high-resolution images and complex and long-range temporal dynamics in surgical videos. To address these challenges, we introduce Surgical SAM 2 (SurgSAM-2), an advanced model to utilize SAM2 with an Efficient Frame Pruning (EFP) mechanism, to facilitate real-time surgical video segmentation. The EFP mechanism dynamically manages the memory bank by selectively retaining only the most informative frames, reducing memory usage and computational cost while maintaining high segmentation accuracy. Our extensive experiments demonstrate that SurgSAM-2 significantly improves both efficiency and segmentation accuracy compared to the vanilla SAM2. Remarkably, SurgSAM-2 achieves a 3times FPS compared with SAM2, while also delivering state-of-the-art performance after fine-tuning with lower-resolution data. These advancements establish SurgSAM-2 as a leading model for surgical video analysis, making real-time surgical video segmentation in resource-constrained environments a feasible reality.

Exploiting partial first-order information in a cyclic way is arguably the most natural strategy to obtain scalable first-order methods. However, despite their wide use in practice, cyclic schemes are far less understood from a theoretical perspective than their randomized counterparts. Motivated by a recent success in analyzing an extrapolated cyclic scheme for generalized variational inequalities, we propose an Accelerated Cyclic Coordinate Dual Averaging with Extrapolation (A-CODER) method for composite convex optimization, where the objective function can be expressed as the sum of a smooth convex function accessible via a gradient oracle and a convex, possibly nonsmooth, function accessible via a proximal oracle. We show that A-CODER attains the optimal convergence rate with improved dependence on the number of blocks compared to prior work. Furthermore, for the setting where the smooth component of the objective function is expressible in a finite sum form, we introduce a variance-reduced variant of A-CODER, VR-A-CODER, with state-of-the-art complexity guarantees. Finally, we demonstrate the effectiveness of our algorithms through numerical experiments.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the L^2 difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

This paper investigates the global convergence of stepsized Newton methods for convex functions. We propose several simple stepsize schedules with fast global convergence guarantees, up to O (k^{-3}), nearly matching lower complexity bounds Omega (k^{-3.5}) of second-order methods. For cases with multiple plausible smoothness parameterizations or an unknown smoothness constant, we introduce a stepsize backtracking procedure that ensures convergence as if the optimal smoothness parameters were known.

We consider the optimization problem of the form min_{x in R^d} f(x) triangleq E_{xi} [F(x; xi)], where the component F(x;xi) is L-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently proposed gradient-free method requires at most O( L^4 d^{3/2} epsilon^{-4} + Delta L^3 d^{3/2} delta^{-1} epsilon^{-4}) stochastic zeroth-order oracle complexity to find a (delta,epsilon)-Goldstein stationary point of objective function, where Delta = f(x_0) - inf_{x in R^d} f(x) and x_0 is the initial point of the algorithm. This paper proposes a more efficient algorithm using stochastic recursive gradient estimators, which improves the complexity to O(L^3 d^{3/2} epsilon^{-3}+ Delta L^2 d^{3/2} delta^{-1} epsilon^{-3}).

We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO ), a gradient-based method that incorporates the interactions between the two players in zero-sum games for optimization updates. We provide continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, CGO predecessors degenerate to their gradient descent ascent (GDA) variants. We provide a rate of convergence to stationary points and further propose a generalized class of alpha-coherent function for which we provide convergence analysis. We show that for strictly alpha-coherent functions, our algorithm convergences to a saddle point. Moreover, we propose optimistic CGO (OCGO), an optimistic variant, for which we show convergence rate to saddle points in alpha-coherent class of functions.

We propose a method that achieves near-optimal rates for smooth stochastic convex optimization and requires essentially no prior knowledge of problem parameters. This improves on prior work which requires knowing at least the initial distance to optimality d0. Our method, U-DoG, combines UniXGrad (Kavis et al., 2019) and DoG (Ivgi et al., 2023) with novel iterate stabilization techniques. It requires only loose bounds on d0 and the noise magnitude, provides high probability guarantees under sub-Gaussian noise, and is also near-optimal in the non-smooth case. Our experiments show consistent, strong performance on convex problems and mixed results on neural network training.

The ability to automatically detect and track surgical instruments in endoscopic videos can enable transformational interventions. Assessing surgical performance and efficiency, identifying skilled tool use and choreography, and planning operational and logistical aspects of OR resources are just a few of the applications that could benefit. Unfortunately, obtaining the annotations needed to train machine learning models to identify and localize surgical tools is a difficult task. Annotating bounding boxes frame-by-frame is tedious and time-consuming, yet large amounts of data with a wide variety of surgical tools and surgeries must be captured for robust training. Moreover, ongoing annotator training is needed to stay up to date with surgical instrument innovation. In robotic-assisted surgery, however, potentially informative data like timestamps of instrument installation and removal can be programmatically harvested. The ability to rely on tool installation data alone would significantly reduce the workload to train robust tool-tracking models. With this motivation in mind we invited the surgical data science community to participate in the challenge, SurgToolLoc 2022. The goal was to leverage tool presence data as weak labels for machine learning models trained to detect tools and localize them in video frames with bounding boxes. We present the results of this challenge along with many of the team's efforts. We conclude by discussing these results in the broader context of machine learning and surgical data science. The training data used for this challenge consisting of 24,695 video clips with tool presence labels is also being released publicly and can be accessed at https://console.cloud.google.com/storage/browser/isi-surgtoolloc-2022.

Weight sharing is a fundamental concept in neural architecture search (NAS), enabling gradient-based methods to explore cell-based architecture spaces significantly faster than traditional blackbox approaches. In parallel, weight entanglement has emerged as a technique for intricate parameter sharing among architectures within macro-level search spaces. %However, the macro structure of such spaces poses compatibility challenges for gradient-based NAS methods. %As a result, blackbox optimization methods have been commonly employed, particularly in conjunction with supernet training, to maintain search efficiency. %Due to the inherent differences in the structure of these search spaces, these Since weight-entanglement poses compatibility challenges for gradient-based NAS methods, these two paradigms have largely developed independently in parallel sub-communities. This paper aims to bridge the gap between these sub-communities by proposing a novel scheme to adapt gradient-based methods for weight-entangled spaces. This enables us to conduct an in-depth comparative assessment and analysis of the performance of gradient-based NAS in weight-entangled search spaces. Our findings reveal that this integration of weight-entanglement and gradient-based NAS brings forth the various benefits of gradient-based methods (enhanced performance, improved supernet training properties and superior any-time performance), while preserving the memory efficiency of weight-entangled spaces. The code for our work is openly accessible https://anonymous.4open.science/r/TangleNAS-527C{here}

Intra-operative recognition of surgical phases holds significant potential for enhancing real-time contextual awareness in the operating room. However, we argue that online recognition, while beneficial, primarily lends itself to post-operative video analysis due to its limited direct impact on the actual surgical decisions and actions during ongoing procedures. In contrast, we contend that the prediction and anticipation of surgical phases are inherently more valuable for intra-operative assistance, as they can meaningfully influence a surgeon's immediate and long-term planning by providing foresight into future steps. To address this gap, we propose a dual approach that simultaneously recognises the current surgical phase and predicts upcoming ones, thus offering comprehensive intra-operative assistance and guidance on the expected remaining workflow. Our novel method, Surgical Phase Recognition and Anticipation (SuPRA), leverages past and current information for accurate intra-operative phase recognition while using future segments for phase prediction. This unified approach challenges conventional frameworks that treat these objectives separately. We have validated SuPRA on two reputed datasets, Cholec80 and AutoLaparo21, where it demonstrated state-of-the-art performance with recognition accuracies of 91.8% and 79.3%, respectively. Additionally, we introduce and evaluate our model using new segment-level evaluation metrics, namely Edit and F1 Overlap scores, for a more temporal assessment of segment classification. In conclusion, SuPRA presents a new multi-task approach that paves the way for improved intra-operative assistance through surgical phase recognition and prediction of future events.

Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it suffers from two issues when applied to federated non-IID data. First, the variance of these estimates increases significantly. Second, delaying communication causes the Markov chains to diverge from the true posterior even for very simple models. To alleviate both these problems, we propose conducive gradients, a simple mechanism that combines local likelihood approximations to correct gradient updates. Notably, conducive gradients are easy to compute, and since we only calculate the approximations once, they incur negligible overhead. We apply conducive gradients to distributed stochastic gradient Langevin dynamics (DSGLD) and call the resulting method federated stochastic gradient Langevin dynamics (FSGLD). We demonstrate that our approach can handle delayed communication rounds, converging to the target posterior in cases where DSGLD fails. We also show that FSGLD outperforms DSGLD for non-IID federated data with experiments on metric learning and neural networks.

While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the computational efficiency through the random projection, yet they suffer from low accuracy if the number of projections is not sufficiently large, because the majority of projections result in trivially small values. In this work, we propose a new family of distance metrics, called augmented sliced Wasserstein distances (ASWDs), constructed by first mapping samples to higher-dimensional hypersurfaces parameterized by neural networks. It is derived from a key observation that (random) linear projections of samples residing on these hypersurfaces would translate to much more flexible nonlinear projections in the original sample space, so they can capture complex structures of the data distribution. We show that the hypersurfaces can be optimized by gradient ascent efficiently. We provide the condition under which the ASWD is a valid metric and show that this can be obtained by an injective neural network architecture. Numerical results demonstrate that the ASWD significantly outperforms other Wasserstein variants for both synthetic and real-world problems.

Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so far. However, we show that even with a perfect approximation to the joint loss, these approaches still suffer from temporary but substantial forgetting when starting to train on a new task. Motivated by this 'stability gap', we propose that continual learning strategies should focus not only on the optimization objective, but also on the way this objective is optimized. While there is some continual learning work that alters the optimization trajectory (e.g., using gradient projection techniques), this line of research is positioned as alternative to improving the optimization objective, while we argue it should be complementary. To evaluate the merits of our proposition, we plan to combine replay-approximated joint objectives with gradient projection-based optimization routines to test whether the addition of the latter provides benefits in terms of (1) alleviating the stability gap, (2) increasing the learning efficiency and (3) improving the final learning outcome.

We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from O(d) to O(d) through step-size sharing, where d is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with non-asymptotic gradient norm guarantees. Our convergence analysis is based on a gradient Lipschitz condition with respect to a Mahalanobis norm, inspired by a recent progress on cyclic block coordinate methods. In deterministic settings, our convergence guarantee matches the guarantee of (full-gradient) gradient descent, but with the gradient Lipschitz constant being defined w.r.t.~a Mahalanobis norm. In stochastic settings, we use recursive variance reduction to decrease the per-iteration cost and match the arithmetic operation complexity of current optimal stochastic full-gradient methods, with a unified analysis for both finite-sum and infinite-sum cases. We prove a faster linear convergence result when a Polyak-{\L}ojasiewicz (P{\L}) condition holds. To our knowledge, this work is the first to provide non-asymptotic convergence guarantees -- variance-reduced or not -- for a cyclic block coordinate method in general composite (smooth + nonsmooth) nonconvex settings. Our experimental results demonstrate the efficacy of the proposed cyclic scheme in training deep neural nets.

This paper presents a novel technique based on gradient boosting to train the final layers of a neural network (NN). Gradient boosting is an additive expansion algorithm in which a series of models are trained sequentially to approximate a given function. A neural network can also be seen as an additive expansion where the scalar product of the responses of the last hidden layer and its weights provide the final output of the network. Instead of training the network as a whole, the proposed algorithm trains the network sequentially in T steps. First, the bias term of the network is initialized with a constant approximation that minimizes the average loss of the data. Then, at each step, a portion of the network, composed of J neurons, is trained to approximate the pseudo-residuals on the training data computed from the previous iterations. Finally, the T partial models and bias are integrated as a single NN with T times J neurons in the hidden layer. Extensive experiments in classification and regression tasks, as well as in combination with deep neural networks, are carried out showing a competitive generalization performance with respect to neural networks trained with different standard solvers, such as Adam, L-BFGS, SGD and deep models. Furthermore, we show that the proposed method design permits to switch off a number of hidden units during test (the units that were last trained) without a significant reduction of its generalization ability. This permits the adaptation of the model to different classification speed requirements on the fly.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex functions, different works have established the optimal O(log(1/delta)log T/T) or O(log(1/delta)/T) high-probability convergence rates for the final iterate, where T is the time horizon and delta is the failure probability. However, to prove these bounds, all the existing works are either limited to compact domains or require almost surely bounded noises. It is natural to ask whether the last iterate of SGD can still guarantee the optimal convergence rate but without these two restrictive assumptions. Besides this important question, there are still lots of theoretical problems lacking an answer. For example, compared with the last-iterate convergence of SGD for non-smooth problems, only few results for smooth optimization have yet been developed. Additionally, the existing results are all limited to a non-composite objective and the standard Euclidean norm. It still remains unclear whether the last-iterate convergence can be provably extended to wider composite optimization and non-Euclidean norms. In this work, to address the issues mentioned above, we revisit the last-iterate convergence of stochastic gradient methods and provide the first unified way to prove the convergence rates both in expectation and in high probability to accommodate general domains, composite objectives, non-Euclidean norms, Lipschitz conditions, smoothness, and (strong) convexity simultaneously. Additionally, we extend our analysis to obtain the last-iterate convergence under heavy-tailed noises.

