Embedding spaces are fundamental to modern AI, translating raw data into high-dimensional vectors that encode rich semantic relationships. Y et, their internal structures remain opaque, with existing approaches often sacrificing semantic coherence for structural regularity or incurring high computational overhead to improve interpretability. To address these challenges, we introduce the Semantic Field Subspace (SFS), a geometry-preserving, context-aware representation that captures local semantic neighborhoods within the embedding space. We also propose SAF ARI (SemAntic Field subspAce deteRmInation), an unsupervised, modality-agnostic algorithm that uncovers hierarchical semantic structures using a novel metric called Semantic Shift, which quantifies how semantics evolve as SFSes evolve. To ensure scalability, we develop an efficient approximation of Semantic Shift that replaces costly SVD computations, achieving a 15 30 speedup with average errors below 0.01. Extensive evaluations across six real-world text and image datasets show that SFSes outperform standard classifiers not only in classification but also in nuanced tasks such as political bias detection, while SAF ARI consistently reveals interpretable and generalizable semantic hierarchies. This work presents a unified framework for structuring, analyzing, and scaling semantic understanding in embedding spaces.

Traditional fuzzy matching often fails when searching for quotes that are semantically identical but syntactically different across documents-a common issue when aligning official written records with speech-to-text transcripts. We introduce TimeStampEval, a benchmark for retrieving precise millisecond timestamps from long transcripts given non-verbatim quotes. Our simple two-stage method dramatically improves retrieval accuracy while cutting inference costs by over 90%. The motivating use case is an automated long-form podcast that assembles Congressional Record clips into AI-hosted narration. The technical challenge: given a sentence-timestamped transcript and a target quote that may differ due to transcription or editorial drift, return exact start and end boundaries. Standard algorithms handle verbatim text but break under fuzzier variants. Evaluating six modern LLMs on a 2,800-sentence (120k-token) transcript revealed four key findings. (1) Prompt design matters more than model choice: placing the query before the transcript and using compact formatting improved accuracy by 3-20 points while reducing token count by 30-40%. (2) Off-by-one errors form a distinct category, showing models understand the task but misplace boundaries. (3) A modest reasoning budget (600-850 tokens) raises accuracy from 37% to 77% for weak setups and to above 90% for strong ones. (4) Our "Assisted Fuzzy" approach-RapidFuzz pre-filtering followed by LLM verification on short snippets-improves fuzzy match accuracy by up to 50 points while halving latency and reducing cost per correct result by up to 96%. Extended tests on ten transcripts (50k-900k tokens, 1989-2025) confirm robustness to transcript length, vocabulary drift, and domain change, maintaining 95-100% rejection accuracy for absent targets.

It provides dense annotations for 48K procedural step segments (430 hours) and high-level goal annotations for 2,807 hours of Ego4D videos.

Electrostatic field matching (EFM) has recently appeared as a novel physics-inspired paradigm for data generation and transfer using the idea of an electric capacitor. However, it requires modeling electrostatic fields using neural networks, which is non-trivial because of the necessity to take into account the complex field outside the capacitor plates. In this paper, we propose Interaction Field Matching (IFM), a generalization of EFM which allows using general interaction fields beyond the electrostatic one. Furthermore, inspired by strong interactions between quarks and antiquarks in physics, we design a particular interaction field realization which solves the problems which arise when modeling electrostatic fields in EFM. We show the performance on a series of toy and image data transfer problems.

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples onto the feasible set; however, repeated projection can distort the learned distribution and induce a mismatch with the data manifold. Thus, recent multi-stage procedures attempt to defer projection to clean samples during sampling, but they increase algorithmic complexity and accumulate errors across steps. This paper addresses these challenges by proposing a novel training-free method, Chance-constrained Flow Matching (CCFM), that integrates stochastic optimization into the sampling process, enabling effective enforcement of hard constraints while maintaining high-fidelity sample generation. Importantly, CCFM guarantees feasibility in the same manner as conventional repeated projection, yet, despite operating directly on noisy intermediate samples, it is theoretically equivalent to projecting onto the feasible set defined by clean samples. This yields a sampler that mitigates distributional distortion. Empirical experiments show that CCFM outperforms current state-of-the-art constrained generative models in modeling complex physical systems governed by partial differential equations and molecular docking problems, delivering higher feasibility and fidelity.

This paper's source code and experimental data are available at

Reward models are key to language model post-training and inference pipelines. Conveniently, recent work showed that every language model defines an implicit reward model (IM-RM), without requiring any architectural changes. However, such IM-RMs tend to generalize worse, especially out-of-distribution, compared to explicit reward models (EX-RMs) that apply a dedicated linear head over the hidden representations of a language model. The existence of a generalization gap is puzzling, as EX-RMs and IM-RMs are nearly identical. They can be trained using the same data, loss function, and language model, and differ only in how the reward is computed. Towards a fundamental understanding of the implicit biases underlying different reward model types, we investigate the root cause of this gap. Our main finding, backed by theory and experiments, is that IM-RMs rely more heavily on superficial token-level cues. Consequently, they often generalize worse than EX-RMs under token-level distribution shifts, as well as in-distribution. Furthermore, we provide evidence against alternative hypotheses for the generalization gap. Most notably, we challenge the intuitive claim that IM-RMs struggle in tasks where generation is harder than verification because they can operate both as a verifier and a generator. Taken together, our results highlight that seemingly minor design choices can substantially impact the generalization behavior of reward models.

Compressing long chain-of-thought (CoT) from large language models (LLMs) is an emerging strategy to improve the reasoning efficiency of LLMs. Despite its promising benefits, existing studies equally compress all thoughts within a long CoT, hindering more concise and effective reasoning. To this end, we first investigate the importance of different thoughts by examining their effectiveness and efficiency in contributing to reasoning through automatic long CoT chunking and Monte Carlo rollouts. Building upon the insights, we propose a theoretically bounded metric to jointly measure the effectiveness and efficiency of different thoughts. We then propose Long$\otimes$Short, an efficient reasoning framework that enables two LLMs to collaboratively solve the problem: a long-thought LLM for more effectively generating important thoughts, while a short-thought LLM for efficiently generating remaining thoughts. Specifically, we begin by synthesizing a small amount of cold-start data to fine-tune LLMs for long-thought and short-thought reasoning styles, respectively. Furthermore, we propose a synergizing-oriented multi-turn reinforcement learning, focusing on the model self-evolution and collaboration between long-thought and short-thought LLMs. Experimental results show that our method enables Qwen2.5-7B and Llama3.1-8B to achieve comparable performance compared to DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-Llama-8B, while reducing token length by over 80% across the MATH500, AIME24/25, AMC23, and GPQA Diamond benchmarks. Our data and code are available at https://github.com/usail-hkust/LongShort.