Think over Trajectories: Leveraging Video Generation to Reconstruct GPS Trajectories from Cellular Signaling

Mobile devices continuously interact with cellular base stations, generating massive volumes of signaling records that provide broad coverage for understanding human mobility. However, such records offer only coarse location cues (e.g., serving-cell identifiers) and therefore limit their direct use in applications that require high-precision GPS trajectories. This paper studies the Sig2GPS problem: reconstructing GPS trajectories from cellular signaling. Inspired by domain experts often lay the signaling trace on the map and sketch the corresponding GPS route, unlike conventional solutions that rely on complex multi-stage engineering pipelines or regress coordinates, Sig2GPS is reframed as an image-to-video generation task that directly operates in the map-visual domain: signaling traces are rendered on a map, and a video generation model is trained to draw a continuous GPS path. To support this paradigm, a paired signaling-to-trajectory video dataset is constructed to fine-tune an open-source video model, and a trajectory-aware reinforcement learning-based optimization method is introduced to improve generation fidelity via rewards. Experiments on large-scale real-world datasets show substantial improvements over strong engineered and learning-based baselines, while additional results on next GPS prediction indicate scalability and cross-city transferability. Overall, these results suggest that map-visual video generation provides a practical interface for trajectory data mining by enabling direct generation and refinement of continuous paths under map constraints.

InstanceAnimator: Multi-Instance Sketch Video Colorization

We propose InstanceAnimator, a novel Diffusion Transformer framework for multi-instance sketch video colorization. Existing methods suffer from three core limitations: inflexible user control due to heavy reliance on single reference frames, poor instance controllability leading to misalignment in multi-character scenarios, and degraded detail fidelity in fine-grained regions. To address these challenges, we introduce three corresponding innovations. First, a Canvas Guidance Condition eliminates workflow fragmentation by allowing free placement of reference elements and background, enabling unprecedented user flexibility. Second, an Instance Matching Mechanism resolves misalignment by integrating instance features with the sketches, ensuring precise control over multiple characters. Third, an Adaptive Decoupled Control Module enhances detail fidelity by injecting semantic features from characters, backgrounds, and text conditions into the diffusion process. Extensive experiments demonstrate that InstanceAnimator achieves superior multi-instance colorization with enhanced user control, high visual quality, and strong instance consistency.

Le MuMo JEPA: Multi-Modal Self-Supervised Representation Learning with Learnable Fusion Tokens

Self-supervised learning has emerged as a powerful paradigm for learning visual representations without manual annotations, yet most methods still operate on a single modality and therefore miss the complementary structure available from heterogeneous sensors. We present Le MuMo JEPA, a self-supervised framework that learns unified representations from RGB images and aligned companion modalities. In our driving experiments, the second modality is camera-aligned LiDAR depth; we also evaluate RGB-thermal training and transfer on the Teledyne FLIR ADAS benchmark. Our approach extends LeJEPA to the multi-modal setting by learning fusion tokens that act as a latent bottleneck between modality-specific patch stems inside a shared transformer. Our default model employs a pruned fusion strategy: after an initial cross-modal attention layer, modality-specific tokens are dropped, forcing cross-modal information into the shared fusion-token grid as an efficient latent bottleneck before Sketched Isotropic Gaussian Regularization (SIGReg) is applied to the joint multimodal CLS embedding. On Waymo, Le MuMo JEPA gives the strongest performance-efficiency trade-off on downstream patch probes among the from-scratch multimodal baselines, improving CenterNet detection and dense depth while remaining competitive on segmentation. Under from-scratch training on nuScenes, Le MuMo JEPA remains the strongest model, and it also gives the best FLIR results, especially after Waymo-initialized fine-tuning. It also retains the best overall accuracy-efficiency balance in our study at substantially lower compute, memory, and estimated training time.

