Daily Papers

A good initialization of deep learning models is essential since it can help them converge better and faster. However, pretraining large models is unaffordable for many researchers, which makes a desired prediction for initial parameters more necessary nowadays. Graph HyperNetworks (GHNs), one approach to predicting model parameters, have recently shown strong performance in initializing large vision models. Unfortunately, predicting parameters of very wide networks relies on copying small chunks of parameters multiple times and requires an extremely large number of parameters to support full prediction, which greatly hinders its adoption in practice. To address this limitation, we propose LoGAH (Low-rank GrAph Hypernetworks), a GHN with a low-rank parameter decoder that expands to significantly wider networks without requiring as excessive increase of parameters as in previous attempts. LoGAH allows us to predict the parameters of 774-million large neural networks in a memory-efficient manner. We show that vision and language models (i.e., ViT and GPT-2) initialized with LoGAH achieve better performance than those initialized randomly or using existing hypernetworks. Furthermore, we show promising transfer learning results w.r.t. training LoGAH on small datasets and using the predicted parameters to initialize for larger tasks. We provide the codes in https://github.com/Blackzxy/LoGAH .

We introduce phi-3-mini, a 3.8 billion parameter language model trained on 3.3 trillion tokens, whose overall performance, as measured by both academic benchmarks and internal testing, rivals that of models such as Mixtral 8x7B and GPT-3.5 (e.g., phi-3-mini achieves 69% on MMLU and 8.38 on MT-bench), despite being small enough to be deployed on a phone. The innovation lies entirely in our dataset for training, a scaled-up version of the one used for phi-2, composed of heavily filtered web data and synthetic data. The model is also further aligned for robustness, safety, and chat format. We also provide some initial parameter-scaling results with a 7B and 14B models trained for 4.8T tokens, called phi-3-small and phi-3-medium, both significantly more capable than phi-3-mini (e.g., respectively 75% and 78% on MMLU, and 8.7 and 8.9 on MT-bench).

Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models presents a substantial challenge, either due to the high computational requirements of model-based approaches or the limited robustness of deep learning (DL) methods. We propose a novel framework that leverages the unique strengths of both approaches in a synergistic manner. Our method incorporates a DL ensemble for initial parameter estimation, facilitating efficient downstream evolutionary sampling initialized with this DL-based prior. We showcase the effectiveness of integrating a rapid deep-learning algorithm with a high-precision evolution strategy in estimating brain tumor cell concentrations from magnetic resonance images. The DL-Prior plays a pivotal role, significantly constraining the effective sampling-parameter space. This reduction results in a fivefold convergence acceleration and a Dice-score of 95%

Compact binary millisecond pulsars (MSPs) with orbital periods lesssim1d are key to understanding binary evolution involving massive neutron stars (NSs). Due to the ablation of the companion by the rapidly spinning pulsar, these systems are also known as spiders and categorized into two main branches: redbacks (RBs; companion mass in the range of 0.1 to 0.5\,\Msun) and black widows (BWs; companion mass lesssim\,0.1\,\Msun). We present models of low- and intermediate-mass X-ray binaries and compare them with observations of Galactic spiders (including the presence or absence of hydrogen lines in their optical spectra), and we constrain and quantify the interaction between the pulsar and the companion. Using MESA, we created the allowed initial parameter space. For the first time in MESA, we also included the detailed evolution of the pulsar spin and modeled the irradiation of the companion by the pulsar wind. Efficient mass accretion onto the NS (at least 70% of the mass transferred is accreted) with an X-ray irradiated disk followed by strong irradiation of the companion can explain most of the properties of the observed spiders. Our RB evolutionary tracks continue to the BW regime, connecting the two branches of spiders. Our models explain the lack of hydrogen in some observed BWs with ultra-light companions. During accretion induced spin up, the mass required to spin up an NS to sub-milliseconds is high enough to collapse it into a black hole. Finally, after analyzing the formation of RB-like spiders with giant companions and orbital periods of several days (huntsmen), we conclude that they are unlikely to produce super-massive NSs (maximum accreted mass lesssim0.5M_{odot}). Cannibalistic MSP binary formation depends heavily on the interplay between accretion onto the pulsar and pulsar wind irradiation.

Training deep neural networks (DNNs) is computationally expensive, which is problematic especially when performing duplicated or similar training runs in model ensemble or fine-tuning pre-trained models, for example. Once we have trained one DNN on some dataset, we have its learning trajectory (i.e., a sequence of intermediate parameters during training) which may potentially contain useful information for learning the dataset. However, there has been no attempt to utilize such information of a given learning trajectory for another training. In this paper, we formulate the problem of "transferring" a given learning trajectory from one initial parameter to another one (learning transfer problem) and derive the first algorithm to approximately solve it by matching gradients successively along the trajectory via permutation symmetry. We empirically show that the transferred parameters achieve non-trivial accuracy before any direct training, and can be trained significantly faster than training from scratch.

Complex vector modes, entangled in spin and orbital angular momentum, are opening burgeoning opportunities for a wide variety of applications. Importantly, the flexible manipulation the various properties of such beams will pave the way to novel applications. As such, in this manuscript, we demonstrate a longitudinal spin-orbit separation of complex vector modes propagating in free space. To achieve this we employed the recently demonstrated circular Airy Gaussian vortex vector (CAGVV) modes, which feature a self-focusing property. More precisely, by properly manipulating the intrinsic parameters of CAGVV modes, the strong coupling between the two constituting orthogonal components of CAGVV mode undergo a spin-orbit separation along the propagation direction namely, while one polarisation component, focuses at a specific plane, the other focuses at a different plane. Such spin-orbit separation, which we demonstrated by numerical simulations and corroborated experimentally, can be adjusted on-demand by simply changing the initial parameters of CAGVV modes. Our findings will be of great relevance, for example in optical tweezers, to manipulate micro- or nano-particles at two different parallel planes.

Coordinate-based neural representations have shown significant promise as an alternative to discrete, array-based representations for complex low dimensional signals. However, optimizing a coordinate-based network from randomly initialized weights for each new signal is inefficient. We propose applying standard meta-learning algorithms to learn the initial weight parameters for these fully-connected networks based on the underlying class of signals being represented (e.g., images of faces or 3D models of chairs). Despite requiring only a minor change in implementation, using these learned initial weights enables faster convergence during optimization and can serve as a strong prior over the signal class being modeled, resulting in better generalization when only partial observations of a given signal are available. We explore these benefits across a variety of tasks, including representing 2D images, reconstructing CT scans, and recovering 3D shapes and scenes from 2D image observations.

We explore a data-driven approach for learning to optimize neural networks. We construct a dataset of neural network checkpoints and train a generative model on the parameters. In particular, our model is a conditional diffusion transformer that, given an initial input parameter vector and a prompted loss, error, or return, predicts the distribution over parameter updates that achieve the desired metric. At test time, it can optimize neural networks with unseen parameters for downstream tasks in just one update. We find that our approach successfully generates parameters for a wide range of loss prompts. Moreover, it can sample multimodal parameter solutions and has favorable scaling properties. We apply our method to different neural network architectures and tasks in supervised and reinforcement learning.

Pruning is a standard technique for reducing the computational cost of deep networks. Many advances in pruning leverage concepts from the Lottery Ticket Hypothesis (LTH). LTH reveals that inside a trained dense network exists sparse subnetworks (tickets) able to achieve similar accuracy (i.e., win the lottery - winning tickets). Pruning at initialization focuses on finding winning tickets without training a dense network. Studies on these concepts share the trend that subnetworks come from weight or filter pruning. In this work, we investigate LTH and pruning at initialization from the lens of layer pruning. First, we confirm the existence of winning tickets when the pruning process removes layers. Leveraged by this observation, we propose to discover these winning tickets at initialization, eliminating the requirement of heavy computational resources for training the initial (over-parameterized) dense network. Extensive experiments show that our winning tickets notably speed up the training phase and reduce up to 51% of carbon emission, an important step towards democratization and green Artificial Intelligence. Beyond computational benefits, our winning tickets exhibit robustness against adversarial and out-of-distribution examples. Finally, we show that our subnetworks easily win the lottery at initialization while tickets from filter removal (the standard structured LTH) hardly become winning tickets.

