#01Nov 4, 2026
cond-mat.mtrl-sci
Thermally Conditioned Time-Series Forecasting of Grain Growth in Polycrystalline Materials
Eliane Younes, Elie Hachem, Marc Bernacki
Grain growth during heat treatment strongly affects the microstructure of polycrystalline materials and, consequently, their mechanical properties. Although numerical methods such as front-tracking or front-capturing simulations can accurately describe grain growth, their high computational cost limits their use for long or non-isothermal thermal cycles. In previous work, grain growth was successfully predicted under isothermal conditions by treating grain size distributions as time series and forecasting their evolution using recurrent neural networks, allowing complete grain growth trajectories to be generated in seconds rather than through costly PDE-based simulations. In the present work, this forecasting framework is reformulated to handle non-isothermal conditions by explicitly incorporating thermal information into the model architecture. Grain size distributions are encoded using a convolutional neural network, thermal descriptors are embedded through a dedicated multilayer perceptron, and temporal evolution is predicted using a recurrent network. Instantaneous temperature and thermal rate are provided at each time step, allowing the model to adapt its predictions to changing thermal conditions. The framework is trained and evaluated on datasets generated from validated front-tracking simulations across a wide range of non-isothermal thermal paths. The results show that the thermally conditioned model accurately reproduces grain growth dynamics under complex thermal histories, achieving, in k-fold cross-validation over all simulations, mean relative errors of 2.99% (one-hour cycles) and 4.51% (four-hour cycles) with coefficients of determination exceeding 0.99, and mean relative errors between 1.91% and 14.66% on ten simulations following four unseen thermal histories of increasing complexity.
#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.LG
Continual Classification Beyond the Kernel Regime: Harnessing the Sparsity Bias of L2 Regularization in Diagonal Linear Networks
Gilad Karpel, Itay Evron, Ron Meir and 1 more
We study logistic regression for continual learning with linear predictors in a high-dimensional statistical setting. Existing theoretical work has largely focused on continual linear regression with variants of L2 regularization, motivated by their analytical simplicity and connection to the kernel regime of neural networks. We first derive the optimal L2 regularization strength for continual linear classification and characterize its generalization performance, recovering behavior analogous to prior results for continual linear regression. Next, we examine the effect of L2 regularization in deeper models using a minimal two-layer diagonal linear network. In the single-task setting, L2 regularization on the weights of such models is known to promote sparsity in the resulting predictor, yielding a rich, sparse feature-learning regime beyond the kernel regime (a similar effect arises in two-layer ReLU networks). However, in continual learning, where L2 regularization is typically centered on previous-task weights, this sparsity bias is no longer preserved. We therefore propose a weighted variant of L2 regularization that extends this beneficial sparsity bias to continual learning. We show theoretically and empirically that, for a sufficiently sparse teacher, our variant converges substantially faster than directly learning a linear predictor with conventional continual L2 or L1 regularization, trading some long-horizon bias for markedly improved performance over moderate task horizons.
#04Nov 4, 2026
cs.RO
Perceptive Humanoid Motion from Simulation
Siyuan Hu, Abulikemu Abuduweili, Yue Meng and 5 more
Humanoid robots have the potential to automate a wide range of physical tasks. Progress toward generalist humanoid autonomy, however, remains constrained by a data bottleneck: mapping pixels and free-form language to low-level joint commands requires paired supervision, and no corpus of such data exists at sufficiently large scale. Some approaches rely on human teleoperation and wearable capture devices, which require at least an hour of human time to produce an hour of data. We present HALO, a humanoid autonomy system powered by a pipeline that synthesizes vision-language-motion data across a thousand procedurally generated homes. The corpus scales with compute rather than human labor. HALO acquires a repertoire of physical skills, including sitting on chairs, navigating to named objects, stepping sideways through half-open doors, crouching and crawling beneath tables, and pushing boxes. It orchestrates these skills to solve composite, long-horizon tasks. Without ever seeing a real home during training, HALO transfers zero-shot to the physical world, achieving a 91% success rate across 360 trials in six unmapped real-world environments. See https://apple-aiml-research.github.io/ml-halo/ for code and videos.
#05Nov 4, 2026
cs.LG
Adaptive Multi Mode: Budget-Aware Routing of Optimizers By Online Landscape Probes
Benjamin Jacob Bodner
The best classical optimizer for a continuous black-box problem depends on its budget and landscape. Existing routers decide from the dimension and budget, past improvement or features fitted to one benchmark, and few test an optimizer's implicit assumptions online. AMM (Adaptive Multi Mode) routes a known budget among quasi-Newton, trust-region, coordinate, multistart and evolution-strategy optimization engines with online probes of curvature, plateaus, separability, kinks, basins and fractal structure. Each probe has a default, a dimension-by-budget validity range and a cost charged to the budget. In its pre-registered development loop on bbob, 32 of 36 predictions held over the last 16 confirmations. AMM was then tested once on held-out bbob instances 101-110 (D=2-40, 10*D-1000*D) against up to seven competitors. It has the highest target share in 382 of 600 function-dimension-budget cells (236 outright, 146 tied) and, by a descriptive posterior rule, is credibly behind in 35, mostly at 10*D and 30*D. At every budget it also leads the controls built from its own engines (the best engine alone, the best engine per dimension and budget, and a greedy schedule), narrowly at 10*D and 30*D, and nevergrad's NgIohTuned. In pre-registered runs its lead over IPOP-CMA-ES holds under affine and box transformations, on box-constrained bbob and, pooled, on rotated f2-f4, but rotating the separable f3 and f4 removes most of the lead there. On held-out MA-BBOB its final share at 2000*D is level with IPOP-CMA-ES's and its anytime area lower. We published AMM as an open-source Python package (pip install amm-optimizer; https://github.com/BjBodner/amm-optimizer).