Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time trajectory increments, state-space partitioning, or repeated simulation of candidate models, which become unreliable or computationally expensive for high-dimensional systems, coarse temporal sampling, or unevenly sampled data. We introduce a data-driven calibration method based on a novel relationship between the coefficients of a stochastic reduced model and the conditional score of the finite-time transition density, defined as the gradient of the logarithm of the transition density with respect to the initial state. The resulting identity expresses derivatives of lagged correlation functions as stationary expectations over observed lagged pairs involving this conditional score and the unknown model coefficients. This formulation allows the drift and diffusion structure to be constrained directly from finite-lag statistics, without differentiating trajectories, partitioning state space, or repeatedly integrating candidate reduced models during calibration, yielding a least-squares fitting problem over stationary lagged pairs. We validate the approach on analytically tractable and data-driven nonequilibrium diffusions, demonstrating that the inferred models preserve the invariant statistics while accurately reproducing finite-lag dynamical correlations. The framework provides a scalable route for learning stochastic reduced-order models from data that reproduce prescribed statistical and dynamical properties.

Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency: practitioners value understanding how a model transforms temporal features, not merely what it predicts. Transformer-based models achieve strong accuracy but their attention weights reveal only token-level relevance, not the functional transformations applied to each feature. This work proposes DECOMPKAN, a lightweight attention-free architecture that combines trend-residual decomposition, channel-wise patching, learned instance normalization, and B-spline Kolmogorov-Arnold Network (KAN) edge functions. Each KAN edge learns an explicit, inspectable 1D scalar function ϕ(x) over learned patch-embedding coordinates that can be directly visualized, offering a form of architectural transparency not directly available in attention-based or MLP-based architectures. On standard benchmarks, DECOMPKAN achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations among selected published baselines, and achieves best or tied-best MSE on 20 of 36 comparisons (25 of 36 MAE; ties counted for all tied models) under a controlled same-recipe evaluation across 9 datasets including the physiological PPG-DaLiA benchmark. The architecture shows particular strength on datasets with smooth temporal dynamics (Solar 17%, ECL 10%vs.

This paper uses a minimum divergence framework to introduce a new way of calculating model weights that can be used to average probabilistic predictions from statistical and machine learning models. The method is general and can be applied regardless of whether the models under consideration are fit to data using frequentist, Bayesian, or some other fitting method. The proposed method is motivated in two different ways and is shown empirically to perform better than or on a par with standard model averaging methods, including model stacking and model averaging that relies on Akaike-style negative exponentiated model weighting, especially when the sample size is small. Our theoretical analysis explains why the method has a small-sample advantage.

In this paper we study continuum-marginal optimal transport. Given a time-continuous family of probability marginals, the problem is to recover the minimum-energy velocity field whose flow reproduces every marginal. This problem is the continuum limit of the classical two-marginal Benamou--Brenier formulation, and also the deterministic limit of the Nelson problem of stochastic optimal transport. We propose a practical mesh-free solver for this problem. The weak continuity equation is embedded in a reproducing kernel Hilbert space, yielding a sample-only objective that requires no spatial discretization. The velocity is parametrized by any linear-in-parameters dictionary or neural network, and is optimized by mini-batch stochastic methods. Synthetic experiments confirm that the method achieves accurate drift recovery and marginal consistency. The same computational framework also applies to the stochastic Nelson problem.

We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect to some semi-metric, around one of its global maxima. Compared to previous works on bandits in general spaces (Kleinberg et al., 2008; Bubeck et al., 2011a) our algorithm does not require the knowledge of this semi-metric. Our algorithm, StoSOO, follows an optimistic strategy to iteratively construct upper confidence bounds over the hierarchical partitions of the function domain to decide which point to sample next. A finite-time analysis of StoSOO shows that it performs almost as well as the best specifically-tuned algorithms even though the local smoothness of the function is not known.

