#01Nov 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.
#02Nov 4, 2026
math.ST
Regularization vs. Convolution in Kernel-Based Hypothesis Testing
Omar Hagrass, Bharath K. Sriperumbudur
The maximum mean discrepancy (MMD) test is a popular nonparametric test on general domains. Two lines of work have studied its optimality through structurally different approaches. The first, a convolution approach on $\mathbb{R}^d$, uses translation-invariant kernels with a shrinking bandwidth and is minimax optimal over Sobolev balls under $L^2$-separation; the second, a regularization approach on general measurable spaces, uses spectral regularization of the kernel covariance operator and is minimax optimal over Hellinger- and $χ^2$-separated alternatives. In this paper, we study the regularization approach over Sobolev balls under $L^2$-separation, which reveals the connection between the two approaches. We show that, with a translation-invariant kernel on $\mathbb{R}^d$, both are ways of meeting a single condition on the kernel's spectral density: the spectral regularized discrepancy captures the $L^2$-separation $Δ$ of a Sobolev alternative of smoothness $s$ as soon as the regularization parameter $λ$ is below the spectral density on frequencies up to $Δ^{-1/(2s)}$. A kernel with a shrinking bandwidth $h$ meets this condition with $λ\asymp h^d$, and under this coupling the constant regularizer, which gives the MMD test itself, attains the Sobolev minimax rate. This explains, from a spectral perspective, the need for a shrinking bandwidth in the convolution approach. With a non-constant spectral regularizer, our analysis requires the bandwidth to shrink only when the spectral density decays faster than any polynomial, as for the Gaussian kernel. Thus, for Matérn and Laplace kernels, a fixed bandwidth with $λ\to 0$ attains the Sobolev minimax rate. Finally, an adaptive test over a grid of bandwidths and regularization parameters is minimax optimal, up to a $\log\log$ factor, over both classes without prior knowledge of the smoothness.
#03Nov 4, 2026
cs.CV
Same Layout, Different Count: What Number Words Do Past Ten in Text-to-Image Models
Liang Yue, Eric A. Vance
Ask SD3.5-Medium for twelve of an object and then, from the same starting noise, for twenty-five. The picture keeps its layout, but the count changes about as much as it would under a new random seed, and in no consistent direction. We study what number words do once a request passes about ten objects, in five open text-to-image models. Holding the object and the starting noise fixed, we change one thing at a time, and people who never see the request count 3,088 of the images. Every model follows the number for small crowds, but only up to a point, its reach: SD3.5-M and FLUX.1-dev stop following it soon after ten, while FLUX.2 [klein] and Qwen-Image follow it loosely up to twenty-five. Beyond SD3.5-M's reach, the coarse part of the starting noise fixes the composition of the picture but not how many objects it holds: redrawing only the noise finer than an eighth of the image keeps the layout as well as a new number does, and already moves the count two-thirds as far. The number word still reaches the denoiser and acts in its first steps, but nothing we tried gives it a clear direction. Shown instead as a noised grid in the starting latent, the count is drawn: people find it in 59% of images, against 4% when it is only told. Past ten, an exact-match score barely separates a model that follows the number loosely from one that ignores it, and a relative-error score can even prefer a constant guess of sixteen. A same-noise test with a few requests per object tells them apart.
#04Nov 4, 2026
cs.AI
ConceptARC at Scale: Studying Conceptual Understanding in Reasoning Models
Philipp Mondorf, Adrien Deliège, Solim LeGris and 5 more
Large reasoning models (LRMs) perform well on challenging benchmarks, yet it remains unclear whether they form generalizable abstractions across conceptually related reasoning tasks. The Abstraction and Reasoning Corpus (ARC) provides a controlled testbed for studying abstraction, requiring solvers to infer transformation rules over two-dimensional grids from a small set of examples. While ARC evaluates rule abstraction within individual tasks, different tasks may share higher-level structure despite requiring different transformations$\unicode{x2014}$for example, several tasks may involve reasoning about objects contained within other objects. Benchmarks such as ConceptARC capture this structure by grouping ARC-style tasks into recurring spatial and semantic concepts, but they often contain only a few manually constructed tasks per concept. We introduce ConceptARC at Scale, a generator for creating thousands of ARC-style tasks targeting a specific concept. Using this generator, we construct ConceptARC-100, a dataset of 1,600 new, manually reviewed tasks, with 100 tasks for each of the 16 concepts defined by ConceptARC$\unicode{x2014}$ten times the size of the original benchmark. We evaluate a range of recent LRMs and models trained from scratch on ConceptARC-100 to characterize which concepts they solve reliably and where they struggle. We further analyze the models' internal representations and find clear semantic structure: task representations cluster according to the operations applied to objects, such as recoloring, removal, or translation, even when realized through substantially different rules and scenarios. Together, our results suggest that models form stable abstractions of transformation operations that generalize across diverse tasks.
#05Nov 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.