Daily Papers

Federated Learning (FL) is a widely used framework for training models in a decentralized manner, ensuring that the central server does not have direct access to data from local clients. However, this approach may still fail to fully preserve data privacy, as models from local clients are exposed to the central server during the aggregation process. This issue becomes even more critical when training vision-language models (VLMs) with FL, as VLMs can easily memorize training data instances, making them vulnerable to membership inference attacks (MIAs). To address this challenge, we propose the FedRand framework, which avoids disclosing the full set of client parameters. In this framework, each client randomly selects subparameters of Low-Rank Adaptation (LoRA) from the server and keeps the remaining counterparts of the LoRA weights as private parameters. After training both parameters on the client's private dataset, only the non-private client parameters are sent back to the server for aggregation. This approach mitigates the risk of exposing client-side VLM parameters, thereby enhancing data privacy. We empirically validate that FedRand improves robustness against MIAs compared to relevant baselines while achieving accuracy comparable to methods that communicate full LoRA parameters across several benchmark datasets.

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses muP parameterized networks, where the optimal hyperparameters for small width networks transfer to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of 1/text{depth} in combination with the muP parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

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.

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific parameterization for second-order optimization that promotes feature learning in a stable manner even if the network width increases significantly. Inspired by a maximal update parameterization, we consider a one-step update of the gradient and reveal the appropriate scales of hyperparameters including random initialization, learning rates, and damping terms. Our approach covers two major second-order optimization algorithms, K-FAC and Shampoo, and we demonstrate that our parameterization achieves higher generalization performance in feature learning. In particular, it enables us to transfer the hyperparameters across models with different widths.

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.

We present BabyLlama-2, a 345 million parameter model distillation-pretrained from two teachers on a 10 million word corpus for the BabyLM competition. On BLiMP and SuperGLUE benchmarks, BabyLlama-2 outperforms baselines trained on both 10 and 100 million word datasets with the same data mix, as well as its teacher models. Through an extensive hyperparameter sweep, we demonstrate that the advantages of distillation cannot be attributed to suboptimal hyperparameter selection of the teachers. Our findings underscore the need for further investigation into distillation techniques, particularly in data-limited settings.

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

Due to the high computational demands executing a rigorous comparison between hyperparameter optimization (HPO) methods is often cumbersome. The goal of this paper is to facilitate a better empirical evaluation of HPO methods by providing benchmarks that are cheap to evaluate, but still represent realistic use cases. We believe these benchmarks provide an easy and efficient way to conduct reproducible experiments for neural hyperparameter search. Our benchmarks consist of a large grid of configurations of a feed forward neural network on four different regression datasets including architectural hyperparameters and hyperparameters concerning the training pipeline. Based on this data, we performed an in-depth analysis to gain a better understanding of the properties of the optimization problem, as well as of the importance of different types of hyperparameters. Second, we exhaustively compared various different state-of-the-art methods from the hyperparameter optimization literature on these benchmarks in terms of performance and robustness.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

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.

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed ell^2 Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP). We provide a ``direct'' parameterization, i.e., a smooth mapping from mathbb R^N onto the set of weights satisfying the SDP-based bound. Moreover, our parameterization is complete, i.e. a neural network satisfies the SDP bound if and only if it can be represented via our parameterization. This enables training using standard gradient methods, without any inner approximation or computationally intensive tasks (e.g. projections or barrier terms) for the SDP constraint. The new parameterization can equivalently be thought of as either a new layer type (the sandwich layer), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. A comprehensive set of experiments on image classification shows that sandwich layers outperform previous approaches on both empirical and certified robust accuracy. Code is available at https://github.com/acfr/LBDN.

In this paper, we present a cross-entropy optimization method for hyperparameter optimization in stochastic gradient-based approaches to train deep neural networks. The value of a hyperparameter of a learning algorithm often has great impact on the performance of a model such as the convergence speed, the generalization performance metrics, etc. While in some cases the hyperparameters of a learning algorithm can be part of learning parameters, in other scenarios the hyperparameters of a stochastic optimization algorithm such as Adam [5] and its variants are either fixed as a constant or are kept changing in a monotonic way over time. We give an in-depth analysis of the presented method in the framework of expectation maximization (EM). The presented algorithm of cross-entropy optimization for hyperparameter optimization of a learning algorithm (CEHPO) can be equally applicable to other areas of optimization problems in deep learning. We hope that the presented methods can provide different perspectives and offer some insights for optimization problems in different areas of machine learning and beyond.

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).

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to acquire. This report proposes several efficient ways to set the hyper-parameters that significantly reduce training time and improves performance. Specifically, this report shows how to examine the training validation/test loss function for subtle clues of underfitting and overfitting and suggests guidelines for moving toward the optimal balance point. Then it discusses how to increase/decrease the learning rate/momentum to speed up training. Our experiments show that it is crucial to balance every manner of regularization for each dataset and architecture. Weight decay is used as a sample regularizer to show how its optimal value is tightly coupled with the learning rates and momentums. Files to help replicate the results reported here are available.

In deep learning, performance is strongly affected by the choice of architecture and hyperparameters. While there has been extensive work on automatic hyperparameter optimization for simple spaces, complex spaces such as the space of deep architectures remain largely unexplored. As a result, the choice of architecture is done manually by the human expert through a slow trial and error process guided mainly by intuition. In this paper we describe a framework for automatically designing and training deep models. We propose an extensible and modular language that allows the human expert to compactly represent complex search spaces over architectures and their hyperparameters. The resulting search spaces are tree-structured and therefore easy to traverse. Models can be automatically compiled to computational graphs once values for all hyperparameters have been chosen. We can leverage the structure of the search space to introduce different model search algorithms, such as random search, Monte Carlo tree search (MCTS), and sequential model-based optimization (SMBO). We present experiments comparing the different algorithms on CIFAR-10 and show that MCTS and SMBO outperform random search. In addition, these experiments show that our framework can be used effectively for model discovery, as it is possible to describe expressive search spaces and discover competitive models without much effort from the human expert. Code for our framework and experiments has been made publicly available.

In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with ell_1-loss, where the goal is to recover a low-rank matrix from a limited number of measurements, a subset of which may be grossly corrupted with noise. We study a scenario where the rank of the true solution is unknown and over-estimated instead. The over-estimation of the rank gives rise to an over-parameterized model in which there are more degrees of freedom than needed. Such over-parameterization may lead to overfitting, or adversely affect the performance of the algorithm. We prove that a simple SubGM with small initialization is agnostic to both over-parameterization and noise in the measurements. In particular, we show that small initialization nullifies the effect of over-parameterization on the performance of SubGM, leading to an exponential improvement in its convergence rate. Moreover, we provide the first unifying framework for analyzing the behavior of SubGM under both outlier and Gaussian noise models, showing that SubGM converges to the true solution, even under arbitrarily large and arbitrarily dense noise values, and--perhaps surprisingly--even if the globally optimal solutions do not correspond to the ground truth. At the core of our results is a robust variant of restricted isometry property, called Sign-RIP, which controls the deviation of the sub-differential of the ell_1-loss from that of an ideal, expected loss. As a byproduct of our results, we consider a subclass of robust low-rank matrix recovery with Gaussian measurements, and show that the number of required samples to guarantee the global convergence of SubGM is independent of the over-parameterized rank.

Large artificial neural networks have become a mainstay of language, vision, and audio processing and synthesis, yet their initializations and learning rates are often set in an unsophisticated fashion, due to the high cost of hyperparameter sweeps at scale. The mu-Parameterization (muP) offers a potential solution to this challenge, yielding scaling rules for model initialization and learning rates while reportedly enabling zero-shot hyperparameter transfer from small to large models. Despite its evident promise, the muP method is not yet widely adopted, perhaps due to higher implementation complexity, many variations, or complex theoretical background. This work investigates muP empirically, focusing on the ubiquitous transformer architecture, and aims to answer a simple question: does mu-Transfer yield optimal learning rates in practice? Studying models of up to 10B parameters and training budgets of up to 190B tokens, we find mu-Transfer works as intended for the majority of important cases, yet also identify a few cases where it may not.

Transformers have shown improved performance when compared to previous architectures for sequence processing such as RNNs. Despite their sizeable performance gains, as recently suggested, the model is computationally expensive to train and with a high parameter budget. In light of this, we explore parameter-sharing methods in Transformers with a specific focus on generative models. We perform an analysis of different parameter sharing/reduction methods and develop the Subformer. Our model combines sandwich-style parameter sharing, which overcomes naive cross-layer parameter sharing in generative models, and self-attentive embedding factorization (SAFE). Experiments on machine translation, abstractive summarization and language modeling show that the Subformer can outperform the Transformer even when using significantly fewer parameters.

The Maximal Update Parametrization (muP) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new scheme, u-muP, which improves upon muP by combining it with Unit Scaling, a method for designing models that makes them easy to train in low-precision. The two techniques have a natural affinity: muP ensures that the scale of activations is independent of model size, and Unit Scaling ensures that activations, weights and gradients begin training with a scale of one. This synthesis opens the door to a simpler scheme, whose default values are near-optimal. This in turn facilitates a more efficient sweeping strategy, with u-muP models reaching a lower loss than comparable muP models and working out-of-the-box in FP8.