Adversarial examples provoke weak reliability and potential security issues in deep neural networks. Although adversarial training has been widely studied to improve adversarial robustness, it works in an over-parameterized regime and requires high computations and large memory budgets. To bridge adversarial robustness and model compression, we propose a novel adversarial pruning method, Masking Adversarial Damage (MAD) that employs second-order information of adversarial loss. By using it, we can accurately estimate adversarial saliency for model parameters and determine which parameters can be pruned without weakening adversarial robustness. Furthermore, we reveal that model parameters of initial layer are highly sensitive to the adversarial examples and show that compressed feature representation retains semantic information for the target objects. Through extensive experiments on three public datasets, we demonstrate that MAD effectively prunes adversarially trained networks without loosing adversarial robustness and shows better performance than previous adversarial pruning methods.

Deep networks often suffer from vanishing or exploding gradients due to inefficient signal propagation, leading to long training times or convergence difficulties. Various architecture designs, sophisticated residual-style networks, and initialization schemes have been shown to improve deep signal propagation. Recently, Pennington et al. used free probability theory to show that dynamical isometry plays an integral role in efficient deep learning. We show that the simplest architecture change of gating each residual connection using a single zero-initialized parameter satisfies initial dynamical isometry and outperforms more complex approaches. Although much simpler than its predecessors, this gate enables training thousands of fully connected layers with fast convergence and better test performance for ResNets trained on CIFAR-10. We apply this technique to language modeling and find that we can easily train 120-layer Transformers. When applied to 12 layer Transformers, it converges 56% faster on enwiki8.

In this work, we explore the use of a novel neural network architecture, the Kolmogorov-Arnold Networks (KANs) as feature extractors for sensor-based (specifically IMU) Human Activity Recognition (HAR). Where conventional networks perform a parameterized weighted sum of the inputs at each node and then feed the result into a statically defined nonlinearity, KANs perform non-linear computations represented by B-SPLINES on the edges leading to each node and then just sum up the inputs at the node. Instead of learning weights, the system learns the spline parameters. In the original work, such networks have been shown to be able to more efficiently and exactly learn sophisticated real valued functions e.g. in regression or PDE solution. We hypothesize that such an ability is also advantageous for computing low-level features for IMU-based HAR. To this end, we have implemented KAN as the feature extraction architecture for IMU-based human activity recognition tasks, including four architecture variations. We present an initial performance investigation of the KAN feature extractor on four public HAR datasets. It shows that the KAN-based feature extractor outperforms CNN-based extractors on all datasets while being more parameter efficient.

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.

Owing to the growing concerns about privacy and regulatory compliance, it is desirable to regulate the output of generative models. To that end, the objective of this work is to prevent the generation of outputs containing undesired features from a pre-trained Generative Adversarial Network (GAN) where the underlying training data set is inaccessible. Our approach is inspired by the observation that the parameter space of GANs exhibits meaningful directions that can be leveraged to suppress specific undesired features. However, such directions usually result in the degradation of the quality of generated samples. Our proposed two-stage method, known as 'Adapt-then-Unlearn,' excels at unlearning such undesirable features while also maintaining the quality of generated samples. In the initial stage, we adapt a pre-trained GAN on a set of negative samples (containing undesired features) provided by the user. Subsequently, we train the original pre-trained GAN using positive samples, along with a repulsion regularizer. This regularizer encourages the learned model parameters to move away from the parameters of the adapted model (first stage) while not degrading the generation quality. We provide theoretical insights into the proposed method. To the best of our knowledge, our approach stands as the first method addressing unlearning within the realm of high-fidelity GANs (such as StyleGAN). We validate the effectiveness of our method through comprehensive experiments, encompassing both class-level unlearning on the MNIST and AFHQ dataset and feature-level unlearning tasks on the CelebA-HQ dataset. Our code and implementation is available at: https://github.com/atriguha/Adapt_Unlearn.

With the increasing size of pre-trained language models (PLMs), fine-tuning all the parameters in the model is not efficient, especially when there are a large number of downstream tasks, which incur significant training and storage costs. Many parameter-efficient fine-tuning (PEFT) approaches have been proposed, among which, Low-Rank Adaptation (LoRA) is a representative approach that injects trainable rank decomposition matrices into every target module. Yet LoRA ignores the importance of parameters in different modules. To address this problem, many works have been proposed to prune the parameters of LoRA. However, under limited training conditions, the upper bound of the rank of the pruned parameter matrix is still affected by the preset values. We, therefore, propose IncreLoRA, an incremental parameter allocation method that adaptively adds trainable parameters during training based on the importance scores of each module. This approach is different from the pruning method as it is not limited by the initial number of training parameters, and each parameter matrix has a higher rank upper bound for the same training overhead. We conduct extensive experiments on GLUE to demonstrate the effectiveness of IncreLoRA. The results show that our method owns higher parameter efficiency, especially when under the low-resource settings where our method significantly outperforms the baselines. Our code is publicly available.

Foundation models encompass an extensive knowledge base and offer remarkable transferability. However, this knowledge becomes outdated or insufficient over time. The challenge lies in continuously updating foundation models to accommodate novel information while retaining their original capabilities. Leveraging the fact that foundation models have initial knowledge on various tasks and domains, we propose a novel approach that, instead of updating all parameters equally, localizes the updates to a sparse set of parameters relevant to the task being learned. We strike a balance between efficiency and new task performance, while maintaining the transferability and generalizability of foundation models. We extensively evaluate our method on foundational vision-language models with a diverse spectrum of continual learning tasks. Our method achieves improvements on the accuracy of the newly learned tasks up to 7% while preserving the pretraining knowledge with a negligible decrease of 0.9% on a representative control set accuracy.

Neural codec language models have achieved state-of-the-art performance in text-to-speech (TTS) synthesis, leveraging scalable architectures like autoregressive transformers and large-scale speech datasets. By framing voice cloning as a prompt continuation task, these models excel at cloning voices from short audio samples. However, this approach is limited in its ability to handle numerous or lengthy speech excerpts, since the concatenation of source and target speech must fall within the maximum context length which is determined during training. In this work, we introduce Lina-Speech, a model that replaces traditional self-attention mechanisms with emerging recurrent architectures like Gated Linear Attention (GLA). Building on the success of initial-state tuning on RWKV, we extend this technique to voice cloning, enabling the use of multiple speech samples and full utilization of the context window in synthesis. This approach is fast, easy to deploy, and achieves performance comparable to fine-tuned baselines when the dataset size ranges from 3 to 15 minutes. Notably, Lina-Speech matches or outperforms state-of-the-art baseline models, including some with a parameter count up to four times higher or trained in an end-to-end style. We release our code and checkpoints. Audio samples are available at https://theodorblackbird.github.io/blog/demo_lina/.

Low-Rank Adaptation (LoRA) has achieved remarkable training results by freezing the original weights and training only low-rank matrices, establishing itself as the predominant fine-tuning method for LLMs. In pursuit of performance closer to full-parameter training, a series of LoRA variants have emerged, such as LoRA+, PISSA, Olora, and LoRA-GA. However, these improvements complicate the initial setup of model training and increase initialization time. More importantly, they overlook the internal interactions of the original weight information. To address these issues, we introduce a novel theory, ``Weight Guide'' aimed at continuously guiding trainable matrices through the original weights during training to enhance the utilization of weight information. Based on this theory, we designed a new PEFT technique called Bone (Block Affine), which not only enhances the utilization of original weight information but also emphasizes the internal connections between weights, leading to faster convergence and better data fitting. Experimental comparisons across two different LLM architectures (LLaMA2, RWKV6) and various parameter scales demonstrate that the Bone structure can achieve rapid convergence and superior data fitting without the need for complex initialization. For example, when fine-tuning LLaMA2-7B on the MetaMathQA dataset and validating on GSM8k and math benchmarks, Bone achieved fine-tuning scores of 49.36 and 8.8, respectively, outperforming PISSA by 5.84\% and 1.96\%.