Federated Learning (FL) is a rising approach towards collaborative and privacy-preserving machine learning where large-scale medical datasets remain localized to each client. However, the issue of data heterogeneity among clients often compels local models to diverge, leading to suboptimal global models. To mitigate the impact of data heterogeneity on FL performance, we start with analyzing how FL training influence FL performance by decomposing the global loss into three terms: local loss, distribution shift loss and aggregation loss. Remarkably, our loss decomposition reveals that existing local training-based FL methods attempt to reduce the distribution shift loss, while the global aggregation-based FL methods propose better aggregation strategies to reduce the aggregation loss. Nevertheless, a comprehensive joint effort to minimize all three terms is currently limited in the literature, leading to subpar performance when dealing with data heterogeneity challenges. To fill this gap, we propose a novel FL method based on global loss decomposition, called FedLD, to jointly reduce these three loss terms. Our FedLD involves a margin control regularization in local training to reduce the distribution shift loss, and a principal gradient-based server aggregation strategy to reduce the aggregation loss. Notably, under different levels of data heterogeneity, our strategies achieve better and more robust performance on retinal and chest X-ray classification compared to other FL algorithms. Our code is available at https://github.com/Zeng-Shuang/FedLD.

Large-scale distributed training requires significant communication bandwidth for gradient exchange that limits the scalability of multi-node training, and requires expensive high-bandwidth network infrastructure. The situation gets even worse with distributed training on mobile devices (federated learning), which suffers from higher latency, lower throughput, and intermittent poor connections. In this paper, we find 99.9% of the gradient exchange in distributed SGD is redundant, and propose Deep Gradient Compression (DGC) to greatly reduce the communication bandwidth. To preserve accuracy during compression, DGC employs four methods: momentum correction, local gradient clipping, momentum factor masking, and warm-up training. We have applied Deep Gradient Compression to image classification, speech recognition, and language modeling with multiple datasets including Cifar10, ImageNet, Penn Treebank, and Librispeech Corpus. On these scenarios, Deep Gradient Compression achieves a gradient compression ratio from 270x to 600x without losing accuracy, cutting the gradient size of ResNet-50 from 97MB to 0.35MB, and for DeepSpeech from 488MB to 0.74MB. Deep gradient compression enables large-scale distributed training on inexpensive commodity 1Gbps Ethernet and facilitates distributed training on mobile. Code is available at: https://github.com/synxlin/deep-gradient-compression.

In a multi-task learning (MTL) setting, a single model is trained to tackle a diverse set of tasks jointly. Despite rapid progress in the field, MTL remains challenging due to optimization issues such as conflicting and dominating gradients. In this work, we propose using a condition number of a linear system of gradients as a stability criterion of an MTL optimization. We theoretically demonstrate that a condition number reflects the aforementioned optimization issues. Accordingly, we present Aligned-MTL, a novel MTL optimization approach based on the proposed criterion, that eliminates instability in the training process by aligning the orthogonal components of the linear system of gradients. While many recent MTL approaches guarantee convergence to a minimum, task trade-offs cannot be specified in advance. In contrast, Aligned-MTL provably converges to an optimal point with pre-defined task-specific weights, which provides more control over the optimization result. Through experiments, we show that the proposed approach consistently improves performance on a diverse set of MTL benchmarks, including semantic and instance segmentation, depth estimation, surface normal estimation, and reinforcement learning. The source code is publicly available at https://github.com/SamsungLabs/MTL .

We propose a minimal path method to simultaneously compute segmentation masks and extract centerlines of tubular structures with line-topology. Minimal path methods are commonly used for the segmentation of tubular structures in a wide variety of applications. Recent methods use features extracted by CNNs, and often outperform methods using hand-tuned features. However, for CNN-based methods, the samples used for training may be generated inappropriately, so that they can be very different from samples encountered during inference. We approach this discrepancy by introducing a novel iterative training scheme, which enables generating better training samples specifically tailored for the minimal path methods without changing existing annotations. In our method, segmentation masks and centerlines are not determined after one another by post-processing, but obtained using the same steps. Our method requires only very few annotated training images. Comparison with seven previous approaches on three public datasets, including satellite images and medical images, shows that our method achieves state-of-the-art results both for segmentation masks and centerlines.

We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments. We study this problem in the context of variationally stable games (a class of continuous games which includes all convex-concave and monotone games), and when the players only have access to noisy estimates of their individual payoff gradients. If the noise is additive, the game-theoretic and purely adversarial settings enjoy similar regret guarantees; however, if the noise is multiplicative, we show that the learners can, in fact, achieve constant regret. We achieve this faster rate via an optimistic gradient scheme with learning rate separation -- that is, the method's extrapolation and update steps are tuned to different schedules, depending on the noise profile. Subsequently, to eliminate the need for delicate hyperparameter tuning, we propose a fully adaptive method that attains nearly the same guarantees as its non-adapted counterpart, while operating without knowledge of either the game or of the noise profile.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ''Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)-the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

Quantization scale and bit-width are the most important parameters when considering how to quantize a neural network. Prior work focuses on optimizing quantization scales in a global manner through gradient methods (gradient descent \& Hessian analysis). Yet, when applying perturbations to quantization scales, we observe a very jagged, highly non-smooth test loss landscape. In fact, small perturbations in quantization scale can greatly affect accuracy, yielding a 0.5-0.8% accuracy boost in 4-bit quantized vision transformers (ViTs). In this regime, gradient methods break down, since they cannot reliably reach local minima. In our work, dubbed Evol-Q, we use evolutionary search to effectively traverse the non-smooth landscape. Additionally, we propose using an infoNCE loss, which not only helps combat overfitting on the small calibration dataset (1,000 images) but also makes traversing such a highly non-smooth surface easier. Evol-Q improves the top-1 accuracy of a fully quantized ViT-Base by 10.30%, 0.78%, and 0.15% for 3-bit, 4-bit, and 8-bit weight quantization levels. Extensive experiments on a variety of CNN and ViT architectures further demonstrate its robustness in extreme quantization scenarios. Our code is available at https://github.com/enyac-group/evol-q

Optimization and generalization are two essential aspects of statistical machine learning. In this paper, we propose a framework to connect optimization with generalization by analyzing the generalization error based on the optimization trajectory under the gradient flow algorithm. The key ingredient of this framework is the Uniform-LGI, a property that is generally satisfied when training machine learning models. Leveraging the Uniform-LGI, we first derive convergence rates for gradient flow algorithm, then we give generalization bounds for a large class of machine learning models. We further apply our framework to three distinct machine learning models: linear regression, kernel regression, and two-layer neural networks. Through our approach, we obtain generalization estimates that match or extend previous results.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

Estimating human pose and shape from monocular images is a long-standing problem in computer vision. Since the release of statistical body models, 3D human mesh recovery has been drawing broader attention. With the same goal of obtaining well-aligned and physically plausible mesh results, two paradigms have been developed to overcome challenges in the 2D-to-3D lifting process: i) an optimization-based paradigm, where different data terms and regularization terms are exploited as optimization objectives; and ii) a regression-based paradigm, where deep learning techniques are embraced to solve the problem in an end-to-end fashion. Meanwhile, continuous efforts are devoted to improving the quality of 3D mesh labels for a wide range of datasets. Though remarkable progress has been achieved in the past decade, the task is still challenging due to flexible body motions, diverse appearances, complex environments, and insufficient in-the-wild annotations. To the best of our knowledge, this is the first survey to focus on the task of monocular 3D human mesh recovery. We start with the introduction of body models and then elaborate recovery frameworks and training objectives by providing in-depth analyses of their strengths and weaknesses. We also summarize datasets, evaluation metrics, and benchmark results. Open issues and future directions are discussed in the end, hoping to motivate researchers and facilitate their research in this area. A regularly updated project page can be found at https://github.com/tinatiansjz/hmr-survey.