Hyperparameter (HP) tuning in deep learning is an expensive process, prohibitively so for neural networks (NNs) with billions of parameters. We show that, in the recently discovered Maximal Update Parametrization (muP), many optimal HPs remain stable even as model size changes. This leads to a new HP tuning paradigm we call muTransfer: parametrize the target model in muP, tune the HP indirectly on a smaller model, and zero-shot transfer them to the full-sized model, i.e., without directly tuning the latter at all. We verify muTransfer on Transformer and ResNet. For example, 1) by transferring pretraining HPs from a model of 13M parameters, we outperform published numbers of BERT-large (350M parameters), with a total tuning cost equivalent to pretraining BERT-large once; 2) by transferring from 40M parameters, we outperform published numbers of the 6.7B GPT-3 model, with tuning cost only 7% of total pretraining cost. A Pytorch implementation of our technique can be found at github.com/microsoft/mup and installable via `pip install mup`.

It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.

Systems based on artificial neural networks (ANNs) have achieved state-of-the-art results in many natural language processing tasks. Although ANNs do not require manually engineered features, ANNs have many hyperparameters to be optimized. The choice of hyperparameters significantly impacts models' performances. However, the ANN hyperparameters are typically chosen by manual, grid, or random search, which either requires expert experiences or is computationally expensive. Recent approaches based on Bayesian optimization using Gaussian processes (GPs) is a more systematic way to automatically pinpoint optimal or near-optimal machine learning hyperparameters. Using a previously published ANN model yielding state-of-the-art results for dialog act classification, we demonstrate that optimizing hyperparameters using GP further improves the results, and reduces the computational time by a factor of 4 compared to a random search. Therefore it is a useful technique for tuning ANN models to yield the best performances for natural language processing tasks.

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.

In this paper, a new parameter perturbation attack on DNNs, called adversarial parameter attack, is proposed, in which small perturbations to the parameters of the DNN are made such that the accuracy of the attacked DNN does not decrease much, but its robustness becomes much lower. The adversarial parameter attack is stronger than previous parameter perturbation attacks in that the attack is more difficult to be recognized by users and the attacked DNN gives a wrong label for any modified sample input with high probability. The existence of adversarial parameters is proved. For a DNN F_{Theta} with the parameter set Theta satisfying certain conditions, it is shown that if the depth of the DNN is sufficiently large, then there exists an adversarial parameter set Theta_a for Theta such that the accuracy of F_{Theta_a} is equal to that of F_{Theta}, but the robustness measure of F_{Theta_a} is smaller than any given bound. An effective training algorithm is given to compute adversarial parameters and numerical experiments are used to demonstrate that the algorithms are effective to produce high quality adversarial parameters.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

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.

Hyperparameter tuning of deep learning models can lead to order-of-magnitude performance gains for the same amount of compute. Despite this, systematic tuning is uncommon, particularly for large models, which are expensive to evaluate and tend to have many hyperparameters, necessitating difficult judgment calls about tradeoffs, budgets, and search bounds. To address these issues and propose a practical method for robustly tuning large models, we present Cost-Aware Pareto Region Bayesian Search (CARBS), a Bayesian optimization algorithm that performs local search around the performance-cost Pareto frontier. CARBS does well even in unbounded search spaces with many hyperparameters, learns scaling relationships so that it can tune models even as they are scaled up, and automates much of the "black magic" of tuning. Among our results, we effectively solve the entire ProcGen benchmark just by tuning a simple baseline (PPO, as provided in the original ProcGen paper). We also reproduce the model size vs. training tokens scaling result from the Chinchilla project (Hoffmann et al. 2022), while simultaneously discovering scaling laws for every other hyperparameter, via an easy automated process that uses significantly less compute and is applicable to any deep learning problem (not just language models).

The optimization algorithm and its hyperparameters can significantly affect the training speed and resulting model accuracy in machine learning applications. The wish list for an ideal optimizer includes fast and smooth convergence to low error, low computational demand, and general applicability. Our recently introduced continual resilient (CoRe) optimizer has shown superior performance compared to other state-of-the-art first-order gradient-based optimizers for training lifelong machine learning potentials. In this work we provide an extensive performance comparison of the CoRe optimizer and nine other optimization algorithms including the Adam optimizer and resilient backpropagation (RPROP) for diverse machine learning tasks. We analyze the influence of different hyperparameters and provide generally applicable values. The CoRe optimizer yields best or competitive performance in every investigated application, while only one hyperparameter needs to be changed depending on mini-batch or batch learning.

Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem (REP) is defined as follows: For n axis-aligned rectangles inside an axis-aligned bounding box B, extend each rectangle in only one of the four directions: up, down, left, or right until it reaches B and the density k is minimized, where k is the maximum number of extensions of rectangles to the boundary that pass through a point inside bounding box B. REP is NP-hard for k>1. If the rectangles are points of a grid (or unit squares of a grid), the problem is called the square escape problem (SEP) and it is still NP-hard. We give a 2-approximation algorithm for SEP with kgeq2 with time complexity O(n^{3/2}k^2). This improves the time complexity of existing algorithms which are at least quadratic. Also, the approximation ratio of our algorithm for kgeq 3 is 3/2 which is tight. We also give a 8-approximation algorithm for REP with time complexity O(nlog n+nk) and give a MPC version of this algorithm for k=O(1) which is the first parallel algorithm for this problem.

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

Convolutional Neural Networks (CNN) have gained great success in many artificial intelligence tasks. However, finding a good set of hyperparameters for a CNN remains a challenging task. It usually takes an expert with deep knowledge, and trials and errors. Genetic algorithms have been used in hyperparameter optimizations. However, traditional genetic algorithms with fixed-length chromosomes may not be a good fit for optimizing deep learning hyperparameters, because deep learning models have variable number of hyperparameters depending on the model depth. As the depth increases, the number of hyperparameters grows exponentially, and searching becomes exponentially harder. It is important to have an efficient algorithm that can find a good model in reasonable time. In this article, we propose to use a variable length genetic algorithm (GA) to systematically and automatically tune the hyperparameters of a CNN to improve its performance. Experimental results show that our algorithm can find good CNN hyperparameters efficiently. It is clear from our experiments that if more time is spent on optimizing the hyperparameters, better results could be achieved. Theoretically, if we had unlimited time and CPU power, we could find the optimized hyperparameters and achieve the best results in the future.

Existing fine-tuning methods either tune all parameters of the pre-trained model (full fine-tuning), which is not efficient, or only tune the last linear layer (linear probing), which suffers a significant accuracy drop compared to the full fine-tuning. In this paper, we propose a new parameter-efficient fine-tuning method termed as SSF, representing that researchers only need to Scale and Shift the deep Features extracted by a pre-trained model to catch up with the performance of full fine-tuning. In this way, SSF also surprisingly outperforms other parameter-efficient fine-tuning approaches even with a smaller number of tunable parameters. Furthermore, different from some existing parameter-efficient fine-tuning methods (e.g., Adapter or VPT) that introduce the extra parameters and computational cost in the training and inference stages, SSF only adds learnable parameters during the training stage, and these additional parameters can be merged into the original pre-trained model weights via re-parameterization in the inference phase. With the proposed SSF, our model obtains 2.46% (90.72% vs. 88.54%) and 11.48% (73.10% vs. 65.57%) performance improvement on FGVC and VTAB-1k in terms of Top-1 accuracy compared to the full fine-tuning but only fine-tuning about 0.3M parameters. We also conduct amounts of experiments in various model families (CNNs, Transformers, and MLPs) and datasets. Results on 26 image classification datasets in total and 3 robustness & out-of-distribution datasets show the effectiveness of SSF. Code is available at https://github.com/dongzelian/SSF.

Recent work has highlighted the complex influence training hyperparameters, e.g., the number of training epochs, can have on the prunability of machine learning models. Perhaps surprisingly, a systematic approach to predict precisely how adjusting a specific hyperparameter will affect prunability remains elusive. To address this gap, we introduce a phenomenological model grounded in the statistical mechanics of learning. Our approach uses temperature-like and load-like parameters to model the impact of neural network (NN) training hyperparameters on pruning performance. A key empirical result we identify is a sharp transition phenomenon: depending on the value of a load-like parameter in the pruned model, increasing the value of a temperature-like parameter in the pre-pruned model may either enhance or impair subsequent pruning performance. Based on this transition, we build a three-regime model by taxonomizing the global structure of the pruned NN loss landscape. Our model reveals that the dichotomous effect of high temperature is associated with transitions between distinct types of global structures in the post-pruned model. Based on our results, we present three case-studies: 1) determining whether to increase or decrease a hyperparameter for improved pruning; 2) selecting the best model to prune from a family of models; and 3) tuning the hyperparameter of the Sharpness Aware Minimization method for better pruning performance.

Machine learning models are often tuned by nesting optimization of model weights inside the optimization of hyperparameters. We give a method to collapse this nested optimization into joint stochastic optimization of weights and hyperparameters. Our process trains a neural network to output approximately optimal weights as a function of hyperparameters. We show that our technique converges to locally optimal weights and hyperparameters for sufficiently large hypernetworks. We compare this method to standard hyperparameter optimization strategies and demonstrate its effectiveness for tuning thousands of hyperparameters.

