Coarse-Graining Hidden Representations: Unsupervised Neuron Selection via Mapping Entropy

2026-09-04

AI Summary

通过映射熵方法无监督选择神经元，解决过参数化神经网络中哪些神经元是关键的问题，优化后子网络在强压缩下表现优于随机子集。

Abstract

Overparameterized neural networks carry far more hidden units than a task nominally requires, raising the question of which neurons are essential and whether that distinction is legible in the representation itself, without labels or gradients. We cast neuron selection as the problem of coarse-graining the hidden layer by retaining a subset of its neurons, and score each putative selection by the mapping entropy (ME). This quantity measures the loss of discriminatory power inherent in discarding part of the network neurons, and the selection that minimises the ME is taken as particularly informative. This criterion is fully unsupervised, in that it depends only on hidden-activation statistics. In teacher-student networks, ME optimisation recovers the minimal teacher-consistent representation and retains extra units in proportion to the hidden layer's residual variability; in a non-linear Gaussian process task, it selects coherent functional-class mappings whose preferred class shifts across training. On this task and on translation-augmented MNIST, ME-selected subnetworks outperform random subsets of equal size, most clearly under strong compression - linking configurational distinguishability to predictive performance.

Problem

• neuron selection
• overparameterized neural networks
• unsupervised learning
• mapping entropy

Innovation

• Unsupervised Neuron Selection
• Mapping Entropy
• Hidden Representations