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

We introduce a gradient-based approach for the problem of Bayesian optimal experimental design to learn causal models in a batch setting -- a critical component for causal discovery from finite data where interventions can be costly or risky. Existing methods rely on greedy approximations to construct a batch of experiments while using black-box methods to optimize over a single target-state pair to intervene with. In this work, we completely dispose of the black-box optimization techniques and greedy heuristics and instead propose a conceptually simple end-to-end gradient-based optimization procedure to acquire a set of optimal intervention target-state pairs. Such a procedure enables parameterization of the design space to efficiently optimize over a batch of multi-target-state interventions, a setting which has hitherto not been explored due to its complexity. We demonstrate that our proposed method outperforms baselines and existing acquisition strategies in both single-target and multi-target settings across a number of synthetic datasets.

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which classical analysis applies only if the loss is either convex or smooth. We show that a very small modification to SGDM closes this gap: simply scale the update at each time point by an exponentially distributed random scalar. The resulting algorithm achieves optimal convergence guarantees. Intriguingly, this result is not derived by a specific analysis of SGDM: instead, it falls naturally out of a more general framework for converting online convex optimization algorithms to non-convex optimization algorithms.

There has been a large literature of neural architecture search, but most existing work made use of heuristic rules that largely constrained the search flexibility. In this paper, we first relax these manually designed constraints and enlarge the search space to contain more than 10^{160} candidates. In the new space, most existing differentiable search methods can fail dramatically. We then propose a novel algorithm named Gradual One-Level Differentiable Neural Architecture Search (GOLD-NAS) which introduces a variable resource constraint to one-level optimization so that the weak operators are gradually pruned out from the super-network. In standard image classification benchmarks, GOLD-NAS can find a series of Pareto-optimal architectures within a single search procedure. Most of the discovered architectures were never studied before, yet they achieve a nice tradeoff between recognition accuracy and model complexity. We believe the new space and search algorithm can advance the search of differentiable NAS.

We present a novel approach to accelerate stochastic gradient descent (SGD) by utilizing curvature information obtained from Hessian-vector products or finite differences of parameters and gradients, similar to the BFGS algorithm. Our approach involves two preconditioners: a matrix-free preconditioner and a low-rank approximation preconditioner. We update both preconditioners online using a criterion that is robust to stochastic gradient noise and does not require line search or damping. To preserve the corresponding symmetry or invariance, our preconditioners are constrained to certain connected Lie groups. The Lie group's equivariance property simplifies the preconditioner fitting process, while its invariance property eliminates the need for damping, which is commonly required in second-order optimizers. As a result, the learning rate for parameter updating and the step size for preconditioner fitting are naturally normalized, and their default values work well in most scenarios. Our proposed approach offers a promising direction for improving the convergence of SGD with low computational overhead. We demonstrate that Preconditioned SGD (PSGD) outperforms SoTA on Vision, NLP, and RL tasks across multiple modern deep-learning architectures. We have provided code for reproducing toy and large scale experiments in this paper.

Recently, flat minima are proven to be effective for improving generalization and sharpness-aware minimization (SAM) achieves state-of-the-art performance. Yet the current definition of flatness discussed in SAM and its follow-ups are limited to the zeroth-order flatness (i.e., the worst-case loss within a perturbation radius). We show that the zeroth-order flatness can be insufficient to discriminate minima with low generalization error from those with high generalization error both when there is a single minimum or multiple minima within the given perturbation radius. Thus we present first-order flatness, a stronger measure of flatness focusing on the maximal gradient norm within a perturbation radius which bounds both the maximal eigenvalue of Hessian at local minima and the regularization function of SAM. We also present a novel training procedure named Gradient norm Aware Minimization (GAM) to seek minima with uniformly small curvature across all directions. Experimental results show that GAM improves the generalization of models trained with current optimizers such as SGD and AdamW on various datasets and networks. Furthermore, we show that GAM can help SAM find flatter minima and achieve better generalization.

Today's deep learning methods focus on how to design the most appropriate objective functions so that the prediction results of the model can be closest to the ground truth. Meanwhile, an appropriate architecture that can facilitate acquisition of enough information for prediction has to be designed. Existing methods ignore a fact that when input data undergoes layer-by-layer feature extraction and spatial transformation, large amount of information will be lost. This paper will delve into the important issues of data loss when data is transmitted through deep networks, namely information bottleneck and reversible functions. We proposed the concept of programmable gradient information (PGI) to cope with the various changes required by deep networks to achieve multiple objectives. PGI can provide complete input information for the target task to calculate objective function, so that reliable gradient information can be obtained to update network weights. In addition, a new lightweight network architecture -- Generalized Efficient Layer Aggregation Network (GELAN), based on gradient path planning is designed. GELAN's architecture confirms that PGI has gained superior results on lightweight models. We verified the proposed GELAN and PGI on MS COCO dataset based object detection. The results show that GELAN only uses conventional convolution operators to achieve better parameter utilization than the state-of-the-art methods developed based on depth-wise convolution. PGI can be used for variety of models from lightweight to large. It can be used to obtain complete information, so that train-from-scratch models can achieve better results than state-of-the-art models pre-trained using large datasets, the comparison results are shown in Figure 1. The source codes are at: https://github.com/WongKinYiu/yolov9.

We develop a multiexposure image fusion method based on texture features, which exploits the edge preserving and intraregion smoothing property of nonlinear diffusion filters based on partial differential equations (PDE). With the captured multiexposure image series, we first decompose images into base layers and detail layers to extract sharp details and fine details, respectively. The magnitude of the gradient of the image intensity is utilized to encourage smoothness at homogeneous regions in preference to inhomogeneous regions. Then, we have considered texture features of the base layer to generate a mask (i.e., decision mask) that guides the fusion of base layers in multiresolution fashion. Finally, well-exposed fused image is obtained that combines fused base layer and the detail layers at each scale across all the input exposures. Proposed algorithm skipping complex High Dynamic Range Image (HDRI) generation and tone mapping steps to produce detail preserving image for display on standard dynamic range display devices. Moreover, our technique is effective for blending flash/no-flash image pair and multifocus images, that is, images focused on different targets.

