#01Nov 4, 2026
cs.LG
Message-passing graph persistence
Jorge Luiz Franco, Arthur Queiroz Moura, Moacir Ponti and 1 more
Message-passing graph neural networks (GNNs) are limited in expressive power by the one-dimensional Weisfeiler-Leman test. Persistent homology (PH) provides topological descriptors that can complement GNN representations, but existing approaches typically compute persistence separately from the representation learning process. In this paper, we introduce Message-Passing Graph Persistence (MGP), a family of topological descriptors that incorporates message passing into graph filtrations. At each filtration step, node embeddings are updated using the current subgraph and associated with persistence events. These embeddings also determine the representatives of connected components during persistence computation. We prove that MGP is invariant under graph isomorphism and that it is strictly more expressive than the PH-based descriptors it extends. We evaluate MGP on an expressivity benchmark and on several graph classification and regression datasets. Experiments show that MGP outperforms other PH-based descriptors on most of these datasets.
#02Nov 4, 2026
math.ST
Fundamental Limits of Coherent Imaging in The Presence of Atmospheric Turbulence
Songbin Liu, Hanyu Yang, Junren Chen and 1 more
We study the fundamental limits of jointly estimating the signal amplitude and the atmospheric phase distortion in complex-valued multi-look coherent imaging, where the measurements are corrupted by multiplicative speckle and additive Gaussian noise, all looks share a known Gaussian sensing matrix, and both parameters belong to structured classes. By analyzing a constrained maximum likelihood estimator, we establish an upper bound on the joint minimax risk that holds uniformly over the admissible parameter classes, while oracle reductions and Fano-type arguments yield worst-case lower bounds over the admissible parameter classes. These results quantify the effects of structural complexity, signal and measurement dimensions, the number of looks, and the noise level, and establish matching minimax rates in several settings, with a remaining gap for phase estimation at low noise when the measurement dimension exceeds the signal dimension. We also construct a two-stage estimator for signal recovery under arbitrary diagonal sign distortions in the real-valued analogue. Under additional conditions, it recovers the signs up to a global sign with high probability and yields a uniform signal risk bound without a distortion-complexity term. Numerical experiments illustrate the dependence of the joint, signal, and phase errors on the model parameters and provide further support for the theoretical analysis.
#03Nov 4, 2026
cs.LG
Reinforcement Learning Enables Scaling Generalist Robot Policy Improvement
Michal Korniak, Marco Bagatella, Ralf Römer and 21 more
The introduction of generalist robot policies has enabled a single, large model to learn to perform a variety of tasks from a vast pre-training corpus. While these models often exhibit powerful zero-shot generalization capabilities, they typically require an adaptation phase to achieve sufficient performance in deployment. Iterated self-improvement via reinforcement learning (RL) has demonstrated promise in enabling this adaptation, yet such approaches have been largely explored in single-task settings - where the goal is to simply improve on a narrow deployment task - which lies in stark contrast to the multi-task capabilities of the base policy. In this work we ask whether generalist robot policies are capable of multi-task, generalist improvement in deployment - targeting many diverse tasks simultaneously - and what algorithmic recipe enables this. To answer this question, we first develop a set of structured evaluations to test generalist improvement capabilities, and systematically evaluate algorithmic and practical design choices regarding value estimation, policy extraction and resource allocation. We show that not only can generalist policies be improved online across diverse tasks, but that the right recipe can enable generalization and increase performance on tasks not considered during online training. We characterize when this generalization occurs and show that both the training task distribution and the use of value-based RL are critical. To the best of our knowledge, this is among the first evidence for online generalist improvement for robot foundation models.
#04Nov 4, 2026
cs.LG
Context--Answer Metamodels: Forecasting LLM Activations Before the First Answer Token
Tommy He, Thomas Jiralerspong
Under stochastic decoding, a single context can elicit many different answers from a language model. Characterizing this variation typically requires many expensive autoregressive rollouts, each revealing only one realization. We ask whether the activations produced while reading the context can directly forecast the model's rollout activations. We train context--answer metamodels that map a context activation sequence to point or distribution forecasts of mean-pooled answer activations. We find that (i) the four metamodel families we study forecast mean-pooled answer activations with high fidelity, and the distribution metamodels also capture rollout variability; (ii) performance improves as the training set grows to 500,000 prompts, and the metamodels generalize zero-shot to out-of-domain datasets; (iii) their forecasts retain behavior-predictive signal; and (iv) context activations from Qwen2.5 predict mean-pooled answer activations from Qwen3.5 and Gemma 4, suggesting that activation forecasts can transfer across models. Together, these results suggest that context activation traces can support scalable forecasts of behaviors in LLM answers before the first answer token is generated.
#05Nov 4, 2026
cond-mat.mtrl-sci
Evolutionary Design of Interpretable Spatial Descriptors for Structure-Property Relationship Discovery
Aditya Raghavan, Sergei V Kalinin
Structure property prediction is a classical task in machine learning, ranging from molecular activity and materials properties to local functional responses measured in microscopy. For image-based regression, two choices define the information available to the predictor: the size of the image neighborhood and the spatial resolution retained within it. A small neighborhood can omit relevant surrounding structure, whereas a large, finely sampled neighborhood can introduce redundant or irrelevant information. Here, we develop a framework for constructing spatial descriptors for prediction of local spectra and hysteresis loops. We benchmark regression models, use SHAP maps to examine their spatial attribution, and explore the effect of the patch size and compression to establish the relationship between predictive accuracy and descriptor dimensionality. We then use a genetic algorithm to optimize spatial partitions and the assignment of mean, minimum, and maximum pooling operations. Each retained region contributes an explicit measurement of the image, allowing the search to balance prediction error against the number of descriptor values. Cartesian and polar constructions provide complementary ways to organize this information. The resulting descriptors make it possible to examine where spatial detail is needed, where regional summaries are sufficient, and how these choices depend on the predictor and the measured response. The same approach can be used for molecules and solids once the genetic algorithm rules for these are established.