Given a sample of size N, it is often useful to select a subsample of smaller size n<N to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning. We assume to be given N unlabeled samples {{boldsymbol x}_i}_{ile N}, and to be given access to a `surrogate model' that can predict labels y_i better than random guessing. Our goal is to select a subset of the samples, to be denoted by {{boldsymbol x}_i}_{iin G}, of size |G|=n<N. We then acquire labels for this set and we use them to train a model via regularized empirical risk minimization. By using a mixture of numerical experiments on real and synthetic data, and mathematical derivations under low- and high- dimensional asymptotics, we show that: (i)~Data selection can be very effective, in particular beating training on the full sample in some cases; (ii)~Certain popular choices in data selection methods (e.g. unbiased reweighted subsampling, or influence function-based subsampling) can be substantially suboptimal.

Pre-training (PT) followed by fine-tuning (FT) is an effective method for training neural networks, and has led to significant performance improvements in many domains. PT can incorporate various design choices such as task and data reweighting strategies, augmentation policies, and noise models, all of which can significantly impact the quality of representations learned. The hyperparameters introduced by these strategies therefore must be tuned appropriately. However, setting the values of these hyperparameters is challenging. Most existing methods either struggle to scale to high dimensions, are too slow and memory-intensive, or cannot be directly applied to the two-stage PT and FT learning process. In this work, we propose an efficient, gradient-based algorithm to meta-learn PT hyperparameters. We formalize the PT hyperparameter optimization problem and propose a novel method to obtain PT hyperparameter gradients by combining implicit differentiation and backpropagation through unrolled optimization. We demonstrate that our method improves predictive performance on two real-world domains. First, we optimize high-dimensional task weighting hyperparameters for multitask pre-training on protein-protein interaction graphs and improve AUROC by up to 3.9%. Second, we optimize a data augmentation neural network for self-supervised PT with SimCLR on electrocardiography data and improve AUROC by up to 1.9%.

This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an infinite hierarchy of non-convex problems via the lifting technique and the Burer-Monteiro factorization. This contrasts with the existing over-parametrization technique where the search rank is limited by the dimension of the matrix and it does not allow a rich over-parametrization of an arbitrary degree. We show that although the spurious solutions of the problem remain stationary points through the hierarchy, they will be transformed into strict saddle points (under some technical conditions) and can be escaped via local search methods. This is the first result in the literature showing that over-parametrization creates a negative curvature for escaping spurious solutions. We also derive a bound on how much over-parametrization is requited to enable the elimination of spurious solutions.

Overparameterized Neural Networks (NN) display state-of-the-art performance. However, there is a growing need for smaller, energy-efficient, neural networks tobe able to use machine learning applications on devices with limited computational resources. A popular approach consists of using pruning techniques. While these techniques have traditionally focused on pruning pre-trained NN (LeCun et al.,1990; Hassibi et al., 1993), recent work by Lee et al. (2018) has shown promising results when pruning at initialization. However, for Deep NNs, such procedures remain unsatisfactory as the resulting pruned networks can be difficult to train and, for instance, they do not prevent one layer from being fully pruned. In this paper, we provide a comprehensive theoretical analysis of Magnitude and Gradient based pruning at initialization and training of sparse architectures. This allows us to propose novel principled approaches which we validate experimentally on a variety of NN architectures.

Post-training has emerged as a crucial paradigm for adapting large-scale pre-trained models to various tasks, whose effects are fully reflected by delta parameters (i.e., the disparity between post-trained and pre-trained parameters). While numerous studies have explored delta parameter properties via operations like pruning, quantization, low-rank approximation, and extrapolation, a unified framework for systematically examining these characteristics has been lacking. In this paper, we propose a novel perspective based on Riemann sum approximation of the loss function to elucidate delta parameter editing operations. Our analysis categorizes existing methods into three classes based on their post-editing performance: competitive, decreased, and improved, explaining how they are expressed by the Riemann sum approximation term and how they alter the model performance. Extensive experiments on both visual and language models, including ViT, LLaMA 3, Qwen 2, and Mistral, corroborate our theoretical findings. Furthermore, we introduce extensions to existing techniques like DARE and BitDelta, highlighting their limitations in leveraging the properties of delta parameters and reorganizing them into general expressions to enhance the applicability and effectiveness of delta parameter editing in post-trained models.

The reproducibility and transparency of large language models are crucial for advancing open research, ensuring the trustworthiness of results, and enabling investigations into data and model biases, as well as potential risks. To this end, we release OpenELM, a state-of-the-art open language model. OpenELM uses a layer-wise scaling strategy to efficiently allocate parameters within each layer of the transformer model, leading to enhanced accuracy. For example, with a parameter budget of approximately one billion parameters, OpenELM exhibits a 2.36% improvement in accuracy compared to OLMo while requiring 2times fewer pre-training tokens. Diverging from prior practices that only provide model weights and inference code, and pre-train on private datasets, our release includes the complete framework for training and evaluation of the language model on publicly available datasets, including training logs, multiple checkpoints, and pre-training configurations. We also release code to convert models to MLX library for inference and fine-tuning on Apple devices. This comprehensive release aims to empower and strengthen the open research community, paving the way for future open research endeavors. Our source code along with pre-trained model weights and training recipes is available at https://github.com/apple/corenet. Additionally, \model models can be found on HuggingFace at: https://huggingface.co/apple/OpenELM.

Training neural networks requires increasing amounts of memory. Parameter sharing can reduce memory and communication costs, but existing methods assume networks have many identical layers and utilize hand-crafted sharing strategies that fail to generalize. We introduce Neural Parameter Allocation Search (NPAS), a novel task where the goal is to train a neural network given an arbitrary, fixed parameter budget. NPAS covers both low-budget regimes, which produce compact networks, as well as a novel high-budget regime, where additional capacity can be added to boost performance without increasing inference FLOPs. To address NPAS, we introduce Shapeshifter Networks (SSNs), which automatically learn where and how to share parameters in a network to support any parameter budget without requiring any changes to the architecture or loss function. NPAS and SSNs provide a complete framework for addressing generalized parameter sharing, and can also be combined with prior work for additional performance gains. We demonstrate the effectiveness of our approach using nine network architectures across four diverse tasks, including ImageNet classification and transformers.

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.

Pre-trained Language Models (PLMs) can be accurately fine-tuned for downstream text processing tasks. Recently, researchers have introduced several parameter-efficient fine-tuning methods that optimize input prompts or adjust a small number of model parameters (e.g LoRA). In this study, we explore the impact of altering the input text of the original task in conjunction with parameter-efficient fine-tuning methods. To most effectively rewrite the input text, we train a few-shot paraphrase model with a Maximum-Marginal Likelihood objective. Using six few-shot text classification datasets, we show that enriching data with paraphrases at train and test time enhances the performance beyond what can be achieved with parameter-efficient fine-tuning alone.

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a sub-family. To understand the importance of this structure in optimization problems we consider the problem of maximizing function value under various types of constraints. To demonstrate the modeling power of submodular order functions we show applications in two different settings. First, we apply our results to the extensively studied problem of assortment optimization. While the objectives in assortment optimization are known to be non-submodular (and non-monotone) even for simple choice models, we show that they are compatible with the notion of submodular order. Consequently, we obtain new and in some cases the first constant factor guarantee for constrained assortment optimization in fundamental choice models. As a second application of submodular order functions, we show an intriguing connection to the maximization of monotone submodular functions in the streaming model. We recover some best known guarantees for this problem as a corollary of our results.

Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L2-regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs).

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.

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

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.

Large pre-trained language models have recently gained significant traction due to their improved performance on various down-stream tasks like text classification and question answering, requiring only few epochs of fine-tuning. However, their large model sizes often prohibit their applications on resource-constrained edge devices. Existing solutions of yielding parameter-efficient BERT models largely rely on compute-exhaustive training and fine-tuning. Moreover, they often rely on additional compute heavy models to mitigate the performance gap. In this paper, we present Sensi-BERT, a sensitivity driven efficient fine-tuning of BERT models that can take an off-the-shelf pre-trained BERT model and yield highly parameter-efficient models for downstream tasks. In particular, we perform sensitivity analysis to rank each individual parameter tensor, that then is used to trim them accordingly during fine-tuning for a given parameter or FLOPs budget. Our experiments show the efficacy of Sensi-BERT across different downstream tasks including MNLI, QQP, QNLI, SST-2 and SQuAD, showing better performance at similar or smaller parameter budget compared to various alternatives.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

Hyperparameters are a critical factor in reliably training well-performing reinforcement learning (RL) agents. Unfortunately, developing and evaluating automated approaches for tuning such hyperparameters is both costly and time-consuming. As a result, such approaches are often only evaluated on a single domain or algorithm, making comparisons difficult and limiting insights into their generalizability. We propose ARLBench, a benchmark for hyperparameter optimization (HPO) in RL that allows comparisons of diverse HPO approaches while being highly efficient in evaluation. To enable research into HPO in RL, even in settings with low compute resources, we select a representative subset of HPO tasks spanning a variety of algorithm and environment combinations. This selection allows for generating a performance profile of an automated RL (AutoRL) method using only a fraction of the compute previously necessary, enabling a broader range of researchers to work on HPO in RL. With the extensive and large-scale dataset on hyperparameter landscapes that our selection is based on, ARLBench is an efficient, flexible, and future-oriented foundation for research on AutoRL. Both the benchmark and the dataset are available at https://github.com/automl/arlbench.

