#01Jul 20, 2026
cs.CV
Certified Training for Convolutional Perturbations
Benedikt Brückner, Alessio Lomuscio
Vision models have been found to be susceptible to perturbations such as motion blur induced at runtime by a shaking camera. This impedes their deployment in critical applications since phenomena such as slightly blurred vision might lead to failures, for example an object detector missing objects. While methods such as data augmentation or Adversarial Training can improve empirical robustness, they lack formal safety guarantees, making it difficult to identify and mitigate hidden vulnerabilities. We introduce a novel Certified Training approach that leverages an efficient encoding of convolutional perturbations to train provably robust models. Our method significantly outperforms Adversarial Training, achieving, for example, over 80% robust accuracy against motion blur of reasonable intensity on CIFAR10 while maintaining comparable standard accuracy.
#02Jul 20, 2026
cs.LG
Do Language Models Dream of Binding Molecules? Benchmarking LLMs under Spatial Constraints
Thomas MacDougall, Maksim Kuznetsov, Roman Schutski and 5 more
Structure-based drug design (SBDD) leverages the 3D structure of protein targets, often complemented by other spatial constraints, to generate candidate binding molecules. While diffusion models have dominated as a leading paradigm for high-quality 3D molecule generation, LLM-based methods are rapidly emerging in molecular design and have shown competitive performance in pocket-conditioned molecular generation. However, their ability to reason about physics and 3D spatial environments is largely underexplored. In this work, we systematically analyze whether current general-purpose LLMs are capable of navigating complex 3D constraints compared to established baselines such as specialized diffusion models. We consider 3D ligand generation conditioned on protein pockets together with ligand- and interaction-derived spatial constraints, including anchor fragments, pharmacophore points, and mandatory pocket-ligand interactions. To enable this evaluation, we introduce 3D-Fit - a token-efficient benchmarking strategy for assessing LLM performance on multi-conditioned spatial molecule generation. Our findings reveal a clear pattern in LLM spatial capabilities: while they still lag behind state-of-the-art approaches, they are promising and can handle multiple spatial constraints simultaneously, enabling scaling to heterogeneous setups.
#03Jul 20, 2026
cs.LG
Enhancing Rubric-based RL via Self-Distillation
Mingxuan Xia, Yuhang Yang, Chao Ye and 7 more
Rubric-based RL has recently shown promise in improving LLMs on open-ended tasks. A widely recognized limitation of rubric-based RL is limited exploration: criteria that no rollout manages to satisfy (Unexplored Criteria, UC) receive no optimization signal. Recent methods address this by incorporating rubric information as external guidance during rollout, yet they introduce a train-inference mismatch: the policy is optimized on rollouts produced under external guidance while this guidance is absent at inference time, causing error accumulation through autoregressive decoding. Moreover, these exploration-focused approaches overlook a fundamentally different failure mode that we term Suppressed Criteria (SC) -- criteria that are satisfied by some rollouts yet whose learning signals are lost during optimization because scalar reward aggregation assigns them non-positive aggregate advantages. Our analysis reveals that SC are remarkably prevalent: over 57% of samples exhibit this failure mode throughout training, with an average of 1.8 SC per sample. To simultaneously address both UC and SC without introducing training-inference mismatch, we propose Criterion-Distilled Policy Optimization (CriPO), which enhances rubric-based RL via on-policy self-distillation. For UC, CriPO constructs a criterion-injection self-teacher and computes a localized forward-KL loss to inject missing behaviors into the policy. For SC, CriPO employs a counterfactual self-teacher to locate criterion-relevant tokens in negative-advantage rollouts and flips their token-level advantages to positive values, preserving useful patterns that would otherwise be suppressed. Experiments on medicine and science benchmarks demonstrate that CriPO consistently outperforms rubric-based RL, achieving stronger final performance with approximately $2\times$ fewer optimization steps.
#04Jul 20, 2026
cs.LG
Sobek: Streaming Equivariant Tensor Product Convolutions
Vladimir Chorošajev, Cédric Bény
Equivariant graph neural networks repeatedly apply edge-conditioned tensor-product convolutions over graph edges. Conventional implementations materialize edge-specific weights, messages, and adjoints, causing tensor-product workspace and memory traffic to grow rapidly with graph size and operator width. This limits feasible workloads and can prevent larger problems from fully utilizing the GPU. We show that these edge-sized intermediates are artifacts of the execution schedule, not requirements of the equivariant operator. By reassociating radial projection, spherical-harmonic coupling, and graph aggregation, edge-local products can be consumed directly into bounded receiver-side state. The resulting streaming formulation preserves fully connected multiplicity mixing and extends through forward, backward, and double backward. We implement this formulation in Sobek, a generated-CUDA backend, and evaluate it across edge-scaling regimes and varied feature structures. Across two operator families and all three differentiation orders, Sobek is faster in all 75 capacity-matched comparisons, with speedups ranging from $1.2\times$ to $49.7\times$, and reduces peak allocated memory by up to 99\%. It also executes workloads up to two orders of magnitude beyond OpenEquivariance's capacity while retaining near-peak throughput. These results show that edge-scaled tensor-product workspace is a property of the conventional schedule, not of equivariant convolution itself.
#05Jul 20, 2026
cs.LG
Generalised Bellman recurrence and three dualities in sequential decision-making
Fernando E. Rosas, David Hyland, Daniel Polani
What gives the Bellman equation its form? We show that the recursive properties of optimal value functions follow from three conditions: that the dynamics decomposes through sufficient statistics, that the return decomposes recursively, and that the aggregation of uncertainty is compatible with both. When all three conditions hold on a common state, the Bellman equation arises from their mutual consistency; when one fails, tractability can often be recovered by augmenting the state or by deforming return or dynamics. The same conditions are shown to give rise to three dualities: one between probability and return, one between return and aggregation, and one between aggregation and probability. Our framework reveals these dualities as arising from a single construction, unifying methods developed separately across reinforcement learning, control, and decision theory.