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We prove a non-asymptotic central limit theorem for vector-valued martingale differences using Stein's method, and use Poisson's equation to extend the result to functions of Markov Chains. We then show that these results can be applied to establish a non-asymptotic central limit theorem for Temporal Difference (TD) learning with averaging.
Diffusion models generate skillful weather ensembles but require costly iterative sampling. We introduce a supervised energy-distance distillation method that compresses a multi-step diffusion teacher into a single-step student by aligning student forecasts with teacher samples and ground-truth observations. Experiments on global forecasting and typhoon-track prediction show that our student outperforms existing distillation methods and preserves skill for extreme events. It matches or surpasses the teacher across key metrics using only one neural function evaluation per autoregressive step.
As several mathematical conjectures have recently been settled using large language models (LLMs), the mathematical community has formulated norms and recommendations regarding the publishing of such results. These norms do not cover the disclosure of the prompts and precise software setup used to obtain those results, nor do they require that results be formalized in a manner that allows for machine verification. I argue that both of these are essential. In addition, since LLM-obtained results may be hard to understand, human authors have the responsibility to invent intuitive explanations.
Many real-world queries over personal data span multiple applications and require structured planning, as individual tools expose only partial information. While LLMs show strong reasoning and tool use, reliably executing multi-step, cross-tool queries remains challenging. We introduce a system that converts natural language queries into structured graphs and executes them via a deterministic planner. Our approach uses depth-first search to resolve dependencies and combine results across tools, improving reliability and enabling queries beyond traditional keyword-based search. We demonstrate high accuracy even with smaller or locally hosted LLMs.
Recommender systems (RS) greatly influence users' consumption decisions, making them attractive targets for malicious shilling attacks that inject fake user profiles to manipulate recommendations. Existing shilling methods can generate effective and stealthy fake profiles when training data only contain rating matrix, but they lack comprehensive solutions for scenarios where side features are present and utilized by the recommender. To address this gap, we extend the Leg-UP framework by enhancing the generator architecture to incorporate side features, enabling the generation of side-feature-aware fake user profiles. Experiments on benchmarks show that our method achieves strong attack performance while maintaining stealthiness.
We propose a multi-task learning approach for multi-party dialogue intent recognition that leverages an auxiliary task that models turn-taking dynamics. Specifically, we introduce turn-transition entropy, a self-supervised target computed from the sequence of speaker transitions, which quantifies the predictability of interaction patterns. Experiments on multiple pre-trained models demonstrate that incorporating this auxiliary task improves intent recognition performance, outperforming existing approaches which ignore multi-party interaction dynamics. We find that our proposed continuous target can be learned as a single-task objective, suggesting that it is an actual signal carrying useful information.
The recently introduced block-sparse featurizer (BSF; Fel et al., 2026) is similar to a sparse autoencoder (SAE), but its atomic unit is a small subspace (a block of directions) rather than a single direction. It is designed for features that live on low-dimensional manifolds, which are especially frequent in vision. This work studies the BSF's strengths and weaknesses, finding how it still somewhat suffers from classic SAE failure modes, like feature splitting and composition. We propose several architectural changes to the BSF, including a Tournament Top-K selection rule that significantly reduces feature splitting, and we also extend the block paradigm to the crosscoder.
The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions. Conventional approaches typically trade off simulation-free training against finite-time generation. We propose a framework for designing the reference process that achieves both simultaneously. The key idea is to prescribe tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals. This framework reveals that score matching is not fundamental to diffusion-model training but instead emerges naturally through reversal of the reference process. We further show that conditional flow matching arises as the small-noise limit of the proposed framework.
Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn how to design them. Modern frameworks such as PyTorch, TensorFlow, and JAX enable this paradigm through efficient automatic differentiation. Embedding first-order methods within these systems allows end-to-end training that improves convergence and solution quality. Guided by Fenchel-Rockafellar duality, the tutorial demonstrates how duality-informed iterative schemes such as the alternating direction method of multipliers, and the primal-dual hybrid gradient can be learned and adapted through representative case studies.
We propose a conjugate and calibrated Gaussian process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained Euclidean representation, turning classification into a GP regression problem with fewer latent dimensions than standard multi-class GP classifiers. This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction. The method is compatible with standard sparse GP regression techniques, enabling scalable inference on larger datasets. Empirical results show well-calibrated and competitive performance across synthetic and real-world datasets.