The existence of a plethora of language models makes the problem of selecting the best one for a custom task challenging. Most state-of-the-art methods leverage transformer-based models (e.g., BERT) or their variants. Training such models and exploring their hyperparameter space, however, is computationally expensive. Prior work proposes several neural architecture search (NAS) methods that employ performance predictors (e.g., surrogate models) to address this issue; however, analysis has been limited to homogeneous models that use fixed dimensionality throughout the network. This leads to sub-optimal architectures. To address this limitation, we propose a suite of heterogeneous and flexible models, namely FlexiBERT, that have varied encoder layers with a diverse set of possible operations and different hidden dimensions. For better-posed surrogate modeling in this expanded design space, we propose a new graph-similarity-based embedding scheme. We also propose a novel NAS policy, called BOSHNAS, that leverages this new scheme, Bayesian modeling, and second-order optimization, to quickly train and use a neural surrogate model to converge to the optimal architecture. A comprehensive set of experiments shows that the proposed policy, when applied to the FlexiBERT design space, pushes the performance frontier upwards compared to traditional models. FlexiBERT-Mini, one of our proposed models, has 3% fewer parameters than BERT-Mini and achieves 8.9% higher GLUE score. A FlexiBERT model with equivalent performance as the best homogeneous model achieves 2.6x smaller size. FlexiBERT-Large, another proposed model, achieves state-of-the-art results, outperforming the baseline models by at least 5.7% on the GLUE benchmark.

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Physics-informed neural networks is a possible choice for a data-driven method to replace linear modal analysis. An architecture that support a random component is necessary for the construction of the stochastic model of the physical system for non-parametric uncertainties, since the goal is to learn the underlying probabilistic distribution of uncertainty in the data. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved convergence results for our problem. The objective of our approach is to train a GAN on data from a finite element method code (Fenics) so as to extract stochastic boundary conditions for faster finite element predictions on a submodel. The submodel and the training data have both the same geometrical support. It is a zone of interest for uncertainty quantification and relevant to engineering purposes. In the exploitation phase, the framework can be viewed as a randomized and parametrized simulation generator on the submodel, which can be used as a Monte Carlo estimator.

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

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

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).

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

Parameter-efficient tuning (PET) methods can effectively drive extremely large pre-trained language models (PLMs) by only training minimal parameters. Different PET methods utilize different manually designed modules. In a small PLM, there are usually noticeable performance differences among PET methods. Nevertheless, when a PLM's scale grows up to tens of billions of parameters, all PET methods achieve almost the same performance and even perform on par with the full-parameter fine-tuning method. Hence, we hypothesize that model scaling can mitigate the design differences (the module structures and the number of trainable parameters) among PET methods. To study this hypothesis, we introduce a more flexible PET method - arbitrary PET (APET) method - to be compatible with arbitrary module structures and any number of trainable parameters. Then, we experiment on 11 NLP tasks of 5 types and 2 representative PLMs. From our investigations, we find that the model scaling (1) mitigates the effects of the arbitrary module structure on the performance of tuning methods, and (2) enables the tuning methods to optimize fewer parameters to achieve the full-parameter fine-tuning performance. Intriguingly, we also observe that all tuning methods require almost the same number of trainable parameters to drive PLMs. We discuss this phenomenon and the above two findings collectively from optimization perspectives to fathom the mechanisms behind them. These conclusions not only demonstrate the positive impact of model scaling on tuning methods but disclose its mechanisms, which help us design more effective and efficient tuning methods on larger-scale PLMs.

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.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear alpha-regret methods that only require bandit feedback, achieving Oleft(T^2{3}log(T)^1{3}right) expected cumulative alpha-regret dependence on the horizon T. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to multiple problems in submodular maximization, adapting approximation algorithms for cardinality and for knapsack constraints. The new CMAB algorithms for knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

We apply augmentations to our dataset to enhance the quality of our predictions and make our final models more resilient to noisy data and domain drifts. Yet the question remains, how are these augmentations going to perform with different hyper-parameters? In this study we evaluate the sensitivity of augmentations with regards to the model's hyper parameters along with their consistency and influence by performing a Local Surrogate (LIME) interpretation on the impact of hyper-parameters when different augmentations are applied to a machine learning model. We have utilized Linear regression coefficients for weighing each augmentation. Our research has proved that there are some augmentations which are highly sensitive to hyper-parameters and others which are more resilient and reliable.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

Adapting large-scale pretrained language models to downstream tasks via fine-tuning is the standard method for achieving state-of-the-art performance on NLP benchmarks. However, fine-tuning all weights of models with millions or billions of parameters is sample-inefficient, unstable in low-resource settings, and wasteful as it requires storing a separate copy of the model for each task. Recent work has developed parameter-efficient fine-tuning methods, but these approaches either still require a relatively large number of parameters or underperform standard fine-tuning. In this work, we propose Compacter, a method for fine-tuning large-scale language models with a better trade-off between task performance and the number of trainable parameters than prior work. Compacter accomplishes this by building on top of ideas from adapters, low-rank optimization, and parameterized hypercomplex multiplication layers. Specifically, Compacter inserts task-specific weight matrices into a pretrained model's weights, which are computed efficiently as a sum of Kronecker products between shared "slow" weights and "fast" rank-one matrices defined per Compacter layer. By only training 0.047% of a pretrained model's parameters, Compacter performs on par with standard fine-tuning on GLUE and outperforms standard fine-tuning on SuperGLUE and low-resource settings. Our code is publicly available at~https://github.com/rabeehk/compacter.

Deep neural networks have shown promise for music audio signal processing applications, often surpassing prior approaches, particularly as end-to-end models in the waveform domain. Yet results to date have tended to be constrained by low sample rates, noise, narrow domains of signal types, and/or lack of parameterized controls (i.e. "knobs"), making their suitability for professional audio engineering workflows still lacking. This work expands on prior research published on modeling nonlinear time-dependent signal processing effects associated with music production by means of a deep neural network, one which includes the ability to emulate the parameterized settings you would see on an analog piece of equipment, with the goal of eventually producing commercially viable, high quality audio, i.e. 44.1 kHz sampling rate at 16-bit resolution. The results in this paper highlight progress in modeling these effects through architecture and optimization changes, towards increasing computational efficiency, lowering signal-to-noise ratio, and extending to a larger variety of nonlinear audio effects. Toward these ends, the strategies employed involved a three-pronged approach: model speed, model accuracy, and model generalizability. Most of the presented methods provide marginal or no increase in output accuracy over the original model, with the exception of dataset manipulation. We found that limiting the audio content of the dataset, for example using datasets of just a single instrument, provided a significant improvement in model accuracy over models trained on more general datasets.

Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theoretical properties, providing several desirable guarantees. Furthermore, we compare Hyperband with popular Bayesian optimization methods on a suite of hyperparameter optimization problems. We observe that Hyperband can provide over an order-of-magnitude speedup over our competitor set on a variety of deep-learning and kernel-based learning problems.

Adaptive optimization methods are widely recognized as among the most popular approaches for training Deep Neural Networks (DNNs). Techniques such as Adam, AdaGrad, and AdaHessian utilize a preconditioner that modifies the search direction by incorporating information about the curvature of the objective function. However, despite their adaptive characteristics, these methods still require manual fine-tuning of the step-size. This, in turn, impacts the time required to solve a particular problem. This paper presents an optimization framework named SANIA to tackle these challenges. Beyond eliminating the need for manual step-size hyperparameter settings, SANIA incorporates techniques to address poorly scaled or ill-conditioned problems. We also explore several preconditioning methods, including Hutchinson's method, which approximates the Hessian diagonal of the loss function. We conclude with an extensive empirical examination of the proposed techniques across classification tasks, covering both convex and non-convex contexts.

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems, respectively. In practice, often at least one of these sub-problems is overparameterized. In this case, there are many ways to choose among optima that achieve equivalent objective values. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of gradient-based algorithms for bilevel optimization. We delineate two standard BLO methods -- cold-start and warm-start -- and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the inner solutions obtained by warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer parameters are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

The common modus operandi of fine-tuning large pre-trained Transformer models entails the adaptation of all their parameters (i.e., full fine-tuning). While achieving striking results on multiple tasks, this approach becomes unfeasible as the model size and the number of downstream tasks increase. In natural language processing and computer vision, parameter-efficient approaches like prompt-tuning and adapters have emerged as solid alternatives by fine-tuning only a small number of extra parameters, without sacrificing performance accuracy. Specifically, adapters, due to their flexibility, have recently garnered significant attention, leading to several variants. For audio classification tasks, the Audio Spectrogram Transformer model shows impressive results. However, surprisingly, how to efficiently adapt it to several downstream tasks has not been tackled before. In this paper, we bridge this gap and present a detailed investigation of common parameter-efficient methods, revealing that adapters consistently outperform the other methods across four benchmarks. This trend is also confirmed in few-shot learning settings and when the total number of trainable parameters increases, demonstrating adapters superior scalability. We finally study the best adapter configuration, as well as the role of residual connections in the learning process. Our code is available at: https://github.com/umbertocappellazzo/PETL AST.

