NerVE: Nonlinear Eigenspectrum Dynamics in LLM Feed-Forward Networks

Nandan Kumar Jha, Brandon Reagen

Keywords: Eigenspectrum, feed-forward networks, training dynamics, latent space geometry, optimizer geometry

TL;DR: We introduce NerVE, an eigenspectral probe of FFN nonlinearities that quantifies how they restructure latent variance, yielding spectral signatures that track generalization and reveal consistent effects of architecure and optimizer design.

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.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Submission Number: 16222