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.

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.

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.

Large Language Models (LLMs) falter in multi-step interactions -- often hallucinating, repeating actions, or misinterpreting user corrections -- due to reliance on linear, unstructured context. This fragility stems from the lack of persistent memory to track evolving goals and task dependencies, undermining trust in autonomous agents. We introduce the Task Memory Engine (TME), a modular memory controller that transforms existing LLMs into robust, revision-aware agents without fine-tuning. TME implements a spatial memory framework that replaces flat context with graph-based structures to support consistent, multi-turn reasoning. Departing from linear concatenation and ReAct-style prompting, TME builds a dynamic task graph -- either a tree or directed acyclic graph (DAG) -- to map user inputs to subtasks, align them with prior context, and enable dependency-tracked revisions. Its Task Representation and Intent Management (TRIM) component models task semantics and user intent to ensure accurate interpretation. Across four multi-turn scenarios-trip planning, cooking, meeting scheduling, and shopping cart editing -- TME eliminates 100% of hallucinations and misinterpretations in three tasks, and reduces hallucinations by 66.7% and misinterpretations by 83.3% across 27 user turns, outperforming ReAct. TME's modular design supports plug-and-play deployment and domain-specific customization, adaptable to both personal assistants and enterprise automation. We release TME's codebase, benchmarks, and components as open-source resources, enabling researchers to develop reliable LLM agents. TME's scalable architecture addresses a critical gap in agent performance across complex, interactive settings.

Microswimmers are sub-millimeter swimming microrobots that show potential as a platform for controllable locomotion in applications including targeted cargo delivery and minimally invasive surgery. To be viable for these target applications, microswimmers will eventually need to be able to navigate in environments with dynamic fluid flows and forces. Experimental studies with microswimmers towards this goal are currently rare because of the difficulty isolating intentional microswimmer motion from environment-induced motion. In this work, we present a method for measuring microswimmer locomotion within a complex flow environment using fiducial microspheres. By tracking the particle motion of ferromagnetic and non-magnetic polystyrene fiducial microspheres, we capture the effect of fluid flow and field gradients on microswimmer trajectories. We then determine the field-driven translation of these microswimmers relative to fluid flow and demonstrate the effectiveness of this method by illustrating the motion of multiple microswimmers through different flows.

Topology optimization is a critical task in engineering design, where the goal is to optimally distribute material in a given space for maximum performance. We introduce Neural Implicit Topology Optimization (NITO), a novel approach to accelerate topology optimization problems using deep learning. NITO stands out as one of the first frameworks to offer a resolution-free and domain-agnostic solution in deep learning-based topology optimization. NITO synthesizes structures with up to seven times better structural efficiency compared to SOTA diffusion models and does so in a tenth of the time. In the NITO framework, we introduce a novel method, the Boundary Point Order-Invariant MLP (BPOM), to represent boundary conditions in a sparse and domain-agnostic manner, moving away from expensive simulation-based approaches. Crucially, NITO circumvents the domain and resolution limitations that restrict Convolutional Neural Network (CNN) models to a structured domain of fixed size -- limitations that hinder the widespread adoption of CNNs in engineering applications. This generalizability allows a single NITO model to train and generate solutions in countless domains, eliminating the need for numerous domain-specific CNNs and their extensive datasets. Despite its generalizability, NITO outperforms SOTA models even in specialized tasks, is an order of magnitude smaller, and is practically trainable at high resolutions that would be restrictive for CNNs. This combination of versatility, efficiency, and performance underlines NITO's potential to transform the landscape of engineering design optimization problems through implicit fields.

In this paper, we aim to model 3D scene dynamics from multi-view videos. Unlike the majority of existing works which usually focus on the common task of novel view synthesis within the training time period, we propose to simultaneously learn the geometry, appearance, and physical velocity of 3D scenes only from video frames, such that multiple desirable applications can be supported, including future frame extrapolation, unsupervised 3D semantic scene decomposition, and dynamic motion transfer. Our method consists of three major components, 1) the keyframe dynamic radiance field, 2) the interframe velocity field, and 3) a joint keyframe and interframe optimization module which is the core of our framework to effectively train both networks. To validate our method, we further introduce two dynamic 3D datasets: 1) Dynamic Object dataset, and 2) Dynamic Indoor Scene dataset. We conduct extensive experiments on multiple datasets, demonstrating the superior performance of our method over all baselines, particularly in the critical tasks of future frame extrapolation and unsupervised 3D semantic scene decomposition. Our code and data are available at https://github.com/vLAR-group/NVFi

With the development of feed-forward models, the default model for sequence modeling has gradually evolved to replace recurrent networks. Many powerful feed-forward models based on convolutional networks and attention mechanism were proposed and show more potential to handle sequence modeling tasks. We wonder that is there an architecture that can not only achieve an approximate substitution of recurrent network, but also absorb the advantages of feed-forward models. So we propose an exploratory architecture referred to Temporal Convolutional Attention-based Network (TCAN) which combines temporal convolutional network and attention mechanism. TCAN includes two parts, one is Temporal Attention (TA) which captures relevant features inside the sequence, the other is Enhanced Residual (ER) which extracts shallow layer's important information and transfers to deep layers. We improve the state-of-the-art results of bpc/perplexity to 30.28 on word-level PTB, 1.092 on character-level PTB, and 9.20 on WikiText-2.