#01Nov 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.
#02Nov 4, 2026
quant-ph
GFlowQEC: Generative Flow Networks that Learn to Sample Quantum LDPC Codes
Nuno Batista, Gabriel Falcao, Penousal Machado
Choosing a quantum error-correcting code for a real device means scoring candidates with circuit-level simulations so slow that only a few hundred can be run. So every evaluation counts, and a search is judged by how many good codes it finds per paid evaluation. Quantum LDPC codes built from a few group elements protect many logical qubits, but good ones are rare in a huge space. We introduce GFlowQEC, to our knowledge the first generative flow network (GFlowNet) for quantum code design. It builds a code one group element at a time and learns to propose codes in proportion to a power of their score. We train it once on scores from earlier searches, freeze it, and let it propose lifted-product codes with 180 physical qubits, scored by their distances. Ranking ten of its draws per paid call, it finds more than twice as many new top-scoring codes (inequivalent to any it was trained on) as tuned parallel tempering, even when tempering starts from GFlowQEC's training codes. It finds more than three and a half times as many as a supervised screen ranking ten random candidates per call. When both rank a hundred, the screen beats GFlowQEC, and does best ranking GFlowQEC's draws. Soft Q-learning, which shares the GFlowNet's optimal policy, does as well at one noise bias and better at the other, so the gain does not depend on the GFlowNet's training loss. Trained proposers can make a budget of expensive evaluations go further when good codes are rare.
#03Nov 4, 2026
cs.CV
CounterFactual Retrieval for Evidence-Aware Individual Animal Identification
Ankit K. Upadhyay, Aleksandr Algasov, Ekaterina Nepovinnykh and 5 more
Automated identification of individual animals is moving from small curated studies toward shared benchmarks and reusable foundation models. This progress is useful, but current evaluation leaves the evidence behind a match unresolved, i.e., high retrieval accuracy does not show whether a model used animal features or identity-correlated shortcuts. We address this with Counterfactual Foreground Retrieval (CFR), an evidence-aware evaluation protocol. CFR evaluates the same query-gallery task under different views: full image, foreground-only, and shortcut-only. The full-image measures standard retrieval performance; the foreground-only measures foreground-supported retrieval; and shortcut-only view measure how much identity signal is recoverable from background, or silhouette. This turns a retrieval score into an evidence profile: how well the model performs on the original images, how much of that performance remains when only the animal is visible, and how much identity signal remains recoverable when the animal is removed. We release around 0.5M masks for 34 datasets and code for mask generation and CFR evaluation.
#04Nov 4, 2026
cs.LG
Systolic Linear Attention: Co-Designing Tile-Grouped Gated Delta Attention for TPUs
Gagik Amirkhanyan, Nuojin Cheng
Gated-delta linear attention layers such as Gated DeltaNet (GDN), Kimi Delta Attention (KDA), and GDN-2 are tuned for GPUs, where small tensor-core tiles and fast vector registers make per-channel decay rescaling and sequential in-block solves cheap. On Google TPUs, which concentrate compute in wide $256 \times 256$ systolic matrix units backed by a slower vector unit, porting these layers directly leaves half of each matrix tile empty and bottlenecks on vector operations. We present \textbf{Systolic Linear Attention (SLA)}, which reshapes gated delta attention around the matrix unit by widening keys to $256$ with grouped value heads, grouping decay gates into four $64$-channel tiles, and computing the chunk solve entirely with block matrix products in a single fused kernel. On TPU v7x, a full \texttt{SLA-R4} layer runs $1.6\times$--$2.5\times$ faster than the open-source Tokamax KDA kernel ($1.4\times$--$2.4\times$ with exact chunk inversion), driven primarily by head sharing and kernel fusion. Across a $2{,}048$-chip TPU v7x pre-training study of sparse Mixture-of-Experts (MoE) models from $6.5\text{B}$ to $63.1\text{B}$ parameters, SLA trains $11\%$--$24\%$ faster than KDA at similar perplexity, and reaches slightly lower perplexity than KDA in smaller matched-seed runs.
#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.