Set Invariance with Probability One for Controlled Diffusion: Score-based Approach

Given a controlled diffusion and a connected, bounded, Lipschitz set, when is it possible to guarantee controlled set invariance with probability one? In this work, we answer this question by deriving the necessary and sufficient conditions for the same in terms of gradients of certain log-likelihoods -- a.k.a. score vector fields -- for two cases: given finite time horizon and infinite time horizon. The deduced conditions comprise a score-based test that provably certifies or falsifies the existence of Markovian controllers for given controlled set invariance problem data. Our results are constructive in the sense when the problem data passes the proposed test, we characterize all controllers guaranteeing the desired set invariance. When the problem data fails the proposed test, there does not exist a controller that can accomplish the desired set invariance with probability one. The computation in the proposed tests involve solving certain Dirichlet boundary value problems, and in the finite horizon case, can also account for additional constraint of hitting a target subset at the terminal time. We illustrate the results using several semi-analytical and numerical examples.

Markov Kernels, Distances and Optimal Control: A Parable of Linear Quadratic Non-Gaussian Distribution Steering

For a controllable linear time-varying (LTV) pair $(\boldsymbol{A}_t,\boldsymbol{B}_t)$ and $\boldsymbol{Q}_{t}$ positive semidefinite, we derive the Markov kernel for the It\^{o} diffusion ${\mathrm{d}}\boldsymbol{x}_{t}=\boldsymbol{A}_{t}\boldsymbol{x}_t {\mathrm{d}} t + \sqrt{2}\boldsymbol{B}_{t}{\mathrm{d}}\boldsymbol{w}_{t}$ with an accompanying killing of probability mass at rate $\frac{1}{2}\boldsymbol{x}^{\top}\boldsymbol{Q}_{t}\boldsymbol{x}$. This Markov kernel is the Green's function for an associated linear reaction-advection-diffusion partial differential equation. Our result generalizes the recently derived kernel for the special case $\left(\boldsymbol{A}_t,\boldsymbol{B}_t\right)=\left(\boldsymbol{0},\boldsymbol{I}\right)$, and depends on the solution of an associated Riccati matrix ODE. A consequence of this result is that the linear quadratic non-Gaussian Schr\"{o}dinger bridge is exactly solvable. This means that the problem of steering a controlled LTV diffusion from a given non-Gaussian distribution to another over a fixed deadline while minimizing an expected quadratic cost can be solved using dynamic Sinkhorn recursions performed with the derived kernel. Our derivation for the $\left(\boldsymbol{A}_t,\boldsymbol{B}_t,\boldsymbol{Q}_t\right)$-parametrized kernel pursues a new idea that relies on finding a state-time dependent distance-like functional given by the solution of a deterministic optimal control problem. This technique breaks away from existing methods, such as generalizing Hermite polynomials or Weyl calculus, which have seen limited success in the reaction-diffusion context. Our technique uncovers a new connection between Markov kernels, distances, and optimal control. This connection is of interest beyond its immediate application in solving the linear quadratic Schr\"{o}dinger bridge problem.

HandSplat: Embedding-Driven Gaussian Splatting for High-Fidelity Hand Rendering

Existing 3D Gaussian Splatting (3DGS) methods for hand rendering rely on rigid skeletal motion with an oversimplified non-rigid motion model, which fails to capture fine geometric and appearance details. Additionally, they perform densification based solely on per-point gradients and process poses independently, ignoring spatial and temporal correlations. These limitations lead to geometric detail loss, temporal instability, and inefficient point distribution. To address these issues, we propose HandSplat, a novel Gaussian Splatting-based framework that enhances both fidelity and stability for hand rendering. To improve fidelity, we extend standard 3DGS attributes with implicit geometry and appearance embeddings for finer non-rigid motion modeling while preserving the static hand characteristic modeled by original 3DGS attributes. Additionally, we introduce a local gradient-aware densification strategy that dynamically refines Gaussian density in high-variation regions. To improve stability, we incorporate pose-conditioned attribute regularization to encourage attribute consistency across similar poses, mitigating temporal artifacts. Extensive experiments on InterHand2.6M demonstrate that HandSplat surpasses existing methods in fidelity and stability while achieving real-time performance. We will release the code and pre-trained models upon acceptance.

