Pedro Savarese

Xin Yuan, Pedro Savarese, Michael Maire

We develop an approach to efficiently grow neural networks, within which parameterization and optimization strategies are designed by considering their effects on the training dynamics. Unlike existing growing methods, which follow simple replication heuristics or utilize auxiliary gradient-based local optimization, we craft a parameterization scheme which dynamically stabilizes weight, activation, and gradient scaling as the architecture evolves, and maintains the inference functionality of the network. To address the optimization difficulty resulting from imbalanced training effort distributed to subnetworks fading in at different growth phases, we propose a learning rate adaption mechanism that rebalances the gradient contribution of these separate subcomponents. Experimental results show that our method achieves comparable or better accuracy than training large fixed-size models, while saving a substantial portion of the original computation budget for training. We demonstrate that these gains translate into real wall-clock training speedups.

David Yunis, Kumar Kshitij Patel, Samuel Wheeler et al.

We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in optimization across various experiments, from small-scale ``grokking'' to large-scale tasks like image classification with ConvNets, image generation with UNets, speech recognition with LSTMs, and language modeling with Transformers. We also demonstrate that weight decay enhances this bias beyond its role as a norm regularizer, even in practical systems. Moreover, we show that these spectral dynamics distinguish memorizing networks from generalizing ones, offering a novel perspective on this longstanding conundrum. Additionally, we leverage spectral dynamics to explore the emergence of well-performing sparse subnetworks (lottery tickets) and the structure of the loss surface through linear mode connectivity. Our findings suggest that spectral dynamics provide a coherent framework to better understand the behavior of neural networks across diverse settings.

Cyrus Zhou, Pedro Savarese, Zack Hassman et al.

Ultra-low-precision inference can sharply reduce memory and latency but often degrades accuracy and relies on specialized hardware. We present SONIQ, a system-optimized, noise-injected quantization framework that learns per-channel mixed precision for both weights and activations while training under the same rules used at inference. By injecting hardware-calibrated quantization noise during training, SONIQ steers models toward the discrete arithmetic used at deployment -- without bespoke runtimes. Across CNNs and Transformers, SONIQ achieves up to 16x and 7x compression, respectively, while matching or exceeding full-precision accuracy. Measured end-to-end, SONIQ delivers up to 7.3x CPU speedup over strong INT8 baselines and up to 6.3x (vector units) / 2.8x (tensor cores) GPU speedup relative to FP16. A practical outcome is that two per-channel precision levels -- one in the 1--4-bit range and one in the 4--8-bit range -- suffice in practice; at inference, each channel selects one of the two, keeping kernels simple and fast. To our knowledge, SONIQ is the first framework to reach or surpass full-precision accuracy under ultra-low (1--4 bits per parameter) regimes while remaining deployable on commodity hardware, narrowing the gap between quantization theory and practical, high-throughput inference.

Pedro Savarese

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep learning technologies. This thesis investigates principled approximation methods for improving the efficiency of deep learning systems, with a particular focus on settings that involve discrete constraints and non-differentiability. We study three main approaches toward improved efficiency: architecture design, model compression, and optimization. For model compression, we propose novel approximations for pruning and quantization that frame the underlying discrete problem as continuous and differentiable, enabling gradient-based training of compression schemes alongside the model's parameters. These approximations allow for fine-grained sparsity and precision configurations, leading to highly compact models without significant fine-tuning. In the context of architecture design, we design an algorithm for neural architecture search that leverages parameter sharing across layers to efficiently explore implicitly recurrent architectures. Finally, we study adaptive optimization, revisiting theoretical properties of widely used methods and proposing an adaptive optimizer that allows for quick hyperparameter tuning. Our contributions center on tackling computationally hard problems via scalable and principled approximations. Experimental results on image classification, language modeling, and generative modeling tasks show that the proposed methods provide significant improvements in terms of training and inference efficiency while maintaining, or even improving, the model's performance.

Pedro Savarese, Sunnie S. Y. Kim, Michael Maire et al.

We study image segmentation from an information-theoretic perspective, proposing a novel adversarial method that performs unsupervised segmentation by partitioning images into maximally independent sets. More specifically, we group image pixels into foreground and background, with the goal of minimizing predictability of one set from the other. An easily computed loss drives a greedy search process to maximize inpainting error over these partitions. Our method does not involve training deep networks, is computationally cheap, class-agnostic, and even applicable in isolation to a single unlabeled image. Experiments demonstrate that it achieves a new state-of-the-art in unsupervised segmentation quality, while being substantially faster and more general than competing approaches.

