arXiv subjects

Kenji Kawaguchi

Publications and source records attributed to Kenji Kawaguchi.

At least 127 records · Page 7Linked to original sources

arXiv2023

Discrete Key-Value Bottleneck

Deep neural networks perform well on classification tasks where data streams are i.i.d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has addressed this challenge involves pre-training of large encoders on volumes of readily available data, followed by task-specific tuning. Given a new task, however, updating the weights of these encoders is challenging as a large number of weights needs to be fine-tuned, and as a result, they forget information about the previous tasks. In the present work, we propose a model architecture to address this issue, building upon a discrete bottleneck containing pairs of separate and learnable key-value codes. Our paradigm will be to encode; process the representation via a discrete bottleneck; and decode. Here, the input is fed to the pre-trained encoder, the output of the encoder is used to select the nearest keys, and the corresponding values are fed to the decoder to solve the current task. The model can only fetch and re-use a sparse number of these key-value pairs during inference, enabling localized and context-dependent model updates. We theoretically investigate the ability of the discrete key-value bottleneck to minimize the effect of learning under distribution shifts and show that it reduces the complexity of the hypothesis class. We empirically verify the proposed method under challenging class-incremental learning scenarios and show that the proposed model - without any task boundaries - reduces catastrophic forgetting across a wide variety of pre-trained models, outperforming relevant baselines on this task.

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arXiv2023

Self-Distillation for Further Pre-training of Transformers

Pre-training a large transformer model on a massive amount of unlabeled data and fine-tuning it on labeled datasets for diverse downstream tasks has proven to be a successful strategy, for a variety of vision and natural language processing tasks. However, direct fine-tuning of the pre-trained model may be suboptimal if there exist large discrepancies across data domains for pre-training and fine-tuning. To tackle this issue, several previous studies have proposed further pre-training strategies, where we continue to pre-train the model on the target unlabeled dataset before fine-tuning. However, all of them solely focus on language models and we empirically find that a Vision Transformer is vulnerable to overfitting as we continue to pretrain the model on target unlabeled data. In order to tackle this limitation, we propose self-distillation as a regularization for a further pre-training stage. Specifically, we first further pre-train the initial pre-trained model on the target unlabeled data and then consider it as a teacher for self-distillation. Then we take the same initial pre-trained model as a student and enforce its hidden representations to be close to those of the teacher while optimizing the student with a masked auto-encoding objective. We empirically validate the efficacy of self-distillation on a variety of benchmark datasets for image and text classification tasks. Experimentally, we show that our proposed method outperforms all the relevant baselines. Theoretically, we analyze the proposed method with a simplified model to understand how self-distillation for further pre-training can potentially help improve the performance of the downstream tasks.

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arXiv2023

Scalable Set Encoding with Universal Mini-Batch Consistency and Unbiased Full Set Gradient Approximation

Recent work on mini-batch consistency (MBC) for set functions has brought attention to the need for sequentially processing and aggregating chunks of a partitioned set while guaranteeing the same output for all partitions. However, existing constraints on MBC architectures lead to models with limited expressive power. Additionally, prior work has not addressed how to deal with large sets during training when the full set gradient is required. To address these issues, we propose a Universally MBC (UMBC) class of set functions which can be used in conjunction with arbitrary non-MBC components while still satisfying MBC, enabling a wider range of function classes to be used in MBC settings. Furthermore, we propose an efficient MBC training algorithm which gives an unbiased approximation of the full set gradient and has a constant memory overhead for any set size for both train- and test-time. We conduct extensive experiments including image completion, text classification, unsupervised clustering, and cancer detection on high-resolution images to verify the efficiency and efficacy of our scalable set encoding framework. Our code is available at github.com/jeffwillette/umbc

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arXiv2023

Auxiliary Learning as an Asymmetric Bargaining Game

Auxiliary learning is an effective method for enhancing the generalization capabilities of trained models, particularly when dealing with small datasets. However, this approach may present several difficulties: (i) optimizing multiple objectives can be more challenging, and (ii) how to balance the auxiliary tasks to best assist the main task is unclear. In this work, we propose a novel approach, named AuxiNash, for balancing tasks in auxiliary learning by formalizing the problem as generalized bargaining game with asymmetric task bargaining power. Furthermore, we describe an efficient procedure for learning the bargaining power of tasks based on their contribution to the performance of the main task and derive theoretical guarantees for its convergence. Finally, we evaluate AuxiNash on multiple multi-task benchmarks and find that it consistently outperforms competing methods.

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arXiv2023

How Does Information Bottleneck Help Deep Learning?

