Implicit Bias of Diagonal Linear Networks Explained by L1 Norm
Summary
This study extends previous work to show that the gradient flow dynamics of deep and two-layer diagonal linear networks, under infinitesimal initialization, can be characterized by a specific algorithm. This algorithm converges to a solution of a modified L1 norm minimization problem, establishing that the implicit bias of these networks corresponds to this modified L1 norm.
Why it matters
Understanding the implicit bias of neural networks is fundamental for predicting their behavior, improving generalization, and designing more robust and interpretable AI models, especially in the context of deep learning theory.
How to implement this in your domain
- 1Review the theoretical underpinnings of implicit bias in neural networks relevant to your model architectures.
- 2Consider how L1 norm minimization principles might influence the sparsity or feature selection in your models.
- 3Investigate the impact of initialization strategies on the implicit bias and generalization performance of your networks.
- 4Apply insights into gradient flow dynamics to better understand and debug training processes for linear networks.
- 5Explore the concept of Structural Invariant Manifolds to analyze the geometric structures shaping your model's learning.
Who benefits
Key takeaways
- The gradient flow dynamics of diagonal linear networks can be characterized by a specific algorithm.
- This algorithm converges to a modified L1 norm minimization problem.
- The implicit bias of these networks, under infinitesimal initialization, corresponds to a modified L1 norm.
- The Structural Invariant Manifold is a key geometric structure shaping the learning process.
Original post by Jiajie Zhao, Jianxing Wang, Junjie Yang, Zhiwei Bai, Yaoyu Zhang
"arXiv:2607.12332v1 Announce Type: new Abstract: We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear net…"
View on XOriginally posted by Jiajie Zhao, Jianxing Wang, Junjie Yang, Zhiwei Bai, Yaoyu Zhang on X · view source
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