A Measure-Theoretic Analysis of Reasoning: Structural Generalization and Approximation Limits

While empirical scaling laws for LLM reasoning are well-documented, the theoretical mechanisms governing out-of-distribution (OOD) generalization remain elusive. We formalize reasoning via optimal transport, projecting discrete trajectories into a continuous metric space to quantify domain shifts using the Wasserstein-1 distance. Invoking Kantorovich duality, we bound OOD generalization via architectural Lipschitz continuity and functional approximation limits. This exposes two primary constraints. First, position-dependent attention (e.g., Absolute Positional Encoding) fails to preserve shift invariance, yielding an $Ω(1)$ Lipschitz constant and expected risk, whereas shift-invariant mechanisms (e.g., Rotary Embeddings) preserve equivariance and bound the error. Second, by mapping sequential backtracking to a Dyck-$k$ language, we establish a strict circuit depth lower bound for $\text{TC}^0$ Transformers. Scaling physical layer depth is necessary to avert representation collapse -- a constraint that scaling representation width cannot bypass due to irreducible approximation bounds in Barron spaces. Evaluations across 54 Transformer configurations on combinatorial search corroborate these bounds, demonstrating that generalization risk degrades monotonically with the Wasserstein domain shift.

LiFT: Lifted Inter-slice Feature Trajectories for 3D Image Generation from 2D Generators

High-resolution 3D medical image generation remains challenging because fully volumetric models are computationally expensive, while efficient 2D slice generators often fail to preserve anatomical consistency across the third dimension. We propose LiFT, a framework for Lifted inter-slice Feature Trajectories that factorizes 3D volume synthesis into per-slice image generation and inter-slice trajectory learning. Rather than modeling the volumetric distribution end-to-end, LiFT treats a volume as an ordered trajectory in feature space, capturing how anatomical structures appear, transform, and disappear across depth. A tri-planar drifting loss aligns the trajectory of generated slices with the trajectories of real volumes, enabling distributional learning over inter-slice progressions in unconditional generation; in paired translation, a bidirectional $z$-context mixer trained against the registered target supplies through-plane coherence while preserving per-slice fidelity. We evaluate LiFT on BraTS 2023 (unconditional and missing-modality MR) and SynthRAD2023 (MR-to-CT). Across these settings, LiFT preserves per-slice quality, approaches the reported cWDM missing-MR reconstruction quality at $\sim$$135\times$ lower inference cost (without formal equivalence testing), and improves through-plane coherence on MR-to-CT relative to a no-mapper ablation, demonstrating that lightweight inter-slice trajectory learning is a viable route to high-resolution 3D medical synthesis.

GeoBrowse: A Geolocation Benchmark for Agentic Tool Use with Expert-Annotated Reasoning Traces

Deep research agents integrate fragmented evidence through multi-step tool use. BrowseComp offers a text-only testbed for such agents, but existing multimodal benchmarks rarely require both weak visual cues composition and BrowseComp-style multi-hop verification. Geolocation is a natural testbed because answers depend on combining multiple ambiguous visual cues and validating them with open-web evidence. Thus, we introduce GeoBrowse, a geolocation benchmark that combines visual reasoning with knowledge-intensive multi-hop queries. Level 1 tests extracting and composing fragmented visual cues, and Level 2 increases query difficulty by injecting long-tail knowledge and obfuscating key entities. To support evaluation, we provide an agentic workflow GATE with five think-with-image tools and four knowledge-intensive tools, and release expert-annotated stepwise traces grounded in verifiable evidence for trajectory-level analysis. Experiments show that GATE outperforms direct inference and open-source agents, indicating that no-tool, search-only or image-only setups are insufficient. Gains come from coherent, level-specific tool-use plans rather than more tool calls, as they more reliably reach annotated key evidence steps and make fewer errors when integrating into the final decision. The GeoBrowse bernchmark and codes are provided in https://github.com/ornamentt/GeoBrowse

Cross-modal Fuzzy Alignment Network for Text-Aerial Person Retrieval and A Large-scale Benchmark

