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Mechanism Design

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Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing

Yunchong Song, Chenghu Zhou, Xinbing Wang, Zhouhan Lin

Most graph neural networks follow the message passing mechanism. However, it faces the over-smoothing problem when multiple times of message passing is applied to a graph, causing indistinguishable node representations and prevents the model to effectively learn dependencies between farther-away nodes. On the other hand, features of neighboring nodes with different labels are likely to be falsely mixed, resulting in the heterophily problem. In this work, we propose to order the messages passing into the node representation, with specific blocks of neurons targeted for message passing within specific hops. This is achieved by aligning the hierarchy of the rooted-tree of a central node with the ordered neurons in its node representation. Experimental results on an extensive set of datasets show that our model can simultaneously achieve the state-of-the-art in both homophily and heterophily settings, without any targeted design. Moreover, its performance maintains pretty well while the model becomes really deep, effectively preventing the over-smoothing problem. Finally, visualizing the gating vectors shows that our model learns to behave differently between homophily and heterophily settings, providing an explainable graph neural model.

AANG : Automating Auxiliary Learning

Lucio M. Dery, Paul Michel, Mikhail Khodak, Graham Neubig, Ameet Talwalkar

Auxiliary objectives, supplementary learning signals that are introduced to help aid learning on data-starved or highly complex end-tasks, are commonplace in machine learning. Whilst much work has been done to formulate useful auxiliary objectives, their construction is still an art which proceeds by slow and tedious hand-design. Intuition for how and when these objectives improve end-task performance has also had limited theoretical backing. In this work, we present an approach for automatically generating a suite of auxiliary objectives. We achieve this by deconstructing existing objectives within a novel unified taxonomy, identifying connections between them, and generating new ones based on the uncovered structure. Next, we theoretically formalize widely-held intuitions about how auxiliary learning improves generalization on the end-task. This leads us to a principled and efficient algorithm for searching the space of generated objectives to find those most useful to a specified end-task. With natural language processing (NLP) as our domain of study, we demonstrate that our automated auxiliary learning pipeline leads to strong improvements over competitive baselines across continued training experiments on a pre-trained model on 5 NLP end-tasks.

Retrieval-based Controllable Molecule Generation

Zichao Wang, Weili Nie, Zhuoran Qiao, Chaowei Xiao, Richard Baraniuk, Anima Anandkumar

Generating new molecules with specified chemical and biological properties via generative models has emerged as a promising direction for drug discovery. However, existing methods require extensive training/fine-tuning with a large dataset, often unavailable in real-world generation tasks. In this work, we propose a new retrieval-based framework for controllable molecule generation. We use a small set of exemplar molecules, i.e., those that (partially) satisfy the design criteria, to steer the pre-trained generative model towards synthesizing molecules that satisfy the given design criteria. We design a retrieval mechanism that retrieves and fuses the exemplar molecules with the input molecule, which is trained by a new self-supervised objective that predicts the nearest neighbor of the input molecule. We also propose an iterative refinement process to dynamically update the generated molecules and retrieval database for better generalization. Our approach is agnostic to the choice of generative models and requires no task-specific fine-tuning. On various tasks ranging from simple design criteria to a challenging real-world scenario for designing lead compounds that bind to the SARS-CoV-2 main protease, we demonstrate our approach extrapolates well beyond the retrieval database, and achieves better performance and wider applicability than previous methods.

Curriculum-based Co-design of Morphology and Control of Voxel-based Soft Robots

Yuxing Wang, Shuang Wu, Haobo Fu, Qiang Fu, Tiantian Zhang, Yongzhe Chang, Xueqian Wang

Co-design of morphology and control of a Voxel-based Soft Robot (VSR) is challenging due to the notorious bi-level optimization. In this paper, we present a Curriculum-based Co-design (CuCo) method for learning to design and control VSRs through an easy-to-difficult process. Specifically, we expand the design space from a small size to the target size gradually through a predefined curriculum. At each learning stage of the curriculum, we use reinforcement learning to simultaneously train the design policy and the control policy, which is enabled by incorporating the design process into the environment and using differentiable policy representations. The converged morphology and the learned policies from last stage are inherited and then serve as the starting point for the next stage. In empirical studies, we show that CuCo is more efficient in creating larger robots with better performance by reusing the practical design and control patterns learned within each stage, in comparison to prior approaches that learn from scratch in the space of target size.

