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Applications · Computer Vision

Huafeng Qin, Xin Jin, Yun Jiang, Mounîm El-Yacoubi, Xinbo Gao

Data mixing augmentation has been widely applied to improve the generalization ability of deep neural networks. Recently, offline data mixing augmentation, e.g. handcrafted and saliency information-based mixup, has been gradually replaced by automatic mixing approaches. Through minimizing two sub-tasks, namely, mixed sample generation and mixup classification in an end-to-end way, AutoMix significantly improves accuracy on image classification tasks. However, as the optimization objective is consistent for the two sub-tasks, this approach is prone to generating consistent instead of diverse mixed samples, which results in overfitting for target task training. In this paper, we propose AdAutomixup, an adversarial automatic mixup augmentation approach that generates challenging samples to train a robust classifier for image classification, by alternatively optimizing the classifier and the mixup sample generator. AdAutomixup comprises two modules, a mixed example generator, and a target classifier. The mixed sample generator aims to produce hard mixed examples to challenge the target classifier, while the target classifier's aim is to learn robust features from hard mixed examples to improve generalization. To prevent the collapse of the inherent meanings of images, we further introduce an exponential moving average (EMA) teacher and cosine similarity to train AdAutomixup in an end-to-end way. Extensive experiments on seven image benchmarks consistently prove that our approach outperforms the state of the art in various classification scenarios. The source code is available at https://github.com/JinXins/Adversarial-AutoMixup.

Optimization · Bilevel optimization

Bo Zhou, Ruiwei Jiang, Siqian Shen

Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision variables have received much less attention, largely due to the ensuing computational intractability and the incapability of gradient-based algorithms for handling discrete optimization formulations. In this paper, we develop deep learning techniques to address this challenge. Specifically, we consider a BP with binary tender, wherein the upper and lower levels are linked via binary variables. We train a neural network to approximate the optimal value of the lower-level problem, as a function of the binary tender. Then, we obtain a single-level reformulation of the BP through a mixed-integer representation of the value function. Furthermore, we conduct a comparative analysis between two types of neural networks: general neural networks and the novel input supermodular neural networks, studying their representational capacities. To solve high-dimensional BPs, we introduce an enhanced sampling method to generate higher-quality samples and implement an iterative process to refine solutions. We demonstrate the performance of these approaches through extensive numerical experiments, whose lower-level problems are linear and mixed-integer programs, respectively.

Theory · Optimization

Libin Zhu, Chaoyue Liu, Adityanarayanan Radhakrishnan, Misha Belkin

While neural networks can be approximated by linear models as their width increases, certain properties of wide neural networks cannot be captured by linear models. In this work we show that recently proposed Neural Quadratic Models can exhibit the "catapult phase" Lewkowycz et al. (2020) that arises when training such models with large learning rates. We then empirically show that the behaviour of quadratic models parallels that of neural networks in generalization, especially in the catapult phase regime. Our analysis further demonstrates that quadratic models are an effective tool for analysis of neural networks.

Applications · Robotics

Kaustubh Sridhar, Souradeep Dutta, Dinesh Jayaraman, James Weimer, Insup Lee

Imitation learning considerably simplifies policy synthesis compared to alternative approaches by exploiting access to expert demonstrations. For such imitation policies, errors away from the training samples are particularly critical. Even rare slip-ups in the policy action outputs can compound quickly over time, since they lead to unfamiliar future states where the policy is still more likely to err, eventually causing task failures. We revisit simple supervised "behavior cloning" for conveniently training the policy from nothing more than pre-recorded demonstrations, but carefully design the model class to counter the compounding error phenomenon. Our "memory-consistent neural network" (MCNN) outputs are hard-constrained to stay within clearly specified permissible regions anchored to prototypical "memory" training samples. We provide a guaranteed upper bound for the sub-optimality gap induced by MCNN policies. Using MCNNs on 10 imitation learning tasks, with MLP, Transformer, and Diffusion backbones, spanning dexterous robotic manipulation and driving, proprioceptive inputs and visual inputs, and varying sizes and types of demonstration data, we find large and consistent gains in performance, validating that MCNNs are better-suited than vanilla deep neural networks for imitation learning applications. Website: https://sites.google.com/view/mcnn-imitation