Interpersonal Memory Matters: A New Task for Proactive Dialogue Utilizing Conversational History

Proactive dialogue systems aim to empower chatbots with the capability of leading conversations towards specific targets, thereby enhancing user engagement and service autonomy. Existing systems typically target pre-defined keywords or entities, neglecting user attributes and preferences implicit in dialogue history, hindering the development of long-term user intimacy. To address these challenges, we take a radical step towards building a more human-like conversational agent by integrating proactive dialogue systems with long-term memory into a unified framework. Specifically, we define a novel task named Memory-aware Proactive Dialogue (MapDia). By decomposing the task, we then propose an automatic data construction method and create the first Chinese Memory-aware Proactive Dataset (ChMapData). Furthermore, we introduce a joint framework based on Retrieval Augmented Generation (RAG), featuring three modules: Topic Summarization, Topic Retrieval, and Proactive Topic-shifting Detection and Generation, designed to steer dialogues towards relevant historical topics at the right time. The effectiveness of our dataset and models is validated through both automatic and human evaluations. We release the open-source framework and dataset at https://github.com/FrontierLabs/MapDia.

A Text-Based Knowledge-Embedded Soft Sensing Modeling Approach for General Industrial Process Tasks Based on Large Language Model

Data-driven soft sensors (DDSS) have become mainstream methods for predicting key performance indicators in process industries. However, DDSS development requires complex and costly customized designs tailored to various tasks during the modeling process. Moreover, DDSS are constrained to a single structured data modality, limiting their ability to incorporate additional contextual knowledge. Furthermore, DDSSs' limited representation learning leads to weak predictive performance with scarce data. To address these challenges, we propose a general framework named LLM-TKESS (large language model for text-based knowledge-embedded soft sensing), harnessing the powerful general problem-solving capabilities, cross-modal knowledge transfer abilities, and few-shot capabilities of LLM for enhanced soft sensing modeling. Specifically, an auxiliary variable series encoder (AVS Encoder) is proposed to unleash LLM's potential for capturing temporal relationships within series and spatial semantic relationships among auxiliary variables. Then, we propose a two-stage fine-tuning alignment strategy: in the first stage, employing parameter-efficient fine-tuning through autoregressive training adjusts LLM to rapidly accommodate process variable data, resulting in a soft sensing foundation model (SSFM). Subsequently, by training adapters, we adapt the SSFM to various downstream tasks without modifying its architecture. Then, we propose two text-based knowledge-embedded soft sensors, integrating new natural language modalities to overcome the limitations of pure structured data models. Furthermore, benefiting from LLM's pre-existing world knowledge, our model demonstrates outstanding predictive capabilities in small sample conditions. Using the thermal deformation of air preheater rotor as a case study, we validate through extensive experiments that LLM-TKESS exhibits outstanding performance.

A Soft Sensor Method with Uncertainty-Awareness and Self-Explanation Based on Large Language Models Enhanced by Domain Knowledge Retrieval

Data-driven soft sensors are crucial in predicting key performance indicators in industrial systems. However, current methods predominantly rely on the supervised learning paradigms of parameter updating, which inherently faces challenges such as high development costs, poor robustness, training instability, and lack of interpretability. Recently, large language models (LLMs) have demonstrated significant potential across various domains, notably through In-Context Learning (ICL), which enables high-performance task execution with minimal input-label demonstrations and no prior training. This paper aims to replace supervised learning with the emerging ICL paradigm for soft sensor modeling to address existing challenges and explore new avenues for advancement. To achieve this, we propose a novel framework called the Few-shot Uncertainty-aware and self-Explaining Soft Sensor (LLM-FUESS), which includes the Zero-shot Auxiliary Variable Selector (LLM-ZAVS) and the Uncertainty-aware Few-shot Soft Sensor (LLM-UFSS). The LLM-ZAVS retrieves from the Industrial Knowledge Vector Storage to enhance LLMs' domain-specific knowledge, enabling zero-shot auxiliary variable selection. In the LLM-UFSS, we utilize text-based context demonstrations of structured data to prompt LLMs to execute ICL for predicting and propose a context sample retrieval augmentation strategy to improve performance. Additionally, we explored LLMs' AIGC and probabilistic characteristics to propose self-explanation and uncertainty quantification methods for constructing a trustworthy soft sensor. Extensive experiments demonstrate that our method achieved state-of-the-art predictive performance, strong robustness, and flexibility, effectively mitigates training instability found in traditional methods. To the best of our knowledge, this is the first work to establish soft sensor utilizing LLMs.

