arXiv cs.AI· Jiankai Huang, Hanwen Shen·· 15 小时前AI 评分24
面向 SE(3) 等变结构预测的 Refined Topology-Pass Scheduling：动态 k-NN 图的阻尼信赖域补偿
Refined Topology-Pass Scheduling: Damped Trust-Region Compensation for Dynamic k-NN Graphs in SE(3)-Equivariant Structure Prediction
AI 导读
针对 SE(3) 等变结构预测中每层重建 k-NN 图开销大的问题，研究提出两遍式拓扑调度：第一遍记录 margin、kNN 半径与位移等少量状态，第二遍做保守补偿，并将图构建基的选择建模为阻尼不动点迭代，其唯一不动点恰为逐块重建（PB）。
正文 · 原文
Abstract:Equivariant structure-prediction pipelines alternate coordinate updates with the construction of a k-nearest-neighbour (kNN) graph whose membership is a discrete, piecewise-constant function of the coordinates. Rebuilding that graph at every block boundary (PB) is the expensive part of an epoch, whereas reusing one frozen graph (F) is fast but leaves a topology gap. We study a two-pass design in which the cheap pass records a small amount of state (margins, kNN radii, measured per-boundary displacements) and a second pass compensates conservatively. We formulate the choice of the graph-construction basis as a damped fixed-point iteration whose unique fixed point is exactly PB, and derive (i) exact non-flip certificates with the two-sided constant $m_i/4$ and one-sided constant $m_i/2$, (ii) the minimum-variance (BLUE) replay gain $\gamma^*$ and the resulting feasibility crossover, (iii) an $\ell_\infty$ trust-region projection that preserves convergence, and (iv) an analytic near-tie spacing law $E[m] \approx r_k/(3k)$ that matches measurements to 1\%. Three compensation levels are implemented in C++ (L1: frozen set with live geometry; L2: margin-gated local repair; L3: damped, projected basis) and validated under a matched-conditions protocol (identical seed, MSA depth and trajectory family, only the topology mode differs). L2 reproduces the PB edge set exactly ($D = 0.0000$ at every boundary), L1 stays within 0.6% and L3 interpolates monotonically: L2 reproduces the PB edge set exactly when the trust region is removed, and L3 interpolates between the frozen and the PB topology. The recorded trajectory itself yields a measured $1.5\times$ Pass-1 and $1.76\times$ epoch speed-up with no measurable loss gap. An open-source implementation of the runtime and of all the experiments reported here is available at this https URL.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.19246 [cs.LG] |
| (or arXiv:2610.19246v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.19246 arXiv-issued DOI via DataCite |
Submission history
From: Jiankai Huang [view email]
[v1]
Tue, 13 Oct 2026 22:01:49 UTC (32 KB)
[v2]
Sat, 24 Oct 2026 03:26:23 UTC (36 KB)
来源：arXiv cs.AI · arxiv.org