NerVE: Nonlinear Eigenspectrum Dynamics in LLM Feed-Forward Networks
This work addresses a fundamental gap in understanding FFN dynamics in LLMs, providing actionable insights for architectural and optimizer design, though it is incremental in building on existing spectral analysis methods.
The paper tackled the problem of understanding high-dimensional dynamics in feed-forward networks (FFNs) of large language models (LLMs) by introducing NerVE, a framework that tracks eigenspectrum dynamics, revealing how nonlinearities and optimizer geometry regulate information flow and correlate with generalization ability across diverse model scales and architectures.
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.