# BMFA: Boundary-Minority Free-Energy Adaptive Screening

arXiv: https://arxiv.org/abs/2607.17656 · HTML: https://mlsanity.com/paper/2607.17656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 30 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [LVIS: A Dataset for Large Vocabulary Instance Segmentation](https://mlsanity.com/paper/1908.03195/) (2019)
- [Token Merging: Your ViT But Faster](https://mlsanity.com/paper/2210.09461/) (2022)
- [DynamicViT: Efficient Vision Transformers with Dynamic Token Sparsification](https://mlsanity.com/paper/2106.02034/) (2021)
- [Segmenter: Transformer for Semantic Segmentation](https://mlsanity.com/paper/2105.05633/) (2021)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [Not All Patches are What You Need: Expediting Vision Transformers via Token Reorganizations](https://mlsanity.com/paper/2202.07800/) (2022)
- [AdaViT: Adaptive Tokens for Efficient Vision Transformer](https://mlsanity.com/paper/2112.07658/) (2021)
- [TokenLearner: What Can 8 Learned Tokens Do for Images and Videos?](https://mlsanity.com/paper/2106.11297/) (2021)
- [Token Fusion: Bridging the Gap between Token Pruning and Token Merging](https://mlsanity.com/paper/2312.01026/) (2023)
- [SpargeAttention: Accurate and Training-free Sparse Attention Accelerating Any Model Inference](https://mlsanity.com/paper/2502.18137/) (2025)
- [SparQ Attention: Bandwidth-Efficient LLM Inference](https://mlsanity.com/paper/2312.04985/) (2023)
- [DiffRate : Differentiable Compression Rate for Efficient Vision Transformers](https://mlsanity.com/paper/2305.17997/) (2023)
- [Zero-TPrune: Zero-Shot Token Pruning through Leveraging of the Attention Graph in Pre-Trained Transformers](https://mlsanity.com/paper/2305.17328/) (2023)
- [CrossGET: Cross-Guided Ensemble of Tokens for Accelerating Vision-Language Transformers](https://mlsanity.com/paper/2305.17455/) (2023)
- [Accelerating Transformers with Spectrum-Preserving Token Merging](https://mlsanity.com/paper/2405.16148/) (2024)
- [Making Vision Transformers Efficient from A Token Sparsification View](https://mlsanity.com/paper/2303.08685/) (2023)
- [ALGM: Adaptive Local-then-Global Token Merging for Efficient Semantic Segmentation with Plain Vision Transformers](https://mlsanity.com/paper/2406.09936/) (2024)
- [Multi-criteria Token Fusion with One-step-ahead Attention for Efficient Vision Transformers](https://mlsanity.com/paper/2403.10030/) (2024)

## Abstract (arXiv)

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.