We propose a tuning-free dynamic SGD step size formula, which we call Distance over Gradients (DoG). The DoG step sizes depend on simple empirical quantities (distance from the initial point and norms of gradients) and have no ``learning rate'' parameter. Theoretically, we show that a slight variation of the DoG formula enjoys strong parameter-free convergence guarantees for stochastic convex optimization assuming only locally bounded stochastic gradients. Empirically, we consider a broad range of vision and language transfer learning tasks, and show that DoG's performance is close to that of SGD with tuned learning rate. We also propose a per-layer variant of DoG that generally outperforms tuned SGD, approaching the performance of tuned Adam. A PyTorch implementation is available at https://github.com/formll/dog

Seminal research in the field of graph neural networks (GNNs) has revealed a direct correspondence between the expressive capabilities of GNNs and the k-dimensional Weisfeiler-Leman (kWL) test, a widely-recognized method for verifying graph isomorphism. This connection has reignited interest in comprehending the specific graph properties effectively distinguishable by the kWL test. A central focus of research in this field revolves around determining the least dimensionality k, for which kWL can discern graphs with different number of occurrences of a pattern graph P. We refer to such a least k as the WL-dimension of this pattern counting problem. This inquiry traditionally delves into two distinct counting problems related to patterns: subgraph counting and induced subgraph counting. Intriguingly, despite their initial appearance as separate challenges with seemingly divergent approaches, both of these problems are interconnected components of a more comprehensive problem: "graph motif parameters". In this paper, we provide a precise characterization of the WL-dimension of labeled graph motif parameters. As specific instances of this result, we obtain characterizations of the WL-dimension of the subgraph counting and induced subgraph counting problem for every labeled pattern P. We additionally demonstrate that in cases where the kWL test distinguishes between graphs with varying occurrences of a pattern P, the exact number of occurrences of P can be computed uniformly using only local information of the last layer of a corresponding GNN. We finally delve into the challenge of recognizing the WL-dimension of various graph parameters. We give a polynomial time algorithm for determining the WL-dimension of the subgraph counting problem for given pattern P, answering an open question from previous work.

The development and training of deep learning models have become increasingly costly and complex. Consequently, software engineers are adopting pre-trained models (PTMs) for their downstream applications. The dynamics of the PTM supply chain remain largely unexplored, signaling a clear need for structured datasets that document not only the metadata but also the subsequent applications of these models. Without such data, the MSR community cannot comprehensively understand the impact of PTM adoption and reuse. This paper presents the PeaTMOSS dataset, which comprises metadata for 281,638 PTMs and detailed snapshots for all PTMs with over 50 monthly downloads (14,296 PTMs), along with 28,575 open-source software repositories from GitHub that utilize these models. Additionally, the dataset includes 44,337 mappings from 15,129 downstream GitHub repositories to the 2,530 PTMs they use. To enhance the dataset's comprehensiveness, we developed prompts for a large language model to automatically extract model metadata, including the model's training datasets, parameters, and evaluation metrics. Our analysis of this dataset provides the first summary statistics for the PTM supply chain, showing the trend of PTM development and common shortcomings of PTM package documentation. Our example application reveals inconsistencies in software licenses across PTMs and their dependent projects. PeaTMOSS lays the foundation for future research, offering rich opportunities to investigate the PTM supply chain. We outline mining opportunities on PTMs, their downstream usage, and cross-cutting questions.

PURPOSE: Subarachnoid hemorrhage (SAH) entails high morbidity and mortality rates. Convolutional neural networks (CNN), a form of deep learning, are capable of generating highly accurate predictions from imaging data. Our objective was to predict mortality in SAH patients by processing the initial CT scan on a CNN based algorithm. METHODS: Retrospective multicentric study of a consecutive cohort of patients with SAH between 2011-2022. Demographic, clinical and radiological variables were analyzed. Pre-processed baseline CT scan images were used as the input for training a CNN using AUCMEDI Framework. Our model's architecture leverages the DenseNet-121 structure, employing transfer learning principles. The output variable was mortality in the first three months. Performance of the model was evaluated by statistical parameters conventionally used in studies involving artificial intelligence methods. RESULTS: Images from 219 patients were processed, 175 for training and validation of the CNN and 44 for its evaluation. 52%(115/219) of patients were female, and the median age was 58(SD=13.06) years. 18.5%(39/219) were idiopathic SAH. Mortality rate was 28.5%(63/219). The model showed good accuracy at predicting mortality in SAH patients exclusively using the images of the initial CT scan (Accuracy=74%, F1=75% and AUC=82%). CONCLUSION: Modern image processing techniques based on AI and CNN make possible to predict mortality in SAH patients with high accuracy using CT scan images as the only input. These models might be optimized by including more data and patients resulting in better training, development and performance on tasks which are beyond the skills of conventional clinical knowledge.

In this work we present BOTS-LM, a series of bilingual language models proficient in both Setswana and English. Leveraging recent advancements in data availability and efficient fine-tuning, BOTS-LM achieves performance similar to models significantly larger than itself while maintaining computational efficiency. Our initial release features an 8 billion parameter generative large language model, with upcoming 0.5 billion and 1 billion parameter large language models and a 278 million parameter encoder-only model soon to be released. We find the 8 billion parameter model significantly outperforms Llama-3-70B and Aya 23 on English-Setswana translation tasks, approaching the performance of dedicated machine translation models, while approaching 70B parameter performance on Setswana reasoning as measured by a machine translated subset of the MMLU benchmark. To accompany the BOTS-LM series of language models, we release the largest Setswana web dataset, SetsText, totalling over 267 million tokens. In addition, we release the largest machine translated Setswana dataset, the first and largest synthetic Setswana dataset, training and evaluation code, training logs, and MMLU-tsn, a machine translated subset of MMLU.

Dataset distillation is the task of synthesizing a small dataset such that a model trained on the synthetic set will match the test accuracy of the model trained on the full dataset. In this paper, we propose a new formulation that optimizes our distilled data to guide networks to a similar state as those trained on real data across many training steps. Given a network, we train it for several iterations on our distilled data and optimize the distilled data with respect to the distance between the synthetically trained parameters and the parameters trained on real data. To efficiently obtain the initial and target network parameters for large-scale datasets, we pre-compute and store training trajectories of expert networks trained on the real dataset. Our method handily outperforms existing methods and also allows us to distill higher-resolution visual data.

We present a novel approach for identifying members of open star clusters using Gaia DR3 data by combining Minimum Spanning Tree (MST) and Gaussian Mixture Model (GMM) techniques. Our method employs a three-step process: initial filtering based on astrometric parameters, MST analysis for spatial distribution filtering, and GMM for final membership probability determination. We tested this methodology on 12+1 open clusters of varying ages, distances, and richness. The method demonstrates superior performance in distinguishing cluster members from field stars, particularly in regions with overlapping populations, as evidenced by its application to clusters like NGC 7790. By effectively reducing the number of probable field stars through MST analysis before applying GMM, our approach enhances both computational efficiency and membership determination accuracy. The results show strong agreement with previous studies while offering improved precision in member identification. This method provides a robust framework for analyzing the extensive datasets provided by Gaia DR3, addressing the challenges of processing large-scale astronomical data while maintaining high accuracy in cluster membership determination.