Mega: Moving Average Equipped Gated Attention

Xuezhe Ma, Chunting Zhou, Xiang Kong, Junxian He, Liangke Gui, Graham Neubig, Jonathan May, Luke Zettlemoyer

The design choices in the Transformer attention mechanism, including weak inductive bias and quadratic computational complexity, have limited its application for modeling long sequences. In this paper, we introduce Mega, a simple, theoretically grounded, single-head gated attention mechanism equipped with (exponential) moving average to incorporate inductive bias of position-aware local dependencies into the position-agnostic attention mechanism. We further propose a variant of Mega that offers linear time and space complexity yet yields only minimal quality loss, by efficiently splitting the whole sequence into multiple chunks with fixed length. Extensive experiments on a wide range of sequence modeling benchmarks, including the Long Range Arena, neural machine translation, auto-regressive language modeling, and image and speech classification, show that Mega achieves significant improvements over other sequence models, including variants of Transformers and recent state space models.

Protein Sequence and Structure Co-Design with Equivariant Translation

Chence Shi, Chuanrui Wang, Jiarui Lu, Bozitao Zhong, Jian Tang

Proteins are macromolecules that perform essential functions in all living organisms. Designing novel proteins with specific structures and desired functions has been a long-standing challenge in the field of bioengineering. Existing approaches generate both protein sequence and structure using either autoregressive models or diffusion models, both of which suffer from high inference costs. In this paper, we propose a new approach capable of protein sequence and structure co-design, which iteratively translates both protein sequence and structure into the desired state from random initialization, based on context features given a priori. Our model consists of a trigonometry-aware encoder that reasons geometrical constraints and interactions from context features, and a roto-translation equivariant decoder that translates protein sequence and structure interdependently. Notably, all protein amino acids are updated in one shot in each translation step, which significantly accelerates the inference process. Experimental results across multiple tasks show that our model outperforms previous state-of-the-art baselines by a large margin, and is able to design proteins of high fidelity as regards both sequence and structure, with running time orders of magnitude less than sampling-based methods.

Neural Architecture Design and Robustness: A Dataset

Steffen Jung, Jovita Lukasik, Margret Keuper

Deep learning models have proven to be successful in a wide range of machine learning tasks. Yet, they are often highly sensitive to perturbations on the input data which can lead to incorrect decisions with high confidence, hampering their deployment for practical use-cases. Thus, finding architectures that are (more) robust against perturbations has received much attention in recent years. Just like the search for well-performing architectures in terms of clean accuracy, this usually involves a tedious trial-and-error process with one additional challenge: the evaluation of a network's robustness is significantly more expensive than its evaluation for clean accuracy. Thus, the aim of this paper is to facilitate better streamlined research on architectural design choices with respect to their impact on robustness as well as, for example, the evaluation of surrogate measures for robustness. We therefore borrow one of the most commonly considered search spaces for neural architecture search for image classification, NAS-Bench-201, which contains a manageable size of 6466 non-isomorphic network designs. We evaluate all these networks on a range of common adversarial attacks and corruption types and introduce a database on neural architecture design and robustness evaluations. We further present three exemplary use cases of this dataset, in which we (i) benchmark robustness measurements based on Jacobian and Hessian matrices for their robustness predictability, (ii) perform neural architecture search on robust accuracies, and (iii) provide an initial analysis of how architectural design choices affect robustness. We find that carefully crafting the topology of a network can have substantial impact on its robustness, where networks with the same parameter count range in mean adversarial robust accuracy from 20%-41%. Code and data is available at http://robustness.vision/.

Emergence of Maps in the Memories of Blind Navigation Agents

Erik Wijmans, Manolis Savva, Irfan Essa, Stefan Lee, Ari S. Morcos, Dhruv Batra

Animal navigation research posits that organisms build and maintain internal spa- tial representations, or maps, of their environment. We ask if machines – specifically, artificial intelligence (AI) navigation agents – also build implicit (or ‘mental’) maps. A positive answer to this question would (a) explain the surprising phenomenon in recent literature of ostensibly map-free neural-networks achieving strong performance, and (b) strengthen the evidence of mapping as a fundamental mechanism for navigation by intelligent embodied agents, whether they be biological or artificial. Unlike animal navigation, we can judiciously design the agent’s perceptual system and control the learning paradigm to nullify alternative navigation mechanisms. Specifically, we train ‘blind’ agents – with sensing limited to only egomotion and no other sensing of any kind – to perform PointGoal navigation (‘go to $\Delta$x, $\Delta$y’) via reinforcement learning. Our agents are composed of navigation-agnostic components (fully-connected and recurrent neural networks), and our experimental setup provides no inductive bias towards mapping. Despite these harsh conditions, we find that blind agents are (1) surprisingly effective navigators in new environments (∼95% success); (2) they utilize memory over long horizons (remembering ∼1,000 steps of past experience in an episode); (3) this memory enables them to exhibit intelligent behavior (following walls, detecting collisions, taking shortcuts); (4) there is emergence of maps and collision detection neurons in the representations of the environment built by a blind agent as it navigates; and (5) the emergent maps are selective and task dependent (e.g. the agent ‘forgets’ exploratory detours). Overall, this paper presents no new techniques for the AI audience, but a surprising finding, an insight, and an explanation.

