NerVE: Nonlinear Eigenspectrum Dynamics in LLM Feed-Forward Networks

TL;DR

NerVE introduces a spectral analysis framework to understand how large language model feed-forward networks organize information, revealing the impact of nonlinearities, optimizer geometry, and architecture on latent space dynamics and generalization.

Contribution

This work presents NerVE, a novel eigenspectral framework that efficiently tracks FFN spectral dynamics, linking them to model design choices and generalization, across various architectures and training setups.

Findings

Spectral signatures correlate with model generalization.

Nonlinearities reinject variance across eigenmodes.

Optimizer geometry influences spectral dynamics.

Abstract

We introduce NerVE, a unified eigenspectral framework for understanding how feed-forward networks (FFNs) in large language models (LLMs) organize and regulate information flow in high-dimensional latent space. Despite FFNs dominating the parameter budget, their high-dimensional dynamics remain poorly understood. NerVE addresses this gap through lightweight, memory-efficient tracking of eigenspectrum dynamics via four complementary metrics: Spectral Entropy (dispersion), Participation Ratio (effective dimensionality), Eigenvalue Early Enrichment (top-heaviness), and Jensen-Shannon divergence (distributional shifts). Our key insight is that FFN nonlinearities reinject variance across eigenmodes, fundamentally governing latent dimension utilization, and that optimizer geometry strongly modulates the extent of this variance reinjection. We validate NerVE across model scales, and diverse architectural and optimizer configurations, each uniquely shaping FFN dynamics: normalization schemes controlling variance flow; FFN weight geometries constraining latent space; positional encoding and activation functions regulating information flow; and optimizer choices redistributing effective capacity across depth. Across these settings, NerVE consistently recovers stable spectral signatures that correlate with model's generalization ability and respond predictably to design choices, generalizing beyond transformer to MLP-Mixer architectures, providing actionable insights for architectural and optimizer choices beyond trial-and-error.