Ensuring safety and meeting temporal specifications are critical challenges for long-term robotic tasks. Signal temporal logic (STL) has been widely used to systematically and rigorously specify these requirements. However, traditional methods of finding the control policy under those STL requirements are computationally complex and not scalable to high-dimensional or systems with complex nonlinear dynamics. Reinforcement learning (RL) methods can learn the policy to satisfy the STL specifications via hand-crafted or STL-inspired rewards, but might encounter unexpected behaviors due to ambiguity and sparsity in the reward. In this paper, we propose a method to directly learn a neural network controller to satisfy the requirements specified in STL. Our controller learns to roll out trajectories to maximize the STL robustness score in training. In testing, similar to Model Predictive Control (MPC), the learned controller predicts a trajectory within a planning horizon to ensure the satisfaction of the STL requirement in deployment. A backup policy is designed to ensure safety when our controller fails. Our approach can adapt to various initial conditions and environmental parameters. We conduct experiments on six tasks, where our method with the backup policy outperforms the classical methods (MPC, STL-solver), model-free and model-based RL methods in STL satisfaction rate, especially on tasks with complex STL specifications while being 10X-100X faster than the classical methods.

Pruning methods have recently grown in popularity as an effective way to reduce the size and computational complexity of deep neural networks. Large numbers of parameters can be removed from trained models with little discernible loss in accuracy after a small number of continued training epochs. However, pruning too many parameters at once often causes an initial steep drop in accuracy which can undermine convergence quality. Iterative pruning approaches mitigate this by gradually removing a small number of parameters over multiple epochs. However, this can still lead to subnetworks that overfit local regions of the loss landscape. We introduce a novel and effective approach to tuning subnetworks through a regularization technique we call Stochastic Subnetwork Annealing. Instead of removing parameters in a discrete manner, we instead represent subnetworks with stochastic masks where each parameter has a probabilistic chance of being included or excluded on any given forward pass. We anneal these probabilities over time such that subnetwork structure slowly evolves as mask values become more deterministic, allowing for a smoother and more robust optimization of subnetworks at high levels of sparsity.

This paper presents a CLIP-based unsupervised learning method for annotation-free multi-label image classification, including three stages: initialization, training, and inference. At the initialization stage, we take full advantage of the powerful CLIP model and propose a novel approach to extend CLIP for multi-label predictions based on global-local image-text similarity aggregation. To be more specific, we split each image into snippets and leverage CLIP to generate the similarity vector for the whole image (global) as well as each snippet (local). Then a similarity aggregator is introduced to leverage the global and local similarity vectors. Using the aggregated similarity scores as the initial pseudo labels at the training stage, we propose an optimization framework to train the parameters of the classification network and refine pseudo labels for unobserved labels. During inference, only the classification network is used to predict the labels of the input image. Extensive experiments show that our method outperforms state-of-the-art unsupervised methods on MS-COCO, PASCAL VOC 2007, PASCAL VOC 2012, and NUS datasets and even achieves comparable results to weakly supervised classification methods.

Existing methods of pruning deep neural networks focus on removing unnecessary parameters of the trained network and fine tuning the model afterwards to find a good solution that recovers the initial performance of the trained model. Unlike other works, our method pays special attention to the quality of the solution in the compressed model and inference computation time by pruning neurons. The proposed algorithm directs the parameters of the compressed model toward a flatter solution by exploring the spectral radius of Hessian which results in better generalization on unseen data. Moreover, the method does not work with a pre-trained network and performs training and pruning simultaneously. Our result shows that it improves the state-of-the-art results on neuron compression. The method is able to achieve very small networks with small accuracy degradation across different neural network models.

We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input data but largely independent of the labels. We find that the singular value spectrum of the Jacobian matrix consists of three distinctive regions: a "chaotic" region of values orders of magnitude greater than one, a large "bulk" region of values extremely close to one, and a "stable" region of values less than one. Along each bulk direction, the left and right singular vectors are nearly identical, indicating that perturbations to the initialization are carried through training almost unchanged. These perturbations have virtually no effect on the network's output in-distribution, yet do have an effect far out-of-distribution. While the Jacobian applies only locally around a single initialization, we find substantial overlap in bulk subspaces for different random seeds. Our code is available at https://github.com/EleutherAI/training-jacobian

Over the years many ellipse detection algorithms spring up and are studied broadly, while the critical issue of detecting ellipses accurately and efficiently in real-world images remains a challenge. In this paper, we propose a valuable industry-oriented ellipse detector by arc-support line segments, which simultaneously reaches high detection accuracy and efficiency. To simplify the complicated curves in an image while retaining the general properties including convexity and polarity, the arc-support line segments are extracted, which grounds the successful detection of ellipses. The arc-support groups are formed by iteratively and robustly linking the arc-support line segments that latently belong to a common ellipse. Afterward, two complementary approaches, namely, locally selecting the arc-support group with higher saliency and globally searching all the valid paired groups, are adopted to fit the initial ellipses in a fast way. Then, the ellipse candidate set can be formulated by hierarchical clustering of 5D parameter space of initial ellipses. Finally, the salient ellipse candidates are selected and refined as detections subject to the stringent and effective verification. Extensive experiments on three public datasets are implemented and our method achieves the best F-measure scores compared to the state-of-the-art methods. The source code is available at https://github.com/AlanLuSun/High-quality-ellipse-detection.

Autonomous agents trained using deep reinforcement learning (RL) often lack the ability to successfully generalise to new environments, even when these environments share characteristics with the ones they have encountered during training. In this work, we investigate how the sampling of individual environment instances, or levels, affects the zero-shot generalisation (ZSG) ability of RL agents. We discover that, for deep actor-critic architectures sharing their base layers, prioritising levels according to their value loss minimises the mutual information between the agent's internal representation and the set of training levels in the generated training data. This provides a novel theoretical justification for the regularisation achieved by certain adaptive sampling strategies. We then turn our attention to unsupervised environment design (UED) methods, which assume control over level generation. We find that existing UED methods can significantly shift the training distribution, which translates to low ZSG performance. To prevent both overfitting and distributional shift, we introduce data-regularised environment design (DRED). DRED generates levels using a generative model trained to approximate the ground truth distribution of an initial set of level parameters. Through its grounding, DRED achieves significant improvements in ZSG over adaptive level sampling strategies and UED methods. Our code and experimental data are available at https://github.com/uoe-agents/dred.

Artificial neural networks for motor control usually adopt generic architectures like fully connected MLPs. While general, these tabula rasa architectures rely on large amounts of experience to learn, are not easily transferable to new bodies, and have internal dynamics that are difficult to interpret. In nature, animals are born with highly structured connectivity in their nervous systems shaped by evolution; this innate circuitry acts synergistically with learning mechanisms to provide inductive biases that enable most animals to function well soon after birth and learn efficiently. Convolutional networks inspired by visual circuitry have encoded useful biases for vision. However, it is unknown the extent to which ANN architectures inspired by neural circuitry can yield useful biases for other AI domains. In this work, we ask what advantages biologically inspired ANN architecture can provide in the domain of motor control. Specifically, we translate C. elegans locomotion circuits into an ANN model controlling a simulated Swimmer agent. On a locomotion task, our architecture achieves good initial performance and asymptotic performance comparable with MLPs, while dramatically improving data efficiency and requiring orders of magnitude fewer parameters. Our architecture is interpretable and transfers to new body designs. An ablation analysis shows that constrained excitation/inhibition is crucial for learning, while weight initialization contributes to good initial performance. Our work demonstrates several advantages of biologically inspired ANN architecture and encourages future work in more complex embodied control.