In many areas of medicine, security, and life sciences, we want to allocate limited resources to different sources in order to detect extreme values. In this paper, we study an efficient way to allocate these resources sequentially under limited feedback. While sequential design of experiments is well studied in bandit theory, the most commonly optimized property is the regret with respect to the maximum mean reward. However, in other problems such as network intrusion detection, we are interested in detecting the most extreme value output by the sources. Therefore, in our work we study extreme regret which measures the efficiency of an algorithm compared to the oracle policy selecting the source with the heaviest tail. We propose the EXTREMEHUNTER algorithm, provide its analysis, and evaluate it empirically on synthetic and real-world experiments.

We consider online learning problems under a partial observability model capturing situations where the information conveyed to the learner is between full information and bandit feedback. In the simplest variant, we assume that in addition to its own loss, the learner also gets to observe losses of some other actions. The revealed losses depend on the learner's action and a directed observation system chosen by the environment. For this setting, we propose the first algorithm that enjoys near-optimal regret guarantees without having to know the observation system before selecting its actions. Along similar lines, we also define a new partial information setting that models online combinatorial optimization problems where the feedback received by the learner is between semi-bandit and full feedback. As the predictions of our first algorithm cannot be always computed efficiently in this setting, we propose another algorithm with similar properties and with the benefit of always being computationally efficient, at the price of a slightly more complicated tuning mechanism. Both algorithms rely on a novel exploration strategy called implicit exploration, which is shown to be more efficient both computationally and information-theoretically than previously studied exploration strategies for the problem.

Machine-learning interatomic potentials (MLIPs) have enabled molecular dynamics at near ab initio accuracy, yet remain limited to energies and forces by construction, leaving electronic observables such as dipole moments and polarizabilities inaccessible. We introduce DenSNet, a density-first approach to machine-learned electronic structure that learns the Hohenberg--Kohn map from nuclear configurations to the ground-state electron density. Our approach employs an SE(3)-equivariant neural network to predict density coefficients of a flexible atom-centered Gaussian basis, combined with a $Δ$-learning strategy that uses superposed atomic densities as a prior to accelerate training. A second equivariant network then maps the predicted density to the total energy, providing a unified framework for molecular dynamics and electronic structure. We validate DenSNet on ethanol, ethanethiol, and resorcinol, where infrared spectra from machine-learned trajectories show excellent agreement with experimental gas-phase measurements. To test scalability, we train on polythiophene oligomers with 1--6 monomers and extrapolate to chains of up to 12 monomers, generating stable long-time trajectories whose infrared spectra agree with reference density functional theory calculations. Here, we show that reinstating the electron density as the central learned quantity opens a practical route to transferable prediction of spectroscopic and electronic observables in large-scale molecular simulations.

We study learning with Chain-of-Thought (CoT) supervision from multiple thinkers, all of whom provide correct but possibly systematically different solutions, e.g., step-by-step solutions to math problems written by different thinkers, or step-by-step execution traces of different programs solving the same problem. We consider classes that are computationally easy to learn using CoT supervision from a single thinker, but hard to learn with only end-result supervision, i.e., without CoT (Joshi et al. 2025). We establish that, under cryptographic assumptions, learning can be hard from CoT supervision provided by two or a few different thinkers, in passive data-collection settings. On the other hand, we provide a generic computationally efficient active learning algorithm that learns with a small amount of CoT data per thinker that is completely independent of the target accuracy $\varepsilon$, a moderate number of thinkers that scales as $\log \frac{1}{\varepsilon}\log \log \frac{1}{\varepsilon}$, and sufficient passive end-result data that scales as $\frac{1}{\varepsilon}\cdot poly\log\frac{1}{\varepsilon}$.

While the optimal sample complexity of binary classification in terms of the VC dimension is well-established, determining the optimal sample complexity of multiclass classification has remained open. The appropriate complexity parameter for multiclass classification is the DS dimension, and despite significant efforts, a gap of $\sqrt{\text{DS}}$ has persisted between the upper and lower bounds on sample complexity. Recent work by Hanneke et al. (2026) shows a novel algebraic characterization of multiclass hypothesis classes in terms of their DS dimension. Building up on this, we show that the maximum hypergraph density of any multiclass hypothesis class is upper-bounded by its DS dimension. This proves a longstanding conjecture of Daniely and Shalev-Shwartz (2014). As a consequence, we determine the optimal dependence of the sample complexity on the DS dimension for multiclass as well as list learning.