Numerous deep learning algorithms have been inspired by and understood via the notion of information bottleneck, where unnecessary information is (often implicitly) minimized while task-relevant information is maximized. However, a rigorous argument for justifying why it is desirable to control information bottlenecks has been elusive. In this paper, we provide the first rigorous learning theory for justifying the benefit of information bottleneck in deep learning by mathematically relating information bottleneck to generalization errors. Our theory proves that controlling information bottleneck is one way to control generalization errors in deep learning, although it is not the only or necessary way. We investigate the merit of our new mathematical findings with experiments across a range of architectures and learning settings. In many cases, generalization errors are shown to correlate with the degree of information bottleneck: i.e., the amount of the unnecessary information at hidden layers. This paper provides a theoretical foundation for current and future methods through the lens of information bottleneck. Our new generalization bounds scale with the degree of information bottleneck, unlike the previous bounds that scale with the number of parameters, VC dimension, Rademacher complexity, stability or robustness. Our code is publicly available at: https://github.com/xu-ji/information-bottleneck

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arXiv2023

Combined Scaling for Zero-shot Transfer Learning

We present a combined scaling method - named BASIC - that achieves 85.7% top-1 accuracy on the ImageNet ILSVRC-2012 validation set without learning from any labeled ImageNet example. This accuracy surpasses best published similar models - CLIP and ALIGN - by 9.3%. Our BASIC model also shows significant improvements in robustness benchmarks. For instance, on 5 test sets with natural distribution shifts such as ImageNet-{A,R,V2,Sketch} and ObjectNet, our model achieves 84.3% top-1 average accuracy, only a small drop from its original ImageNet accuracy. To achieve these results, we scale up the contrastive learning framework of CLIP and ALIGN in three dimensions: data size, model size, and batch size. Our dataset has 6.6B noisy image-text pairs, which is 4x larger than ALIGN, and 16x larger than CLIP. Our largest model has 3B weights, which is 3.75x larger in parameters and 8x larger in FLOPs than ALIGN and CLIP. Finally, our batch size is 65536 which is 2x more than CLIP and 4x more than ALIGN. We encountered two main challenges with the scaling rules of BASIC. First, the main challenge with implementing the combined scaling rules of BASIC is the limited memory of accelerators, such as GPUs and TPUs. To overcome the memory limit, we propose two simple methods which make use of gradient checkpointing and model parallelism. Second, while increasing the dataset size and the model size has been the defacto method to improve the performance of deep learning models like BASIC, the effect of a large contrastive batch size on such contrastive-trained image-text models is not well-understood. To shed light on the benefits of large contrastive batch sizes, we develop a theoretical framework which shows that larger contrastive batch sizes lead to smaller generalization gaps for image-text models such as BASIC.

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arXiv2023

D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory

Kohn-Sham Density Functional Theory (KS-DFT) has been traditionally solved by the Self-Consistent Field (SCF) method. Behind the SCF loop is the physics intuition of solving a system of non-interactive single-electron wave functions under an effective potential. In this work, we propose a deep learning approach to KS-DFT. First, in contrast to the conventional SCF loop, we propose to directly minimize the total energy by reparameterizing the orthogonal constraint as a feed-forward computation. We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity from O(N^4) to O(N^3). Second, the numerical integration which involves a summation over the quadrature grids can be amortized to the optimization steps. At each step, stochastic gradient descent (SGD) is performed with a sampled minibatch of the grids. Extensive experiments are carried out to demonstrate the advantage of our approach in terms of efficiency and stability. In addition, we show that our approach enables us to explore more complex neural-based wave functions.

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arXiv2023

Clustering Aware Classification for Risk Prediction and Subtyping in Clinical Data

In data containing heterogeneous subpopulations, classification performance benefits from incorporating the knowledge of cluster structure in the classifier. Previous methods for such combined clustering and classification either 1) are classifier-specific and not generic, or 2) independently perform clustering and classifier training, which may not form clusters that can potentially benefit classifier performance. The question of how to perform clustering to improve the performance of classifiers trained on the clusters has received scant attention in previous literature, despite its importance in several real-world applications. In this paper, first, we theoretically analyze the generalization performance of classifiers trained on clustered data and find conditions under which clustering can potentially aid classification. This motivates the design of a simple k-means-based classification algorithm called Clustering Aware Classification (CAC) and its neural variant {DeepCAC}. DeepCAC effectively leverages deep representation learning to learn latent embeddings and finds clusters in a manner that make the clustered data suitable for training classifiers for each underlying subpopulation. Our experiments on synthetic and real benchmark datasets demonstrate the efficacy of DeepCAC over previous methods for combined clustering and classification.