Applications · Neuroscience, Cognitive Science

Nanda H Krishna, Colin Bredenberg, Daniel Levenstein, Blake A Richards, Guillaume Lajoie

During periods of quiescence, such as sleep, neural activity in many brain circuits resembles that observed during periods of task engagement. However, the precise conditions under which task-optimized networks can autonomously reactivate the same network states responsible for online behavior is poorly understood. In this study, we develop a mathematical framework that outlines sufficient conditions for the emergence of neural reactivation in circuits that encode features of smoothly varying stimuli. We demonstrate mathematically that noisy recurrent networks optimized to track environmental state variables using change-based sensory information naturally develop denoising dynamics, which, in the absence of input, cause the network to revisit state configurations observed during periods of online activity. We validate our findings using numerical experiments on two canonical neuroscience tasks: spatial position estimation based on self-motion cues, and head direction estimation based on angular velocity cues. Overall, our work provides theoretical support for modeling offline reactivation as an emergent consequence of task optimization in noisy neural circuits.

Deep Learning · Other Representation Learning

Vladimir Kostic, Pietro Novelli, Riccardo Grazzi, Karim Lounici, massimiliano pontil

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

Optimization · Optimization and Learning under Uncertainty

Justin Dumouchelle, Esther Julien, Jannis Kurtz, Elias Khalil

Robust optimization provides a mathematical framework for modeling and solving decision-making problems under worst-case uncertainty. This work addresses two-stage robust optimization (2RO) problems (also called *adjustable robust optimization*), wherein first-stage and second-stage decisions are made before and after uncertainty is realized, respectively. This results in a nested min-max-min optimization problem which is extremely challenging computationally, especially when the decisions are discrete. We propose Neur2RO, an efficient machine learning-driven instantiation of column-and-constraint generation (CCG), a classical iterative algorithm for 2RO. Specifically, we learn to estimate the value function of the second-stage problem via a novel neural network architecture that is easy to optimize over by design. Embedding our neural network into CCG yields high-quality solutions quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital budgeting. For knapsack, Neur2RO finds solutions that are within roughly $2$% of the best-known values in a few seconds compared to the three hours of the state-of-the-art exact branch-and-price algorithm; for larger and more complex instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO outperforms three variants of the $k$-adaptability algorithm, particularly on the largest instances, with a $10$ to $100$-fold reduction in solution time. Our code and data are available at https://github.com/khalil-research/Neur2RO.

Probabilistic Methods · Variational Inference

Junbo Li, Zichen Miao, Qiang Qiu, Ruqi Zhang

Bayesian neural networks (BNNs) offer uncertainty quantification but come with the downside of substantially increased training and inference costs. Sparse BNNs have been investigated for efficient inference, typically by either slowly introducing sparsity throughout the training or by post-training compression of dense BNNs. The dilemma of how to cut down massive training costs remains, particularly given the requirement to learn about the uncertainty. To solve this challenge, we introduce Sparse Subspace Variational Inference (SSVI), the first fully sparse BNN framework that maintains a consistently sparse Bayesian model throughout the training and inference phases. Starting from a randomly initialized low-dimensional sparse subspace, our approach alternately optimizes the sparse subspace basis selection and its associated parameters. While basis selection is characterized as a non-differentiable problem, we approximate the optimal solution with a removal-and-addition strategy, guided by novel criteria based on weight distribution statistics. Our extensive experiments show that SSVI sets new benchmarks in crafting sparse BNNs, achieving, for instance, a 10-20× compression in model size with under 3\% performance drop, and up to 20× FLOPs reduction during training. Remarkably, SSVI also demonstrates enhanced robustness to hyperparameters, reducing the need for intricate tuning in VI and occasionally even surpassing VI-trained dense BNNs.