Learning Symbolic Models for Graph-structured Physical Mechanism

Hongzhi Shi, Jingtao Ding, Yufan Cao, Quanming Yao, Li Liu, Yong Li

Graph-structured physical mechanisms are ubiquitous in real-world scenarios, thus revealing underneath formulas is of great importance for scientific discovery. However, classical symbolic regression methods fail on this task since they can only handle input-output pairs that are not graph-structured. In this paper, we propose a new approach that generalizes symbolic regression to graph-structured physical mechanisms. The essence of our method is to model the formula skeleton with a message-passing flow, which helps transform the discovery of the skeleton into the search for the message-passing flow. Such a transformation guarantees that we are able to search a message-passing flow, which is efficient and Pareto-optimal in terms of both accuracy and simplicity. Subsequently, the underneath formulas can be identified by interpreting component functions of the searched message-passing flow, reusing classical symbolic regression methods. We conduct extensive experiments on datasets from different physical domains, including mechanics, electricity, and thermology, and on real-world datasets of pedestrian dynamics without ground-truth formulas. The experimental results not only verify the rationale of our design but also demonstrate that the proposed method can automatically learn precise and interpretable formulas for graph-structured physical mechanisms.

Towards a Unified Theoretical Understanding of Non-contrastive Learning via Rank Differential Mechanism

Zhijian Zhuo, Yifei Wang, Jinwen Ma, Yisen Wang

Recently, a variety of methods under the name of non-contrastive learning (like BYOL, SimSiam, SwAV, DINO) show that when equipped with some asymmetric architectural designs, aligning positive pairs alone is sufficient to attain good performance in self-supervised visual learning. Despite some understandings of some specific modules (like the predictor in BYOL), there is yet no unified theoretical understanding of how these seemingly different asymmetric designs can all avoid feature collapse, particularly considering methods that also work without the predictor (like DINO). In this work, we propose a unified theoretical understanding for existing variants of non-contrastive learning. Our theory named Rank Differential Mechanism (RDM) shows that all these asymmetric designs create a consistent rank difference in their dual-branch output features. This rank difference will provably lead to an improvement of effective dimensionality and alleviate either complete or dimensional feature collapse. Different from previous theories, our RDM theory is applicable to different asymmetric designs (with and without the predictor), and thus can serve as a unified understanding of existing non-contrastive learning methods. Besides, our RDM theory also provides practical guidelines for designing many new non-contrastive variants. We show that these variants indeed achieve comparable performance to existing methods on benchmark datasets, and some of them even outperform the baselines. Our code is available at \url{https://github.com/PKU-ML/Rank-Differential-Mechanism}.

SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments

Tsun-Hsuan Wang, Pingchuan Ma, Andrew Everett Spielberg, Zhou Xian, Hao Zhang, Joshua B. Tenenbaum, Daniela Rus, Chuang Gan

While significant research progress has been made in robot learning for control, unique challenges arise when simultaneously co-optimizing morphology. Existing work has typically been tailored for particular environments or representations. In order to more fully understand inherent design and performance tradeoffs and accelerate the development of new breeds of soft robots, a comprehensive virtual platform — with well-established tasks, environments, and evaluation metrics — is needed. In this work, we introduce SoftZoo, a soft robot co-design platform for locomotion in diverse environments. SoftZoo supports an extensive, naturally-inspired material set, including the ability to simulate environments such as flat ground, desert, wetland, clay, ice, snow, shallow water, and ocean. Further, it provides a variety of tasks relevant for soft robotics, including fast locomotion, agile turning, and path following, as well as differentiable design representations for morphology and control. Combined, these elements form a feature-rich platform for analysis and development of soft robot co-design algorithms. We benchmark prevalent representations and co-design algorithms, and shed light on 1) the interplay between environment, morphology, and behavior (2) the importance of design space representations 3) the ambiguity in muscle formation and controller synthesis and 4) the value of differentiable physics. We envision that SoftZoo will serve as a standard platform and template an approach toward the development of novel representations and algorithms for co-designing soft robots’ behavioral and morphological intelligence. Demos are available on our project page.