Xin Yuan, Pedro Savarese, Michael Maire

We develop an approach to growing deep network architectures over the course of training, driven by a principled combination of accuracy and sparsity objectives. Unlike existing pruning or architecture search techniques that operate on full-sized models or supernet architectures, our method can start from a small, simple seed architecture and dynamically grow and prune both layers and filters. By combining a continuous relaxation of discrete network structure optimization with a scheme for sampling sparse subnetworks, we produce compact, pruned networks, while also drastically reducing the computational expense of training. For example, we achieve $49.7\%$ inference FLOPs and $47.4\%$ training FLOPs savings compared to a baseline ResNet-50 on ImageNet, while maintaining $75.2\%$ top-1 accuracy -- all without any dedicated fine-tuning stage. Experiments across CIFAR, ImageNet, PASCAL VOC, and Penn Treebank, with convolutional networks for image classification and semantic segmentation, and recurrent networks for language modeling, demonstrate that we both train faster and produce more efficient networks than competing architecture pruning or search methods.

Blake Woodworth, Suriya Gunasekar, Jason D. Lee et al.

A recent line of work studies overparametrized neural networks in the "kernel regime," i.e. when the network behaves during training as a kernelized linear predictor, and thus training with gradient descent has the effect of finding the minimum RKHS norm solution. This stands in contrast to other studies which demonstrate how gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. Building on an observation by Chizat and Bach, we show how the scale of the initialization controls the transition between the "kernel" (aka lazy) and "rich" (aka active) regimes and affects generalization properties in multilayer homogeneous models. We also highlight an interesting role for the width of a model in the case that the predictor is not identically zero at initialization. We provide a complete and detailed analysis for a family of simple depth-$D$ models that already exhibit an interesting and meaningful transition between the kernel and rich regimes, and we also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.

Pedro Savarese, Hugo Silva, Michael Maire

The search for efficient, sparse deep neural network models is most prominently performed by pruning: training a dense, overparameterized network and removing parameters, usually via following a manually-crafted heuristic. Additionally, the recent Lottery Ticket Hypothesis conjectures that, for a typically-sized neural network, it is possible to find small sub-networks which, when trained from scratch on a comparable budget, match the performance of the original dense counterpart. We revisit fundamental aspects of pruning algorithms, pointing out missing ingredients in previous approaches, and develop a method, Continuous Sparsification, which searches for sparse networks based on a novel approximation of an intractable $\ell_0$ regularization. We compare against dominant heuristic-based methods on pruning as well as ticket search -- finding sparse subnetworks that can be successfully re-trained from an early iterate. Empirical results show that we surpass the state-of-the-art for both objectives, across models and datasets, including VGG trained on CIFAR-10 and ResNet-50 trained on ImageNet. In addition to setting a new standard for pruning, Continuous Sparsification also offers fast parallel ticket search, opening doors to new applications of the Lottery Ticket Hypothesis.

Pedro Savarese, David McAllester, Sudarshan Babu et al.

From a simplified analysis of adaptive methods, we derive AvaGrad, a new optimizer which outperforms SGD on vision tasks when its adaptability is properly tuned. We observe that the power of our method is partially explained by a decoupling of learning rate and adaptability, greatly simplifying hyperparameter search. In light of this observation, we demonstrate that, against conventional wisdom, Adam can also outperform SGD on vision tasks, as long as the coupling between its learning rate and adaptability is taken into account. In practice, AvaGrad matches the best results, as measured by generalization accuracy, delivered by any existing optimizer (SGD or adaptive) across image classification (CIFAR, ImageNet) and character-level language modelling (Penn Treebank) tasks.

Daniel Specht Menezes, Pedro Savarese, Ruy Luiz Milidiú

With the recent progress in machine learning, boosted by techniques such as deep learning, many tasks can be successfully solved once a large enough dataset is available for training. Nonetheless, human-annotated datasets are often expensive to produce, especially when labels are fine-grained, as is the case of Named Entity Recognition (NER), a task that operates with labels on a word-level. In this paper, we propose a method to automatically generate labeled datasets for NER from public data sources by exploiting links and structured data from DBpedia and Wikipedia. Due to the massive size of these data sources, the resulting dataset -- SESAME Available at https://sesame-pt.github.io -- is composed of millions of labeled sentences. We detail the method to generate the dataset, report relevant statistics, and design a baseline using a neural network, showing that our dataset helps building better NER predictors.

Pedro Savarese

Adaptive gradient methods such as Adam have gained extreme popularity due to their success in training complex neural networks and less sensitivity to hyperparameter tuning compared to SGD. However, it has been recently shown that Adam can fail to converge and might cause poor generalization -- this lead to the design of new, sophisticated adaptive methods which attempt to generalize well while being theoretically reliable. In this technical report we focus on AdaBound, a promising, recently proposed optimizer. We present a stochastic convex problem for which AdaBound can provably take arbitrarily long to converge in terms of a factor which is not accounted for in the convergence rate guarantee of Luo et al. (2019). We present a new $O(\sqrt T)$ regret guarantee under different assumptions on the bound functions, and provide empirical results on CIFAR suggesting that a specific form of momentum SGD can match AdaBound's performance while having less hyperparameters and lower computational costs.

Blake Woodworth, Suriya Gunasekar, Pedro Savarese et al.

