Research
Refined Topology-Pass Scheduling: Damped Trust-Region Compensation for Dynamic k-NN Graphs in SE(3)-Equivariant Structure Prediction
arXiv:2610.19246v1 Announce Type: new Abstract: Equivariant structure-prediction pipelines alternate coordinate updates with the construction of a k-nearest-neighbour (kNN) graph whose membership is a
arXiv:2610.19246v1 Announce Type: new 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 1.5imes Pass-1 and 1.76imes 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 https://github.com/AlbertHuang96/ProteinPredictMachineLearning.
Related
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- XANE(3): An E(3)-Equivariant Graph Neural Network for Accurate Prediction of XANES Spectra from Atomic Structures
- Not All Neighbors Matter: Understanding the Impact of Graph Sparsification on GNN Pipelines
Source: arXiv cs.LG | 2026-10-15