Parameter-Efficient Fine-Tuning Design Spaces

Jiaao Chen, Aston Zhang, Xingjian Shi, Mu Li, Alex Smola, Diyi Yang

Parameter-efficient fine-tuning aims to achieve comparable performances of fine-tuning with much fewer trainable parameters. Recently, various tuning strategies (e.g., Adapters, Prefix Tuning, BitFit, and LoRA) have been proposed. However, their designs are hand-crafted separately, and it remains unclear whether certain design patterns exist for parameter-efficient fine-tuning. Thus, we present a parameter-efficient fine-tuning design paradigm and discover design patterns that are applicable to different experimental settings. Instead of focusing on designing another individual tuning strategy, we introduce parameter-efficient fine-tuning design spaces that parameterize tuning structures and tuning strategies. Specifically, any design space is characterized by four components: layer grouping, trainable parameter allocation, tunable groups, and strategy assignment. Our comprehensive empirical study leads to the discovery of design patterns: (i) grouping layers in a spindle pattern, (ii) uniformly allocating the number of trainable parameters to layers, (ii) tuning all the groups, and (iv) tuning different groups with proper strategies. Our discovered design patterns result in new parameter-efficient fine-tuning methods. Experiments show that these methods consistently outperform investigated parameter-efficient fine-tuning strategies across different backbone models and different tasks in natural language processing.

Neural Design for Genetic Perturbation Experiments

Aldo Pacchiano, Drausin Wulsin, Robert A Barton, Luis Voloch

The problem of how to genetically modify cells in order to maximize a certain cellular phenotype has taken center stage in drug development over the last few years (with, for example, genetically edited CAR-T, CAR-NK, and CAR-NKT cells entering cancer clinical trials). Exhausting the search space for all possible genetic edits (perturbations) or combinations thereof is infeasible due to cost and experimental limitations. This work provides a theoretically sound framework for iteratively exploring the space of perturbations in pooled batches in order to maximize a target phenotype under an experimental budget. Inspired by this application domain, we study the problem of batch query bandit optimization and introduce the Optimistic Arm Elimination ($\mathrm{OAE}$) principle designed to find an almost optimal arm under different functional relationships between the queries (arms) and the outputs (rewards). We analyze the convergence properties of $\mathrm{OAE}$ by relating it to the Eluder dimension of the algorithm's function class and validate that $\mathrm{OAE}$ outperforms other strategies in finding optimal actions in experiments on simulated problems, public datasets well-studied in bandit contexts, and in genetic perturbation datasets when the regression model is a deep neural network. OAE also outperforms the benchmark algorithms in 3 of 4 datasets in the GeneDisco experimental planning challenge.

Neuromechanical Autoencoders: Learning to Couple Elastic and Neural Network Nonlinearity

Deniz Oktay, Mehran Mirramezani, Eder Medina, Ryan P Adams

Intelligent biological systems are characterized by their embodiment in a complex environment and the intimate interplay between their nervous systems and the nonlinear mechanical properties of their bodies. This coordination, in which the dynamics of the motor system co-evolved to reduce the computational burden on the brain, is referred to as "mechanical intelligence" or "morphological computation". In this work, we seek to develop machine learning analogs of this process, in which we jointly learn the morphology of complex nonlinear elastic solids along with a deep neural network to control it. By using a specialized differentiable simulator of elastic mechanics coupled to conventional deep learning architectures---which we refer to as neuromechanical autoencoders---we are able to learn to perform morphological computation via gradient descent. Key to our approach is the use of mechanical metamaterials---cellular solids, in particular---as the morphological substrate. Just as deep neural networks provide flexible and massively-parametric function approximators for perceptual and control tasks, cellular solid metamaterials are promising as a rich and learnable space for approximating a variety of actuation tasks. In this work we take advantage of these complementary computational concepts to co-design materials and neural network controls to achieve nonintuitive mechanical behavior. We demonstrate in simulation how it is possible to achieve translation, rotation, and shape matching, as well as a "digital MNIST" task. We additionally manufacture and evaluate one of the designs to verify its real-world behavior.