Text-to-3D Gaussian Splatting with Physics-Grounded Motion Generation

Text-to-3D generation is a valuable technology in virtual reality and digital content creation. While recent works have pushed the boundaries of text-to-3D generation, producing high-fidelity 3D objects with inefficient prompts and simulating their physics-grounded motion accurately still remain unsolved challenges. To address these challenges, we present an innovative framework that utilizes the Large Language Model (LLM)-refined prompts and diffusion priors-guided Gaussian Splatting (GS) for generating 3D models with accurate appearances and geometric structures. We also incorporate a continuum mechanics-based deformation map and color regularization to synthesize vivid physics-grounded motion for the generated 3D Gaussians, adhering to the conservation of mass and momentum. By integrating text-to-3D generation with physics-grounded motion synthesis, our framework renders photo-realistic 3D objects that exhibit physics-aware motion, accurately reflecting the behaviors of the objects under various forces and constraints across different materials. Extensive experiments demonstrate that our approach achieves high-quality 3D generations with realistic physics-grounded motion.

Geometry-guided Cross-view Diffusion for One-to-many Cross-view Image Synthesis

This paper presents a novel approach for cross-view synthesis aimed at generating plausible ground-level images from corresponding satellite imagery or vice versa. We refer to these tasks as satellite-to-ground (Sat2Grd) and ground-to-satellite (Grd2Sat) synthesis, respectively. Unlike previous works that typically focus on one-to-one generation, producing a single output image from a single input image, our approach acknowledges the inherent one-to-many nature of the problem. This recognition stems from the challenges posed by differences in illumination, weather conditions, and occlusions between the two views. To effectively model this uncertainty, we leverage recent advancements in diffusion models. Specifically, we exploit random Gaussian noise to represent the diverse possibilities learnt from the target view data. We introduce a Geometry-guided Cross-view Condition (GCC) strategy to establish explicit geometric correspondences between satellite and street-view features. This enables us to resolve the geometry ambiguity introduced by camera pose between image pairs, boosting the performance of cross-view image synthesis. Through extensive quantitative and qualitative analyses on three benchmark cross-view datasets, we demonstrate the superiority of our proposed geometry-guided cross-view condition over baseline methods, including recent state-of-the-art approaches in cross-view image synthesis. Our method generates images of higher quality, fidelity, and diversity than other state-of-the-art approaches.

Single Image, Any Face: Generalisable 3D Face Generation

The creation of 3D human face avatars from a single unconstrained image is a fundamental task that underlies numerous real-world vision and graphics applications. Despite the significant progress made in generative models, existing methods are either less suited in design for human faces or fail to generalise from the restrictive training domain to unconstrained facial images. To address these limitations, we propose a novel model, Gen3D-Face, which generates 3D human faces with unconstrained single image input within a multi-view consistent diffusion framework. Given a specific input image, our model first produces multi-view images, followed by neural surface construction. To incorporate face geometry information in a generalisable manner, we utilise input-conditioned mesh estimation instead of ground-truth mesh along with synthetic multi-view training data. Importantly, we introduce a multi-view joint generation scheme to enhance appearance consistency among different views. To the best of our knowledge, this is the first attempt and benchmark for creating photorealistic 3D human face avatars from single images for generic human subject across domains. Extensive experiments demonstrate the superiority of our method over previous alternatives for out-of-domain singe image 3D face generation and top competition for in-domain setting.

Weyl Calculus and Exactly Solvable Schrödinger Bridges with Quadratic State Cost

Schr\"{o}dinger bridge--a stochastic dynamical generalization of optimal mass transport--exhibits a learning-control duality. Viewed as a stochastic control problem, the Schr\"{o}dinger bridge finds an optimal control policy that steers a given joint state statistics to another while minimizing the total control effort subject to controlled diffusion and deadline constraints. Viewed as a stochastic learning problem, the Schr\"{o}dinger bridge finds the most-likely distribution-valued trajectory connecting endpoint distributional observations, i.e., solves the two point boundary-constrained maximum likelihood problem over the manifold of probability distributions. Recent works have shown that solving the Schr\"{o}dinger bridge problem with state cost requires finding the Markov kernel associated with a reaction-diffusion PDE where the state cost appears as a state-dependent reaction rate. We explain how ideas from Weyl calculus in quantum mechanics, specifically the Weyl operator and the Weyl symbol, can help determine such Markov kernels. We illustrate these ideas by explicitly finding the Markov kernel for the case of quadratic state cost via Weyl calculus, recovering our earlier results but avoiding tedious computation with Hermite polynomials.