#01Nov 9, 2026
cs.LG
Attention Is Only as Good as Its Witnesses: When Higher-Order Layers Help, and When They Do Not
Mostafa 'Neo' Mohsenvand
Transformers stop learning graph search as graphs grow, and learn the card game SET only after many distinct questions, although attention can represent both. We read these failures, and the uneven record of higher-order attention, from what a layer sums over: each layer we study computes the partition function of a family of witnesses and reads it at a temperature. Two laws follow. The depth law is a known result of logic, which we state for these layers: L layers over two-step walks reach exactly 2^L - 1 steps, just as a logical statement with L nested clauses of the form "there is a vertex such that" sees exactly that far. We build a construction that reaches this far, checked in Lean, and, when vertices carry no names, no such network reaches further. The size law is the cost of reading at a temperature, which logic does not have: existence is read correctly at every size, in the worst case, if and only if inverse temperature times margin is at least the logarithm of the number of candidates. Layers built on these laws, and on two principles that we test, learn where Transformers fail. One propagator layer trained on 49-vertex graphs answers every question at every search depth on 250-vertex graphs. Given the modulus 3, exponential Newton computes the softmax of 2-simplicial attention over pairs exactly in 3^d n operations for d clocks; with six clocks it learns SET from as few deals as 2-simplicial attention and transfers from 8- to 20-card tables. On CLRS-30 without hints, a 186,000-parameter block of OR-join and power-mean channels matches (within half a point) or beats a model of at least 73 million parameters on 9 of 12 graph tasks of the official test set, and on 8 of 12 with freshly drawn test graphs. The same account explains where pair layers did not help and where parallel layers must loop.
#02Nov 9, 2026
cs.LG
Scalable Bayesian Optimization for Efficient Exploration of Moire Patterns
Panagiotis Krokidas, Christos Lazaridis, Vassilis Sioros and 3 more
Large materials design spaces often contain rare high-performing configurations that are difficult to identify through trial-and-error exploration or purely representative machine-learning (ML) sampling. In this work, we present FruBO, a flexible Bayesian Optimization framework for accelerating the discovery of optimal configurations in computationally demanding materials design problems. As a case study, we investigate multilayer Moiré patterns generated by the superposition of six rotated hexagonal lattices, where the objective is to identify the rotational conformation that maximizes pore-size uniformity, quantified using the Jain fairness index. The resulting benchmark contains 600,000 unique configurations and exhibits a highly skewed objective distribution, making the global optimum difficult to locate by random sampling. We compare random exploration, Gaussian Process-based Bayesian Optimization, and Bayesian Optimization using a lightweight CatBoost surrogate with committee-based uncertainty estimation. Random sampling identifies the global optimum only after 533,012 evaluations, requiring approximately 31 hours, while Gaussian Process-based BO becomes impractical due to GPU memory exhaustion after 290 acquired samples. In contrast, FruBO with CatBoost identifies the global optimum after 1,470 acquired samples and approximately 1.15 hours. These results demonstrate that scalable surrogate models can substantially improve the feasibility and efficiency of BO in large nanomaterials design spaces.
#03Nov 9, 2026
cs.LG
FocusBranch: Combinatorial Branch-and-Bound for $\ell_0$ Neural Network Robustness Verification
Renwei Deng, Yang He, Linyi Li and 1 more
Verifying the local robustness of neural networks under $\ell_0$ perturbations is inherently combinatorial, as it must reason over all sparse subsets of $ε$ perturbed pixels. This paper presents FocusBranch, a combinatorial branch-and-bound framework for $\ell_0$ robustness verification. The key insight is to make the $\ell_0$-ball decomposable and branchable using a node abstraction, which consists of a focus pixel set $\mathcal{S}$ and a level $l$, permitting at most $ε-l$ pixels outside $\mathcal{S}$. This abstraction unifies two branching mechanisms: concrete nodes branch through upper shadows to fix additional perturbed locations, while super nodes branch through covering designs to cover many perturbation cases with fewer child nodes. FocusBranch proves node safety by concretizing linear relaxations over node-constrained $\ell_0$-balls and recursively branches on unknown nodes. Rather than relying on a fixed verification plan, it samples nodes across levels to estimate safe rates and costs, then selects a starting level and branching strategy predicted to minimize verification time. Experiments on fully connected and convolutional classifiers for MNIST, Fashion-MNIST, and CIFAR-10 show that FocusBranch verifies $\ell_0$ robustness effectively across architectures and outperforms state-of-the-art verifiers. The code is available at: https://github.com/simpl-group/FocusBranch.