Deep Learning · Theory

Yuto Nishimura, Taiji Suzuki

Recent deep learning applications, exemplified by text-to-image tasks, often involve high-dimensional inputs and outputs. While several studies have investigated the function estimation capabilities of deep learning, research on dilated convolutional neural networks (CNNs) has mainly focused on cases where input dimensions are infinite but output dimensions are one-dimensional, similar to many other studies. However, many practical deep learning tasks involve high-dimensional (or even infinite dimensional) inputs and outputs.In this paper, we investigate the optimality of dilated CNNs for estimating a map between infinite-dimensional input and output spaces by analyzing their approximation and estimation abilities. For that purpose, we first show that approximation and estimation errors depend only on the smoothness and decay rate with respect to the infinity norm of the output, and their estimation accuracy actually achieve the {\it minimax optimal} rate of convergence.Second, we demonstrate that the dilated CNNs outperform {\it any} linear estimators including kernel ridge regression and $k$-NN estimators in a minimax error sense, highlighting the usefulness of feature learning realized by deep neural networks.Our theoretical analysis particularly explains the success of deep learning in recent high-dimensional input-output tasks.

Social Aspects · Accountability, Transparency and Interpretability

Xiaoqi Wang, Han Wei Shen

While Graph Neural Networks (GNNs) have achieved remarkable performance on various machine learning tasks on graph data, they also raised questions regarding their transparency and interpretability. Recently, there have been extensive research efforts to explain the decision-making process of GNNs. These efforts often focus on explaining why a certain prediction is made for a particular instance, or what discriminative features the GNNs try to detect for each class. However, to the best of our knowledge, there is no existing study on understanding the decision boundaries of GNNs, even though the decision-making process of GNNs is directly determined by the decision boundaries. To bridge this research gap, we propose a model-level explainability method called GNNBoundary, which attempts to gain deeper insights into the decision boundaries of graph classifiers. Specifically, we first develop an algorithm to identify the pairs of classes whose decision regions are adjacent. For an adjacent class pair, the near-boundary graphs between them are effectively generated by optimizing a novel objective function specifically designed for boundary graph generation. Thus, by analyzing the nearboundary graphs, the important characteristics of decision boundaries can be uncovered. To evaluate the efficacy of GNNBoundary, we conduct experiments on both synthetic and public real-world datasets. The results demonstrate that, via the analysis of faithful near-boundary graphs generated by GNNBoundary, we can thoroughly assess the robustness and generalizability of the explained GNNs. The official implementation can be found at https://github.com/yolandalalala/GNNBoundary.

Deep Learning · Algorithms

Satoki Ishikawa, Ryo Karakida

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 parametrization, 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 parametrization achieves higher generalization performance in feature learning.In particular, it enables us to transfer the hyperparameters across models with different widths.

Optimization · Everything Else

Shangmin Guo, YI REN, Stefano Albrecht, Kenny Smith

Although much research has been done on proposing new models or loss functions to improve the generalisation of artificial neural networks (ANNs), less attention has been directed to the impact of the training data on generalisation. In this work, we start from approximating the interaction between samples, i.e. how learning one sample would modify the model's prediction on other samples. Through analysing the terms involved in weight updates in supervised learning, we find that labels influence the interaction between samples. Therefore, we propose the labelled pseudo Neural Tangent Kernel (lpNTK) which takes label information into consideration when measuring the interactions between samples. We first prove that lpNTK asymptotically converges to the empirical neural tangent kernel in terms of the Frobenius norm under certain assumptions. Secondly, we illustrate how lpNTK helps to understand learning phenomena identified in previous work, specifically the learning difficulty of samples and forgetting events during learning. Moreover, we also show that using lpNTK to identify and remove poisoning training samples does not hurt the generalisation performance of ANNs.

Applications

Zitao Song, Wendi Ren, Shuang Li

Excitatory point processes (i.e., event flows) occurring over dynamic graphs (i.e., evolving topologies) provide a fine-grained model to capture how discrete events may spread over time and space. How to effectively steer the event flows by modifying the dynamic graph structures presents an interesting problem, motivated by curbing the spread of infectious diseases through strategically locking down cities to mitigating traffic congestion via traffic light optimization. To address the intricacies of planning and overcome the high dimensionality inherent to such decision-making problems, we design an Amortized Network Interventions (ANI) framework, allowing for the pooling of optimal policies from history and other contexts while ensuring a permutation equivalent property. This property enables efficient knowledge transfer and sharing across diverse contexts. Each task is solved by an H-step lookahead model-based reinforcement learning, where neural ODEs are introduced to model the dynamics of the excitatory point processes. Instead of simulating rollouts from the dynamics model, we derive an analytical mean-field approximation for the event flows given the dynamics, making the online planning more efficiently solvable. We empirically illustrate that this ANI approach substantially enhances policy learning for unseen dynamics and exhibits promising outcomes in steering event flows through network intervention using synthetic and real COVID datasets.