Sketch2Simulation: Automating Flowsheet Generation via Multi Agent Large Language Models

Converting process sketches into executable simulation models remains a major bottleneck in process systems engineering, requiring substantial manual effort and simulator-specific expertise. Recent advances in generative AI have improved both engineering-diagram interpretation and LLM-assisted flowsheet generation, but these remain largely disconnected: diagram-understanding methods often stop at extracted graphs, while text-to-simulation workflows assume structured inputs rather than raw visual artifacts. To bridge this gap, we present an end-to-end multi-agent large language model system that converts process diagrams directly into executable Aspen HYSYS flowsheets. The framework decomposes the task into three coordinated layers: diagram parsing and interpretation, simulation model synthesis, and multi-level validation. Specialized agents handle visual interpretation, graph-based intermediate representation construction, code generation for the HYSYS COM interface, execution, and structural verification. We evaluate the framework on four chemical engineering case studies of increasing complexity, from a simple desalting process to an industrial aromatic production flowsheet with multiple recycle loops. The system produces executable HYSYS models in all cases, achieving complete structural fidelity on the two simpler cases and strong performance on the more complex ones, with connection consistency above 0.93 and stream consistency above 0.96. These results demonstrate a viable end-to-end sketch-to-simulation workflow while highlighting remaining challenges in dense recycle structures, implicit diagram semantics, and simulator-interface constraints.

Sketch2CT: Multimodal Diffusion for Structure-Aware 3D Medical Volume Generation

Diffusion probabilistic models have demonstrated significant potential in generating high-quality, realistic medical images, providing a promising solution to the persistent challenge of data scarcity in the medical field. Nevertheless, producing 3D medical volumes with anatomically consistent structures under multimodal conditions remains a complex and unresolved problem. We introduce Sketch2CT, a multimodal diffusion framework for structure-aware 3D medical volume generation, jointly guided by a user-provided 2D sketch and a textual description that captures 3D geometric semantics. The framework initially generates 3D segmentation masks of the target organ from random noise, conditioned on both modalities. To effectively align and fuse these inputs, we propose two key modules that refine sketch features with localized textual cues and integrate global sketch-text representations. Built upon a capsule-attention backbone, these modules leverage the complementary strengths of sketches and text to produce anatomically accurate organ shapes. The synthesized segmentation masks subsequently guide a latent diffusion model for 3D CT volume synthesis, enabling realistic reconstruction of organ appearances that are consistent with user-defined sketches and descriptions. Extensive experiments on public CT datasets demonstrate that Sketch2CT achieves superior performance in generating multimodal medical volumes. Its controllable, low-cost generation pipeline enables principled, efficient augmentation of medical datasets. Code is available at https://github.com/adlsn/Sketch2CT.

GeoFusion-CAD: Structure-Aware Diffusion with Geometric State Space for Parametric 3D Design

Parametric Computer-Aided Design (CAD) is fundamental to modern 3D modeling, yet existing methods struggle to generate long command sequences, especially under complex geometric and topological dependencies. Transformer-based architectures dominate CAD sequence generation due to their strong dependency modeling, but their quadratic attention cost and limited context windowing hinder scalability to long programs. We propose GeoFusion-CAD, an end-to-end diffusion framework for scalable and structure-aware generation. Our proposal encodes CAD programs as hierarchical trees, jointly capturing geometry and topology within a state-space diffusion process. Specifically, a lightweight C-Mamba block models long-range structural dependencies through selective state transitions, enabling coherent generation across extended command sequences. To support long-sequence evaluation, we introduce DeepCAD-240, an extended benchmark that increases the sequence length ranging from 40 to 240 while preserving sketch-extrusion semantics from the ABC dataset. Extensive experiments demonstrate that GeoFusion-CAD achieves superior performance on both short and long command ranges, maintaining high geometric fidelity and topological consistency where Transformer-based models degrade. Our approach sets new state-of-the-art scores for long-sequence parametric CAD generation, establishing a scalable foundation for next-generation CAD modeling systems. Code and datasets are available at GitHub.

