Understanding Chain-of-Thought in Large Language Models via Topological Data Analysis

With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging the power of long reasoning chains, we cannot help but wonder: Why do different reasoning chains perform differently in reasoning? What components of the reasoning chains play a key role? Existing studies mainly focus on evaluating reasoning chains from a functional perspective, with little attention paid to their structural mechanisms. To address this gap, this work is the first to analyze and evaluate the quality of the reasoning chain from a structural perspective. We apply persistent homology from Topological Data Analysis (TDA) to map reasoning steps into semantic space, extract topological features, and analyze structural changes. These changes reveal semantic coherence, logical redundancy, and identify logical breaks and gaps. By calculating homology groups, we assess connectivity and redundancy at various scales, using barcode and persistence diagrams to quantify stability and consistency. Our results show that the topological structural complexity of reasoning chains correlates positively with accuracy. More complex chains identify correct answers sooner, while successful reasoning exhibits simpler topologies, reducing redundancy and cycles, enhancing efficiency and interpretability. This work provides a new perspective on reasoning chain quality assessment and offers guidance for future optimization.

START: Traversing Sparse Footholds with Terrain Reconstruction

Traversing terrains with sparse footholds like legged animals presents a promising yet challenging task for quadruped robots, as it requires precise environmental perception and agile control to secure safe foot placement while maintaining dynamic stability. Model-based hierarchical controllers excel in laboratory settings, but suffer from limited generalization and overly conservative behaviors. End-to-end learning-based approaches unlock greater flexibility and adaptability, but existing state-of-the-art methods either rely on heightmaps that introduce noise and complex, costly pipelines, or implicitly infer terrain features from egocentric depth images, often missing accurate critical geometric cues and leading to inefficient learning and rigid gaits. To overcome these limitations, we propose START, a single-stage learning framework that enables agile, stable locomotion on highly sparse and randomized footholds. START leverages only low-cost onboard vision and proprioception to accurately reconstruct local terrain heightmap, providing an explicit intermediate representation to convey essential features relevant to sparse foothold regions. This supports comprehensive environmental understanding and precise terrain assessment, reducing exploration cost and accelerating skill acquisition. Experimental results demonstrate that START achieves zero-shot transfer across diverse real-world scenarios, showcasing superior adaptability, precise foothold placement, and robust locomotion.

Robot Learning from a Physical World Model

We introduce PhysWorld, a framework that enables robot learning from video generation through physical world modeling. Recent video generation models can synthesize photorealistic visual demonstrations from language commands and images, offering a powerful yet underexplored source of training signals for robotics. However, directly retargeting pixel motions from generated videos to robots neglects physics, often resulting in inaccurate manipulations. PhysWorld addresses this limitation by coupling video generation with physical world reconstruction. Given a single image and a task command, our method generates task-conditioned videos and reconstructs the underlying physical world from the videos, and the generated video motions are grounded into physically accurate actions through object-centric residual reinforcement learning with the physical world model. This synergy transforms implicit visual guidance into physically executable robotic trajectories, eliminating the need for real robot data collection and enabling zero-shot generalizable robotic manipulation. Experiments on diverse real-world tasks demonstrate that PhysWorld substantially improves manipulation accuracy compared to previous approaches. Visit \href{https://pointscoder.github.io/PhysWorld_Web/}{the project webpage} for details.

Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction

Neural operators are promising surrogates for dynamical systems but when trained with standard L2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling overcomes this limitation. We consider three practical turbulent-flow challenges where conventional neural operators fail: spatio-temporal super-resolution, forecasting, and sparse flow reconstruction. For Schlieren jet super-resolution, an adversarially trained neural operator (adv-NO) reduces the energy-spectrum error by 15x while preserving sharp gradients at neural operator-like inference cost. For 3D homogeneous isotropic turbulence, adv-NO trained on only 160 timesteps from a single trajectory forecasts accurately for five eddy-turnover times and offers 114x wall-clock speed-up at inference than the baseline diffusion-based forecasters, enabling near-real-time rollouts. For reconstructing cylinder wake flows from highly sparse Particle Tracking Velocimetry-like inputs, a conditional generative model infers full 3D velocity and pressure fields with correct phase alignment and statistics. These advances enable accurate reconstruction and forecasting at low compute cost, bringing near-real-time analysis and control within reach in experimental and computational fluid mechanics. See our project page: https://vivekoommen.github.io/Gen4Turb/

Exploring Contextual Attribute Density in Referring Expression Counting

Referring expression counting (REC) algorithms are for more flexible and interactive counting ability across varied fine-grained text expressions. However, the requirement for fine-grained attribute understanding poses challenges for prior arts, as they struggle to accurately align attribute information with correct visual patterns. Given the proven importance of ''visual density'', it is presumed that the limitations of current REC approaches stem from an under-exploration of ''contextual attribute density'' (CAD). In the scope of REC, we define CAD as the measure of the information intensity of one certain fine-grained attribute in visual regions. To model the CAD, we propose a U-shape CAD estimator in which referring expression and multi-scale visual features from GroundingDINO can interact with each other. With additional density supervision, we can effectively encode CAD, which is subsequently decoded via a novel attention procedure with CAD-refined queries. Integrating all these contributions, our framework significantly outperforms state-of-the-art REC methods, achieves $30\%$ error reduction in counting metrics and a $10\%$ improvement in localization accuracy. The surprising results shed light on the significance of contextual attribute density for REC. Code will be at github.com/Xu3XiWang/CAD-GD.