This is the 1st part of the dissertation for my master degree and compares the power consumption using the default floating point (32bit) and Nvidia mixed precision (16bit and 32bit) while training a classification ML model. A custom PC with specific hardware was built to perform the experiments, and different ML hyper-parameters, such as batch size, neurons, and epochs, were chosen to build Deep Neural Networks (DNN). Additionally, various software was used during the experiments to collect the power consumption data in Watts from the Graphics Processing Unit (GPU), Central Processing Unit (CPU), Random Access Memory (RAM) and manually from a wattmeter connected to the wall. A benchmarking test with default hyper parameter values for the DNN was used as a reference, while the experiments used a combination of different settings. The results were recorded in Excel, and descriptive statistics were chosen to calculate the mean between the groups and compare them using graphs and tables. The outcome was positive when using mixed precision combined with specific hyper-parameters. Compared to the benchmarking, the optimisation for the classification reduced the power consumption between 7 and 11 Watts. Similarly, the carbon footprint is reduced because the calculation uses the same power consumption data. Still, a consideration is required when configuring hyper-parameters because it can negatively affect hardware performance. However, this research required inferential statistics, specifically ANOVA and T-test, to compare the relationship between the means. Furthermore, tests indicated no statistical significance of the relationship between the benchmarking and experiments. However, a more extensive implementation with a cluster of GPUs can increase the sample size significantly, as it is an essential factor and can change the outcome of the statistical analysis.

By classifying infinite-width neural networks and identifying the *optimal* limit, Tensor Programs IV and V demonstrated a universal way, called muP, for *widthwise hyperparameter transfer*, i.e., predicting optimal hyperparameters of wide neural networks from narrow ones. Here we investigate the analogous classification for *depthwise parametrizations* of deep residual networks (resnets). We classify depthwise parametrizations of block multiplier and learning rate by their infinite-width-then-depth limits. In resnets where each block has only one layer, we identify a unique optimal parametrization, called Depth-muP that extends muP and show empirically it admits depthwise hyperparameter transfer. We identify *feature diversity* as a crucial factor in deep networks, and Depth-muP can be characterized as maximizing both feature learning and feature diversity. Exploiting this, we find that absolute value, among all homogeneous nonlinearities, maximizes feature diversity and indeed empirically leads to significantly better performance. However, if each block is deeper (such as modern transformers), then we find fundamental limitations in all possible infinite-depth limits of such parametrizations, which we illustrate both theoretically and empirically on simple networks as well as Megatron transformer trained on Common Crawl.

State-of-the-art parameter-efficient fine-tuning methods rely on introducing adapter modules between the layers of a pretrained language model. However, such modules are trained separately for each task and thus do not enable sharing information across tasks. In this paper, we show that we can learn adapter parameters for all layers and tasks by generating them using shared hypernetworks, which condition on task, adapter position, and layer id in a transformer model. This parameter-efficient multi-task learning framework allows us to achieve the best of both worlds by sharing knowledge across tasks via hypernetworks while enabling the model to adapt to each individual task through task-specific adapters. Experiments on the well-known GLUE benchmark show improved performance in multi-task learning while adding only 0.29% parameters per task. We additionally demonstrate substantial performance improvements in few-shot domain generalization across a variety of tasks. Our code is publicly available in https://github.com/rabeehk/hyperformer.

A supervised learning algorithm searches over a set of functions A to B parametrised by a space P to find the best approximation to some ideal function fcolon A to B. It does this by taking examples (a,f(a)) in Atimes B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.

We introduce TabRepo, a new dataset of tabular model evaluations and predictions. TabRepo contains the predictions and metrics of 1310 models evaluated on 200 classification and regression datasets. We illustrate the benefit of our dataset in multiple ways. First, we show that it allows to perform analysis such as comparing Hyperparameter Optimization against current AutoML systems while also considering ensembling at marginal cost by using precomputed model predictions. Second, we show that our dataset can be readily leveraged to perform transfer-learning. In particular, we show that applying standard transfer-learning techniques allows to outperform current state-of-the-art tabular systems in accuracy, runtime and latency.

As the most basic application and implementation of deep learning, image classification has grown in popularity. Various datasets are provided by renowned data science communities for benchmarking machine learning algorithms and pre-trained models. The ASSIRA Cats & Dogs dataset is one of them and is being used in this research for its overall acceptance and benchmark standards. A comparison of various pre-trained models is demonstrated by using different types of optimizers and loss functions. Hyper-parameters are changed to gain the best result from a model. By applying this approach, we have got higher accuracy without major changes in the training model. To run the experiment, we used three different computer architectures: a laptop equipped with NVIDIA GeForce GTX 1070, a laptop equipped with NVIDIA GeForce RTX 3080Ti, and a desktop equipped with NVIDIA GeForce RTX 3090. The acquired results demonstrate supremacy in terms of accuracy over the previously done experiments on this dataset. From this experiment, the highest accuracy which is 99.65% is gained using the NASNet Large.

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 train a suite of multimodal foundation models (MMFM) using the popular LLaVA framework with the recently released Gemma family of large language models (LLMs). Of particular interest is the 2B parameter Gemma model, which provides opportunities to construct capable small-scale MMFMs. In line with findings from other papers in this space, we test the effect of ablating three design features: pretraining the connector, utilizing a more powerful image backbone, and increasing the size of the language backbone. The resulting models, which we call LLaVA-Gemma, exhibit moderate performance on an array of evaluations, but fail to improve past the current comparably sized SOTA models. Closer analysis of performance shows mixed effects; skipping pretraining tends to reduce performance, larger vision models sometimes improve performance, and increasing language model size has inconsistent effects. We publicly release training recipes, code and weights for our models for the LLaVA-Gemma models.

Instruction fine-tuning pretrained LLMs for diverse downstream tasks has demonstrated remarkable success and has captured the interest of both academics and practitioners. To ensure such fine-tuned LLMs align with human preferences, techniques such as RLHF and DPO have emerged. At the same time, there is increasing interest in smaller parameter counts for models. In this work, using OpenLLaMA 3Bv2 as a base model, we describe the recipe used to fine-tune the OpenBezoar family of models. In this recipe: We first generate synthetic instruction fine-tuning data using an open and commercially non-restrictive instruction fine-tuned variant of the Falcon-40B model under three schemes based on: LaMini-LM, WizardLM/Evol-Instruct (with databricks-dolly-15k as a seed dataset) and Orca (with the Flan Collection as a seed dataset), then filter these generations using GPT-4 as a human proxy. We then perform cost-effective QLoRA-based supervised fine-tuning sequentially with each scheme. The resulting checkpoint is further fine-tuned with a subset of the HH-RLHF dataset to minimize distribution shift prior to using the DPO loss to obtain the final checkpoint. Evaluation is done with the LM Eval Harness tasks/metrics as well as on MT-Bench using the "LLM-as-a-judge" framework with Claude 2.1, with the finding that the final checkpoint, "OpenBezoar-HH-RLHF-DPO", demonstrates superior performance over many models at the 3B parameter scale, even outperforming the top model in one of the categories on the Huggingface Open LLM Leaderboard. We release "OpenBezoar-SFT", "OpenBezoar-HH-RLHF-SFT", "OpenBezoar-HH-RLHF-DPO" checkpoints, alongside our generated datasets on HuggingFace at https://huggingface.co/collections/SurgeGlobal/open-bezoar-6620a24923e12127e9e2b9cc and our codebase at https://bitbucket.org/paladinanalytics/workspace/projects/OP.

This paper presents a systematic overview and comparison of parameter-efficient fine-tuning methods covering over 40 papers published between February 2019 and February 2023. These methods aim to resolve the infeasibility and impracticality of fine-tuning large language models by only training a small set of parameters. We provide a taxonomy that covers a broad range of methods and present a detailed method comparison with a specific focus on real-life efficiency and fine-tuning multibillion-scale language models.

Math reasoning is a highly active area of Large Language Model (LLM) research because it is a hallmark of artificial intelligence. However, few works have explored how math reasoning is encoded within LLM parameters and if it is a skill that can be isolated within a model. Doing so could allow targeted intervention to improve math performance without altering non-math behavior and foster understanding of how models encode math reasoning. We introduce Math Neurosurgery (MathNeuro), a method for isolating math-specific parameters in LLMs using only forward passes. MathNeuro builds on existing work by using weights and activations to calculate parameter importance, but isolates math-specific parameters by removing those important for general language tasks. Pruning parameters MathNeuro identifies deletes a LLM's math reasoning ability without destroying its general language ability. Scaling these parameters by a small constant improves a pretrained or instruction-tuned LLM's performance by 4-17% on GSM8K while leaving non-math behavior unaltered. MathNeuro is also data efficient: most of its effectiveness holds when identifying math-specific parameters using a single sample. MathNeuro highlights the potential for future work to intervene on math-specific parameters.

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.

Large Language Model training with 8-bit floating point (FP8) formats promises significant efficiency improvements, but reduced numerical precision makes training challenging. It is currently possible to train in FP8 only if one is willing to tune various hyperparameters, reduce model scale, or accept the overhead of computing dynamic scale factors. We demonstrate simple, scalable FP8 training that requires no dynamic scaling factors or special hyperparameters, even at large model sizes. Our method, munit Scaling (muS), also enables simple hyperparameter transfer across model widths, matched numerics across training and inference, and other desirable properties. munit Scaling is straightforward to implement, consisting of a set of minimal interventions based on a first-principles analysis of common transformer operations. We validate our method by training models from 1B to 13B parameters, performing all hidden linear layer computations in FP8. We achieve quality equal to higher precision baselines while also training up to 33% faster.