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function y(x). We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels y(x) are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

State space models (SSMs) have demonstrated state-of-the-art sequence modeling performance in some modalities, but underperform attention in language modeling. Moreover, despite scaling nearly linearly in sequence length instead of quadratically, SSMs are still slower than Transformers due to poor hardware utilization. In this paper, we make progress on understanding the expressivity gap between SSMs and attention in language modeling, and on reducing the hardware barrier between SSMs and attention. First, we use synthetic language modeling tasks to understand the gap between SSMs and attention. We find that existing SSMs struggle with two capabilities: recalling earlier tokens in the sequence and comparing tokens across the sequence. To understand the impact on language modeling, we propose a new SSM layer, H3, that is explicitly designed for these abilities. H3 matches attention on the synthetic languages and comes within 0.4 PPL of Transformers on OpenWebText. Furthermore, a hybrid 125M-parameter H3-attention model that retains two attention layers surprisingly outperforms Transformers on OpenWebText by 1.0 PPL. Next, to improve the efficiency of training SSMs on modern hardware, we propose FlashConv. FlashConv uses a fused block FFT algorithm to improve efficiency on sequences up to 8K, and introduces a novel state passing algorithm that exploits the recurrent properties of SSMs to scale to longer sequences. FlashConv yields 2times speedup on the long-range arena benchmark and allows hybrid language models to generate text 2.4times faster than Transformers. Using FlashConv, we scale hybrid H3-attention language models up to 2.7B parameters on the Pile and find promising initial results, achieving lower perplexity than Transformers and outperforming Transformers in zero- and few-shot learning on a majority of tasks in the SuperGLUE benchmark.

Recent advancements in text-to-image diffusion models have shown remarkable creative capabilities with textual prompts, but generating personalized instances based on specific subjects, known as subject-driven generation, remains challenging. To tackle this issue, we present a new hybrid framework called HybridBooth, which merges the benefits of optimization-based and direct-regression methods. HybridBooth operates in two stages: the Word Embedding Probe, which generates a robust initial word embedding using a fine-tuned encoder, and the Word Embedding Refinement, which further adapts the encoder to specific subject images by optimizing key parameters. This approach allows for effective and fast inversion of visual concepts into textual embedding, even from a single image, while maintaining the model's generalization capabilities.

Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only available supervision is a differentiable metric defined on the generated contents. Since the sampling procedure of DPMs involves recursive calls to the denoising UNet, na\"ive gradient backpropagation requires storing the intermediate states of all iterations, resulting in extremely high memory consumption. To overcome this issue, we propose a novel method AdjointDPM, which first generates new samples from diffusion models by solving the corresponding probability-flow ODEs. It then uses the adjoint sensitivity method to backpropagate the gradients of the loss to the models' parameters (including conditioning signals, network weights, and initial noises) by solving another augmented ODE. To reduce numerical errors in both the forward generation and gradient backpropagation processes, we further reparameterize the probability-flow ODE and augmented ODE as simple non-stiff ODEs using exponential integration. Finally, we demonstrate the effectiveness of AdjointDPM on three interesting tasks: converting visual effects into identification text embeddings, finetuning DPMs for specific types of stylization, and optimizing initial noise to generate adversarial samples for security auditing.

High dynamic range (HDR) novel view synthesis (NVS) aims to create photorealistic images from novel viewpoints using HDR imaging techniques. The rendered HDR images capture a wider range of brightness levels containing more details of the scene than normal low dynamic range (LDR) images. Existing HDR NVS methods are mainly based on NeRF. They suffer from long training time and slow inference speed. In this paper, we propose a new framework, High Dynamic Range Gaussian Splatting (HDR-GS), which can efficiently render novel HDR views and reconstruct LDR images with a user input exposure time. Specifically, we design a Dual Dynamic Range (DDR) Gaussian point cloud model that uses spherical harmonics to fit HDR color and employs an MLP-based tone-mapper to render LDR color. The HDR and LDR colors are then fed into two Parallel Differentiable Rasterization (PDR) processes to reconstruct HDR and LDR views. To establish the data foundation for the research of 3D Gaussian splatting-based methods in HDR NVS, we recalibrate the camera parameters and compute the initial positions for Gaussian point clouds. Experiments demonstrate that our HDR-GS surpasses the state-of-the-art NeRF-based method by 3.84 and 1.91 dB on LDR and HDR NVS while enjoying 1000x inference speed and only requiring 6.3% training time.

Few-shot learning aims at leveraging knowledge learned by one or more deep learning models, in order to obtain good classification performance on new problems, where only a few labeled samples per class are available. Recent years have seen a fair number of works in the field, introducing methods with numerous ingredients. A frequent problem, though, is the use of suboptimally trained models to extract knowledge, leading to interrogations on whether proposed approaches bring gains compared to using better initial models without the introduced ingredients. In this work, we propose a simple methodology, that reaches or even beats state of the art performance on multiple standardized benchmarks of the field, while adding almost no hyperparameters or parameters to those used for training the initial deep learning models on the generic dataset. This methodology offers a new baseline on which to propose (and fairly compare) new techniques or adapt existing ones.

Textured 3D morphing creates smooth and plausible interpolation sequences between two 3D objects, focusing on transitions in both shape and texture. This is important for creative applications like visual effects in filmmaking. Previous methods rely on establishing point-to-point correspondences and determining smooth deformation trajectories, which inherently restrict them to shape-only morphing on untextured, topologically aligned datasets. This restriction leads to labor-intensive preprocessing and poor generalization. To overcome these challenges, we propose a method for 3D regenerative morphing using a 3D diffusion prior. Unlike previous methods that depend on explicit correspondences and deformations, our method eliminates the additional need for obtaining correspondence and uses the 3D diffusion prior to generate morphing. Specifically, we introduce a 3D diffusion model and interpolate the source and target information at three levels: initial noise, model parameters, and condition features. We then explore an Attention Fusion strategy to generate more smooth morphing sequences. To further improve the plausibility of semantic interpolation and the generated 3D surfaces, we propose two strategies: (a) Token Reordering, where we match approximate tokens based on semantic analysis to guide implicit correspondences in the denoising process of the diffusion model, and (b) Low-Frequency Enhancement, where we enhance low-frequency signals in the tokens to improve the quality of generated surfaces. Experimental results show that our method achieves superior smoothness and plausibility in 3D morphing across diverse cross-category object pairs, offering a novel regenerative method for 3D morphing with textured representations.

Recently, image-to-3D approaches have significantly advanced the generation quality and speed of 3D assets based on large reconstruction models, particularly 3D Gaussian reconstruction models. Existing large 3D Gaussian models directly map 2D image to 3D Gaussian parameters, while regressing 2D image to 3D Gaussian representations is challenging without 3D priors. In this paper, we propose a large Point-to-Gaussian model, that inputs the initial point cloud produced from large 3D diffusion model conditional on 2D image to generate the Gaussian parameters, for image-to-3D generation. The point cloud provides initial 3D geometry prior for Gaussian generation, thus significantly facilitating image-to-3D Generation. Moreover, we present the Attention mechanism, Projection mechanism, and Point feature extractor, dubbed as APP block, for fusing the image features with point cloud features. The qualitative and quantitative experiments extensively demonstrate the effectiveness of the proposed approach on GSO and Objaverse datasets, and show the proposed method achieves state-of-the-art performance.

Generative Language Models (LMs) such as ChatGPT have exhibited remarkable performance across various downstream tasks. Nevertheless, one of their most prominent drawbacks is generating inaccurate or false information with a confident tone. Previous studies have devised sophisticated pipelines and prompts to induce large LMs to exhibit the capability for self-correction. However, large LMs are explicitly prompted to verify and modify its answers separately rather than completing all steps spontaneously like humans. Moreover, these complex prompts are extremely challenging for small LMs to follow. In this paper, we introduce the Intrinsic Self-Correction (ISC) in generative language models, aiming to correct the initial output of LMs in a self-triggered manner, even for those small LMs with 6 billion parameters. Specifically, we devise a pipeline for constructing self-correction data and propose Partial Answer Masking (PAM), aiming to endow the model with the capability for intrinsic self-correction through fine-tuning. We conduct experiments using LMs with parameters sizes ranging from 6 billion to 13 billion in two tasks, including commonsense reasoning and factual knowledge reasoning. Our experiments demonstrate that the outputs generated using ISC outperform those generated without self-correction. We believe that the output quality of even small LMs can be further improved by empowering them with the ability to intrinsic self-correct.

