Emergence of Innovative Frameworks in Deep Learning

The field of deep learning is witnessing a significant shift towards understanding the underlying dynamics of feature emergence and generalization. Researchers are developing novel frameworks to characterize the behavior of neural networks, including the study of grokking, delayed generalization, and the role of key hyperparameters. These efforts aim to provide a deeper understanding of how neural networks learn and generalize, leading to the development of more efficient and effective models. Noteworthy papers in this area include:

  • A framework that captures the three key stages of grokking behavior in 2-layer nonlinear networks, providing insights into the emergence of features and their generalizability.
  • A study that derives a new Rademacher complexity bound for deep neural networks using Koopman operators and reproducing kernel Hilbert spaces, shedding light on why high-rank models generalize well.
  • A paper that introduces a generalized information bottleneck theory, reformulating the original principle through the lens of synergy and demonstrating its potential for improved generalization. These innovative frameworks and theories are poised to advance the field of deep learning, enabling the development of more powerful and efficient models.

Sources

$\mathbf{Li_2}$: A Framework on Dynamics of Feature Emergence and Delayed Generalization

Why High-rank Neural Networks Generalize?: An Algebraic Framework with RKHSs

A Law of Data Reconstruction for Random Features (and Beyond)

Bridging Kolmogorov Complexity and Deep Learning: Asymptotically Optimal Description Length Objectives for Transformers

IIET: Efficient Numerical Transformer via Implicit Iterative Euler Method

Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime

Gradient Descent with Large Step Sizes: Chaos and Fractal Convergence Region

How Does Preconditioning Guide Feature Learning in Deep Neural Networks?

A Generalized Information Bottleneck Theory of Deep Learning

On the Benefits of Weight Normalization for Overparameterized Matrix Sensing

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