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arXiv2022

Discrete Factorial Representations as an Abstraction for Goal Conditioned Reinforcement Learning

Goal-conditioned reinforcement learning (RL) is a promising direction for training agents that are capable of solving multiple tasks and reach a diverse set of objectives. How to \textit{specify} and \textit{ground} these goals in such a way that we can both reliably reach goals during training as well as generalize to new goals during evaluation remains an open area of research. Defining goals in the space of noisy and high-dimensional sensory inputs poses a challenge for training goal-conditioned agents, or even for generalization to novel goals. We propose to address this by learning factorial representations of goals and processing the resulting representation via a discretization bottleneck, for coarser goal specification, through an approach we call DGRL. We show that applying a discretizing bottleneck can improve performance in goal-conditioned RL setups, by experimentally evaluating this method on tasks ranging from maze environments to complex robotic navigation and manipulation. Additionally, we prove a theorem lower-bounding the expected return on out-of-distribution goals, while still allowing for specifying goals with expressive combinatorial structure.

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arXiv2022

Interpolation Consistency Training for Semi-Supervised Learning

We introduce Interpolation Consistency Training (ICT), a simple and computation efficient algorithm for training Deep Neural Networks in the semi-supervised learning paradigm. ICT encourages the prediction at an interpolation of unlabeled points to be consistent with the interpolation of the predictions at those points. In classification problems, ICT moves the decision boundary to low-density regions of the data distribution. Our experiments show that ICT achieves state-of-the-art performance when applied to standard neural network architectures on the CIFAR-10 and SVHN benchmark datasets. Our theoretical analysis shows that ICT corresponds to a certain type of data-adaptive regularization with unlabeled points which reduces overfitting to labeled points under high confidence values.

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arXiv2022

Interpolated Adversarial Training: Achieving Robust Neural Networks without Sacrificing Too Much Accuracy

Adversarial robustness has become a central goal in deep learning, both in the theory and the practice. However, successful methods to improve the adversarial robustness (such as adversarial training) greatly hurt generalization performance on the unperturbed data. This could have a major impact on how the adversarial robustness affects real world systems (i.e. many may opt to forego robustness if it can improve accuracy on the unperturbed data). We propose Interpolated Adversarial Training, which employs recently proposed interpolation based training methods in the framework of adversarial training. On CIFAR-10, adversarial training increases the standard test error (when there is no adversary) from 4.43% to 12.32%, whereas with our Interpolated adversarial training we retain the adversarial robustness while achieving a standard test error of only 6.45%. With our technique, the relative increase in the standard error for the robust model is reduced from 178.1% to just 45.5%. Moreover, we provide mathematical analysis of Interpolated Adversarial Training to confirm its efficiencies and demonstrate its advantages in terms of robustness and generalization.

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arXiv2022

When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability. Recently, Extended PINNs (XPINNs) based on domain decomposition methods have attracted considerable attention due to their effectiveness in modeling multiscale and multiphysics problems and their parallelization. However, theoretical understanding on their convergence and generalization properties remains unexplored. In this study, we take an initial step towards understanding how and when XPINNs outperform PINNs. Specifically, for general multi-layer PINNs and XPINNs, we first provide a prior generalization bound via the complexity of the target functions in the PDE problem, and a posterior generalization bound via the posterior matrix norms of the networks after optimization. Moreover, based on our bounds, we analyze the conditions under which XPINNs improve generalization. Concretely, our theory shows that the key building block of XPINN, namely the domain decomposition, introduces a tradeoff for generalization. On the one hand, XPINNs decompose the complex PDE solution into several simple parts, which decreases the complexity needed to learn each part and boosts generalization. On the other hand, decomposition leads to less training data being available in each subdomain, and hence such model is typically prone to overfitting and may become less generalizable. Empirically, we choose five PDEs to show when XPINNs perform better than, similar to, or worse than PINNs, hence demonstrating and justifying our new theory.

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arXiv2022

MGNNI: Multiscale Graph Neural Networks with Implicit Layers

Recently, implicit graph neural networks (GNNs) have been proposed to capture long-range dependencies in underlying graphs. In this paper, we introduce and justify two weaknesses of implicit GNNs: the constrained expressiveness due to their limited effective range for capturing long-range dependencies, and their lack of ability to capture multiscale information on graphs at multiple resolutions. To show the limited effective range of previous implicit GNNs, We first provide a theoretical analysis and point out the intrinsic relationship between the effective range and the convergence of iterative equations used in these models. To mitigate the mentioned weaknesses, we propose a multiscale graph neural network with implicit layers (MGNNI) which is able to model multiscale structures on graphs and has an expanded effective range for capturing long-range dependencies. We conduct comprehensive experiments for both node classification and graph classification to show that MGNNI outperforms representative baselines and has a better ability for multiscale modeling and capturing of long-range dependencies.