Despite the popularity of guitar effects, there is very little existing research on classification and parameter estimation of specific plugins or effect units from guitar recordings. In this paper, convolutional neural networks were used for classification and parameter estimation for 13 overdrive, distortion and fuzz guitar effects. A novel dataset of processed electric guitar samples was assembled, with four sub-datasets consisting of monophonic or polyphonic samples and discrete or continuous settings values, for a total of about 250 hours of processed samples. Results were compared for networks trained and tested on the same or on a different sub-dataset. We found that discrete datasets could lead to equally high performance as continuous ones, whilst being easier to design, analyse and modify. Classification accuracy was above 80\%, with confusion matrices reflecting similarities in the effects timbre and circuits design. With parameter values between 0.0 and 1.0, the mean absolute error is in most cases below 0.05, while the root mean square error is below 0.1 in all cases but one.

While fine-tuning pretrained models has become common practice, these models often underperform outside their specific domains. Recently developed model merging techniques enable the direct integration of multiple models, each fine-tuned for distinct tasks, into a single model. This strategy promotes multitasking capabilities without requiring retraining on the original datasets. However, existing methods fall short in addressing potential conflicts and complex correlations between tasks, especially in parameter-level adjustments, posing a challenge in effectively balancing parameter competition across various tasks. This paper introduces an innovative technique named PCB-Merging (Parameter Competition Balancing), a lightweight and training-free technique that adjusts the coefficients of each parameter for effective model merging. PCB-Merging employs intra-balancing to gauge parameter significance within individual tasks and inter-balancing to assess parameter similarities across different tasks. Parameters with low importance scores are dropped, and the remaining ones are rescaled to form the final merged model. We assessed our approach in diverse merging scenarios, including cross-task, cross-domain, and cross-training configurations, as well as out-of-domain generalization. The experimental results reveal that our approach achieves substantial performance enhancements across multiple modalities, domains, model sizes, number of tasks, fine-tuning forms, and large language models, outperforming existing model merging methods. The code is publicly available at: https://github.com/duguodong7/pcb-merging.

In order to improve reproducibility, deep reinforcement learning (RL) has been adopting better scientific practices such as standardized evaluation metrics and reporting. However, the process of hyperparameter optimization still varies widely across papers, which makes it challenging to compare RL algorithms fairly. In this paper, we show that hyperparameter choices in RL can significantly affect the agent's final performance and sample efficiency, and that the hyperparameter landscape can strongly depend on the tuning seed which may lead to overfitting. We therefore propose adopting established best practices from AutoML, such as the separation of tuning and testing seeds, as well as principled hyperparameter optimization (HPO) across a broad search space. We support this by comparing multiple state-of-the-art HPO tools on a range of RL algorithms and environments to their hand-tuned counterparts, demonstrating that HPO approaches often have higher performance and lower compute overhead. As a result of our findings, we recommend a set of best practices for the RL community, which should result in stronger empirical results with fewer computational costs, better reproducibility, and thus faster progress. In order to encourage the adoption of these practices, we provide plug-and-play implementations of the tuning algorithms used in this paper at https://github.com/facebookresearch/how-to-autorl.

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

We carry out an information-theoretical analysis of a two-layer neural network trained from input-output pairs generated by a teacher network with matching architecture, in overparametrized regimes. Our results come in the form of bounds relating i) the mutual information between training data and network weights, or ii) the Bayes-optimal generalization error, to the same quantities but for a simpler (generalized) linear model for which explicit expressions are rigorously known. Our bounds, which are expressed in terms of the number of training samples, input dimension and number of hidden units, thus yield fundamental performance limits for any neural network (and actually any learning procedure) trained from limited data generated according to our two-layer teacher neural network model. The proof relies on rigorous tools from spin glasses and is guided by ``Gaussian equivalence principles'' lying at the core of numerous recent analyses of neural networks. With respect to the existing literature, which is either non-rigorous or restricted to the case of the learning of the readout weights only, our results are information-theoretic (i.e. are not specific to any learning algorithm) and, importantly, cover a setting where all the network parameters are trained.

Weight sharing promises to make neural architecture search (NAS) tractable even on commodity hardware. Existing methods in this space rely on a diverse set of heuristics to design and train the shared-weight backbone network, a.k.a. the super-net. Since heuristics and hyperparameters substantially vary across different methods, a fair comparison between them can only be achieved by systematically analyzing the influence of these factors. In this paper, we therefore provide a systematic evaluation of the heuristics and hyperparameters that are frequently employed by weight-sharing NAS algorithms. Our analysis uncovers that some commonly-used heuristics for super-net training negatively impact the correlation between super-net and stand-alone performance, and evidences the strong influence of certain hyperparameters and architectural choices. Our code and experiments set a strong and reproducible baseline that future works can build on.

We present the task description of the Detection and Classification of Acoustic Scenes and Events (DCASE) 2023 Challenge Task 2: ``First-shot unsupervised anomalous sound detection (ASD) for machine condition monitoring''. The main goal is to enable rapid deployment of ASD systems for new kinds of machines without the need for hyperparameter tuning. In the past ASD tasks, developed methods tuned hyperparameters for each machine type, as the development and evaluation datasets had the same machine types. However, collecting normal and anomalous data as the development dataset can be infeasible in practice. In 2023 Task 2, we focus on solving the first-shot problem, which is the challenge of training a model on a completely novel machine type. Specifically, (i) each machine type has only one section (a subset of machine type) and (ii) machine types in the development and evaluation datasets are completely different. Analysis of 86 submissions from 23 teams revealed that the keys to outperform baselines were: 1) sampling techniques for dealing with class imbalances across different domains and attributes, 2) generation of synthetic samples for robust detection, and 3) use of multiple large pre-trained models to extract meaningful embeddings for the anomaly detector.

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.

Recent advances in Neural Architecture Search (NAS) which extract specialized hardware-aware configurations (a.k.a. "sub-networks") from a hardware-agnostic "super-network" have become increasingly popular. While considerable effort has been employed towards improving the first stage, namely, the training of the super-network, the search for derivative high-performing sub-networks is still largely under-explored. For example, some recent network morphism techniques allow a super-network to be trained once and then have hardware-specific networks extracted from it as needed. These methods decouple the super-network training from the sub-network search and thus decrease the computational burden of specializing to different hardware platforms. We propose a comprehensive system that automatically and efficiently finds sub-networks from a pre-trained super-network that are optimized to different performance metrics and hardware configurations. By combining novel search tactics and algorithms with intelligent use of predictors, we significantly decrease the time needed to find optimal sub-networks from a given super-network. Further, our approach does not require the super-network to be refined for the target task a priori, thus allowing it to interface with any super-network. We demonstrate through extensive experiments that our system works seamlessly with existing state-of-the-art super-network training methods in multiple domains. Moreover, we show how novel search tactics paired with evolutionary algorithms can accelerate the search process for ResNet50, MobileNetV3 and Transformer while maintaining objective space Pareto front diversity and demonstrate an 8x faster search result than the state-of-the-art Bayesian optimization WeakNAS approach.

We present Generalized LoRA (GLoRA), an advanced approach for universal parameter-efficient fine-tuning tasks. Enhancing Low-Rank Adaptation (LoRA), GLoRA employs a generalized prompt module to optimize pre-trained model weights and adjust intermediate activations, providing more flexibility and capability across diverse tasks and datasets. Moreover, GLoRA facilitates efficient parameter adaptation by employing a scalable, modular, layer-wise structure search that learns individual adapter of each layer. Originating from a unified mathematical formulation, GLoRA exhibits strong transfer learning, few-shot learning and domain generalization abilities, as it adjusts to new tasks through additional dimensions on weights and activations. Comprehensive experiments demonstrate that GLoRA outperforms all previous methods in natural, specialized, and structured benchmarks, achieving superior accuracy with fewer parameters and computations on various datasets. Furthermore, our structural re-parameterization design ensures that GLoRA incurs no extra inference cost, rendering it a practical solution for resource-limited applications. Code is available at: https://github.com/Arnav0400/ViT-Slim/tree/master/GLoRA.

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.

Efficient hyperparameter or architecture search methods have shown remarkable results, but each of them is only applicable to searching for either hyperparameters (HPs) or architectures. In this work, we propose a unified pipeline, AutoHAS, to efficiently search for both architectures and hyperparameters. AutoHAS learns to alternately update the shared network weights and a reinforcement learning (RL) controller, which learns the probability distribution for the architecture candidates and HP candidates. A temporary weight is introduced to store the updated weight from the selected HPs (by the controller), and a validation accuracy based on this temporary weight serves as a reward to update the controller. In experiments, we show AutoHAS is efficient and generalizable to different search spaces, baselines and datasets. In particular, AutoHAS can improve the accuracy over popular network architectures, such as ResNet and EfficientNet, on CIFAR-10/100, ImageNet, and four more other datasets.

In this work, we propose a communication-efficient parameterization, FedPara, for federated learning (FL) to overcome the burdens on frequent model uploads and downloads. Our method re-parameterizes weight parameters of layers using low-rank weights followed by the Hadamard product. Compared to the conventional low-rank parameterization, our FedPara method is not restricted to low-rank constraints, and thereby it has a far larger capacity. This property enables to achieve comparable performance while requiring 3 to 10 times lower communication costs than the model with the original layers, which is not achievable by the traditional low-rank methods. The efficiency of our method can be further improved by combining with other efficient FL optimizers. In addition, we extend our method to a personalized FL application, pFedPara, which separates parameters into global and local ones. We show that pFedPara outperforms competing personalized FL methods with more than three times fewer parameters.

