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Yihang Chen 0003

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3 papers

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ICLR Conference 2024 Conference Paper

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Yihang Chen 0003
Fanghui Liu 0001
Yiping Lu
Grigorios Chrysos 0002
Volkan Cevher

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of which the gradient flow is described by a partial differential equation in the large-neural network limit, i.e., the mean-field regime. To derive the generalization bounds under this setting, our analysis necessitates a shift from the conventional time-invariant Gram matrix employed in the lazy training regime to a time-variant, distribution-dependent version. To this end, we provide a global lower bound on the minimum eigenvalue of the Gram matrix under the mean-field regime. Besides, for the traceability of the dynamic of Kullback-Leibler (KL) divergence, we establish the linear convergence of the empirical error and estimate the upper bound of the KL divergence over parameters distribution. Finally, we build the uniform convergence for generalization bound via Rademacher complexity. Our results offer new insights into the generalization ability of deep ResNet beyond the lazy training regime and contribute to advancing the understanding of the fundamental properties of deep neural networks.

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ICML Conference 2024 Conference Paper

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Yihang Chen 0003
Fanghui Liu 0001
Taiji Suzuki
Volkan Cevher

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposition, we theoretically demonstrate that the re-weighting strategy allows for decreasing the variance. For bias, we analyze the regularization of the arbitrary or well-chosen scale, showing that the bias can behave very differently under different regularization scales. In our analysis, the bias and variance can be characterized by the spectral decay of a data-dependent regularized kernel: the original kernel matrix associated with an additional re-weighting matrix, and thus the re-weighting strategy can be regarded as a data-dependent regularization for better understanding. Besides, our analysis provides asymptotic expansion of kernel functions/vectors under covariate shift, which has its own interest.

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ICLR Conference 2024 Conference Paper

Order-Preserving GFlowNets

Yihang Chen 0003
Lukas Mauch

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates with probabilities proportional to a given reward. However, GFlowNets can only be used with a predefined scalar reward, which can be either computationally expensive or not directly accessible, in the case of multi-objective optimization (MOO) tasks for example. Moreover, to prioritize identifying high-reward candidates, the conventional practice is to raise the reward to a higher exponent, the optimal choice of which may vary across different environments. To address these issues, we propose Order-Preserving GFlowNets (OP-GFNs), which sample with probabilities in proportion to a learned reward function that is consistent with a provided (partial) order on the candidates, thus eliminating the need for an explicit formulation of the reward function. We theoretically prove that the training process of OP-GFNs gradually sparsifies the learned reward landscape in single-objective maximization tasks. The sparsification concentrates on candidates of a higher hierarchy in the ordering, ensuring exploration at the beginning and exploitation towards the end of the training. We demonstrate OP-GFN's state-of-the-art performance in single-objective maximization (totally ordered) and multi-objective Pareto front approximation (partially ordered) tasks, including synthetic datasets, molecule generation, and neural architecture search.

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