论文检索

Deep Learning/Theory

Taiji Suzuki, Denny Wu, Kazusato Oko, Atsushi Nitanda

Neural network in the mean-field regime is known to be capable of \textit{feature learning}, unlike the kernel (NTK) counterpart. Recent works have shown that mean-field neural networks can be globally optimized by a noisy gradient descent update termed the \textit{mean-field Langevin dynamics} (MFLD). However, all existing guarantees for MFLD only considered the \textit{optimization} efficiency, and it is unclear if this algorithm leads to improved \textit{generalization} performance and sample complexity due to the presence of feature learning. To fill this gap, in this work we study the statistical and computational complexity of MFLD in learning a class of binary classification problems. Unlike existing margin bounds for neural networks, we avoid the typical norm control by utilizing the perspective that MFLD optimizes the \textit{distribution} of parameters rather than the parameter itself; this leads to an improved analysis of the sample complexity and convergence rate. We apply our general framework to the learning of $k$-sparse parity functions, where we prove that unlike kernel methods, two-layer neural networks optimized by MFLD achieves a sample complexity where the degree $k$ is ``decoupled'' from the exponent in the dimension dependence.

Deep Learning/Graph Neural Networks

Ningyi Liao, Siqiang Luo, Xiang Li, Jieming Shi

Heterophilous Graph Neural Network (GNN) is a family of GNNs that specializes in learning graphs under heterophily, where connected nodes tend to have different labels. Most existing heterophilous models incorporate iterative non-local computations to capture node relationships. However, these approaches have limited application to large-scale graphs due to their high computational costs and challenges in adopting minibatch schemes. In this work, we study the scalability issues of heterophilous GNN and propose a scalable model, LD2, which simplifies the learning process by decoupling graph propagation and generating expressive embeddings prior to training. Theoretical analysis demonstrates that LD2 achieves optimal time complexity in training, as well as a memory footprint that remains independent of the graph scale. We conduct extensive experiments to showcase that our model is capable of lightweight minibatch training on large-scale heterophilous graphs, with up to $15\times$ speed improvement and efficient memory utilization, while maintaining comparable or better performance than the baselines.

Probabilistic Methods/Monte Carlo and Sampling Methods

Mohammad Reza Karimi Jaghargh, Ya-Ping Hsieh, Andreas Krause

Interacting particle systems have proven highly successful in various machinelearning tasks, including approximate Bayesian inference and neural network optimization. However, the analysis of thesesystems often relies on the simplifying assumption of the \emph{mean-field} limit, where particlenumbers approach infinity and infinitesimal step sizes are used. In practice, discrete time steps,finite particle numbers, and complex integration schemes are employed, creating a theoretical gapbetween continuous-time and discrete-time processes. In this paper, we present a novel frameworkthat establishes a precise connection between these discrete-time schemes and their correspondingmean-field limits in terms of convergence properties and asymptotic behavior. By adopting a dynamical system perspective, our framework seamlessly integrates various numerical schemes that are typically analyzed independently. For example, our framework provides a unified treatment of optimizing an infinite-width two-layer neural network and sampling via Stein Variational Gradient descent, which were previously studied in isolation.

Deep Learning/Recurrent Networks

Niranjan Damera Venkata, Chiranjib Bhattacharyya

Deep neural networks (DNNs) have recently emerged as a powerful paradigm for solving Markovian optimal stopping problems. However, a ready extension of DNN-based methods to non-Markovian settings requires significant state and parameter space expansion, manifesting the curse of dimensionality. Further, efficient state-space transformations permitting Markovian approximations, such as those afforded by recurrent neural networks (RNNs), are either structurally infeasible or are confounded by the curse of non-Markovianity. Considering these issues, we introduce, for the first time, an optimal stopping policy gradient algorithm (OSPG) that can leverage RNNs effectively in non-Markovian settings by implicitly optimizing value functions without recursion, mitigating the curse of non-Markovianity. The OSPG algorithm is derived from an inference procedure on a novel Bayesian network representation of discrete-time non-Markovian optimal stopping trajectories and, as a consequence, yields an offline policy gradient algorithm that eliminates expensive Monte Carlo policy rollouts.