AI-driven tumor analysis has garnered increasing attention in healthcare. However, its progress is significantly hindered by the lack of annotated tumor cases, which requires radiologists to invest a lot of effort in collecting and annotation. In this paper, we introduce a highly practical solution for robust tumor synthesis and segmentation, termed FreeTumor, which refers to annotation-free synthetic tumors and our desire to free patients that suffering from tumors. Instead of pursuing sophisticated technical synthesis modules, we aim to design a simple yet effective tumor synthesis paradigm to unleash the power of large-scale data. Specifically, FreeTumor advances existing methods mainly from three aspects: (1) Existing methods only leverage small-scale labeled data for synthesis training, which limits their ability to generalize well on unseen data from different sources. To this end, we introduce the adversarial training strategy to leverage large-scale and diversified unlabeled data in synthesis training, significantly improving tumor synthesis. (2) Existing methods largely ignored the negative impact of low-quality synthetic tumors in segmentation training. Thus, we employ an adversarial-based discriminator to automatically filter out the low-quality synthetic tumors, which effectively alleviates their negative impact. (3) Existing methods only used hundreds of cases in tumor segmentation. In FreeTumor, we investigate the data scaling law in tumor segmentation by scaling up the dataset to 11k cases. Extensive experiments demonstrate the superiority of FreeTumor, e.g., on three tumor segmentation benchmarks, average +8.9% DSC over the baseline that only using real tumors and +6.6% DSC over the state-of-the-art tumor synthesis method. Code will be available.

We present 3DGS-LM, a new method that accelerates the reconstruction of 3D Gaussian Splatting (3DGS) by replacing its ADAM optimizer with a tailored Levenberg-Marquardt (LM). Existing methods reduce the optimization time by decreasing the number of Gaussians or by improving the implementation of the differentiable rasterizer. However, they still rely on the ADAM optimizer to fit Gaussian parameters of a scene in thousands of iterations, which can take up to an hour. To this end, we change the optimizer to LM that runs in conjunction with the 3DGS differentiable rasterizer. For efficient GPU parallization, we propose a caching data structure for intermediate gradients that allows us to efficiently calculate Jacobian-vector products in custom CUDA kernels. In every LM iteration, we calculate update directions from multiple image subsets using these kernels and combine them in a weighted mean. Overall, our method is 30% faster than the original 3DGS while obtaining the same reconstruction quality. Our optimization is also agnostic to other methods that acclerate 3DGS, thus enabling even faster speedups compared to vanilla 3DGS.

We propose a method for dynamic scene reconstruction using deformable 3D Gaussians that is tailored for monocular video. Building upon the efficiency of Gaussian splatting, our approach extends the representation to accommodate dynamic elements via a deformable set of Gaussians residing in a canonical space, and a time-dependent deformation field defined by a multi-layer perceptron (MLP). Moreover, under the assumption that most natural scenes have large regions that remain static, we allow the MLP to focus its representational power by additionally including a static Gaussian point cloud. The concatenated dynamic and static point clouds form the input for the Gaussian Splatting rasterizer, enabling real-time rendering. The differentiable pipeline is optimized end-to-end with a self-supervised rendering loss. Our method achieves results that are comparable to state-of-the-art dynamic neural radiance field methods while allowing much faster optimization and rendering. Project website: https://lynl7130.github.io/gaufre/index.html

Application of deep learning on histopathological whole slide images (WSIs) holds promise of improving diagnostic efficiency and reproducibility but is largely dependent on the ability to write computer code or purchase commercial solutions. We present a code-free pipeline utilizing free-to-use, open-source software (QuPath, DeepMIB, and FastPathology) for creating and deploying deep learning-based segmentation models for computational pathology. We demonstrate the pipeline on a use case of separating epithelium from stroma in colonic mucosa. A dataset of 251 annotated WSIs, comprising 140 hematoxylin-eosin (HE)-stained and 111 CD3 immunostained colon biopsy WSIs, were developed through active learning using the pipeline. On a hold-out test set of 36 HE and 21 CD3-stained WSIs a mean intersection over union score of 96.6% and 95.3% was achieved on epithelium segmentation. We demonstrate pathologist-level segmentation accuracy and clinical acceptable runtime performance and show that pathologists without programming experience can create near state-of-the-art segmentation solutions for histopathological WSIs using only free-to-use software. The study further demonstrates the strength of open-source solutions in its ability to create generalizable, open pipelines, of which trained models and predictions can seamlessly be exported in open formats and thereby used in external solutions. All scripts, trained models, a video tutorial, and the full dataset of 251 WSIs with ~31k epithelium annotations are made openly available at https://github.com/andreped/NoCodeSeg to accelerate research in the field.

We present Direct Reward Fine-Tuning (DRaFT), a simple and effective method for fine-tuning diffusion models to maximize differentiable reward functions, such as scores from human preference models. We first show that it is possible to backpropagate the reward function gradient through the full sampling procedure, and that doing so achieves strong performance on a variety of rewards, outperforming reinforcement learning-based approaches. We then propose more efficient variants of DRaFT: DRaFT-K, which truncates backpropagation to only the last K steps of sampling, and DRaFT-LV, which obtains lower-variance gradient estimates for the case when K=1. We show that our methods work well for a variety of reward functions and can be used to substantially improve the aesthetic quality of images generated by Stable Diffusion 1.4. Finally, we draw connections between our approach and prior work, providing a unifying perspective on the design space of gradient-based fine-tuning algorithms.

We propose a new dataset distillation algorithm using reparameterization and convexification of implicit gradients (RCIG), that substantially improves the state-of-the-art. To this end, we first formulate dataset distillation as a bi-level optimization problem. Then, we show how implicit gradients can be effectively used to compute meta-gradient updates. We further equip the algorithm with a convexified approximation that corresponds to learning on top of a frozen finite-width neural tangent kernel. Finally, we improve bias in implicit gradients by parameterizing the neural network to enable analytical computation of final-layer parameters given the body parameters. RCIG establishes the new state-of-the-art on a diverse series of dataset distillation tasks. Notably, with one image per class, on resized ImageNet, RCIG sees on average a 108% improvement over the previous state-of-the-art distillation algorithm. Similarly, we observed a 66% gain over SOTA on Tiny-ImageNet and 37% on CIFAR-100.

Designing a high-efficiency and high-quality expressive network architecture has always been the most important research topic in the field of deep learning. Most of today's network design strategies focus on how to integrate features extracted from different layers, and how to design computing units to effectively extract these features, thereby enhancing the expressiveness of the network. This paper proposes a new network design strategy, i.e., to design the network architecture based on gradient path analysis. On the whole, most of today's mainstream network design strategies are based on feed forward path, that is, the network architecture is designed based on the data path. In this paper, we hope to enhance the expressive ability of the trained model by improving the network learning ability. Due to the mechanism driving the network parameter learning is the backward propagation algorithm, we design network design strategies based on back propagation path. We propose the gradient path design strategies for the layer-level, the stage-level, and the network-level, and the design strategies are proved to be superior and feasible from theoretical analysis and experiments.