LongCat-Flash-Prover: Advancing Native Formal Reasoning via Agentic Tool-Integrated Reinforcement Learning

We introduce LongCat-Flash-Prover, a flagship 560-billion-parameter open-source Mixture-of- Experts (MoE) model that advances Native Formal Reasoning in Lean4 through agentic tool-integrated reasoning (TIR). We decompose the native formal reasoning task into three independent formal capabilities, i.e., auto-formalization, sketching, and proving. To facilitate these capabilities, we propose a Hybrid-Experts Iteration Framework to expand high-quality task trajectories, including generating a formal statement based on a given informal problem, producing a whole-proof directly from the statement, or a lemma-style sketch. During agentic RL, we present a Hierarchical Importance Sampling Policy Optimization (HisPO) algorithm, which aims to stabilize the MoE model training on such long-horizon tasks. It employs a gradient masking strategy that accounts for the policy staleness and the inherent train-inference engine discrepancies at both sequence and token levels. Additionally, we also incorporate theorem consistency and legality detection mechanisms to eliminate reward hacking issues. Extensive evaluations show that our LongCat-Flash-Prover sets a new state-of-the-art for open-weights models in both auto-formalization and theorem proving. Demonstrating remarkable sample efficiency, it achieves a 97.1% pass rate on MiniF2F-Test using only 72 inference budget per problem. On more challenging benchmarks, it solves 70.8% of ProverBench and 41.5% of PutnamBench with no more than 220 attempts per problem, significantly outperforming existing open-weights baselines.

ProactiveBench: Benchmarking Proactiveness in Multimodal Large Language Models

Effective collaboration begins with knowing when to ask for help. For example, when trying to identify an occluded object, a human would ask someone to remove the obstruction. Can MLLMs exhibit a similar "proactive" behavior by requesting simple user interventions? To investigate this, we introduce ProactiveBench, a benchmark built from seven repurposed datasets that tests proactiveness across different tasks such as recognizing occluded objects, enhancing image quality, and interpreting coarse sketches. We evaluate 22 MLLMs on ProactiveBench, showing that (i) they generally lack proactiveness; (ii) proactiveness does not correlate with model capacity; (iii) "hinting" at proactiveness yields only marginal gains. Surprisingly, we found that conversation histories and in-context learning introduce negative biases, hindering performance. Finally, we explore a simple fine-tuning strategy based on reinforcement learning: its results suggest that proactiveness can be learned, even generalizing to unseen scenarios. We publicly release ProactiveBench as a first step toward building proactive multimodal models.

Teaching an Agent to Sketch One Part at a Time

We develop a method for producing vector sketches one part at a time. To do this, we train a multi-modal language model-based agent using a novel multi-turn process-reward reinforcement learning following supervised fine-tuning. Our approach is enabled by a new dataset we call ControlSketch-Part, containing rich part-level annotations for sketches, obtained using a novel, generic automatic annotation pipeline that segments vector sketches into semantic parts and assigns paths to parts with a structured multi-stage labeling process. Our results indicate that incorporating structured part-level data and providing agent with the visual feedback through the process enables interpretable, controllable, and locally editable text-to-vector sketch generation.

Global Convergence of Multiplicative Updates for the Matrix Mechanism: A Collaborative Proof with Gemini 3

We analyze a fixed-point iteration $v \leftarrow φ(v)$ arising in the optimization of a regularized nuclear norm objective involving the Hadamard product structure, posed in~\cite{denisov} in the context of an optimization problem over the space of algorithms in private machine learning. We prove that the iteration $v^{(k+1)} = \text{diag}((D_{v^{(k)}}^{1/2} M D_{v^{(k)}}^{1/2})^{1/2})$ converges monotonically to the unique global optimizer of the potential function $J(v) = 2 \text{Tr}((D_v^{1/2} M D_v^{1/2})^{1/2}) - \sum v_i$, closing a problem left open there. The bulk of this proof was provided by Gemini 3, subject to some corrections and interventions. Gemini 3 also sketched the initial version of this note. Thus, it represents as much a commentary on the practical use of AI in mathematics as it represents the closure of a small gap in the literature. As such, we include a small narrative description of the prompting process, and some resulting principles for working with AI to prove mathematics.