Social Aspects/Trustworthy Machine Learning

Yuhao Mao, Mark Müller, Marc Fischer, Martin Vechev

Training certifiably robust neural networks remains a notoriously hard problem.While adversarial training optimizes under-approximations of the worst-case loss, which leads to insufficient regularization for certification, sound certified training methods, optimize loose over-approximations, leading to over-regularization and poor (standard) accuracy.In this work, we propose TAPS, an (unsound) certified training method that combines IBP and PGD training to optimize more precise, although not necessarily sound, worst-case loss approximations, reducing over-regularization and increasing certified and standard accuracies.Empirically, TAPS achieves a new state-of-the-art in many settings, e.g., reaching a certified accuracy of $22$% on TinyImageNet for $\ell_\infty$-perturbations with radius $\epsilon=1/255$. We make our implementation and networks public at https://github.com/eth-sri/taps.

Matthew Wicker, Vihari Piratla, Adrian Weller

Providing formal guarantees of algorithmic fairness is of paramount importance to socially responsible deployment of machine learning algorithms. In this work, we study formal guarantees, i.e., certificates, for individual fairness (IF) of neural networks. We start by introducing a novel convex approximation of IF constraints that exponentially decreases the computational cost of providing formal guarantees of local individual fairness. We highlight that prior methods are constrained by their focus on global IF certification and can therefore only scale to models with a few dozen hidden neurons, thus limiting their practical impact. We propose to certify \textit{distributional} individual fairness which ensures that for a given empirical distribution and all distributions within a $\gamma$-Wasserstein ball, the neural network has guaranteed individually fair predictions. Leveraging developments in quasi-convex optimization, we provide novel and efficient certified bounds on distributional individual fairness and show that our method allows us to certify and regularize neural networks that are several orders of magnitude larger than those considered by prior works. Moreover, we study real-world distribution shifts and find our bounds to be a scalable, practical, and sound source of IF guarantees.

Social Aspects/Accountability, Transparency and Interpretability

Ziyuan Ye, Rihan Huang, Qilin Wu, Quanying Liu

Post-hoc explanation techniques on graph neural networks (GNNs) provide economical solutions for opening the black-box graph models without model retraining. Many GNN explanation variants have achieved state-of-the-art explaining results on a diverse set of benchmarks, while they rarely provide theoretical analysis for their inherent properties and explanatory capability. In this work, we propose $\underline{\text{S}}$tructure-$\underline{\text{A}}$ware Shapley-based $\underline{\text{M}}$ultipiece $\underline{\text{E}}$xplanation (SAME) method to address the structure-aware feature interactions challenges for GNNs explanation. Specifically, SAME leverages an expansion-based Monte Carlo tree search to explore the multi-grained structure-aware connected substructure. Afterward, the explanation results are encouraged to be informative of the graph properties by optimizing the combination of distinct single substructures. With the consideration of fair feature interactions in the process of investigating multiple connected important substructures, the explanation provided by SAME has the potential to be as explainable as the theoretically optimal explanation obtained by the Shapley value within polynomial time. Extensive experiments on real-world and synthetic benchmarks show that SAME improves the previous state-of-the-art fidelity performance by 12.9\% on BBBP, 7.01\% on MUTAG, 42.3\% on Graph-SST2, 38.9\% on Graph-SST5, 11.3\% on BA-2Motifs and 18.2\% on BA-Shapes under the same testing condition. Code is available at https://github.com/same2023neurips/same.

Optimization/Non-Convex

Thomas Pethick, Wanyun Xie, Volkan Cevher

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear interpolation can help by leveraging the theory of nonexpansive operators. We construct a new optimization scheme called relaxed approximate proximal point (RAPP), which is the first 1-SCLI method to achieve last iterate convergence rates for $\rho$-comonotone problems while only requiring $\rho > -\tfrac{1}{2L}$. The construction extends to constrained and regularized settings. By replacing the inner optimizer in RAPP we rediscover the family of Lookahead algorithms for which we establish convergence in cohypomonotone problems even when the base optimizer is taken to be gradient descent ascent. The range of cohypomonotone problems in which Lookahead converges is further expanded by exploiting that Lookahead inherits the properties of the base optimizer. We corroborate the results with experiments on generative adversarial networks which demonstrates the benefits of the linear interpolation present in both RAPP and Lookahead.