Large language models (LLMs) often demonstrate inconsistencies with human preferences. Previous research gathered human preference data and then aligned the pre-trained models using reinforcement learning or instruction tuning, the so-called finetuning step. In contrast, aligning frozen LLMs without any extra data is more appealing. This work explores the potential of the latter setting. We discover that by integrating self-evaluation and rewind mechanisms, unaligned LLMs can directly produce responses consistent with human preferences via self-boosting. We introduce a novel inference method, Rewindable Auto-regressive INference (RAIN), that allows pre-trained LLMs to evaluate their own generation and use the evaluation results to guide backward rewind and forward generation for AI safety. Notably, RAIN operates without the need of extra data for model alignment and abstains from any training, gradient computation, or parameter updates; during the self-evaluation phase, the model receives guidance on which human preference to align with through a fixed-template prompt, eliminating the need to modify the initial prompt. Experimental results evaluated by GPT-4 and humans demonstrate the effectiveness of RAIN: on the HH dataset, RAIN improves the harmlessness rate of LLaMA 30B over vanilla inference from 82% to 97%, while maintaining the helpfulness rate. Under the leading adversarial attack llm-attacks on Vicuna 33B, RAIN establishes a new defense baseline by reducing the attack success rate from 94% to 19%.

The entry of large language models (LLMs) into research and commercial spaces has led to a trend of ever-larger models, with initial promises of generalisability, followed by a widespread desire to downsize and create specialised models without the need for complete fine-tuning, using Parameter Efficient Fine-tuning (PEFT) methods. We present an investigation into the suitability of different PEFT methods to clinical decision-making tasks, across a range of model sizes, including extremely small models with as few as 25 million parameters. Our analysis shows that the performance of most PEFT approaches varies significantly from one task to another, with the exception of LoRA, which maintains relatively high performance across all model sizes and tasks, typically approaching or matching full fine-tuned performance. The effectiveness of PEFT methods in the clinical domain is evident, particularly for specialised models which can operate on low-cost, in-house computing infrastructure. The advantages of these models, in terms of speed and reduced training costs, dramatically outweighs any performance gain from large foundation LLMs. Furthermore, we highlight how domain-specific pre-training interacts with PEFT methods and model size, and discuss how these factors interplay to provide the best efficiency-performance trade-off. Full code available at: tbd.

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time R^3times R, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually R^3 times {0}. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

We use two-dimensional particle-in-cell simulations to investigate the generation and evolution of the magnetic field associated with the propagation of a jet for various initial conditions. We demonstrate that, in general, the magnetic field is initially grown by the Weibel and Mushroom instabilities. However, the field is saturated by the Alfv'en current limit. For initially non-magnetized plasma, we show that the growth of the magnetic field is delayed when the matter density of the jet environment is lower, which are in agreement with simple analytical predictions. We show that the higher Lorentz factor (gtrsim 2) prevents rapid growth of the magnetic fields. When the initial field is troidal, the position of the magnetic filaments moves away from the jet as the field strength increases. The axial initial field helps the jet maintain its shape more effectively than the troidal initial field.

While prompt tuning approaches have achieved competitive performance with high efficiency, we observe that they invariably employ the same initialization process, wherein the soft prompt is either randomly initialized or derived from an existing embedding vocabulary. In contrast to these conventional methods, this study aims to investigate an alternative way to derive soft prompt. Our empirical studies show that the soft prompt typically exhibits a low intrinsic rank characteristic. With such observations, we propose decomposed prompt tuning, a novel approach that utilizes low-rank matrices to initialize the soft prompt. Through the low-rank reparameterization, our method significantly reduces the number of trainable parameters while maintaining effectiveness. Experimental results on the SuperGLUE benchmark in both high-resource and low-resource scenarios demonstrate the effectiveness of the proposed method.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

The initial state of neural networks plays a central role in conditioning the subsequent training dynamics. In the context of classification problems, we provide a theoretical analysis demonstrating that the structure of a neural network can condition the model to assign all predictions to the same class, even before the beginning of training, and in the absence of explicit biases. We show that the presence of this phenomenon, which we call "Initial Guessing Bias" (IGB), depends on architectural choices such as activation functions, max-pooling layers, and network depth. Our analysis of IGB has practical consequences, in that it guides architecture selection and initialization. We also highlight theoretical consequences, such as the breakdown of node-permutation symmetry, the violation of self-averaging, the validity of some mean-field approximations, and the non-trivial differences arising with depth.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

The pre-training phase of language models often begins with randomly initialized parameters. With the current trends in scaling models, training their large number of parameters can be extremely slow and costly. In contrast, small language models are less expensive to train, but they often cannot achieve the accuracy of large models. In this paper, we explore an intriguing idea to connect these two different regimes: Can we develop a method to initialize large language models using smaller pre-trained models? Will such initialization bring any benefits in terms of training time and final accuracy? In this paper, we introduce HyperCloning, a method that can expand the parameters of a pre-trained language model to those of a larger model with increased hidden dimensions. Our method ensures that the larger model retains the functionality of the smaller model. As a result, the larger model already inherits the predictive power and accuracy of the smaller model before the training starts. We demonstrate that training such an initialized model results in significant savings in terms of GPU hours required for pre-training large language models.

The performance of an algorithm often critically depends on its parameter configuration. While a variety of automated algorithm configuration methods have been proposed to relieve users from the tedious and error-prone task of manually tuning parameters, there is still a lot of untapped potential as the learned configuration is static, i.e., parameter settings remain fixed throughout the run. However, it has been shown that some algorithm parameters are best adjusted dynamically during execution, e.g., to adapt to the current part of the optimization landscape. Thus far, this is most commonly achieved through hand-crafted heuristics. A promising recent alternative is to automatically learn such dynamic parameter adaptation policies from data. In this article, we give the first comprehensive account of this new field of automated dynamic algorithm configuration (DAC), present a series of recent advances, and provide a solid foundation for future research in this field. Specifically, we (i) situate DAC in the broader historical context of AI research; (ii) formalize DAC as a computational problem; (iii) identify the methods used in prior-art to tackle this problem; (iv) conduct empirical case studies for using DAC in evolutionary optimization, AI planning, and machine learning.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance varepsilon, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as varepsilon varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from varepsilon=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of varepsilon. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

There often is a dilemma between ease of optimization and robust out-of-distribution (OoD) generalization. For instance, many OoD methods rely on penalty terms whose optimization is challenging. They are either too strong to optimize reliably or too weak to achieve their goals. We propose to initialize the networks with a rich representation containing a palette of potentially useful features, ready to be used by even simple models. On the one hand, a rich representation provides a good initialization for the optimizer. On the other hand, it also provides an inductive bias that helps OoD generalization. Such a representation is constructed with the Rich Feature Construction (RFC) algorithm, also called the Bonsai algorithm, which consists of a succession of training episodes. During discovery episodes, we craft a multi-objective optimization criterion and its associated datasets in a manner that prevents the network from using the features constructed in the previous iterations. During synthesis episodes, we use knowledge distillation to force the network to simultaneously represent all the previously discovered features. Initializing the networks with Bonsai representations consistently helps six OoD methods achieve top performance on ColoredMNIST benchmark. The same technique substantially outperforms comparable results on the Wilds Camelyon17 task, eliminates the high result variance that plagues other methods, and makes hyperparameter tuning and model selection more reliable.

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.

Weight initialization plays an important role in neural network training. Widely used initialization methods are proposed and evaluated for networks that are trained from scratch. However, the growing number of pretrained models now offers new opportunities for tackling this classical problem of weight initialization. In this work, we introduce weight selection, a method for initializing smaller models by selecting a subset of weights from a pretrained larger model. This enables the transfer of knowledge from pretrained weights to smaller models. Our experiments demonstrate that weight selection can significantly enhance the performance of small models and reduce their training time. Notably, it can also be used together with knowledge distillation. Weight selection offers a new approach to leverage the power of pretrained models in resource-constrained settings, and we hope it can be a useful tool for training small models in the large-model era. Code is available at https://github.com/OscarXZQ/weight-selection.