Maximizing a monotone submodular function under cardinality constraint k is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a 1{2} -epsilon approximation ratio and a query complexity bounded by poly(log(n),log(k),epsilon^{-1}). However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a 1{2}+epsilon approximation ratio must have an amortized query complexity that is polynomial in n. In this paper, we develop a simpler algorithm for the problem that maintains a (1{2}-epsilon)-approximate solution for submodular maximization under cardinality constraint k using a polylogarithmic amortized update time.

SberQuAD -- a large scale analog of Stanford SQuAD in the Russian language - is a valuable resource that has not been properly presented to the scientific community. We fill this gap by providing a description, a thorough analysis, and baseline experimental results.

Language model pretraining has led to significant performance gains but careful comparison between different approaches is challenging. Training is computationally expensive, often done on private datasets of different sizes, and, as we will show, hyperparameter choices have significant impact on the final results. We present a replication study of BERT pretraining (Devlin et al., 2019) that carefully measures the impact of many key hyperparameters and training data size. We find that BERT was significantly undertrained, and can match or exceed the performance of every model published after it. Our best model achieves state-of-the-art results on GLUE, RACE and SQuAD. These results highlight the importance of previously overlooked design choices, and raise questions about the source of recently reported improvements. We release our models and code.

Fine-tuning large pretrained language models on a limited training corpus usually suffers from poor generalization. Prior works show that the recently-proposed sharpness-aware minimization (SAM) optimization method can improve the model generalization. However, SAM adds a perturbation to each model parameter equally (but not all parameters contribute equally to the optimization of training), which we argue is sub-optimal and will lead to excessive computation. In this paper, we propose a novel optimization procedure, namely FSAM, which introduces a Fisher mask to improve the efficiency and performance of SAM. In short, instead of adding perturbation to all parameters, FSAM uses the Fisher information to identity the important parameters and formulates a Fisher mask to obtain the sparse perturbation, i.e., making the optimizer focus on these important parameters. Experiments on various tasks in GLUE and SuperGLUE benchmarks show that FSAM consistently outperforms the vanilla SAM by 0.67~1.98 average score among four different pretrained models. We also empirically show that FSAM works well in other complex scenarios, e.g., fine-tuning on generation tasks or limited training data. Encouragingly, when training data is limited, FSAM improves the SAM by a large margin, i.e., up to 15.1.

As language models scale up, it becomes increasingly expensive to verify research ideas because conclusions on small models do not trivially transfer to large ones. A possible solution is to establish a generic system that directly predicts some metrics for large models solely based on the results and hyperparameters from small models. Existing methods based on scaling laws require hyperparameter search on the largest models, which is impractical with limited resources. We address this issue by presenting our discoveries indicating that Maximal Update parametrization (Mup) enables accurate fitting of scaling laws for hyperparameters close to common loss basins, without any search. Thus, different models can be directly compared on large scales with loss prediction even before the training starts. We propose a new paradigm as a first step towards reliable academic research for any model scale without heavy computation. Code is publicly available at https://github.com/cofe-ai/Mu-scaling.

We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets (i.e., "foundation models"), in both vision and language domains. In this setting, we identify the first scaling law describing the relationship between weight sparsity, number of non-zero parameters, and amount of training data, which we validate empirically across model and data scales; on ViT/JFT-4B and T5/C4. These results allow us to characterize the "optimal sparsity", the sparsity level which yields the best performance for a given effective model size and training budget. For a fixed number of non-zero parameters, we identify that the optimal sparsity increases with the amount of data used for training. We also extend our study to different sparsity structures (such as the hardware-friendly n:m pattern) and strategies (such as starting from a pretrained dense model). Our findings shed light on the power and limitations of weight sparsity across various parameter and computational settings, offering both theoretical understanding and practical implications for leveraging sparsity towards computational efficiency improvements.

Recent efforts to scale Transformer models have demonstrated rapid progress across a wide range of tasks (Wei et al., 2022). However, fine-tuning these models for downstream tasks is expensive due to their large parameter counts. Parameter-efficient fine-tuning (PEFT) approaches have emerged as a viable alternative by allowing us to fine-tune models by updating only a small number of parameters. In this work, we propose a general framework for parameter efficient fine-tuning (PEFT), based on structured unrestricted-rank matrices (SURM) which can serve as a drop-in replacement for popular approaches such as Adapters and LoRA. Unlike other methods like LoRA, SURMs provides more flexibility in finding the right balance between compactness and expressiveness. This is achieved by using low displacement rank matrices (LDRMs), which hasn't been used in this context before. SURMs remain competitive with baselines, often providing significant quality improvements while using a smaller parameter budget. SURMs achieve 5-7% accuracy gains on various image classification tasks while replacing low-rank matrices in LoRA. It also results in up to 12x reduction of the number of parameters in adapters (with virtually no loss in quality) on the GLUE benchmark.

Recent success in deep learning has partially been driven by training increasingly overparametrized networks on ever larger datasets. It is therefore natural to ask: how much of the data is superfluous, which examples are important for generalization, and how do we find them? In this work, we make the striking observation that, in standard vision datasets, simple scores averaged over several weight initializations can be used to identify important examples very early in training. We propose two such scores -- the Gradient Normed (GraNd) and the Error L2-Norm (EL2N) scores -- and demonstrate their efficacy on a range of architectures and datasets by pruning significant fractions of training data without sacrificing test accuracy. In fact, using EL2N scores calculated a few epochs into training, we can prune half of the CIFAR10 training set while slightly improving test accuracy. Furthermore, for a given dataset, EL2N scores from one architecture or hyperparameter configuration generalize to other configurations. Compared to recent work that prunes data by discarding examples that are rarely forgotten over the course of training, our scores use only local information early in training. We also use our scores to detect noisy examples and study training dynamics through the lens of important examples -- we investigate how the data distribution shapes the loss surface and identify subspaces of the model's data representation that are relatively stable over training.

We open-source a state-of-the-art 7.5B-parameter generative model series named PhoGPT for Vietnamese, which includes the base pre-trained monolingual model PhoGPT-7B5 and its instruction-following variant, PhoGPT-7B5-Instruct. In addition, we also demonstrate its superior performance compared to previous open-source models through a human evaluation experiment. GitHub: https://github.com/VinAIResearch/PhoGPT

This study addresses the challenge of noise in training datasets for Direct Preference Optimization (DPO), a method for aligning Large Language Models (LLMs) with human preferences. We categorize noise into pointwise noise, which includes low-quality data points, and pairwise noise, which encompasses erroneous data pair associations that affect preference rankings. Utilizing Distributionally Robust Optimization (DRO), we enhance DPO's resilience to these types of noise. Our theoretical insights reveal that DPO inherently embeds DRO principles, conferring robustness to pointwise noise, with the regularization coefficient beta playing a critical role in its noise resistance. Extending this framework, we introduce Distributionally Robustifying DPO (Dr. DPO), which integrates pairwise robustness by optimizing against worst-case pairwise scenarios. The novel hyperparameter beta' in Dr. DPO allows for fine-tuned control over data pair reliability, providing a strategic balance between exploration and exploitation in noisy training environments. Empirical evaluations demonstrate that Dr. DPO substantially improves the quality of generated text and response accuracy in preference datasets, showcasing enhanced performance in both noisy and noise-free settings. The code is available at https://github.com/junkangwu/Dr_DPO.

Despite extensive studies, the underlying reason as to why overparameterized neural networks can generalize remains elusive. Existing theory shows that common stochastic optimizers prefer flatter minimizers of the training loss, and thus a natural potential explanation is that flatness implies generalization. This work critically examines this explanation. Through theoretical and empirical investigation, we identify the following three scenarios for two-layer ReLU networks: (1) flatness provably implies generalization; (2) there exist non-generalizing flattest models and sharpness minimization algorithms fail to generalize, and (3) perhaps most surprisingly, there exist non-generalizing flattest models, but sharpness minimization algorithms still generalize. Our results suggest that the relationship between sharpness and generalization subtly depends on the data distributions and the model architectures and sharpness minimization algorithms do not only minimize sharpness to achieve better generalization. This calls for the search for other explanations for the generalization of over-parameterized neural networks.

While existing work on neural architecture search (NAS) tunes hyperparameters in a separate post-processing step, we demonstrate that architectural choices and other hyperparameter settings interact in a way that can render this separation suboptimal. Likewise, we demonstrate that the common practice of using very few epochs during the main NAS and much larger numbers of epochs during a post-processing step is inefficient due to little correlation in the relative rankings for these two training regimes. To combat both of these problems, we propose to use a recent combination of Bayesian optimization and Hyperband for efficient joint neural architecture and hyperparameter search.