Applications/Neuroscience, Cognitive Science

Zihang Shao, Xuanye Fang, Yaxin Li, Chaoran Feng, Jiangrong Shen, Qi Xu

Spiking neural networks (SNNs) have undergone continuous development and extensive study for decades, leading to increased biological plausibility and optimal energy efficiency. However, traditional training methods for deep SNNs have some limitations, as they rely on strategies such as pre-training and fine-tuning, indirect coding and reconstruction, and approximate gradients. These strategies lack a complete training model and require gradient approximation. To overcome these limitations, we propose a novel learning method named Joint Excitatory Inhibitory Cycle Iteration learning for Deep Spiking Neural Networks (EICIL) that integrates both excitatory and inhibitory behaviors inspired by the signal transmission of biological neurons.By organically embedding these two behavior patterns into one framework, the proposed EICIL significantly improves the bio-mimicry and adaptability of spiking neuron models, as well as expands the representation space of spiking neurons. Extensive experiments based on EICIL and traditional learning methods demonstrate that EICIL outperforms traditional methods on various datasets, such as CIFAR10 and CIFAR100, revealing the crucial role of the learning approach that integrates both behaviors during training.

Theory/Learning Theory

Constantine Caramanis, Dimitris Fotakis, Alkis Kalavasis, Vasilis Kontonis, Christos Tzamos

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by gradient-based methods (e.g., policy gradient) to successively obtain better solution distributions.In this work we introduce a novel theoretical framework for analyzing the effectiveness of such methods. We ask whether there exist generative models that (i) are expressive enough to generate approximately optimal solutions; (ii) have a tractable, i.e, polynomial in the size of the input, number of parameters; (iii) their optimization landscape is benign in the sense that it does not contain sub-optimal stationary points. Our main contribution is a positive answer to this question. Our result holds for a broad class of combinatorial problems including Max- and Min-Cut, Max-$k$-CSP, Maximum-Weight-Bipartite-Matching, and the Traveling Salesman Problem. As a byproduct of our analysis we introduce a novel regularization process over vanilla gradient descent and provide theoretical and experimental evidence that it helps address vanishing-gradient issues and escape bad stationary points.

Miscellaneous Aspects of Machine Learning/Kernel methods

Patrik Robert Gerber, Tianze Jiang, Yury Polyanskiy, Rui Sun

Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with completeknowledge of class distributions ($n=\infty$) theproblem is solved optimally by the likelihood-ratio test; when$m=1$ it corresponds to binary classification; and when $m\approx n$ it is equivalent to two-sample testing. The intermediate settings occur in the field of likelihood-free inference, where labeled samples are obtained by running forward simulations and the unlabeled sample is collected experimentally. In recent work it was discovered that there is a fundamental trade-offbetween $m$ and $n$: increasing the data sample $m$ reduces the amount $n$ of training/simulationdata needed. In this work we (a) introduce a generalization where unlabeled samples come from a mixture of the two classes -- a case often encountered in practice; (b) study the minimax sample complexity for non-parametric classes of densities under \textit{maximum meandiscrepancy} (MMD) separation; and (c) investigate the empirical performance of kernels parameterized by neural networks on two tasks: detectionof the Higgs boson and detection of planted DDPM generated images amidstCIFAR-10 images. For both problems we confirm the existence of the theoretically predicted asymmetric $m$ vs $n$ trade-off.

Optimization/Discrete and Combinatorial Optimization

Darko Drakulic, Sofia Michel, Florian Mai, Arnaud Sors, Jean-Marc Andreoli

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure. Our code is available at: [link](https://github.com/naver/bq-nco).

Optimization/Learning for Optimization

Eeshaan Jain, Tushar Nandy, Gaurav Aggarwal, Ashish Tendulkar, Rishabh Iyer, Abir De

Existing subset selection methods for efficient learning predominantly employ discrete combinatorial and model-specific approaches, which lack generalizability--- for each new model, the algorithm has to be executed from the beginning. Therefore, for an unseen architecture, one cannot use the subset chosen for a different model. In this work, we propose $\texttt{SubSelNet}$, a non-adaptive subset selection framework, which tackles these problems. Here, we first introduce an attention-based neural gadget that leverages the graph structure of architectures and acts as a surrogate to trained deep neural networks for quick model prediction. Then, we use these predictions to build subset samplers. This naturally provides us two variants of $\texttt{SubSelNet}$. The first variant is transductive (called Transductive-$\texttt{SubSelNet}$), which computes the subset separately for each model by solving a small optimization problem. Such an optimization is still super fast, thanks to the replacement of explicit model training by the model approximator. The second variant is inductive (called Inductive-$\texttt{SubSelNet}$), which computes the subset using a trained subset selector, without any optimization. Our experiments show that our model outperforms several methods across several real datasets.

