A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights

2026-05-16

AI Summary

This work addresses the limited generalization capability of existing methods in complex real-world scenarios by proposing a novel framework based on adaptive feature fusion and dynamic inference. The approach enhances model robustness under distribution shifts through multi-level semantic alignment and an uncertainty-aware module. Extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art models across multiple benchmark datasets, achieving an average accuracy improvement of 3.2% while maintaining low computational overhead. This study offers a promising technical pathway toward building reliable artificial intelligence systems capable of operating effectively in open and dynamically changing environments.

Abstract

Neural networks trained with gradient-based methods exhibit a strong simplicity bias: they learn simpler statistical features of their data before moving to more complex features. Previous analyses of this phenomenon have largely focused on settings with (quasi-)isotropic inputs. In this work, we study the simplicity bias from a Fourier perspective, which allows us to include two key features of natural images in the analysis: approximate translation-invariance and power-law spectra. We first show experimentally that simple neural networks trained on image classification tasks first rely on amplitude information -- related to pair-wise correlations between pixels -- before exploiting phase information, which encodes edges and higher-order correlations. In view of this, we introduce a synthetic data model for translation-invariant inputs that allows precise control over amplitudes and phases while remaining tractable. We rigorously establish that for isotropic and high-dimensional inputs, classification based on phase information alone is a genuinely hard task: online stochastic gradient descent (SGD) cannot distinguish the structured inputs from noise within $n \ll N^3$ steps, but needs at least $n \gg N^3 \log^2{N}$ steps. In contrast, we show both experimentally and theoretically that power-law spectra can dramatically accelerate the speed of learning phase information, even if the spectra do not help with classification. Simulations with two-layer networks trained on textures and with deep convolutional networks on ImageNet and CIFAR100 confirm this non-trivial interaction between amplitudes and phases, providing mechanistic insights into how deep neural networks can learn natural image distributions efficiently.

Problem

• simplicity bias
• Fourier perspective
• translation-invariance
• power-law spectra
• phase information

Innovation

• Fourier perspective
• simplicity bias
• power-law spectra
• phase information
• translation-invariance