# Avoiding Premature Collapse: Adaptive Annealing for Entropy-Regularized Structural Inference

arXiv: https://arxiv.org/abs/2601.23039 · HTML: https://mlsanity.com/paper/2601.23039/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 14 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 9 of 9)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [mHC: Manifold-Constrained Hyper-Connections](https://mlsanity.com/paper/2512.24880/) (2025)
- [Hyper-Connections](https://mlsanity.com/paper/2409.19606/) (2024)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [A Unified Framework for Implicit Sinkhorn Differentiation](https://mlsanity.com/paper/2205.06688/) (2022)
- [An explicit analysis of the entropic penalty in linear programming](https://mlsanity.com/paper/1806.01879/) (2018)
- [Annealed Sinkhorn for Optimal Transport: convergence, regularization path and debiasing](https://mlsanity.com/paper/2408.11620/) (2024)

## Built on by (most cited first, 1 of 1)

- [The Birkhoff Geometry of Manifold-Constrained Hyper-Connections: Two Channels, Vertex Viscosity, and Sinkhorn as a Retraction](https://mlsanity.com/paper/2610.06653/) (2026)

## Abstract (arXiv)

Differentiable matching layers and residual connection paradigms, often implemented via entropy-regularized Optimal Transport (OT), serve as critical mechanisms in structural prediction and architectural scaling. However, recovering discrete permutations or maintaining identity mappings via annealing ε → 0 is notoriously unstable. In this work, we identify a fundamental mechanism for this failure: Premature Mode Collapse. By analyzing the non-normal dynamics of the Sinkhorn fixed-point map, we reveal a theoretical thermodynamic speed limit: standard exponential cooling outpaces the contraction rate of the inference operator, which degrades as O(1/ε). To address this, we propose Efficient Piecewise Hybrid Adaptive Stability Control (EPH-ASC), an adaptive scheduling algorithm that monitors the stability of the inference process. We demonstrate that EPH-ASC is essential for stabilizing Manifold-Constrained Hyper-Connections (mHC) during large-scale training on the FineWeb-Edu dataset, effectively preventing late-stage gradient explosions by enforcing a linear stability law.