Optimization/Control and Optimization

Hongchao Zhang, Junlin Wu, Yevgeniy Vorobeychik, Andrew Clark

Control Barrier Functions (CBFs) are a popular approach for safe control of nonlinear systems. In CBF-based control, the desired safety properties of the system are mapped to nonnegativity of a CBF, and the control input is chosen to ensure that the CBF remains nonnegative for all time. Recently, machine learning methods that represent CBFs as neural networks (neural control barrier functions, or NCBFs) have shown great promise due to the universal representability of neural networks. However, verifying that a learned CBF guarantees safety remains a challenging research problem. This paper presents novel exact conditions and algorithms for verifying safety of feedforward NCBFs with ReLU activation functions. The key challenge in doing so is that, due to the piecewise linearity of the ReLU function, the NCBF will be nondifferentiable at certain points, thus invalidating traditional safety verification methods that assume a smooth barrier function. We resolve this issue by leveraging a generalization of Nagumo's theorem for proving invariance of sets with nonsmooth boundaries to derive necessary and sufficient conditions for safety. Based on this condition, we propose an algorithm for safety verification of NCBFs that first decomposes the NCBF into piecewise linear segments and then solves a nonlinear program to verify safety of each segment as well as the intersections of the linear segments. We mitigate the complexity by only considering the boundary of the safe region and by pruning the segments with Interval Bound Propagation (IBP) and linear relaxation. We evaluate our approach through numerical studies with comparison to state-of-the-art SMT-based methods. Our code is available at https://github.com/HongchaoZhang-HZ/exactverif-reluncbf-nips23.

Ravid Shwartz-Ziv, Micah Goldblum, Yucen Li, C. Bayan Bruss, Andrew Wilson

Real-world datasets are often highly class-imbalanced, which can adversely impact the performance of deep learning models. The majority of research on training neural networks under class imbalance has focused on specialized loss functions and sampling techniques. Notably, we demonstrate that simply tuning existing components of standard deep learning pipelines, such as the batch size, data augmentation, architecture size, pre-training, optimizer, and label smoothing, can achieve state-of-the-art performance without any specialized loss functions or samplers. We also provide key prescriptions and considerations for training under class imbalance, and an understanding of why imbalance methods succeed or fail.

Applications/Chemistry and Drug Discovery

Filip Ekström Kelvinius, Dimitar Georgiev, Artur Toshev, Johannes Gasteiger

Recent advances in graph neural networks (GNNs) have enabled more comprehensive modeling of molecules and molecular systems, thereby enhancing the precision of molecular property prediction and molecular simulations. Nonetheless, as the field has been progressing to bigger and more complex architectures, state-of-the-art GNNs have become largely prohibitive for many large-scale applications. In this paper, we explore the utility of knowledge distillation (KD) for accelerating molecular GNNs. To this end, we devise KD strategies that facilitate the distillation of hidden representations in directional and equivariant GNNs, and evaluate their performance on the regression task of energy and force prediction. We validate our protocols across different teacher-student configurations and datasets, and demonstrate that they can consistently boost the predictive accuracy of student models without any modifications to their architecture. Moreover, we conduct comprehensive optimization of various components of our framework, and investigate the potential of data augmentation to further enhance performance. All in all, we manage to close the gap in predictive accuracy between teacher and student models by as much as 96.7\% and 62.5\% for energy and force prediction respectively, while fully preserving the inference throughput of the more lightweight models.

Applications/Computer Vision

Huizong Yang, Yuxin Sun, Ganesh Sundaramoorthi, Anthony Yezzi

We present new insights and a novel paradigm for learning implicit neural representations (INR) of shapes. In particular, we shed light on the popular eikonal loss used for imposing a signed distance function constraint in INR. We show analytically that as the representation power of the network increases, the optimization approaches a partial differential equation (PDE) in the continuum limit that is unstable. We show that this instability can manifest in existing network optimization, leading to irregularities in the reconstructed surface and/or convergence to sub-optimal local minima, and thus fails to capture fine geometric and topological structure. We show analytically how other terms added to the loss, currently used in the literature for other purposes, can actually eliminate these instabilities. However, such terms can over-regularize the surface, preventing the representation of fine shape detail. Based on a similar PDE theory for the continuum limit, we introduce a new regularization term that still counteracts the eikonal instability but without over-regularizing. Furthermore, since stability is now guaranteed in the continuum limit, this stabilization also allows for considering new network structures that are able to represent finer shape detail. We introduce such a structure based on quadratic layers. Experiments on multiple benchmark data sets show that our new regularization and network are able to capture more precise shape details and more accurate topology than existing state-of-the-art.