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

Domain adaptation (DA) has drawn high interest for its capacity to adapt a model trained on labeled source data to perform well on unlabeled or weakly labeled target data from a different domain. Most common DA techniques require concurrent access to the input images of both the source and target domains. However, in practice, privacy concerns often impede the availability of source images in the adaptation phase. This is a very frequent DA scenario in medical imaging, where, for instance, the source and target images could come from different clinical sites. We introduce a source-free domain adaptation for image segmentation. Our formulation is based on minimizing a label-free entropy loss defined over target-domain data, which we further guide with a domain-invariant prior on the segmentation regions. Many priors can be derived from anatomical information. Here, a class ratio prior is estimated from anatomical knowledge and integrated in the form of a Kullback Leibler (KL) divergence in our overall loss function. Furthermore, we motivate our overall loss with an interesting link to maximizing the mutual information between the target images and their label predictions. We show the effectiveness of our prior aware entropy minimization in a variety of domain-adaptation scenarios, with different modalities and applications, including spine, prostate, and cardiac segmentation. Our method yields comparable results to several state of the art adaptation techniques, despite having access to much less information, as the source images are entirely absent in our adaptation phase. Our straightforward adaptation strategy uses only one network, contrary to popular adversarial techniques, which are not applicable to a source-free DA setting. Our framework can be readily used in a breadth of segmentation problems, and our code is publicly available: https://github.com/mathilde-b/SFDA

Adversarial training improves the robustness of neural networks against adversarial attacks, albeit at the expense of the trade-off between standard and robust generalization. To unveil the underlying factors driving this phenomenon, we examine the layer-wise learning capabilities of neural networks during the transition from a standard to an adversarial setting. Our empirical findings demonstrate that selectively updating specific layers while preserving others can substantially enhance the network's learning capacity. We therefore propose CURE, a novel training framework that leverages a gradient prominence criterion to perform selective conservation, updating, and revision of weights. Importantly, CURE is designed to be dataset- and architecture-agnostic, ensuring its applicability across various scenarios. It effectively tackles both memorization and overfitting issues, thus enhancing the trade-off between robustness and generalization and additionally, this training approach also aids in mitigating "robust overfitting". Furthermore, our study provides valuable insights into the mechanisms of selective adversarial training and offers a promising avenue for future research.

Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve optimization, such as unsupervised pretraining. However, modern neural networks are able to achieve negligible training error on complex tasks, using only direct training with stochastic gradient descent. We introduce a simple analysis technique to look for evidence that such networks are overcoming local optima. We find that, in fact, on a straight path from initialization to solution, a variety of state of the art neural networks never encounter any significant obstacles.

With the growing size of pre-trained models, full fine-tuning and storing all the parameters for various downstream tasks is costly and infeasible. In this paper, we propose a new parameter-efficient fine-tuning method, Gradient-based Parameter Selection (GPS), demonstrating that only tuning a few selected parameters from the pre-trained model while keeping the remainder of the model frozen can generate similar or better performance compared with the full model fine-tuning method. Different from the existing popular and state-of-the-art parameter-efficient fine-tuning approaches, our method does not introduce any additional parameters and computational costs during both the training and inference stages. Another advantage is the model-agnostic and non-destructive property, which eliminates the need for any other design specific to a particular model. Compared with the full fine-tuning, GPS achieves 3.33% (91.78% vs. 88.45%, FGVC) and 9.61% (73.1% vs. 65.57%, VTAB) improvement of the accuracy with tuning only 0.36% parameters of the pre-trained model on average over 24 image classification tasks; it also demonstrates a significant improvement of 17% and 16.8% in mDice and mIoU, respectively, on medical image segmentation task. Moreover, GPS achieves state-of-the-art performance compared with existing PEFT methods.

We derive a simple and model-independent formula for the change in the generalization gap due to a gradient descent update. We then compare the change in the test error for stochastic gradient descent to the change in test error from an equivalent number of gradient descent updates and show explicitly that stochastic gradient descent acts to regularize generalization error by decorrelating nearby updates. These calculations depends on the details of the model only through the mean and covariance of the gradient distribution, which may be readily measured for particular models of interest. We discuss further improvements to these calculations and comment on possible implications for stochastic optimization.

In distributed deep learning with data parallelism, synchronizing gradients at each training step can cause a huge communication overhead, especially when many nodes work together to train large models. Local gradient methods, such as Local SGD, address this issue by allowing workers to compute locally for H steps without synchronizing with others, hence reducing communication frequency. While H has been viewed as a hyperparameter to trade optimization efficiency for communication cost, recent research indicates that setting a proper H value can lead to generalization improvement. Yet, selecting a proper H is elusive. This work proposes a theory-grounded method for determining H, named the Quadratic Synchronization Rule (QSR), which recommends dynamically setting H in proportion to 1{eta^2} as the learning rate eta decays over time. Extensive ImageNet experiments on ResNet and ViT show that local gradient methods with QSR consistently improve the test accuracy over other synchronization strategies. Compared with the standard data parallel training, QSR enables Local AdamW on ViT-B to cut the training time on 16 or 64 GPUs down from 26.7 to 20.2 hours or from 8.6 to 5.5 hours and, at the same time, achieves 1.16% or 0.84% higher top-1 validation accuracy.

We investigate a primal-dual (PD) method for the saddle point problem (SPP) that uses a linear approximation of the primal function instead of the standard proximal step, resulting in a linearized PD (LPD) method. For convex-strongly concave SPP, we observe that the LPD method has a suboptimal dependence on the Lipschitz constant of the primal function. To fix this issue, we combine features of Accelerated Gradient Descent with the LPD method resulting in a single-loop Accelerated Linearized Primal-Dual (ALPD) method. ALPD method achieves the optimal gradient complexity when the SPP has a semi-linear coupling function. We also present an inexact ALPD method for SPPs with a general nonlinear coupling function that maintains the optimal gradient evaluations of the primal parts and significantly improves the gradient evaluations of the coupling term compared to the ALPD method. We verify our findings with numerical experiments.

Surgical scene perception via videos are critical for advancing robotic surgery, telesurgery, and AI-assisted surgery, particularly in ophthalmology. However, the scarcity of diverse and richly annotated video datasets has hindered the development of intelligent systems for surgical workflow analysis. Existing datasets for surgical workflow analysis, which typically face challenges such as small scale, a lack of diversity in surgery and phase categories, and the absence of time-localized annotations, limit the requirements for action understanding and model generalization validation in complex and diverse real-world surgical scenarios. To address this gap, we introduce OphNet, a large-scale, expert-annotated video benchmark for ophthalmic surgical workflow understanding. OphNet features: 1) A diverse collection of 2,278 surgical videos spanning 66 types of cataract, glaucoma, and corneal surgeries, with detailed annotations for 102 unique surgical phases and 150 granular operations; 2) It offers sequential and hierarchical annotations for each surgery, phase, and operation, enabling comprehensive understanding and improved interpretability; 3) Moreover, OphNet provides time-localized annotations, facilitating temporal localization and prediction tasks within surgical workflows. With approximately 205 hours of surgical videos, OphNet is about 20 times larger than the largest existing surgical workflow analysis benchmark. Our dataset and code have been made available at: https://github.com/minghu0830/OphNet-benchmark.

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy function into account. We empirically establish its superior performance and reduced variance for several natural sciences applications.