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty is giving appropriate initial conditions or initial guesses, to which the widely used time-marching schemes and Newton's iteration method are very sensitive in finding solutions for complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first reveal that PINNs, when combined with random initialization and deep ensemble method -- originally developed for uncertainty quantification -- can effectively uncover multiple solutions to nonlinear ordinary and partial differential equations (ODEs/PDEs). Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen-Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear differential equations.

PUGS: Zero-shot Physical Understanding with Gaussian Splatting

Current robotic systems can understand the categories and poses of objects well. But understanding physical properties like mass, friction, and hardness, in the wild, remains challenging. We propose a new method that reconstructs 3D objects using the Gaussian splatting representation and predicts various physical properties in a zero-shot manner. We propose two techniques during the reconstruction phase: a geometry-aware regularization loss function to improve the shape quality and a region-aware feature contrastive loss function to promote region affinity. Two other new techniques are designed during inference: a feature-based property propagation module and a volume integration module tailored for the Gaussian representation. Our framework is named as zero-shot physical understanding with Gaussian splatting, or PUGS. PUGS achieves new state-of-the-art results on the standard benchmark of ABO-500 mass prediction. We provide extensive quantitative ablations and qualitative visualization to demonstrate the mechanism of our designs. We show the proposed methodology can help address challenging real-world grasping tasks. Our codes, data, and models are available at https://github.com/EverNorif/PUGS

Subconscious Robotic Imitation Learning

Although robotic imitation learning (RIL) is promising for embodied intelligent robots, existing RIL approaches rely on computationally intensive multi-model trajectory predictions, resulting in slow execution and limited real-time responsiveness. Instead, human beings subconscious can constantly process and store vast amounts of information from their experiences, perceptions, and learning, allowing them to fulfill complex actions such as riding a bike, without consciously thinking about each. Inspired by this phenomenon in action neurology, we introduced subconscious robotic imitation learning (SRIL), wherein cognitive offloading was combined with historical action chunkings to reduce delays caused by model inferences, thereby accelerating task execution. This process was further enhanced by subconscious downsampling and pattern augmented learning policy wherein intent-rich information was addressed with quantized sampling techniques to improve manipulation efficiency. Experimental results demonstrated that execution speeds of the SRIL were 100\% to 200\% faster over SOTA policies for comprehensive dual-arm tasks, with consistently higher success rates.

FocusChat: Text-guided Long Video Understanding via Spatiotemporal Information Filtering

Recently, multi-modal large language models have made significant progress. However, visual information lacking of guidance from the user's intention may lead to redundant computation and involve unnecessary visual noise, especially in long, untrimmed videos. To address this issue, we propose FocusChat, a text-guided multi-modal large language model (LLM) that emphasizes visual information correlated to the user's prompt. In detail, Our model first undergoes the semantic extraction module, which comprises a visual semantic branch and a text semantic branch to extract image and text semantics, respectively. The two branches are combined using the Spatial-Temporal Filtering Module (STFM). STFM enables explicit spatial-level information filtering and implicit temporal-level feature filtering, ensuring that the visual tokens are closely aligned with the user's query. It lowers the essential number of visual tokens inputted into the LLM. FocusChat significantly outperforms Video-LLaMA in zero-shot experiments, using an order of magnitude less training data with only 16 visual tokens occupied. It achieves results comparable to the state-of-the-art in few-shot experiments, with only 0.72M pre-training data.

Towards Degradation-Robust Reconstruction in Generalizable NeRF

Generalizable Neural Radiance Field (GNeRF) across scenes has been proven to be an effective way to avoid per-scene optimization by representing a scene with deep image features of source images. However, despite its potential for real-world applications, there has been limited research on the robustness of GNeRFs to different types of degradation present in the source images. The lack of such research is primarily attributed to the absence of a large-scale dataset fit for training a degradation-robust generalizable NeRF model. To address this gap and facilitate investigations into the degradation robustness of 3D reconstruction tasks, we construct the Objaverse Blur Dataset, comprising 50,000 images from over 1000 settings featuring multiple levels of blur degradation. In addition, we design a simple and model-agnostic module for enhancing the degradation robustness of GNeRFs. Specifically, by extracting 3D-aware features through a lightweight depth estimator and denoiser, the proposed module shows improvement on different popular methods in GNeRFs in terms of both quantitative and visual quality over varying degradation types and levels. Our dataset and code will be made publicly available.