#04Nov 9, 2026
cs.LG
HyInv Technical Report
Haowei Lin, Cai Zhou, Xiangxin Zhou
Inverse folding designs amino-acid sequences for a given protein backbone, and screening needs many candidates that are both diverse and well folded. We present HyInv, a 1.96-million-parameter backbone-conditioned graph network with an encoder-decoder architecture, trained by Hyra 2.0, the research agent developed by our team: pretrained with random-order autoregressive sequence modeling, followed by structure-reward reinforcement learning. At inference, a grouped draft-and-rewrite sampler that uses separate draft and rewrite temperatures improves refolding TM-score at matched diversity. An optimized implementation with BF16 numerics designs 128 sequences for a 402-residue backbone in 50.6 ms on a single NVIDIA H20 GPU, about 52 times faster than the reference sampler, and an exact FP32 path that returns the reference sequences is 8.7 times faster. Across five benchmark datasets and seven dataset-predictor combinations, HyInv reaches a higher average scTM than all ten external baselines at comparable or higher sequence diversity, with large margins over ProteinMPNN and ProteinZero V2. The same default setting supports de novo backbones, pocket-constrained libraries, enzyme redesign with the catalytic site kept, and loop redesign. We have released our code and model at https://github.com/Tencent-Hunyuan/Hyra-results/tree/main/AI4Science/hyinv.
#05Nov 9, 2026
cs.LG
ShiftCache: Fast and Exact Indel Effect Prediction by Reusing Shifted Reference Encodings
Sina Barazandeh, Arth Banka, Jose Lugo-Martinez
Sequence-to-function models such as AlphaGenome and Borzoi read up to a megabase of DNA and score a genetic variant by comparing their predictions for the reference and alternate sequences. Insertions and deletions (indels) are costly to score, because an indel usually shifts the unchanged DNA after it onto a different pooling grid, which prevents direct reuse of the reference's encoder activations. The AlphaGenome Atlas scored more than 100 million indels with three full model passes each, although the DNA after an indel matches the reference shifted by the indel's length. We present ShiftCache, an exact reuse system that encodes each shifted reference once and shares it among all variants scored in the same window with the same shift. ShiftCache copies every encoder output a variant can reuse and recomputes the rest in batched tiles. On held-out AlphaGenome windows shared by many indels, in strict fp32 on one A6000, ShiftCache is 3.5 to 6.5$\times$ faster than deduplicated dense execution and 1.6 to 2.7$\times$ faster than our adaptation of layer-by-layer reuse to indels. It is 3.5 to 4.1$\times$ faster than dense reimplementations of two published analyses with Borzoi and AlphaGenome, and 2.6$\times$ faster than dense execution with Enformer. Scoring each variant in its own centered 131 kb window makes ShiftCache only 1.36$\times$ faster than deduplicated dense execution, and highly diverse insertion lengths or many dispersed edits can make it slower than layer-by-layer reuse or dense execution. For encoders that meet our conditions, ShiftCache computes the same predictions as dense execution in exact arithmetic. On an A6000, every checked output of the default AlphaGenome and Borzoi runs matches dense execution within an absolute and relative tolerance of $10^{-5}$. With larger tile batches, with Enformer or on an H100, a small fraction of values exceeds this tolerance.