Existing distribution compression methods, like Kernel Herding (KH), were originally developed for unlabelled data.

Reinforcement learning with general utilities (RLGU) offers a unifying framework to capture several problems beyond standard expected returns, including imitation learning, pure exploration, and safe RL. Despite recent fundamental advances in the theoretical analysis of policy gradient (PG) methods for standard RL and recent efforts in RLGU, the understanding of these PG algorithms and their scope of application in RLGU still remain limited. In this work, we establish global optimality guarantees of PG methods for RLGU in which the objective is a general concave utility function of the state-action occupancy measure. In the tabular setting, we provide global optimality results using a new proof technique building on recent theoretical developments on the convergence of PG methods for standard RL using gradient domination. Our proof technique opens avenues for analyzing policy parameterizations beyond the direct policy parameterization for RLGU. In addition, we provide global optimality results for large state-action space settings beyond prior work which has mostly focused on the tabular setting. In this large scale setting, we adapt PG methods by approximating occupancy measures within a function approximation class using maximum likelihood estimation. Our sample complexity only scales with the dimension induced by our approximation class instead of the size of the state-action space.

Self-Supervised Learning (SSL) for Combinatorial Optimization (CO) is an emerging paradigm for solving combinatorial problems using neural networks. In this paper, we address a central challenge of SSL for CO: solving problems with discrete constraints. We design an end-to-end differentiable framework that enables us to solve discrete constrained optimization problems with neural networks. Concretely, we leverage algorithmic techniques from the literature on convex geometry and Carathéodory's theorem to decompose neural network outputs into convex combinations of polytope corners that correspond to feasible sets. This decomposition-based approach enables self-supervised training but also ensures efficient quality-preserving rounding of the neural net output into feasible solutions. Extensive experiments in cardinality-constrained optimization show that our approach can consistently outperform neural baselines. We further provide workedout examples of how our method can be applied beyond cardinality-constrained problems to a diverse set of combinatorial optimization tasks, including finding independent sets in graphs, and solving matroid-constrained problems.

Human cognition is theorized to operate in two modes: fast, intuitive System 1 thinking and slow, deliberate System 2 thinking. While current Large Reasoning Models (LRMs) excel at System 2 thinking, their inability to perform fast thinking leads to high computational overhead and latency. In this work, we enable LRMs to approximate human intelligence through dynamic thinking speed adjustment, optimizing accuracy-efficiency trade-offs. Our approach addresses two key questions: (1) how to control thinking speed in LRMs, and (2) when to adjust it for optimal performance. For the first question, we identify the steering vector that governs slow-fast thinking transitions in LRMs' representation space.

The advent of single-cell Assay for Transposase-Accessible Chromatin using sequencing (scATAC-seq) offers an innovative perspective for deciphering regulatory mechanisms by assembling a vast repository of single-cell chromatin accessibility data. While foundation models have achieved significant success in single-cell transcriptomics, there is currently no foundation model for scATAC-seq that supports zero-shot high-quality cell identification and comprehensive multi-omics analysis simultaneously. Key challenges lie in the high dimensionality and sparsity of scATAC-seq data, as well as the lack of a standardized schema for representing open chromatin regions (OCRs). Here, we present ChromFound, a foundation model tailored for scATAC-seq. ChromFound utilizes a hybrid architecture and genome-aware tokenization to effectively capture genome-wide long contexts and regulatory signals from dynamic chromatin landscapes. Pretrained on 1.97 million cells from 30 tissues and 6 disease conditions, ChromFound demonstrates broad applicability across 6 diverse tasks. Notably, it achieves robust zero-shot performance in generating universal cell representations and exhibits excellent transferability in cell type annotation and cross-omics prediction. By uncovering enhancer-gene links undetected by existing computational methods, ChromFound offers a promising framework for understanding disease risk variants in the noncoding genome.

We propose Shallow Flow Matching (SFM), a novel mechanism that enhances flow matching (FM)-based text-to-speech (TTS) models within a coarse-to-fine generation paradigm. Unlike conventional FM modules, which use the coarse representations from the weak generator as conditions, SFM constructs intermediate states along the FM paths from these representations. During training, we introduce an orthogonal projection method to adaptively determine the temporal position of these states, and apply a principled construction strategy based on a singlesegment piecewise flow. The SFM inference starts from the intermediate state rather than pure noise, thereby focusing computation on the latter stages of the FM paths. We integrate SFM into multiple TTS models with a lightweight SFM head. Experiments demonstrate that SFM yields consistent gains in speech naturalness across both objective and subjective evaluations, and significantly accelerates inference when using adaptive-step ODE solvers. Demo and codes are available at https://ydqmkkx.github.io/SFMDemo/.

Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.

Occlusion is one of the fundamental challenges in crowd counting. In the community, various data-driven approaches have been developed to address this issue, yet their effectiveness is limited. This is mainly because most existing crowd counting datasets on which the methods are trained are based on passive cameras, restricting their ability to fully sense the environment. Recently, embodied navigation methods have shown significant potential in precise object detection in interactive scenes. These methods incorporate active camera settings, holding promise in addressing the fundamental issues in crowd counting.

Data-driven algorithm selection is a powerful approach for choosing effective heuristics for computational problems. It operates by evaluating a set of candidate algorithms on a collection of representative training instances and selecting the one with the best empirical performance. However, running each algorithm on every training instance is computationally expensive, making scalability a central challenge. In practice, a common workaround is to evaluate algorithms on smaller proxy instances derived from the original inputs. However, this practice has remained largely ad hoc and lacked theoretical grounding. We provide the first theoretical foundations for this practice by formalizing the notion of size generalization: predicting an algorithm's performance on a large instance by evaluating it on a smaller, representative instance, subsampled from the original instance. We provide size generalization guarantees for three widely used clustering algorithms (single-linkage, k-means++, and Gonzalez's k-centers heuristic) and two canonical max-cut algorithms (Goemans-Williamson and Greedy). We characterize the subsample size sufficient to ensure that performance on the subsample reflects performance on the full instance, and our experiments support these findings.

In Transformer language models, activation vectors transform from current token embeddings to next token predictions as they pass through the model. To isolate a minimal form of this transformation, we identify language model subnetworks that make bigram predictions, naive next token predictions based only on the current token. We find that bigram subnetworks can be found in fully trained language models up to 1B parameters, and these subnetworks are critical for model performance even when they consist of less than 0.2% of model parameters. Bigram subnetworks are concentrated in the first Transformer MLP layer, and they overlap significantly with subnetworks trained to optimally prune a given model. Mechanistically, the bigram subnetworks often recreate a pattern from the full models where the first layer induces a sharp change that aligns activations with next token predictions rather than current token representations. Our results demonstrate that bigram subnetworks comprise a minimal subset of parameters that are both necessary and sufficient for basic next token predictions in language models, and they help drive the transformation from current to next token activations in the residual stream. These subnetworks can lay a foundation for studying more complex language model circuits by building up from a minimal circuit.1