#01Nov 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.
#02Nov 4, 2026
cs.LG
Transforming Integer Grids to Spatial Intuition: Perception, Not Planning, Governs ARC-AGI-3
Harsidak Singh Banwait
Sample-efficient fluid intelligence requires agents that rapidly form working models of unfamiliar interactive environments. ARC-AGI-3 tests this across uninstructed visual games scored by Relative Human Action Efficiency, which penalizes exploratory waste quadratically. When frontier models read raw integer grids, serialization destroys spatial topology, and they spend hundreds of actions rediscovering basic boundaries and symmetries. We introduce SARBLOH, an open-weight agent built on the premise that spatial perception, not planning capacity, governs interactive reasoning on ARC-AGI-3. A zero-parameter O(HW) perception engine turns each frame, in 35 ms, into an object inventory with bipartite temporal tracking, a geometric briefing that separates proven invariants from affordance hypotheses, and an annotated canvas. Paired with a code-as-action runtime, the agent writes algorithmic hypotheses instead of low-level moves. Across eight presentations, grounded perception raises the rubric score from 3/28 to 25/28 points while cutting token use by 89.4%. On 23 held-out games, geometric invariants generalize with 100% accuracy, while single-frame affordance guesses fall to 6-50%, so active verification probes remain necessary. On the public set, Run A (briefing off) solved 143 of 183 levels in 8.2 hours at 59.4% single-pass efficiency; Run B (briefing on) reached 63.5%. Within the nine-hour budget on one Kaggle RTX PRO 6000 GPU, SARBLOH scored 16.53 on the hidden Kaggle evaluation, 13.7x the first Milestone winner.
#03Nov 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.
#04Nov 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.
#05Nov 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.