Text-aerial person retrieval aims to identify targets in UAV-captured images from eyewitness descriptions, supporting intelligent transportation and public security applications. Compared to ground-view text--image person retrieval, UAV-captured images often suffer from degraded visual information due to drastic variations in viewing angles and flight altitudes, making semantic alignment with textual descriptions very challenging. To address this issue, we propose a novel Cross-modal Fuzzy Alignment Network, which quantifies the token-level reliability by fuzzy logic to achieve accurate fine-grained alignment and incorporates ground-view images as a bridge agent to further mitigate the gap between aerial images and text descriptions, for text--aerial person retrieval. In particular, we design the Fuzzy Token Alignment module that employs the fuzzy membership function to dynamically model token-level association strength and suppress the influence of unobservable or noisy tokens. It can alleviate the semantic inconsistencies caused by missing visual cues and significantly enhance the robustness of token-level semantic alignment. Moreover, to further mitigate the gap between aerial images and text descriptions, we design a Context-Aware Dynamic Alignment module to incorporate the ground-view agent as a bridge in text--aerial alignment and adaptively combine direct alignment and agent-assisted alignment to improve the robustness. In addition, we construct a large-scale benchmark dataset called AERI-PEDES by using a chain-of-thought to decompose text generation into attribute parsing, initial captioning, and refinement, thus boosting textual accuracy and semantic consistency. Experiments on AERI-PEDES and TBAPR demonstrate the superiority of our method.

Vision Also You Need: Navigating Out-of-Distribution Detection with Multimodal Large Language Model

Out-of-Distribution (OOD) detection is a critical task that has garnered significant attention. The emergence of CLIP has spurred extensive research into zero-shot OOD detection, often employing a training-free approach. Current methods leverage expert knowledge from large language models (LLMs) to identify potential outliers. However, these approaches tend to over-rely on knowledge in the text space, neglecting the inherent challenges involved in detecting out-of-distribution samples in the image space. In this paper, we propose a novel pipeline, MM-OOD, which leverages the multimodal reasoning capabilities of MLLMs and their ability to conduct multi-round conversations for enhanced outlier detection. Our method is designed to improve performance in both near OOD and far OOD tasks. Specifically, (1) for near OOD tasks, we directly feed ID images and corresponding text prompts into MLLMs to identify potential outliers; and (2) for far OOD tasks, we introduce the sketch-generate-elaborate framework: first, we sketch outlier exposure using text prompts, then generate corresponding visual OOD samples, and finally elaborate by using multimodal prompts. Experiments demonstrate that our method achieves significant improvements on widely used multimodal datasets such as Food-101, while also validating its scalability on ImageNet-1K.

STEP3-VL-10B Technical Report

We present STEP3-VL-10B, a lightweight open-source foundation model designed to redefine the trade-off between compact efficiency and frontier-level multimodal intelligence. STEP3-VL-10B is realized through two strategic shifts: first, a unified, fully unfrozen pre-training strategy on 1.2T multimodal tokens that integrates a language-aligned Perception Encoder with a Qwen3-8B decoder to establish intrinsic vision-language synergy; and second, a scaled post-training pipeline featuring over 1k iterations of reinforcement learning. Crucially, we implement Parallel Coordinated Reasoning (PaCoRe) to scale test-time compute, allocating resources to scalable perceptual reasoning that explores and synthesizes diverse visual hypotheses. Consequently, despite its compact 10B footprint, STEP3-VL-10B rivals or surpasses models 10$\times$-20$\times$ larger (e.g., GLM-4.6V-106B, Qwen3-VL-235B) and top-tier proprietary flagships like Gemini 2.5 Pro and Seed-1.5-VL. Delivering best-in-class performance, it records 92.2% on MMBench and 80.11% on MMMU, while excelling in complex reasoning with 94.43% on AIME2025 and 75.95% on MathVision. We release the full model suite to provide the community with a powerful, efficient, and reproducible baseline.

Max-Entropy Reinforcement Learning with Flow Matching and A Case Study on LQR

Soft actor-critic (SAC) is a popular algorithm for max-entropy reinforcement learning. In practice, the energy-based policies in SAC are often approximated using simple policy classes for efficiency, sacrificing the expressiveness and robustness. In this paper, we propose a variant of the SAC algorithm that parameterizes the policy with flow-based models, leveraging their rich expressiveness. In the algorithm, we evaluate the flow-based policy utilizing the instantaneous change-of-variable technique and update the policy with an online variant of flow matching developed in this paper. This online variant, termed importance sampling flow matching (ISFM), enables policy update with only samples from a user-specified sampling distribution rather than the unknown target distribution. We develop a theoretical analysis of ISFM, characterizing how different choices of sampling distributions affect the learning efficiency. Finally, we conduct a case study of our algorithm on the max-entropy linear quadratic regulator problems, demonstrating that the proposed algorithm learns the optimal action distribution.