Deep Learning (DL) has the potential to optimize machine learning in both the scientific and clinical communities. However, greater expertise is required to develop DL algorithms, and the variability of implementations hinders their reproducibility, translation, and deployment. Here we present the community-driven Generally Nuanced Deep Learning Framework (GaNDLF), with the goal of lowering these barriers. GaNDLF makes the mechanism of DL development, training, and inference more stable, reproducible, interpretable, and scalable, without requiring an extensive technical background. GaNDLF aims to provide an end-to-end solution for all DL-related tasks in computational precision medicine. We demonstrate the ability of GaNDLF to analyze both radiology and histology images, with built-in support for k-fold cross-validation, data augmentation, multiple modalities and output classes. Our quantitative performance evaluation on numerous use cases, anatomies, and computational tasks supports GaNDLF as a robust application framework for deployment in clinical workflows.

We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend to require possibly expensive calculations regarding Hessians of lower-level objectives, or lack rigorous finite-time performance guarantees. In this work, we propose a Fully First-order Stochastic Approximation (F2SA) method, and study its non-asymptotic convergence properties. Specifically, we show that F2SA converges to an epsilon-stationary solution of the bilevel problem after epsilon^{-7/2}, epsilon^{-5/2}, and epsilon^{-3/2} iterations (each iteration using O(1) samples) when stochastic noises are in both level objectives, only in the upper-level objective, and not present (deterministic settings), respectively. We further show that if we employ momentum-assisted gradient estimators, the iteration complexities can be improved to epsilon^{-5/2}, epsilon^{-4/2}, and epsilon^{-3/2}, respectively. We demonstrate even superior practical performance of the proposed method over existing second-order based approaches on MNIST data-hypercleaning experiments.

Differentiable architecture search (DARTS) yields highly efficient gradient-based neural architecture search (NAS) by relaxing the discrete operation selection to optimize continuous architecture parameters that maps NAS from the discrete optimization to a continuous problem. DARTS then remaps the relaxed supernet back to the discrete space by one-off post-search pruning to obtain the final architecture (finalnet). Some emerging works argue that this remap is inherently prone to mismatch the network between training and evaluation which leads to performance discrepancy and even model collapse in extreme cases. We propose to close the gap between the relaxed supernet in training and the pruned finalnet in evaluation through utilizing small temperature to sparsify the continuous distribution in the training phase. To this end, we first formulate sparse-noisy softmax to get around gradient saturation. We then propose an exponential temperature schedule to better control the outbound distribution and elaborate an entropy-based adaptive scheme to finally achieve the enhancement. We conduct extensive experiments to verify the efficiency and efficacy of our method.

Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain neural networks such as recurrent neural networks (RNNs) and long-short-term memory networks (LSTMs) exhibit potential unbounded smoothness, rendering conventional bilevel optimization algorithms unsuitable. In this paper, we design a new bilevel optimization algorithm, namely BO-REP, to address this challenge. This algorithm updates the upper-level variable using normalized momentum and incorporates two novel techniques for updating the lower-level variable: initialization refinement and periodic updates. Specifically, once the upper-level variable is initialized, a subroutine is invoked to obtain a refined estimate of the corresponding optimal lower-level variable, and the lower-level variable is updated only after every specific period instead of each iteration. When the upper-level problem is nonconvex and unbounded smooth, and the lower-level problem is strongly convex, we prove that our algorithm requires mathcal{O}(1/epsilon^4) iterations to find an epsilon-stationary point in the stochastic setting, where each iteration involves calling a stochastic gradient or Hessian-vector product oracle. Notably, this result matches the state-of-the-art complexity results under the bounded smoothness setting and without mean-squared smoothness of the stochastic gradient, up to logarithmic factors. Our proof relies on novel technical lemmas for the periodically updated lower-level variable, which are of independent interest. Our experiments on hyper-representation learning, hyperparameter optimization, and data hyper-cleaning for text classification tasks demonstrate the effectiveness of our proposed algorithm.

Efficiently approximating local curvature information of the loss function is a key tool for optimization and compression of deep neural networks. Yet, most existing methods to approximate second-order information have high computational or storage costs, which can limit their practicality. In this work, we investigate matrix-free, linear-time approaches for estimating Inverse-Hessian Vector Products (IHVPs) for the case when the Hessian can be approximated as a sum of rank-one matrices, as in the classic approximation of the Hessian by the empirical Fisher matrix. We propose two new algorithms as part of a framework called M-FAC: the first algorithm is tailored towards network compression and can compute the IHVP for dimension d, if the Hessian is given as a sum of m rank-one matrices, using O(dm^2) precomputation, O(dm) cost for computing the IHVP, and query cost O(m) for any single element of the inverse Hessian. The second algorithm targets an optimization setting, where we wish to compute the product between the inverse Hessian, estimated over a sliding window of optimization steps, and a given gradient direction, as required for preconditioned SGD. We give an algorithm with cost O(dm + m^2) for computing the IHVP and O(dm + m^3) for adding or removing any gradient from the sliding window. These two algorithms yield state-of-the-art results for network pruning and optimization with lower computational overhead relative to existing second-order methods. Implementations are available at [9] and [17].

Bilevel optimization enjoys a wide range of applications in hyper-parameter optimization, meta-learning and reinforcement learning. However, bilevel optimization problems are difficult to solve. Recent progress on scalable bilevel algorithms mainly focuses on bilevel optimization problems where the lower-level objective is either strongly convex or unconstrained. In this work, we tackle the bilevel problem through the lens of the penalty method. We show that under certain conditions, the penalty reformulation recovers the solutions of the original bilevel problem. Further, we propose the penalty-based bilevel gradient descent (PBGD) algorithm and establish its finite-time convergence for the constrained bilevel problem without lower-level strong convexity. Experiments showcase the efficiency of the proposed PBGD algorithm.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the gradients of linear layers are computed by matrix multiplications, we consider methods for randomized matrix multiplications and demonstrate that they require less memory with a moderate decrease of the test accuracy. Also, we investigate the variance of the gradient estimate induced by the randomized matrix multiplication. We compare this variance with the variance coming from gradient estimation based on the batch of samples. We demonstrate the benefits of the proposed method on the fine-tuning of the pre-trained RoBERTa model on GLUE tasks.

Robotic dexterous grasping is important for interacting with the environment. To unleash the potential of data-driven models for dexterous grasping, a large-scale, high-quality dataset is essential. While gradient-based optimization offers a promising way for constructing such datasets, previous works suffer from limitations, such as inefficiency, strong assumptions in the grasp quality energy, or limited object sets for experiments. Moreover, the lack of a standard benchmark for comparing different methods and datasets hinders progress in this field. To address these challenges, we develop a highly efficient synthesis system and a comprehensive benchmark with MuJoCo for dexterous grasping. We formulate grasp synthesis as a bilevel optimization problem, combining a novel lower-level quadratic programming (QP) with an upper-level gradient descent process. By leveraging recent advances in CUDA-accelerated robotic libraries and GPU-based QP solvers, our system can parallelize thousands of grasps and synthesize over 49 grasps per second on a single 3090 GPU. Our synthesized grasps for Shadow, Allegro, and Leap hands all achieve a success rate above 75% in simulation, with a penetration depth under 1 mm, outperforming existing baselines on nearly all metrics. Compared to the previous large-scale dataset, DexGraspNet, our dataset significantly improves the performance of learning models, with a success rate from around 40% to 80% in simulation. Real-world testing of the trained model on the Shadow Hand achieves an 81% success rate across 20 diverse objects. The codes and datasets are released on our project page: https://pku-epic.github.io/BODex.