A recent line of work studies overparametrized neural networks in the "kernel regime," i.e. when the network behaves during training as a kernelized linear predictor, and thus training with gradient descent has the effect of finding the minimum RKHS norm solution. This stands in contrast to other studies which demonstrate how gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. Building on an observation by Chizat and Bach, we show how the scale of the initialization controls the transition between the "kernel" (aka lazy) and "rich" (aka active) regimes and affects generalization properties in multilayer homogeneous models. We provide a complete and detailed analysis for a simple two-layer model that already exhibits an interesting and meaningful transition between the kernel and rich regimes, and we demonstrate the transition for more complex matrix factorization models and multilayer non-linear networks.

Pedro Savarese, Michael Maire

We introduce a parameter sharing scheme, in which different layers of a convolutional neural network (CNN) are defined by a learned linear combination of parameter tensors from a global bank of templates. Restricting the number of templates yields a flexible hybridization of traditional CNNs and recurrent networks. Compared to traditional CNNs, we demonstrate substantial parameter savings on standard image classification tasks, while maintaining accuracy. Our simple parameter sharing scheme, though defined via soft weights, in practice often yields trained networks with near strict recurrent structure; with negligible side effects, they convert into networks with actual loops. Training these networks thus implicitly involves discovery of suitable recurrent architectures. Though considering only the design aspect of recurrent links, our trained networks achieve accuracy competitive with those built using state-of-the-art neural architecture search (NAS) procedures. Our hybridization of recurrent and convolutional networks may also represent a beneficial architectural bias. Specifically, on synthetic tasks which are algorithmic in nature, our hybrid networks both train faster and extrapolate better to test examples outside the span of the training set.

Pedro Savarese, Itay Evron, Daniel Soudry et al.

We consider the question of what functions can be captured by ReLU networks with an unbounded number of units (infinite width), but where the overall network Euclidean norm (sum of squares of all weights in the system, except for an unregularized bias term for each unit) is bounded; or equivalently what is the minimal norm required to approximate a given function. For functions $f : \mathbb R \rightarrow \mathbb R$ and a single hidden layer, we show that the minimal network norm for representing $f$ is $\max(\int |f''(x)| dx, |f'(-\infty) + f'(+\infty)|)$, and hence the minimal norm fit for a sample is given by a linear spline interpolation.

Mor Shpigel Nacson, Jason D. Lee, Suriya Gunasekar et al.

We provide a detailed study on the implicit bias of gradient descent when optimizing loss functions with strictly monotone tails, such as the logistic loss, over separable datasets. We look at two basic questions: (a) what are the conditions on the tail of the loss function under which gradient descent converges in the direction of the $L_2$ maximum-margin separator? (b) how does the rate of margin convergence depend on the tail of the loss function and the choice of the step size? We show that for a large family of super-polynomial tailed losses, gradient descent iterates on linear networks of any depth converge in the direction of $L_2$ maximum-margin solution, while this does not hold for losses with heavier tails. Within this family, for simple linear models we show that the optimal rates with fixed step size is indeed obtained for the commonly used exponentially tailed losses such as logistic loss. However, with a fixed step size the optimal convergence rate is extremely slow as $1/\log(t)$, as also proved in Soudry et al. (2018). For linear models with exponential loss, we further prove that the convergence rate could be improved to $\log (t) /\sqrt{t}$ by using aggressive step sizes that compensates for the rapidly vanishing gradients. Numerical results suggest this method might be useful for deep networks.

Pedro H. P. Savarese, Mayank Kakodkar, Bruno Ribeiro

We propose a Las Vegas transformation of Markov Chain Monte Carlo (MCMC) estimators of Restricted Boltzmann Machines (RBMs). We denote our approach Markov Chain Las Vegas (MCLV). MCLV gives statistical guarantees in exchange for random running times. MCLV uses a stopping set built from the training data and has maximum number of Markov chain steps K (referred as MCLV-K). We present a MCLV-K gradient estimator (LVS-K) for RBMs and explore the correspondence and differences between LVS-K and Contrastive Divergence (CD-K), with LVS-K significantly outperforming CD-K training RBMs over the MNIST dataset, indicating MCLV to be a promising direction in learning generative models.

Pedro H. P. Savarese, Leonardo O. Mazza, Daniel R. Figueiredo

We propose a new layer design by adding a linear gating mechanism to shortcut connections. By using a scalar parameter to control each gate, we provide a way to learn identity mappings by optimizing only one parameter. We build upon the motivation behind Residual Networks, where a layer is reformulated in order to make learning identity mappings less problematic to the optimizer. The augmentation introduces only one extra parameter per layer, and provides easier optimization by making degeneration into identity mappings simpler. We propose a new model, the Gated Residual Network, which is the result when augmenting Residual Networks. Experimental results show that augmenting layers provides better optimization, increased performance, and more layer independence. We evaluate our method on MNIST using fully-connected networks, showing empirical indications that our augmentation facilitates the optimization of deep models, and that it provides high tolerance to full layer removal: the model retains over 90% of its performance even after half of its layers have been randomly removed. We also evaluate our model on CIFAR-10 and CIFAR-100 using Wide Gated ResNets, achieving 3.65% and 18.27% error, respectively.