# BMFA: Boundary-Minority Free-Energy Adaptive Screening

Source: [BMFA: Boundary-Minority Free-Energy Adaptive Screening](<https://www.sota2.com/research/paper/6a5efd7a17e2c828503ba4c4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-22T05:00:13.060Z

Authors: Wenyan Xu, Alizer Wong

Published: 2026-07-20T08:07:18.000Z

## Abstract

Vision Transformers process spatially redundant tokens efficiently only when coarse token summaries preserve the evidence required by exponential attention aggregation. We identify a boundary-minority underestimation failure in which a spatially small, high-response region contributes dominant Gibbs mass while remaining nearly invisible to a block mean. We formalize the failure through the discrepancy between normalized log-mean-exp free energy and mean summarization, prove that minority Gibbs mass can remain non-vanishing as its spatial support and mean contribution vanish, and characterize the limitations of finite-order moment corrections. Building on the resulting analysis, we introduce Boundary-Minority Free-Energy Adaptive Screening (BMFA), which constructs a hierarchical piecewise-constant approximation and recursively refines blocks according to a computable lower-bound increment of local free energy. Controlled synthetic tests, COCO and LVIS diagnostic probes, closed-loop DeiT-Tiny evaluations, and ImageNet-1K experiments establish a consistent evidence chain. BMFA reduces the mean synthetic underestimate from 2.582 to 0.261 at a 5.794% leaf ratio, lowers the COCO image-edge mean gap from 2.254 to 0.526, and preserves 71.520% ImageNet Top-1 accuracy at a 55.861% leaf ratio. The current prototype evaluates selection quality after full QK computation; the reported leaf ratio therefore characterizes representation granularity rather than verified sparse-kernel speedup.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2607.17656>)

[PDF](<https://arxiv.org/pdf/2607.17656.pdf>)