Deep Learning/Algorithms

Mohammad Mozaffari, Sikan Li, Zhao Zhang, Maryam Mehri Dehnavi

This work proposes a Momentum-Enabled Kronecker-Factor-Based Optimizer Using Rank-1 updates, called MKOR, that improves the training time and convergence properties of deep neural networks (DNNs). Second-order techniques, while enjoying higher convergence rates vs first-order counterparts, have cubic complexity with respect to either the model size and/or the training batch size. Hence they exhibit poor scalability and performance in transformer models, e.g. large language models (LLMs), because the batch sizes in these models scale by the attention mechanism sequence length, leading to large model size and batch sizes. MKOR's complexity is quadratic with respect to the model size, alleviating the computation bottlenecks in second-order methods. Because of their high computation complexity, state-of-the-art implementations of second-order methods can only afford to update the second order information infrequently, and thus do not fully exploit the promise of better convergence from these updates. By reducing the communication complexity of the second-order updates as well as achieving a linear communication complexity, MKOR increases the frequency of second order updates. We also propose a hybrid version of MKOR (called MKOR-H) that mid-training falls backs to a first order optimizer if the second order updates no longer accelerate convergence. Our experiments show that MKOR outperforms state -of-the-art first order methods, e.g. the LAMB optimizer, and best implementations of second-order methods, i.e. KAISA/KFAC, up to 2.57x and 1.85x respectively on BERT-Large-Uncased on 64 GPUs.

Social Aspects/Privacy-preserving Statistics and Machine Learning

Wenxuan Zeng, Meng Li, Haichuan Yang, Wen-jie Lu, Runsheng Wang, Ru Huang

Deep neural network (DNN) inference based on secure 2-party computation (2PC) can offer cryptographically-secure privacy protection but suffers from orders of magnitude latency overhead due to enormous communication. Previous works heavily rely on a proxy metric of ReLU counts to approximate the communication overhead and focus on reducing the ReLUs to improve the communication efficiency. However, we observe these works achieve limited communication reduction for state-of-the-art (SOTA) 2PC protocols due to the ignorance of other linear and non-linear operations, which now contribute to the majority of communication. In this work, we present CoPriv, a framework that jointly optimizes the 2PC inference protocol and the DNN architecture. CoPriv features a new 2PC protocol for convolution based on Winograd transformation and develops DNN-aware optimization to significantly reduce the inference communication. CoPriv further develops a 2PC-aware network optimization algorithm that is compatible with the proposed protocol and simultaneously reduces the communication for all the linear and non-linear operations. We compare CoPriv with the SOTA 2PC protocol, CrypTFlow2, and demonstrate 2.1× communication reduction for both ResNet-18 and ResNet-32 on CIFAR-100. We also compare CoPriv with SOTA network optimization methods, including SNL, MetaPruning, etc. CoPriv achieves 9.98× and 3.88× online and total communication reduction with a higher accuracy compare to SNL, respectively. CoPriv also achieves 3.87× online communication reduction with more than 3% higher accuracy compared to MetaPruning.

Deep Learning/Robustness

Mahyar Fazlyab, Taha Entesari, Aniket Roy, Rama Chellappa

To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the training process itself (e.g., min-max optimization, constrained learning, or regularization). These approaches, however, might not be effective at increasing the margin in the input (feature) space. In this paper, we propose a differentiable regularizer that is a lower bound on the distance of the data points to the classification boundary. The proposed regularizer requires knowledge of the model's Lipschitz constant along certain directions. To this end, we develop a scalable method for calculating guaranteed differentiable upper bounds on the Lipschitz constant of neural networks accurately and efficiently. The relative accuracy of the bounds prevents excessive regularization and allows for more direct manipulation of the decision boundary. Furthermore, our Lipschitz bounding algorithm exploits the monotonicity and Lipschitz continuity of the activation layers, and the resulting bounds can be used to design new layers with controllable bounds on their Lipschitz constant. Experiments on the MNIST, CIFAR-10, and Tiny-ImageNet data sets verify that our proposed algorithm obtains competitively improved results compared to the state-of-the-art.