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph G=(V, D,B) is parameterized by a rational function with parameters for each vertex and edge in G. This rational parametrization naturally allows for the study of these models from an algebraic and combinatorial point of view. Indeed, this point of view has led to a collection of results in the literature, mainly focusing on questions related to identifiability and determining relationships between covariances (i.e., finding polynomials in the Gaussian vanishing ideal). So far, a large proportion of these results has focused on the case when D, the directed part of the mixed graph G, is acyclic. This is due to the fact that in the acyclic case, the parametrization becomes polynomial and there is a description of the entries of the covariance matrices in terms of a finite sum. We move beyond the acyclic case and give a closed form expression for the entries of the covariance matrices in terms of the one-connections in a graph obtained from D through some small operations. This closed form expression then allows us to show that if G is simple, then the parametrization map is generically finite-to-one. Finally, having a closed form expression for the covariance matrices allows for the development of an algorithm for systematically exploring possible polynomials in the Gaussian vanishing ideal.

Aligning large language models (LLMs) with human preferences is critical for real-world deployment, yet existing methods like RLHF face computational and stability challenges. While DPO establishes an offline paradigm with single hyperparameter beta, subsequent methods like SimPO reintroduce complexity through dual parameters (beta, gamma). We propose {ReLU-based Preference Optimization (RePO)}, a streamlined algorithm that eliminates beta via two advances: (1) retaining SimPO's reference-free margins but removing beta through gradient analysis, and (2) adopting a ReLU-based max-margin loss that naturally filters trivial pairs. Theoretically, RePO is characterized as SimPO's limiting case (beta to infty), where the logistic weighting collapses to binary thresholding, forming a convex envelope of the 0-1 loss. Empirical results on AlpacaEval 2 and Arena-Hard show that RePO outperforms DPO and SimPO across multiple base models, requiring only one hyperparameter to tune.

Parameter-efficient fine-tuning optimizes large, pre-trained foundation models by updating a subset of parameters; in this class, Low-Rank Adaptation (LoRA) is particularly effective. Inspired by an effort to investigate the different roles of LoRA matrices during fine-tuning, this paper characterizes and leverages unexpected asymmetry in the importance of low-rank adapter matrices. Specifically, when updating the parameter matrices of a neural network by adding a product BA, we observe that the B and A matrices have distinct functions: A extracts features from the input, while B uses these features to create the desired output. Based on this observation, we demonstrate that fine-tuning B is inherently more effective than fine-tuning A, and that a random untrained A should perform nearly as well as a fine-tuned one. Using an information-theoretic lens, we also bound the generalization of low-rank adapters, showing that the parameter savings of exclusively training B improves the bound. We support our conclusions with experiments on RoBERTa, BART-Large, LLaMA-2, and ViTs.

Triggered by the realization that AI emulators can rival the performance of traditional numerical weather prediction models running on HPC systems, there is now an increasing number of large AI models that address use cases such as forecasting, downscaling, or nowcasting. While the parallel developments in the AI literature focus on foundation models -- models that can be effectively tuned to address multiple, different use cases -- the developments on the weather and climate side largely focus on single-use cases with particular emphasis on mid-range forecasting. We close this gap by introducing Prithvi WxC, a 2.3 billion parameter foundation model developed using 160 variables from the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). Prithvi WxC employs an encoder-decoder-based architecture, incorporating concepts from various recent transformer models to effectively capture both regional and global dependencies in the input data. The model has been designed to accommodate large token counts to model weather phenomena in different topologies at fine resolutions. Furthermore, it is trained with a mixed objective that combines the paradigms of masked reconstruction with forecasting. We test the model on a set of challenging downstream tasks namely: Autoregressive rollout forecasting, Downscaling, Gravity wave flux parameterization, and Extreme events estimation. The pretrained model with 2.3 billion parameters, along with the associated fine-tuning workflows, has been publicly released as an open-source contribution via Hugging Face.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Learned optimizers (LOs) can significantly reduce the wall-clock training time of neural networks, substantially reducing training costs. However, they often suffer from poor meta-generalization, especially when training networks larger than those seen during meta-training. To address this, we use the recently proposed Maximal Update Parametrization (muP), which allows zero-shot generalization of optimizer hyperparameters from smaller to larger models. We extend muP theory to learned optimizers, treating the meta-training problem as finding the learned optimizer under muP. Our evaluation shows that LOs meta-trained with muP substantially improve meta-generalization as compared to LOs trained under standard parametrization (SP). Notably, when applied to large-width models, our best muLO, trained for 103 GPU-hours, matches or exceeds the performance of VeLO, the largest publicly available learned optimizer, meta-trained with 4000 TPU-months of compute. Moreover, muLOs demonstrate better generalization than their SP counterparts to deeper networks and to much longer training horizons (25 times longer) than those seen during meta-training.

We present miniF2F, a dataset of formal Olympiad-level mathematics problems statements intended to provide a unified cross-system benchmark for neural theorem proving. The miniF2F benchmark currently targets Metamath, Lean, Isabelle (partially) and HOL Light (partially) and consists of 488 problem statements drawn from the AIME, AMC, and the International Mathematical Olympiad (IMO), as well as material from high-school and undergraduate mathematics courses. We report baseline results using GPT-f, a neural theorem prover based on GPT-3 and provide an analysis of its performance. We intend for miniF2F to be a community-driven effort and hope that our benchmark will help spur advances in neural theorem proving.

We introduce a new framework for sample-efficient model evaluation that we call active testing. While approaches like active learning reduce the number of labels needed for model training, existing literature largely ignores the cost of labeling test data, typically unrealistically assuming large test sets for model evaluation. This creates a disconnect to real applications, where test labels are important and just as expensive, e.g. for optimizing hyperparameters. Active testing addresses this by carefully selecting the test points to label, ensuring model evaluation is sample-efficient. To this end, we derive theoretically-grounded and intuitive acquisition strategies that are specifically tailored to the goals of active testing, noting these are distinct to those of active learning. As actively selecting labels introduces a bias; we further show how to remove this bias while reducing the variance of the estimator at the same time. Active testing is easy to implement and can be applied to any supervised machine learning method. We demonstrate its effectiveness on models including WideResNets and Gaussian processes on datasets including Fashion-MNIST and CIFAR-100.

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

Pre-training and fine-tuning have achieved significant advances in the information retrieval (IR). A typical approach is to fine-tune all the parameters of large-scale pre-trained models (PTMs) on downstream tasks. As the model size and the number of tasks increase greatly, such approach becomes less feasible and prohibitively expensive. Recently, a variety of parameter-efficient tuning methods have been proposed in natural language processing (NLP) that only fine-tune a small number of parameters while still attaining strong performance. Yet there has been little effort to explore parameter-efficient tuning for IR. In this work, we first conduct a comprehensive study of existing parameter-efficient tuning methods at both the retrieval and re-ranking stages. Unlike the promising results in NLP, we find that these methods cannot achieve comparable performance to full fine-tuning at both stages when updating less than 1\% of the original model parameters. More importantly, we find that the existing methods are just parameter-efficient, but not learning-efficient as they suffer from unstable training and slow convergence. To analyze the underlying reason, we conduct a theoretical analysis and show that the separation of the inserted trainable modules makes the optimization difficult. To alleviate this issue, we propose to inject additional modules alongside the PTM to make the original scattered modules connected. In this way, all the trainable modules can form a pathway to smooth the loss surface and thus help stabilize the training process. Experiments at both retrieval and re-ranking stages show that our method outperforms existing parameter-efficient methods significantly, and achieves comparable or even better performance over full fine-tuning.

Approximating Stochastic Gradient Descent (SGD) as a Stochastic Differential Equation (SDE) has allowed researchers to enjoy the benefits of studying a continuous optimization trajectory while carefully preserving the stochasticity of SGD. Analogous study of adaptive gradient methods, such as RMSprop and Adam, has been challenging because there were no rigorously proven SDE approximations for these methods. This paper derives the SDE approximations for RMSprop and Adam, giving theoretical guarantees of their correctness as well as experimental validation of their applicability to common large-scaling vision and language settings. A key practical result is the derivation of a square root scaling rule to adjust the optimization hyperparameters of RMSprop and Adam when changing batch size, and its empirical validation in deep learning settings.

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.

In this paper, we compare the three most popular algorithms for hyperparameter optimization (Grid Search, Random Search, and Genetic Algorithm) and attempt to use them for neural architecture search (NAS). We use these algorithms for building a convolutional neural network (search architecture). Experimental results on CIFAR-10 dataset further demonstrate the performance difference between compared algorithms. The comparison results are based on the execution time of the above algorithms and accuracy of the proposed models.

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous works have focused on embedding dynamical systems into networks through two approaches: learning a single solution operator (i.e., the mapping from input parametrized functions to solutions) or learning the governing system of equations (i.e., the constitutive model relative to the state variables). Both of these approaches yield different representations for the same underlying data or function. Additionally, observing that families of differential equations often share key characteristics, we seek one network representation across a wide range of equations. Our method, called Predicting Operators and Symbolic Expressions (PROSE), learns maps from multimodal inputs to multimodal outputs, capable of generating both numerical predictions and mathematical equations. By using a transformer structure and a feature fusion approach, our network can simultaneously embed sets of solution operators for various parametric differential equations using a single trained network. Detailed experiments demonstrate that the network benefits from its multimodal nature, resulting in improved prediction accuracy and better generalization. The network is shown to be able to handle noise in the data and errors in the symbolic representation, including noisy numerical values, model misspecification, and erroneous addition or deletion of terms. PROSE provides a new neural network framework for differential equations which allows for more flexibility and generality in learning operators and governing equations from data.