← 研踪 PaperTrailarXiv:2610.39717 · v1
Implicit Bias of (Stochastic) Gradient Descent on Deep Linear Diagonal Networks
首次提交 2026-10-29 17:49
版本更新 2026-10-29 17:49
雷达观测 2026-10-30 13:28
摘要
Modern machine learning models are often overparameterized, i.e., have more parameters than training data. This typically implies that the loss function admits multiple minimizers so that training methods (and their hyperparameter choices) have significant influence on the computed solution. We study this so-called implicit bias phenomenon in the context of training deep linear diagonal networks. Previous work has shown that the gradient flow for learning such networks converges to (almost) sparse solutions when initialized small. For an arbitrary number of layers, we extend this analysis to the practically more realistic (stochastic) gradient descent iterations. Our approach identifies (stochastic) gradient descent as a perturbed (stochastic) mirror gradient descent. This allows us to establish convergence and characterize the limiting solution, relating it to weighted $\ell_1$-minimization. Moreover, we provide sufficient conditions on the step sizes and quantify the influence of the step sizes on the implicit bias.
作者备注：38 pages, 14 figures
观测到的版本
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v1 · 2026-10-29 17:49 · 最新观测版本
Implicit Bias of (Stochastic) Gradient Descent on Deep Linear Diagonal Networks
Modern machine learning models are often overparameterized, i.e., have more parameters than training data. This typically implies that the loss function admits multiple minimizers so that training methods (and their hyperparameter choices) have significant influence on the computed solution. We study this so-called implicit bias phenomenon in the context of training deep linear diagonal networks. Previous work has shown that the gradient flow for learning such networks converges to (almost) sparse solutions when initialized small. For an arbitrary number of layers, we extend this analysis to the practically more realistic (stochastic) gradient descent iterations. Our approach identifies (stochastic) gradient descent as a perturbed (stochastic) mirror gradient descent. This allows us to establish convergence and characterize the limiting solution, relating it to weighted $\ell_1$-minimization. Moreover, we provide sufficient conditions on the step sizes and quantify the influence of the step sizes on the implicit bias.
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