FlyKites: Human-centric Interactive Exploration and Assistance under Limited Communication

Fleets of autonomous robots have been deployed for exploration of unknown scenes for features of interest, e.g., subterranean exploration, reconnaissance, search and rescue missions. During exploration, the robots may encounter un-identified targets, blocked passages, interactive objects, temporary failure, or other unexpected events, all of which require consistent human assistance with reliable communication for a time period. This however can be particularly challenging if the communication among the robots is severely restricted to only close-range exchange via ad-hoc networks, especially in extreme environments like caves and underground tunnels. This paper presents a novel human-centric interactive exploration and assistance framework called FlyKites, for multi-robot systems under limited communication. It consists of three interleaved components: (I) the distributed exploration and intermittent communication (called the "spread mode"), where the robots collaboratively explore the environment and exchange local data among the fleet and with the operator; (II) the simultaneous optimization of the relay topology, the operator path, and the assignment of robots to relay roles (called the "relay mode"), such that all requested assistance can be provided with minimum delay; (III) the human-in-the-loop online execution, where the robots switch between different roles and interact with the operator adaptively. Extensive human-in-the-loop simulations and hardware experiments are performed over numerous challenging scenes.

MoRoCo: Multi-operator-robot Coordination, Interaction and Exploration under Restricted Communication

Fleets of autonomous robots are increasingly deployed alongside multiple human operators to explore unknown environments, identify salient features, and perform complex tasks in scenarios such as subterranean exploration, reconnaissance, and search-and-rescue missions. In these contexts, communication is often severely limited to short-range exchanges via ad-hoc networks, posing challenges to coordination. While recent studies have addressed multi-robot exploration under communication constraints, they largely overlook the essential role of human operators and their real-time interaction with robotic teams. Operators may demand timely updates on the exploration progress and robot status, reprioritize or cancel tasks dynamically, or request live video feeds and control access. Conversely, robots may seek human confirmation for anomalous events or require help recovering from motion or planning failures. To enable such bilateral, context-aware interactions under restricted communication, this work proposes MoRoCo, a unified framework for online coordination and exploration in multi-operator, multi-robot systems. MoRoCo enables the team to adaptively switch among three coordination modes: spread mode for parallelized exploration with intermittent data sharing, migrate mode for coordinated relocation, and chain mode for maintaining high-bandwidth connectivity through multi-hop links. These transitions are managed through distributed algorithms via only local communication. Extensive large-scale human-in-the-loop simulations and hardware experiments validate the necessity of incorporating human robot interactions and demonstrate that MoRoCo enables efficient, reliable coordination under limited communication, marking a significant step toward robust human-in-the-loop multi-robot autonomy in challenging environments.

Embedding based retrieval for long tail search queries in ecommerce

In this abstract we present a series of optimizations we performed on the two-tower model architecture [14], training and evaluation datasets to implement semantic product search at Best Buy. Search queries on bestbuy.com follow the pareto distribution whereby a minority of them account for most searches. This leaves us with a long tail of search queries that have low frequency of issuance. The queries in the long tail suffer from very spare interaction signals. Our current work focuses on building a model to serve the long tail queries. We present a series of optimizations we have done to this model to maximize conversion for the purpose of retrieval from the catalog. The first optimization we present is using a large language model to improve the sparsity of conversion signals. The second optimization is pretraining an off-the-shelf transformer-based model on the Best Buy catalog data. The third optimization we present is on the finetuning front. We use query-to-query pairs in addition to query-to-product pairs and combining the above strategies for finetuning the model. We also demonstrate how merging the weights of these finetuned models improves the evaluation metrics. Finally, we provide a recipe for curating an evaluation dataset for continuous monitoring of model performance with human-in-the-loop evaluation. We found that adding this recall mechanism to our current term match-based recall improved conversion by 3% in an online A/B test.