Deep Gradient Leakage (DGL) is a highly effective attack that recovers private training images from gradient vectors. This attack casts significant privacy challenges on distributed learning from clients with sensitive data, where clients are required to share gradients. Defending against such attacks requires but lacks an understanding of when and how privacy leakage happens, mostly because of the black-box nature of deep networks. In this paper, we propose a novel Inversion Influence Function (I^2F) that establishes a closed-form connection between the recovered images and the private gradients by implicitly solving the DGL problem. Compared to directly solving DGL, I^2F is scalable for analyzing deep networks, requiring only oracle access to gradients and Jacobian-vector products. We empirically demonstrate that I^2F effectively approximated the DGL generally on different model architectures, datasets, attack implementations, and noise-based defenses. With this novel tool, we provide insights into effective gradient perturbation directions, the unfairness of privacy protection, and privacy-preferred model initialization. Our codes are provided in https://github.com/illidanlab/inversion-influence-function.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

In the domain of medical imaging, many supervised learning based methods for segmentation face several challenges such as high variability in annotations from multiple experts, paucity of labelled data and class imbalanced datasets. These issues may result in segmentations that lack the requisite precision for clinical analysis and can be misleadingly overconfident without associated uncertainty quantification. We propose the PULASki for biomedical image segmentation that accurately captures variability in expert annotations, even in small datasets. Our approach makes use of an improved loss function based on statistical distances in a conditional variational autoencoder structure (Probabilistic UNet), which improves learning of the conditional decoder compared to the standard cross-entropy particularly in class imbalanced problems. We analyse our method for two structurally different segmentation tasks (intracranial vessel and multiple sclerosis (MS) lesion) and compare our results to four well-established baselines in terms of quantitative metrics and qualitative output. Empirical results demonstrate the PULASKi method outperforms all baselines at the 5\% significance level. The generated segmentations are shown to be much more anatomically plausible than in the 2D case, particularly for the vessel task. Our method can also be applied to a wide range of multi-label segmentation tasks and and is useful for downstream tasks such as hemodynamic modelling (computational fluid dynamics and data assimilation), clinical decision making, and treatment planning.

This paper addresses the challenge of grading visual features in lumbar spine MRI using Deep Learning. Such a method is essential for the automatic quantification of structural changes in the spine, which is valuable for understanding low back pain. Multiple recent studies investigated different architecture designs, and the most recent success has been attributed to the use of transformer architectures. In this work, we argue that with a well-tuned three-stage pipeline comprising semantic segmentation, localization, and classification, convolutional networks outperform the state-of-the-art approaches. We conducted an ablation study of the existing methods in a population cohort, and report performance generalization across various subgroups. Our code is publicly available to advance research on disc degeneration and low back pain.

Coronary microvascular disease constitutes a substantial risk to human health. Employing computer-aided analysis and diagnostic systems, medical professionals can intervene early in disease progression, with 3D vessel segmentation serving as a crucial component. Nevertheless, conventional U-Net architectures tend to yield incoherent and imprecise segmentation outcomes, particularly for small vessel structures. While models with attention mechanisms, such as Transformers and large convolutional kernels, demonstrate superior performance, their extensive computational demands during training and inference lead to increased time complexity. In this study, we leverage Fourier domain learning as a substitute for multi-scale convolutional kernels in 3D hierarchical segmentation models, which can reduce computational expenses while preserving global receptive fields within the network. Furthermore, a zero-parameter frequency domain fusion method is designed to improve the skip connections in U-Net architecture. Experimental results on a public dataset and an in-house dataset indicate that our novel Fourier transformation-based network achieves remarkable dice performance (84.37\% on ASACA500 and 80.32\% on ImageCAS) in tubular vessel segmentation tasks and substantially reduces computational requirements without compromising global receptive fields.

The sheer size of modern neural networks makes model serving a serious computational challenge. A popular class of compression techniques overcomes this challenge by pruning or sparsifying the weights of pretrained networks. While useful, these techniques often face serious tradeoffs between computational requirements and compression quality. In this work, we propose a novel optimization-based pruning framework that considers the combined effect of pruning (and updating) multiple weights subject to a sparsity constraint. Our approach, CHITA, extends the classical Optimal Brain Surgeon framework and results in significant improvements in speed, memory, and performance over existing optimization-based approaches for network pruning. CHITA's main workhorse performs combinatorial optimization updates on a memory-friendly representation of local quadratic approximation(s) of the loss function. On a standard benchmark of pretrained models and datasets, CHITA leads to significantly better sparsity-accuracy tradeoffs than competing methods. For example, for MLPNet with only 2% of the weights retained, our approach improves the accuracy by 63% relative to the state of the art. Furthermore, when used in conjunction with fine-tuning SGD steps, our method achieves significant accuracy gains over the state-of-the-art approaches.

Pruning is an effective method to reduce the memory footprint and FLOPs associated with neural network models. However, existing structured-pruning methods often result in significant accuracy degradation for moderate pruning levels. To address this problem, we introduce a new Hessian Aware Pruning (HAP) method coupled with a Neural Implant approach that uses second-order sensitivity as a metric for structured pruning. The basic idea is to prune insensitive components and to use a Neural Implant for moderately sensitive components, instead of completely pruning them. For the latter approach, the moderately sensitive components are replaced with with a low rank implant that is smaller and less computationally expensive than the original component. We use the relative Hessian trace to measure sensitivity, as opposed to the magnitude based sensitivity metric commonly used in the literature. We test HAP for both computer vision tasks and natural language tasks, and we achieve new state-of-the-art results. Specifically, HAP achieves less than 0.1%/0.5% degradation on PreResNet29/ResNet50 (CIFAR-10/ImageNet) with more than 70\%/50\% of parameters pruned. Meanwhile, HAP also achieves significantly better performance (up to 0.8\% with 60\% of parameters pruned) as compared to gradient based method for head pruning on transformer-based models. The framework has been open sourced and available online.

Second-order training methods have better convergence properties than gradient descent but are rarely used in practice for large-scale training due to their computational overhead. This can be viewed as a hardware limitation (imposed by digital computers). Here we show that natural gradient descent (NGD), a second-order method, can have a similar computational complexity per iteration to a first-order method, when employing appropriate hardware. We present a new hybrid digital-analog algorithm for training neural networks that is equivalent to NGD in a certain parameter regime but avoids prohibitively costly linear system solves. Our algorithm exploits the thermodynamic properties of an analog system at equilibrium, and hence requires an analog thermodynamic computer. The training occurs in a hybrid digital-analog loop, where the gradient and Fisher information matrix (or any other positive semi-definite curvature matrix) are calculated at given time intervals while the analog dynamics take place. We numerically demonstrate the superiority of this approach over state-of-the-art digital first- and second-order training methods on classification tasks and language model fine-tuning tasks.