We present the data release and data reduction process for the Epoch 1 NIRCam observations for the Cosmic Evolution Early Release Science Survey (CEERS). These data consist of NIRCam imaging in six broadband filters (F115W, F150W, F200W, F277W, F356W and F444W) and one medium band filter (F410M) over four pointings, obtained in parallel with primary CEERS MIRI observations (Yang et al. in prep). We reduced the NIRCam imaging with the JWST Calibration Pipeline, with custom modifications and reduction steps designed to address additional features and challenges with the data. Here we provide a detailed description of each step in our reduction and a discussion of future expected improvements. Our reduction process includes corrections for known pre-launch issues such as 1/f noise, as well as in-flight issues including snowballs, wisps, and astrometric alignment. Many of our custom reduction processes were first developed with pre-launch simulated NIRCam imaging over the full 10 CEERS NIRCam pointings. We present a description of the creation and reduction of this simulated dataset in the Appendix. We provide mosaics of the real images in a public release, as well as our reduction scripts with detailed explanations to allow users to reproduce our final data products. These represent one of the first official public datasets released from the Directors Discretionary Early Release Science (DD-ERS) program.

Most deep neural networks are trained under fixed network architectures and require retraining when the architecture changes. If expanding the network's size is needed, it is necessary to retrain from scratch, which is expensive. To avoid this, one can grow from a small network by adding random weights over time to gradually achieve the target network size. However, this naive approach falls short in practice as it brings too much noise to the growing process. Prior work tackled this issue by leveraging the already learned weights and training data for generating new weights through conducting a computationally expensive analysis step. In this paper, we introduce MixtureGrowth, a new approach to growing networks that circumvents the initialization overhead in prior work. Before growing, each layer in our model is generated with a linear combination of parameter templates. Newly grown layer weights are generated by using a new linear combination of existing templates for a layer. On one hand, these templates are already trained for the task, providing a strong initialization. On the other, the new coefficients provide flexibility for the added layer weights to learn something new. We show that our approach boosts top-1 accuracy over the state-of-the-art by 2-2.5% on CIFAR-100 and ImageNet datasets, while achieving comparable performance with fewer FLOPs to a larger network trained from scratch. Code is available at https://github.com/chaudatascience/mixturegrowth.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm -- using only the number of iterations as feedback -- can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

This technical report presents Prithvi-EO-2.0, a new geospatial foundation model that offers significant improvements over its predecessor, Prithvi-EO-1.0. Trained on 4.2M global time series samples from NASA's Harmonized Landsat and Sentinel-2 data archive at 30m resolution, the new 300M and 600M parameter models incorporate temporal and location embeddings for enhanced performance across various geospatial tasks. Through extensive benchmarking with GEO-Bench, the 600M version outperforms the previous Prithvi-EO model by 8\% across a range of tasks. It also outperforms six other geospatial foundation models when benchmarked on remote sensing tasks from different domains and resolutions (i.e. from 0.1m to 15m). The results demonstrate the versatility of the model in both classical earth observation and high-resolution applications. Early involvement of end-users and subject matter experts (SMEs) are among the key factors that contributed to the project's success. In particular, SME involvement allowed for constant feedback on model and dataset design, as well as successful customization for diverse SME-led applications in disaster response, land use and crop mapping, and ecosystem dynamics monitoring. Prithvi-EO-2.0 is available on Hugging Face and IBM terratorch, with additional resources on GitHub. The project exemplifies the Trusted Open Science approach embraced by all involved organizations.

In this work, we obtain the error estimate of the rotation parameter beta from the core bounce phase of the characteristic gravitational wave signal of a rapidly rotating core collapse supernova (CCSN). We quantify the error with asymptotic expansions of the covariance of a Maximum Likelihood Estimator (MLE) in terms of inverse powers of Signal-Noise Ratio (SNR), this method has been previously applied to parameter estimation for compact binary coalescences. When the second order of this expansion is negligible, it indicates that the first order is a good approximation of the error that will have a matching filter approach when estimating beta. The analysis indicates that we should be able to resolve the presence of rotation for the galactic and nearby extragalactic progenitors. We show that the estimation error Delta beta can be as small as a few percent and is larger for small values of beta.

Practical identifiability is a critical concern in data-driven modeling of mathematical systems. In this paper, we propose a novel framework for practical identifiability analysis to evaluate parameter identifiability in mathematical models of biological systems. Starting with a rigorous mathematical definition of practical identifiability, we demonstrate its equivalence to the invertibility of the Fisher Information Matrix. Our framework establishes the relationship between practical identifiability and coordinate identifiability, introducing a novel metric that simplifies and accelerates the evaluation of parameter identifiability compared to the profile likelihood method. Additionally, we introduce new regularization terms to address non-identifiable parameters, enabling uncertainty quantification and improving model reliability. To guide experimental design, we present an optimal data collection algorithm that ensures all model parameters are practically identifiable. Applications to Hill functions, neural networks, and dynamic biological models demonstrate the feasibility and efficiency of the proposed computational framework in uncovering critical biological processes and identifying key observable variables.

A primary cost driver for training large models is wall-clock training time. We show that popular time estimates based on FLOPs are poor estimates, and construct a more accurate proxy based on memory copies. We show that with some simple accounting, we can estimate the training speed of a transformer model from its hyperparameters. Combined with a scaling law curve like Chinchilla, this lets us estimate the final loss of the model. We fit our estimate to real data with a linear regression, and apply the result to rewrite Chinchilla in terms of a model's estimated training time as opposed to the amount of training data. This gives an expression for the loss in terms of the model's hyperparameters alone. We show that this expression is accurate across a wide range of model hyperparameter values, enabling us to analytically make architectural decisions and train models more efficiently.

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.

The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? It is known that many different parameter settings can determine the same function. Moreover, the degree of this redundancy is inhomogeneous: for some networks, the only symmetries are permutation of neurons in a layer and positive scaling of parameters at a neuron, while other networks admit additional hidden symmetries. In this work, we prove that, for any network architecture where no layer is narrower than the input, there exist parameter settings with no hidden symmetries. We also describe a number of mechanisms through which hidden symmetries can arise, and empirically approximate the functional dimension of different network architectures at initialization. These experiments indicate that the probability that a network has no hidden symmetries decreases towards 0 as depth increases, while increasing towards 1 as width and input dimension increase.

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship between, loss, or task performance, and scale. All components of this process vary, from the specific equation being fit, to the training setup, to the optimization method. Each of these factors may affect the fitted law, and therefore, the conclusions of a given study. We discuss discrepancies in the conclusions that several prior works reach, on questions such as the optimal token to parameter ratio. We augment this discussion with our own analysis of the critical impact that changes in specific details may effect in a scaling study, and the resulting altered conclusions. Additionally, we survey over 50 papers that study scaling trends: while 45 of these papers quantify these trends using a power law, most under-report crucial details needed to reproduce their findings. To mitigate this, we we propose a checklist for authors to consider while contributing to scaling law research.

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 propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

What makes a good Large Language Model (LLM)? That it performs well on the relevant benchmarks -- which hopefully measure, with some validity, the presence of capabilities that are also challenged in real application. But what makes the model perform well? What gives a model its abilities? We take a recently introduced type of benchmark that is meant to challenge capabilities in a goal-directed, agentive context through self-play of conversational games, and analyse how performance develops as a function of model characteristics like number of parameters, or type of training. We find that while there is a clear relationship between number of parameters and performance, there is still a wide spread of performance points within a given size bracket, which is to be accounted for by training parameters such as fine-tuning data quality and method. From a more practical angle, we also find a certain degree of unpredictability about performance across access methods, possible due to unexposed sampling parameters, and a, very welcome, performance stability against at least moderate weight quantisation during inference.

