#01Nov 4, 2026
physics.flu-dyn
FlowReconBench: Accuracy, calibration and cost of learned and classical flow reconstruction from sparse sensors
Nicolas Tricard, Linzheng Wang, Jason Chen and 1 more
Reconstructing full flow fields from sparse sensors requires prior assumptions about unmeasured regions and physical variables. Yet it remains unclear when learned models outperform classical estimators and which aspects of their predictions can be trusted. FlowReconBench evaluates ten learned and five classical methods on three regimes: a laminar cylinder wake across Reynolds numbers, two-dimensional Kolmogorov turbulence and a large-scale three-dimensional (3D) isotropic turbulence. Methods share leakage-controlled splits and sensor draws and are scored on per-channel error, ensemble spread, calibration, spectra and cost. The leading method changes for each regime. Classical methods perform strongly in low-order and dense-sensing regimes. On the cylinder wake, linear stochastic estimation and gappy proper orthogonal decomposition lead, including for unobserved pressure. In 3D, inverse-distance weighting matches the best learned methods on observed channels. Data-driven methods become superior at decreasing sensor density or poor sensor observability. On Kolmogorov flow, continuous ranked probability score and error yield different method rankings: generative models offer broader but underdispersed ensembles, while deterministic models prioritize pointwise error. Generative models balance this tradeoff through their sampler budget, with a larger budget improving ensemble quality at higher computational cost. In 3D, scaling tests demonstrate that queryable methods are flat in memory, while full-grid construction methods run out of memory. Observing only 2 of 4 fields leaves the problem kinematically underconstrained, yet a latent model can reproduce structural similarities to the ground truth.
#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
cs.LG
FedFiOT: Fisher-Weighted Optimal Transport for Model Merging in One-Shot and Few-Round Federated Learning
Quan Minh Nguyen, Hoang M. Ngo, Bhakti Chowkwale and 2 more
One-shot and few-round federated learning (FL) reduce communication burden by constructing a global model within one or a few communication rounds, but often achieve lower performance than conventional multi-round FL. Without frequent synchronization, client models may drift apart, causing neurons that learn similar features to occupy different positions across clients. At the same time, local data heterogeneity can cause corresponding parameters to differ in their importance to each client's predictions. Together, these challenges cause direct averaging to combine mismatched neurons and assign equal weight to parameters despite differences in their importance. We propose FedFiOT, a Fisher-weighted optimal transport framework for one-shot and few-round FL that leverages Fisher information to quantify parameter importance and guide neuron alignment and model aggregation. FedFiOT jointly optimizes neuron correspondences and global model parameters through alternating minimization of a shared Fisher-weighted objective. Theoretically, we show that FedFiOT's optimization procedure monotonically decreases the layer-wise merging objective and establish a stationarity bound that quantifies the effects of client heterogeneity and nonuniform Fisher weighting.Experiments across multiple datasets demonstrate consistent improvements over competing baselines in both one-shot and few-round federated learning settings.
#04Nov 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.
#05Nov 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.