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

TL;DR

This paper introduces the Overfitting--Underfitting Indicator (OUI), an activation-based measure that provides early, label-free insights into training regimes across various neural network tasks, promoting an activation-centric view of training dynamics.

Contribution

It proposes OUI as a practical, activation-based observable that predicts training outcomes early, supporting a new activation-centric perspective on neural network training dynamics.

Findings

OUI predicts poor or promising training regimes before convergence.

OUI anticipates weight decay regimes in supervised learning.

OUI discriminates learning-rate regimes early in reinforcement learning.

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.