Dilated convolution with learnable spacings

Ismail Khalfaoui Hassani, Thomas Pellegrini, Timothée Masquelier

Recent works indicate that convolutional neural networks (CNN) need large receptive fields (RF) to compete with visual transformers and their attention mechanism. In CNNs, RFs can simply be enlarged by increasing the convolution kernel sizes. Yet the number of trainable parameters, which scales quadratically with the kernel's size in the 2D case, rapidly becomes prohibitive, and the training is notoriously difficult. This paper presents a new method to increase the RF size without increasing the number of parameters. The dilated convolution (DC) has already been proposed for the same purpose. DC can be seen as a convolution with a kernel that contains only a few non-zero elements placed on a regular grid. Here we present a new version of the DC in which the spacings between the non-zero elements, or equivalently their positions, are no longer fixed but learnable via backpropagation thanks to an interpolation technique. We call this method “Dilated Convolution with Learnable Spacings” (DCLS) and generalize it to the n-dimensional convolution case. However, our main focus here will be on the 2D case. We first tried our approach on ResNet50: we drop-in replaced the standard convolutions with DCLS ones, which increased the accuracy of ImageNet1k classification at iso-parameters, but at the expense of the throughput. Next, we used the recent ConvNeXt state-of-the-art convolutional architecture and drop-in replaced the depthwise convolutions with DCLS ones. This not only increased the accuracy of ImageNet1k classification but also of typical downstream and robustness tasks, again at iso-parameters but this time with negligible cost on throughput, as ConvNeXt uses separable convolutions. Conversely, classic DC led to poor performance with both ResNet50 and ConvNeXt. The code of the method is based on PyTorch and available at: https://github.com/K-H-Ismail/Dilated-Convolution-with-Learnable-Spacings-PyTorch.

DySR: Adaptive Super-Resolution via Algorithm and System Co-design

Syed Zawad, Cheng Li, Zhewei Yao, Elton Zheng, Yuxiong He, Feng Yan

Super resolution (SR) is a promising approach for improving the quality of low resolution steaming services on mobile devices. On mobile devices, the available computing and memory resources change dynamically depending on other running applications. Due to the high computation and memory demands of SR models, it is essential to adapt the model according to available resources to harvest the best possible model performance while maintaining quality of service (QoS), such as meeting a minimum framerate and avoiding interruptions. Nevertheless, there is no SR model or machine learning system that supports adaptive SR, and enabling adaptive SR model on mobile devices is challenging because adapting model can cause significant framerate drop or even service interruption. To address this challenge, we take an algorithm and system co-design approach and propose DySR that maintains QoS while maximizing the model performance. During the training stage, DySR employs an adaption-aware one-shot Neural Architecture Search to produce sub-graphs that share kernel operation weights for low model adaption overhead while striking a balance between performance and framerate. During the inference stage, an incremental model adaption method is developed for further reducing the model adaption overhead. We evaluate on a diverse set of hardware and datasets to show that DySR can generate models close to the Pareto frontier while maintaining a steady framerate throughput with a memory footprint of around 40\% less compared to baseline methods.

DamoFD: Digging into Backbone Design on Face Detection

Yang Liu, Jiankang Deng, Fei Wang, Lei Shang, Xuansong Xie, Baigui Sun

Face detection (FD) has achieved remarkable success over the past few years, yet, these leaps often arrive when consuming enormous computation costs. Moreover, when considering a realistic situation, i.e., building a lightweight face detector under a computation-scarce scenario, such heavy computation cost limits the application of the face detector. To remedy this, several pioneering works design tiny face detectors through off-the-shelf neural architecture search (NAS) technologies, which are usually applied to the classification task. Thus, the searched architectures are sub-optimal for the face detection task since some design criteria between detection and classification task are different. As a representative, the face detection backbone design needs to guarantee the stage-level detection ability while it is not required for the classification backbone. Furthermore, the detection backbone consumes a vast body of inference budgets in the whole detection framework. Considering the intrinsic design requirement and the virtual importance role of the face detection backbone, we thus ask a critical question: How to employ NAS to search FD-friendly backbone architecture? To cope with this question, we propose a distribution-dependent stage-aware ranking score (DDSAR-Score) to explicitly characterize the stage-level expressivity and identify the individual importance of each stage, thus satisfying the aforementioned design criterion of the FD backbone. Based on our proposed DDSAR-Score, we conduct comprehensive experiments on the challenging Wider Face benchmark dataset and achieve dominant performance across a wide range of compute regimes. In particular, compared to the tiniest face detector SCRFD-0.5GF, our method is +2.5 % better in Average Precision (AP) score when using the same amount of FLOPs. The code is avaliable at https://github.com/ly19965/FaceMaas/tree/master/face_project/face_detection/DamoFD.