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arXiv2022

Simplicial Embeddings in Self-Supervised Learning and Downstream Classification

Simplicial Embeddings (SEM) are representations learned through self-supervised learning (SSL), wherein a representation is projected into $L$ simplices of $V$ dimensions each using a softmax operation. This procedure conditions the representation onto a constrained space during pretraining and imparts an inductive bias for group sparsity. For downstream classification, we formally prove that the SEM representation leads to better generalization than an unnormalized representation. Furthermore, we empirically demonstrate that SSL methods trained with SEMs have improved generalization on natural image datasets such as CIFAR-100 and ImageNet. Finally, when used in a downstream classification task, we show that SEM features exhibit emergent semantic coherence where small groups of learned features are distinctly predictive of semantically-relevant classes.

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arXiv2022

Robustness Implies Generalization via Data-Dependent Generalization Bounds

This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds in two directions, to solve an open problem that has seen little development since 2010. The first is to reduce the dependence on the covering number. The second is to remove the dependence on the hypothesis space. We present several examples, including ones for lasso and deep learning, in which our bounds are provably preferable. The experiments on real-world data and theoretical models demonstrate near-exponential improvements in various situations. To achieve these improvements, we do not require additional assumptions on the unknown distribution; instead, we only incorporate an observable and computable property of the training samples. A key technical innovation is an improved concentration bound for multinomial random variables that is of independent interest beyond robustness and generalization.

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arXiv2022

When and How Mixup Improves Calibration

In many machine learning applications, it is important for the model to provide confidence scores that accurately capture its prediction uncertainty. Although modern learning methods have achieved great success in predictive accuracy, generating calibrated confidence scores remains a major challenge. Mixup, a popular yet simple data augmentation technique based on taking convex combinations of pairs of training examples, has been empirically found to significantly improve confidence calibration across diverse applications. However, when and how Mixup helps calibration is still a mystery. In this paper, we theoretically prove that Mixup improves calibration in \textit{high-dimensional} settings by investigating natural statistical models. Interestingly, the calibration benefit of Mixup increases as the model capacity increases. We support our theories with experiments on common architectures and datasets. In addition, we study how Mixup improves calibration in semi-supervised learning. While incorporating unlabeled data can sometimes make the model less calibrated, adding Mixup training mitigates this issue and provably improves calibration. Our analysis provides new insights and a framework to understand Mixup and calibration.

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arXiv2022

Multi-Task Learning as a Bargaining Game

In Multi-task learning (MTL), a joint model is trained to simultaneously make predictions for several tasks. Joint training reduces computation costs and improves data efficiency; however, since the gradients of these different tasks may conflict, training a joint model for MTL often yields lower performance than its corresponding single-task counterparts. A common method for alleviating this issue is to combine per-task gradients into a joint update direction using a particular heuristic. In this paper, we propose viewing the gradients combination step as a bargaining game, where tasks negotiate to reach an agreement on a joint direction of parameter update. Under certain assumptions, the bargaining problem has a unique solution, known as the Nash Bargaining Solution, which we propose to use as a principled approach to multi-task learning. We describe a new MTL optimization procedure, Nash-MTL, and derive theoretical guarantees for its convergence. Empirically, we show that Nash-MTL achieves state-of-the-art results on multiple MTL benchmarks in various domains.

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arXiv2022

Understanding Dynamics of Nonlinear Representation Learning and Its Application

Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images. Representation learning allows us to automatically discover suitable representations from raw sensory data. For example, given raw sensory data, a deep neural network learns nonlinear representations at its hidden layers, which are subsequently used for classification (or regression) at its output layer. This happens implicitly during training through minimizing a supervised or unsupervised loss in common practical regimes of deep learning, unlike the neural tangent kernel (NTK) regime. In this paper, we study the dynamics of such implicit nonlinear representation learning, which is beyond the NTK regime. We identify a pair of a new assumption and a novel condition, called the common model structure assumption and the data-architecture alignment condition. Under the common model structure assumption, the data-architecture alignment condition is shown to be sufficient for the global convergence and necessary for the global optimality. Moreover, our theory explains how and when increasing the network size does and does not improve the training behaviors in the practical regime. Our results provide practical guidance for designing a model structure: e.g., the common model structure assumption can be used as a justification for using a particular model structure instead of others. We also derive a new training framework based on the theory. The proposed framework is empirically shown to maintain competitive (practical) test performances while providing global convergence guarantees for deep residual neural networks with convolutions, skip connections, and batch normalization with standard benchmark datasets, including CIFAR-10, CIFAR-100, and SVHN.

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