Recent machine learning research has increasingly focused on equilibrium analysis in non-cooperative games rather than solely on optimal solutions. Many such problems involve shared constraints and can be formulated as Generalized Nash Equilibrium Problems (GNEPs). For strongly monotone games, existing methods compute consensus-based variational GNEs (v-GNEs) by exchanging Lagrange multipliers. We propose a fully distributed continuous-time algorithm for shared linear equality constraints that converges without multiplier exchange and reaches any GNE, reducing communication overhead and improving privacy. Discrete-time schemes are also provided, and the method is validated on a multi-robot placement task.
Existing GNN quantization methods suffer from considerable quantization overhead, which severely limits their practical usage in real-world scenarios. To this end, we present TopGQ, an accurate post-training GNN quantization framework, alleviating redundant quantization overhead. We propose dual-axis scale absorption, which enables activation quantization along both the outer and inner dimensions by merging one into the adjacency matrix. On top of that, we introduce TopPIN, a proxy for nodes' local structure, and use it to group nodes with similar topology during quantization. Experimental results show that TopGQ reduces quantization time by an order of magnitude while preserving accuracy.
We extend the FLOP (fast learning of order and parents) algorithm recently proposed by Wienöbst et al. (2026) from observational to interventional data. In particular, we use the interventional BIC score of Hauser and Bühlmann (2012), adapting it to be used with the iterative Cholesky-based score updates that are partly responsible for FLOP's speed. We show that, in the sample limit, I-FLOP recovers a DAG in the same interventional Markov equivalence class as the data-generating DAG. We compare I-FLOP to existing causal structure learning algorithms on real and simulated interventional data, where it performs favorably in terms of both performance and run time.
This paper presents ContrastWSD, a RoBERTa-based metaphor detection model that integrates the Metaphor Identification Procedure (MIP) and Word Sense Disambiguation (WSD) to extract and contrast the contextual meaning with the basic meaning of a word to determine whether it is used metaphorically in a sentence. By utilizing the word senses derived from a WSD model, our model enhances the metaphor detection process and outperforms other methods that rely solely on contextual embeddings or integrate only the basic definitions and other external knowledge. We evaluate our approach on various benchmark datasets and compare it with strong baselines, indicating the effectiveness in advancing metaphor detection.
We propose a novel test for assessing partial effects in Fréchet regression with responses lying on the Bures-Wasserstein manifold. Under the null hypothesis, we show that the statistic admits a degenerate V-statistic approximation whose limiting distribution is a weighted mixture of chi-squared random variables, with weights determined by the eigenvalues of an integral operator associated with a reproducing kernel Hilbert space (RKHS) kernel. We establish the asymptotic validity and consistency of the proposed test. Its finite-sample performance is examined through simulation studies. We apply the proposed test to study the effect of age, while controlling for other covariates, on gene co-expression structure in single-cell data.
Training effective foundation models requires massive and organized datasets, yet scientific domains such as nuclear fusion present unique challenges due to largely heterogeneous and sparse data. Here we characterize the data used in developing such a model: with over 20 sensor types spanning 5 orders of magnitude in sampling rate, mixed tensor structures (point measurements, spectrograms, images), and nonstationary physics. We analyze our input complexity and discuss trade-offs between temporal context and frequency resolution. Our analysis provides a template for representing multi-modal fluctuation data at scale, with implications for both multi-modal control systems and nuclear fusion.
We present CheXtriev, a graph-based, anatomy-aware framework for chest radiograph retrieval. Unlike prior methods focussed on global features, our method leverages graph transformers to extract informative features from specific anatomical regions. Furthermore, it captures spatial context and the interplay between anatomical location and findings. This contextualization, grounded in evidence-based anatomy, results in a richer anatomy-aware representation and leads to more accurate, effective and efficient retrieval, particularly for less prevalent findings. CheXtriv outperforms state-of-the-art global and local approaches by 18% to 26% in retrieval accuracy and 11% to 23% in ranking quality. The code is available at https://github.com/cvit-mip/chextriev.
Large language models (LLMs) exhibit remarkable reasoning capabilities, but their task-specific fine-tuning is notoriously plagued by overconfidence, severely hindering trustworthy deployment. We propose Data-Adaptive Lower-Rank Adaptation (DALorRA), a simple and effective variational Bayesian sparse framework that shifts the paradigm of uncertainty quantification from the dense parameter space to the lightweight rank level of low-rank adaptation (LoRA). With the insight that LoRA essentially aggregates multiple rank-one components that may provide superfluous model capacity, DALorRA imposes stochastic masking on rank dimensions, enabling Bayesian regularization of model capacity during training and ensemble-like calibration during inference. Extensive experiments demonstrate DALorRA's excellent calibration of LLMs without compromising reasoning accuracy.