Miscellaneous Aspects of Machine Learning · Representation Learning

Ilmin Kang, HyounYoung Bae, Kangil Kim

Most neural networks for classification primarily learn features differentiated by input-domain related information such as visual similarity of objects in an image. While this focus is natural behavior, it can inadvertently introduce an inductive bias that conflicts with unseen relations in an implicit output-domain determined by human labeling based on their own world knowledge. Such conflicts can limit generalization of models by potential dominance of the input-domain focused bias in inference.To overcome this limitation without external resources, we introduce Output-Domain focused Biasing (ODB) training strategy that constructs inductive biases on features differentiated by only output labels. It has four steps: 1) it learns intermediate latent object features in an unsupervised manner; 2) it decouples their visual dependencies by assigning new independent embedding parameters; 3) it captures structured features optimized for the original classification task; and 4) it integrates the structured features with the original visual features for the final prediction.We implement the ODB on a vision transformer architecture, and achieved significant improvements on image classification benchmarks. This paper offers a straightforward and effective method to obtain and utilize output-domain focused inductive bias for classification mapping two different domains.

Optimization · Learning for Optimization

Yufei Kuang, Jie Wang, Haoyang Liu, Fangzhou Zhu, Xijun Li, Jia Zeng, Jianye HAO, Bin Li, Feng Wu

Machine learning (ML) has been shown to successfully accelerate solving NP-hard combinatorial optimization (CO) problems under the branch and bound framework. However, the high training and inference cost and limited interpretability of ML approaches severely limit their wide application to modern exact CO solvers. In contrast, human-designed policies---though widely integrated in modern CO solvers due to their compactness and reliability---can not capture data-driven patterns for higher performance. To combine the advantages of the two paradigms, we propose the first symbolic discovery framework---namely, deep symbolic discovery for exact combinatorial optimization solver (Symb4CO)---to learn high-performance symbolic policies on the branching task. Specifically, we show the potential existence of small symbolic policies empirically, employ a large neural network to search in the high-dimensional discrete space, and compile the learned symbolic policies directly for fast deployment. Experiments show that the Symb4CO learned purely CPU-based policies consistently achieve *comparable* performance to previous GPU-based state-of-the-art approaches. Furthermore, the appealing features of Symb4CO include its high training (*ten training instances*) and inference (*one CPU core*) efficiency and good interpretability (*one-line expressions*), making it simple and reliable for deployment. The results show encouraging potential for the *wide* deployment of ML to modern CO solvers.

Probabilistic Methods · Monte Carlo and Sampling Methods

Kejun Tang, Jiayu Zhai, Xiaoliang Wan, Chao Yang

Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its flexible meshless discretization and its potential for high-dimensional problems. One fundamental numerical difficulty is that random samples in the training set introduce statistical errors into the discretization of the loss functional which may become the dominant error in the final approximation, and therefore overshadow the modeling capability of the neural network. In this work, we propose a new minmax formulation to optimize simultaneously the approximate solution, given by a neural network model, and the random samples in the training set, provided by a deep generative model. The key idea is to use a deep generative model to adjust the random samples in the training set such that the residual induced by the neural network model can maintain a smooth profile in the training process. Such an idea is achieved by implicitly embedding the Wasserstein distance between the residual-induced distribution and the uniform distribution into the loss, which is then minimized together with the residual. A nearly uniform residual profile means that its variance is small for any normalized weight function such that the Monte Carlo approximation error of the loss functional is reduced significantly for a certain sample size. The adversarial adaptive sampling (AAS) approach proposed in this work is the first attempt to formulate two essential components, minimizing the residual and seeking the optimal training set, into one minmax objective functional for the neural network approximation of PDEs.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Chengming Hu, Haolun Wu, Xuan Li, Chen Ma, Xi Chen, Boyu Wang, Jun Yan, Xue Liu

