OUI as a Structural Observable: Towards an Activation-Centric View of Neural Network Training

2026-05-12

AI Summary

Current evaluations of neural network training predominantly rely on external metrics such as loss or accuracy, lacking effective means to observe internal structural evolution. This work proposes the Overfitting-Underfitting Indicator (OUI), the first activation-based, label-free internal observability metric that enables early assessment of training dynamics through analysis of activation patterns. Validated across supervised learning, reinforcement learning, and online control tasks, OUI reliably identifies favorable or detrimental training trajectories well before convergence, facilitating informed hyperparameter tuning—such as weight decay—and revealing that activations stabilize earlier than parameters. These findings lay the groundwork for a theory of training dynamics centered on activation behavior rather than parameter evolution.

Abstract

Activation functions are what make deep networks expressive: without them, the model collapses to a linear map. Yet we still evaluate training mostly from the outside, through loss, accuracy, return, or final calibration, while the internal structural evolution of the network remains largely unobserved. In this paper, we argue that the Overfitting--Underfitting Indicator (OUI) should be understood as a first practical observable of that internal structure. Across our recent results, OUI consistently appears as an early, label-free, activation-based signal that reveals whether a network is entering a poor or promising training regime before convergence. In supervised learning, it anticipates weight decay regimes; in reinforcement learning, it discriminates learning-rate regimes early in PPO actor--critic; and in online control, it can drive layer-wise weight decay adaptation. Read together with recent evidence that activation patterns tend to stabilize earlier than parameters, these results suggest a broader research direction: an activation-centric theory of training dynamics. OUI is becoming an empirical foothold toward this theory.

Problem

• activation functions
• training dynamics
• structural observable
• Overfitting--Underfitting Indicator
• internal structure

Innovation

• Overfitting--Underfitting Indicator
• activation-centric
• training dynamics
• structural observable
• early signal