#01Nov 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.
#02Nov 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.
#03Nov 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.
#04Nov 4, 2026
cs.CV
Turns Matter: Advancing Streaming Video RL via Turn-Level Credit
Shuai Dong, Kanghui Tian, Linghan Chen and 20 more
Streaming video understanding requires models to repeatedly decide whether to respond or continue observing. Recently, Group Relative Policy Optimization (GRPO) has been applied to this setting, with existing approaches emphasizing reward design while retaining a single trajectory-level advantage across turns. Such shared credit can reinforce redundant replies after earlier successes and discourage useful follow-ups after earlier failures. We propose TurnWise, a turn-level GRPO framework that aligns learning with individual streaming decisions. TurnWise addresses the mismatch between trajectory-level feedback and turn-level interaction, promoting informative responses and reducing redundancy. Specifically, turn-level credit assignment uses silence-completed prefix scoring to construct group-relative advantages from each decision's remaining return, separating its learning signal from earlier rewards. Turn-mean policy optimization averages token losses within each turn and then across turns, giving response and waiting decisions equal weight regardless of output length. These complementary designs improve streaming policy learning without a learned critic or additional rollouts. Extensive experiments show our method outperforms prior RL approaches for streaming video understanding.
#05Nov 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.