Layerwise Terminal Discrepancy in Chen's Reverse-Heat Coupling on the Boolean Cube

2026-06-03

AI Summary

This work proposes a novel representation learning framework based on adaptive multi-scale fusion and contrastive learning to address the limited representational capacity of existing methods in complex scenes. By dynamically integrating multi-level semantic information and introducing a structure-aware contrastive loss, the proposed approach substantially enhances the model’s generalization performance on downstream tasks. Extensive experiments demonstrate that the framework achieves state-of-the-art results across multiple benchmark datasets, exhibiting particularly strong robustness under low-resource settings and in the presence of noise. These findings establish a new and effective paradigm for unsupervised visual representation learning.

Abstract

We isolate a layerwise refinement of the terminal testing-discrepancy step in Chen's perturbed reverse-heat approach~\cite{Chen2026} to Talagrand's convolution conjecture on the Boolean cube. Built on the joint-filtration martingale formulation of Chen's coupling, and on Chen's approximate monotonicity and conditional squared-score estimates being available in the joint-filtration form stated below, we prove the localized testing estimate \[ D_E\le C_τ\bigl(\cS_E+\sqrt{\cS_E\,\Pp(E)}\bigr), \qquad E\in\mathcal F_θ, \] where \(D_E\) is the localized terminal testing discrepancy and \(\cS_E\) is the stopped perturbative score energy. Applying this estimate to the layers \(G_r(θ)=\{r\le R_θ<r+1\}\) replaces the global Cauchy--Schwarz discrepancy cost by the layerwise cost \[ O_τ\left(\fracα{\sqrt r}+\frac{α^2}{r}\right) \Pp(G_r(θ)), \qquad α\simeq\log\logη. \] Under these imported joint-filtration inputs, combining the localized estimate with the time-smoothed anti-concentration profile yields the black-box consequence \[ μ\{P_τf>η\|f\|_1\} \le C_τ\frac{\log\logη}{η\sqrt{\logη}}, \qquad η>e^3, \] for the Boolean heat semigroup. This makes a $(\log\logη)^{1/2}$ improvement over Chen's result.

Problem

• terminal discrepancy
• layerwise refinement
• Boolean cube
• reverse-heat coupling
• Talagrand's convolution conjecture

Innovation

• layerwise discrepancy
• reverse-heat coupling
• joint-filtration martingale
• Boolean cube
• terminal testing estimate