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

arXiv: https://arxiv.org/abs/2605.11570 · HTML: https://mlsanity.com/paper/2605.11570/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Model collapse from synthetic data, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 3 of its 5 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Model collapse from synthetic data](https://mlsanity.com/synth/model-collapse-from-synthetic-data/)

## Builds on (most cited first, 3 of 3)

- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [OUI Need to Talk About Weight Decay: A New Perspective on Overfitting Detection](https://mlsanity.com/paper/2504.17160/) (2025)
- [Regime Change Hypothesis: Foundations for Decoupled Dynamics in Neural Network Training](https://mlsanity.com/paper/2602.08333/) (2026)

## Abstract (arXiv)

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.