The Homogeneity Trap: Spectral Collapse in Doubly-Stochastic Deep Networks

📝 Original Info

• Title: The Homogeneity Trap: Spectral Collapse in Doubly-Stochastic Deep Networks
• ArXiv ID: 2601.02080
• Date: 2026-01-05
• Authors: Yizhi Liu

📝 Abstract

Doubly-stochastic matrices (DSM) are increasingly utilized in deep learning-particularly within Optimal Transport layers and Sinkhorn-based attention-to enforce structural stability. However, we identify a critical spectral degradation phenomenon termed the Homogeneity Trap: imposing maximum-entropy constraints systematically suppresses the subdominant singular value σ 2 (M ). We prove that strictly contractive DSM dynamics accelerate this decay, acting as a low-pass filter that eliminates detail components. We derive a finite-n probability bound linking Signal-to-Noise Ratio (SNR) degradation to orthogonal collapse, explicitly quantifying the relationship between spectral contraction and geometric loss using rigorous concentration inequalities. Furthermore, we demonstrate that Residual Connections fail to mitigate this collapse, instead forcing the network into a regime of Identity Stagnation. Source code and reproduction scripts are provided in the supplementary material.

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