We propose Inner Loop Feedback (ILF), a novel approach to accelerate diffusion models' inference. ILF trains a lightweight module to predict future features in the denoising process by leveraging the outputs from a chosen diffusion backbone block at a given time step. This approach exploits two key intuitions; (1) the outputs of a given block at adjacent time steps are similar, and (2) performing partial computations for a step imposes a lower burden on the model than skipping the step entirely. Our method is highly flexible, since we find that the feedback module itself can simply be a block from the diffusion backbone, with all settings copied. Its influence on the diffusion forward can be tempered with a learnable scaling factor from zero initialization. We train this module using distillation losses; however, unlike some prior work where a full diffusion backbone serves as the student, our model freezes the backbone, training only the feedback module. While many efforts to optimize diffusion models focus on achieving acceptable image quality in extremely few steps (1-4 steps), our emphasis is on matching best case results (typically achieved in 20 steps) while significantly reducing runtime. ILF achieves this balance effectively, demonstrating strong performance for both class-to-image generation with diffusion transformer (DiT) and text-to-image generation with DiT-based PixArt-alpha and PixArt-sigma. The quality of ILF's 1.7x-1.8x speedups are confirmed by FID, CLIP score, CLIP Image Quality Assessment, ImageReward, and qualitative comparisons. Project information is available at https://mgwillia.github.io/ilf.

In an industrial group like Safran, numerical simulations of physical phenomena are integral to most design processes. At Safran's corporate research center, we enhance these processes by developing fast and reliable surrogate models for various physics. We focus here on two technologies developed in recent years. The first is a physical reduced-order modeling method for non-linear structural mechanics and thermal analysis, used for calculating the lifespan of high-pressure turbine blades and performing heat analysis of high-pressure compressors. The second technology involves learning physics simulations with non-parameterized geometrical variability using classical machine learning tools, such as Gaussian process regression. Finally, we present our contributions to the open-source and open-data community.

All current formulations of thermodynamics invoke some form of coarse-graining or ensembles as the supposed link between their own laws and the microscopic laws of motion. They deal only with ensemble-averages, expectation values, macroscopic limits, infinite heat baths, etc., not with the details of physical variables of individual microscopic systems. They are consistent with the laws of motion for finite systems only in certain approximations, which improve with increasing scale, given various assumptions about initial conditions which are neither specified precisely nor even thought to hold exactly in nature. Here I propose a new formulation of the zeroth, first and second laws, improving upon the axiomatic approach to thermodynamics (Carath\'eodory, 1909; Lieb & Yngvason, 1999), via the principles of the recently proposed constructor theory. Specifically, I provide a non-approximative, scale-independent formulation of 'adiabatic accessibility'; this in turn provides a non-approximative, scale-independent distinction between work and heat and reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second). It also achieves the long-sought unification of the axiomatic approach with Kelvin's.

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where M^* in R^{n times n} is a positive semi-definite unknown matrix of rank r ll n, and one uses a symmetric parameterization XX^top to learn M^*. Here X in R^{n times k} with k > r is the factor matrix. We give a novel Omega (1/T^2) lower bound of randomly initialized GD for the over-parameterized case (k >r) where T is the number of iterations. This is in stark contrast to the exact-parameterization scenario (k=r) where the convergence rate is exp (-Omega (T)). Next, we study asymmetric setting where M^* in R^{n_1 times n_2} is the unknown matrix of rank r ll min{n_1,n_2}, and one uses an asymmetric parameterization FG^top to learn M^* where F in R^{n_1 times k} and G in R^{n_2 times k}. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case (k=r) with an exp (-Omega(T)) rate. Furthermore, we give the first global exact convergence result for the over-parameterization case (k>r) with an exp(-Omega(alpha^2 T)) rate where alpha is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from Omega (1/T^2) to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of alpha, recovering the rate in the exact-parameterization case.

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a robust framework for extracting theoretical insights from observational data. However, its computational demands can be substantial, primarily due to the need for numerous likelihood function evaluations. Our proposed method utilizes the power of deep learning, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process. Unlike traditional approaches, our method trains neural networks on-the-fly using the current set of live points as training data, without the need for pre-training. This flexibility enables adaptation to various theoretical models and datasets. We perform simple hyperparameter optimization using genetic algorithms to suggest initial neural network architectures for learning each likelihood function. Once sufficient accuracy is achieved, the neural network replaces the original likelihood function. The implementation integrates with nested sampling algorithms and has been thoroughly evaluated using both simple cosmological dark energy models and diverse observational datasets. Additionally, we explore the potential of genetic algorithms for generating initial live points within nested sampling inference, opening up new avenues for enhancing the efficiency and effectiveness of Bayesian inference methods.

State-of-the-art space science missions increasingly rely on automation due to spacecraft complexity and the costs of human oversight. The high volume of data, including scientific and telemetry data, makes manual inspection challenging. Machine learning offers significant potential to meet these demands. The Euclid space telescope, in its survey phase since February 2024, exemplifies this shift. Euclid's success depends on accurate monitoring and interpretation of housekeeping telemetry and science-derived data. Thousands of telemetry parameters, monitored as time series, may or may not impact the quality of scientific data. These parameters have complex interdependencies, often due to physical relationships (e.g., proximity of temperature sensors). Optimising science operations requires careful anomaly detection and identification of hidden parameter states. Moreover, understanding the interactions between known anomalies and physical quantities is crucial yet complex, as related parameters may display anomalies with varied timing and intensity. We address these challenges by analysing temperature anomalies in Euclid's telemetry from February to August 2024, focusing on eleven temperature parameters and 35 covariates. We use a predictive XGBoost model to forecast temperatures based on historical values, detecting anomalies as deviations from predictions. A second XGBoost model predicts anomalies from covariates, capturing their relationships to temperature anomalies. We identify the top three anomalies per parameter and analyse their interactions with covariates using SHAP (Shapley Additive Explanations), enabling rapid, automated analysis of complex parameter relationships. Our method demonstrates how machine learning can enhance telemetry monitoring, offering scalable solutions for other missions with similar data challenges.

Let L denote the Laplacian matrix of a graph G. We study continuous quantum walks on G defined by the transition matrix U(t)=expleft(itLright). The initial state is of the pair state form, e_a-e_b with a,b being any two vertices of G. We provide two ways to construct infinite families of graphs that have perfect pair transfer. We study a "transitivity" phenomenon which cannot occur in vertex state transfer. We characterize perfect pair state transfer on paths and cycles. We also study the case when quantum walks are generated by the unsigned Laplacians of underlying graphs and the initial states are of the plus state form, e_a+e_b. When the underlying graphs are bipartite, plus state transfer is equivalent to pair state transfer.

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

The weather forecasting system is important for science and society, and significant achievements have been made in applying artificial intelligence (AI) to medium-range weather forecasting. However, existing AI-based weather forecasting models rely on analysis or reanalysis products from traditional numerical weather prediction (NWP) systems as initial conditions for making predictions. Initial states are typically generated by traditional data assimilation components, which are computational expensive and time-consuming. Here we present an AI-based data assimilation model, i.e., Adas, for global weather variables. By introducing the confidence matrix, Adas employs gated convolution to handle sparse observations and gated cross-attention for capturing the interactions between the background and observations. Further, we combine Adas with the advanced AI-based forecasting model (i.e., FengWu) to construct the first end-to-end AI-based global weather forecasting system: FengWu-Adas. We demonstrate that Adas can assimilate global observations to produce high-quality analysis, enabling the system operate stably for long term. Moreover, we are the first to apply the methods to real-world scenarios, which is more challenging and has considerable practical application potential. We have also achieved the forecasts based on the analyses generated by AI with a skillful forecast lead time exceeding that of the IFS for the first time.