CktGNN: Circuit Graph Neural Network for Electronic Design Automation

Zehao Dong, Weidong Cao, Muhan Zhang, Dacheng Tao, Yixin Chen, Xuan Zhang

The electronic design automation of analog circuits has been a longstanding challenge in the integrated circuit field due to the huge design space and complex design trade-offs among circuit specifications. In the past decades, intensive research efforts have only been paid to automate the transistor sizing with a given circuit topology. By recognizing the graph nature of circuits, this paper presents a Circuit Graph Neural Network (CktGNN) that simultaneously automates the circuit topology generation and device sizing based on the encoder-dependent optimization subroutines. Particularly, CktGNN encodes circuit graphs using a two-level GNN framework (of nested GNN) where circuits are represented as combinations of subgraphs in a known subgraph basis. In this way, it significantly improves efficiency by reducing the number of subgraphs to perform message passing. Nonetheless, another critical roadblock to advancing learning-assisted circuit design automation is a lack of public benchmarks to perform canonical assessment and reproducible research. To tackle the challenge, we introduce Open Circuit Benchmark (OCB), an open-sourced dataset that contains $10$K distinct operational amplifiers with carefully-extracted circuit specifications from physical implementations. OCB also equips with communicative circuit generation and evaluation capabilities such that it can be used to generalize the applicability of CktGNN to design various analog circuits by efficiently producing corresponding datasets. Experiments on OCB show the extraordinary advantages of CktGNN through representation-based optimization frameworks over other recent powerful GNN baselines and manual design from human experts. Our work paves the way toward a learning-based open-sourced design automation flow for analog circuits.

Conditional Antibody Design as 3D Equivariant Graph Translation

Xiangzhe Kong, Wenbing Huang, Yang Liu

Antibody design is valuable for therapeutic usage and biological research. Existing deep-learning-based methods encounter several key issues: 1) incomplete context for Complementarity-Determining Regions (CDRs) generation; 2) incapability of capturing the entire 3D geometry of the input structure; 3) inefficient prediction of the CDR sequences in an autoregressive manner. In this paper, we propose Multi-channel Equivariant Attention Network (MEAN) to co-design 1D sequences and 3D structures of CDRs. To be specific, MEAN formulates antibody design as a conditional graph translation problem by importing extra components including the target antigen and the light chain of the antibody. Then, MEAN resorts to E(3)-equivariant message passing along with a proposed attention mechanism to better capture the geometrical correlation between different components. Finally, it outputs both the 1D sequences and 3D structure via a multi-round progressive full-shot scheme, which enjoys more efficiency and precision against previous autoregressive approaches. Our method significantly surpasses state-of-the-art models in sequence and structure modeling, antigen-binding CDR design, and binding affinity optimization. Specifically, the relative improvement to baselines is about 23\% in antigen-binding CDR design and 34\% for affinity optimization.

Disentangling the Mechanisms Behind Implicit Regularization in SGD

Zachary Novack, Simran Kaur, Tanya Marwah, Saurabh Garg, Zachary Chase Lipton

A number of competing hypotheses have been proposed to explain why small-batch Stochastic Gradient Descent (SGD) leads to improved generalization over the full-batch regime, with recent work crediting the implicit regularization of various quantities throughout training. However, to date, empirical evidence assessing the explanatory power of these hypotheses is lacking. In this paper, we conduct an extensive empirical evaluation, focusing on the ability of various theorized mechanisms to close the small-to-large batch generalization gap. Additionally, we characterize how the quantities that SGD has been claimed to (implicitly) regularize change over the course of training. By using micro-batches, i.e. disjoint smaller subsets of each mini-batch, we empirically show that explicitly penalizing the gradient norm or the Fisher Information Matrix trace, averaged over micro-batches, in the large-batch regime recovers small-batch SGD generalization, whereas Jacobian-based regularizations fail to do so. This generalization performance is shown to often be correlated with how well the regularized model’s gradient norms resemble those of small-batch SGD. We additionally show that this behavior breaks down as the micro-batch size approaches the batch size. Finally, we note that in this line of inquiry, positive experimental findings on CIFAR10 are often reversed on other datasets like CIFAR100, highlighting the need to test hypotheses on a wider collection of datasets.

Mechanism Design · ICLR 2023 | paperlist.ai