Knowledge distillation aims to train a compact student network using soft supervision from a larger teacher network and hard supervision from ground truths. However, determining an optimal knowledge fusion ratio that balances these supervisory signals remains challenging. Prior methods generally resort to a constant or heuristic-based fusion ratio, which often falls short of a proper balance. In this study, we introduce a novel adaptive method for learning a sample-wise knowledge fusion ratio, exploiting both the correctness of teacher and student, as well as how well the student mimics the teacher on each sample. Our method naturally leads to the \textit{intra-sample} trilateral geometric relations among the student prediction ($\mathcal{S}$), teacher prediction ($\mathcal{T}$), and ground truth ($\mathcal{G}$). To counterbalance the impact of outliers, we further extend to the \textit{inter-sample} relations, incorporating the teacher's global average prediction ($\mathcal{\bar{T}})$ for samples within the same class. A simple neural network then learns the implicit mapping from the intra- and inter-sample relations to an adaptive, sample-wise knowledge fusion ratio in a bilevel-optimization manner. Our approach provides a simple, practical, and adaptable solution for knowledge distillation that can be employed across various architectures and model sizes. Extensive experiments demonstrate consistent improvements over other loss re-weighting methods on image classification, attack detection, and click-through rate prediction.

Optimization

Antoine Bambade, Fabian Schramm, Adrien Taylor, Justin Carpentier

Optimization layers within neural network architectures have become increasingly popular for their ability to solve a wide range of machine learning tasks and to model domain-specific knowledge. However, designing optimization layers requires careful consideration as the underlying optimization problems might be infeasible during training. Motivated by applications in learning, control and robotics, this work focuses on convex quadratic programming (QP) layers. The specific structure of this type of optimization layer can be efficiently exploited for faster computations while still allowing rich modeling capabilities. We leverage primal-dual augmented Lagrangian techniques for computing derivatives of both feasible and infeasible QP solutions. More precisely, we propose a unified approach which tackles the differentiability of the closest feasible QP solutions in a classical $\ell_2$ sense. We then harness this approach to enrich the expressive capabilities of existing QP layers. More precisely, we show how differentiating through infeasible QPs during training enables to drive towards feasibility at test time a new range of QP layers. These layers notably demonstrate superior predictive performance in some conventional learning tasks. Additionally, we present alternative formulations that enhance numerical robustness, speed, and accuracy for training such layers. Along with these contributions, we provide an open-source C++ software package called QPLayer for differentiating feasible and infeasible convex QPs and which can be interfaced with modern learning frameworks.

Applications · Computer Vision

Jisu Nam, Gyuseong Lee, Seonwoo Kim, Inès Hyeonsu Kim, Hyoungwon Cho, Seyeon Kim, Seungryong Kim

The objective for establishing dense correspondence between paired images con- sists of two terms: a data term and a prior term. While conventional techniques focused on defining hand-designed prior terms, which are difficult to formulate, re- cent approaches have focused on learning the data term with deep neural networks without explicitly modeling the prior, assuming that the model itself has the capacity to learn an optimal prior from a large-scale dataset. The performance improvement was obvious, however, they often fail to address inherent ambiguities of matching, such as textureless regions, repetitive patterns, large displacements, or noises. To address this, we propose DiffMatch, a novel conditional diffusion-based framework designed to explicitly model both the data and prior terms for dense matching. This is accomplished by leveraging a conditional denoising diffusion model that explic- itly takes matching cost and injects the prior within generative process. However, limited input resolution of the diffusion model is a major hindrance. We address this with a cascaded pipeline, starting with a low-resolution model, followed by a super-resolution model that successively upsamples and incorporates finer details to the matching field. Our experimental results demonstrate significant performance improvements of our method over existing approaches, and the ablation studies validate our design choices along with the effectiveness of each component. Code and pretrained weights are available at https://ku-cvlab.github.io/DiffMatch.

Probabilistic Methods

Gianluca Bencomo, Jake Snell, Thomas L. Griffiths

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires matrix storage, inversion, and multiplication or Monte Carlo estimation, none of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we consider the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.