Safe and Robust Domains of Attraction for Discrete-Time Systems: A Set-Based Characterization and Certifiable Neural Network Estimation

Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging due to both theoretical and computational limitations, particularly in the presence of uncertainties and state constraints. In this paper, we propose a novel framework for the accurate estimation of safe (state-constrained) and robust DOAs for discrete-time nonlinear uncertain systems with continuous dynamics, open safe sets, compact disturbance sets, and uniformly locally $\ell_p$-stable compact RISs. The notion of uniform $\ell_p$ stability is quite general and encompasses, as special cases, uniform exponential and polynomial stability. The DOAs are characterized via newly introduced value functions defined on metric spaces of compact sets. We establish their fundamental mathematical properties and derive the associated Bellman-type (Zubov-type) functional equations. Building on this characterization, we develop a physics-informed neural network (NN) framework to learn the corresponding value functions by embedding the derived Bellman-type equations directly into the training process. To obtain certifiable estimates of the safe robust DOAs from the learned neural approximations, we further introduce a verification procedure that leverages existing formal verification tools. The effectiveness and applicability of the proposed methodology are demonstrated through four numerical examples involving nonlinear uncertain systems subject to state constraints, and its performance is compared with existing methods from the literature.

A Boundary Integral-based Neural Operator for Mesh Deformation

This paper presents an efficient mesh deformation method based on boundary integration and neural operators, formulating the problem as a linear elasticity boundary value problem (BVP). To overcome the high computational cost of traditional finite element methods and the limitations of existing neural operators in handling Dirichlet boundary conditions for vector fields, we introduce a direct boundary integral representation using a Dirichlet-type Green's tensor. This formulation expresses the internal displacement field solely as a function of boundary displacements, eliminating the need to solve for unknown tractions. Building on this, we design a Boundary-Integral-based Neural Operator (BINO) that learns the geometry- and material-aware Green's traction kernel. A key technical advantage of our framework is the mathematical decoupling of the physical integration process from the geometric representation via geometric descriptors. While this study primarily demonstrates robust generalization across diverse boundary conditions, the architecture inherently possesses potential for cross-geometry adaptation. Numerical experiments, including large deformations of flexible beams and rigid-body motions of NACA airfoils, confirm the model's high accuracy and strict adherence to the principles of linearity and superposition. The results demonstrate that the proposed framework ensures mesh quality and computational efficiency, providing a reliable new paradigm for parametric mesh generation and shape optimization in engineering.

LogicGraph : Benchmarking Multi-Path Logical Reasoning via Neuro-Symbolic Generation and Verification

Evaluations of large language models (LLMs) primarily emphasize convergent logical reasoning, where success is defined by producing a single correct proof. However, many real-world reasoning problems admit multiple valid derivations, requiring models to explore diverse logical paths rather than committing to one route. To address this limitation, we introduce LogicGraph, the first benchmark aimed to systematically evaluate multi-path logical reasoning, constructed via a neuro-symbolic framework that leverages backward logic generation and semantic instantiation. This pipeline yields solver-verified reasoning problems formalized by high-depth multi-path reasoning and inherent logical distractions, where each instance is associated with an exhaustive set of minimal proofs. We further propose a reference-free evaluation framework to rigorously assess model performance in both convergent and divergent regimes. Experiments on state-of-the-art language models reveal a common limitation: models tend to commit early to a single route and fail to explore alternatives, and the coverage gap grows substantially with reasoning depth. LogicGraph exposes this divergence gap and provides actionable insights to motivate future improvements. Our code and data will be released at https://github.com/kkkkarry/LogicGraph.

Physical Human-Robot Interaction for Grasping in Augmented Reality via Rigid-Soft Robot Synergy

Hybrid rigid-soft robots combine the precision of rigid manipulators with the compliance and adaptability of soft arms, offering a promising approach for versatile grasping in unstructured environments. However, coordinating hybrid robots remains challenging, due to difficulties in modeling, perception, and cross-domain kinematics. In this work, we present a novel augmented reality (AR)-based physical human-robot interaction framework that enables direct teleoperation of a hybrid rigid-soft robot for simple reaching and grasping tasks. Using an AR headset, users can interact with a simulated model of the robotic system integrated into a general-purpose physics engine, which is superimposed on the real system, allowing simulated execution prior to real-world deployment. To ensure consistent behavior between the virtual and physical robots, we introduce a real-to-simulation parameter identification pipeline that leverages the inherent geometric properties of the soft robot, enabling accurate modeling of its static and dynamic behavior as well as the control system's response.

Locomo-Plus: Beyond-Factual Cognitive Memory Evaluation Framework for LLM Agents

Long-term conversational memory is a core capability for LLM-based dialogue systems, yet existing benchmarks and evaluation protocols primarily focus on surface-level factual recall. In realistic interactions, appropriate responses often depend on implicit constraints such as user state, goals, or values that are not explicitly queried later. To evaluate this setting, we introduce \textbf{LoCoMo-Plus}, a benchmark for assessing cognitive memory under cue--trigger semantic disconnect, where models must retain and apply latent constraints across long conversational contexts. We further show that conventional string-matching metrics and explicit task-type prompting are misaligned with such scenarios, and propose a unified evaluation framework based on constraint consistency. Experiments across diverse backbone models, retrieval-based methods, and memory systems demonstrate that cognitive memory remains challenging and reveals failures not captured by existing benchmarks. Our code and evaluation framework are publicly available at: https://github.com/xjtuleeyf/Locomo-Plus.

POP: Online Structural Pruning Enables Efficient Inference of Large Foundation Models

Large foundation models (LFMs) achieve strong performance through scaling, yet current structural pruning methods derive fixed pruning decisions during inference, overlooking sparsity patterns that emerge in the autoregressive token generation. In this paper, we propose POP (Partition-guided Online Pruning), an efficient online structural pruning framework that enables context-conditioned dynamic pruning with minimal computational overhead. POP partitions model channels into retained, candidate, and pruned regions, where prefilling defines a coarse pruning partition, and the decoding stage generates a fine-grained mask within the candidate region, avoiding full-channel re-evaluation. The coarse pruning partition preserves consistently important weights, while the fine-grained masking provides context-conditioned variation during decoding. Moreover, POP is a lightweight, plug-and-play method that requires no preprocessing, including offline calibration, retraining, or learning predictors. Extensive evaluations across diverse LFMs, including large language models (LLMs), mixture-of-experts models (MoEs), and vision-language models (VLMs), demonstrate that POP consistently delivers higher accuracy than existing pruning approaches while incurring smaller computational overhead and minimizing inference latency.

OdysseyArena: Benchmarking Large Language Models For Long-Horizon, Active and Inductive Interactions

The rapid advancement of Large Language Models (LLMs) has catalyzed the development of autonomous agents capable of navigating complex environments. However, existing evaluations primarily adopt a deductive paradigm, where agents execute tasks based on explicitly provided rules and static goals, often within limited planning horizons. Crucially, this neglects the inductive necessity for agents to discover latent transition laws from experience autonomously, which is the cornerstone for enabling agentic foresight and sustaining strategic coherence. To bridge this gap, we introduce OdysseyArena, which re-centers agent evaluation on long-horizon, active, and inductive interactions. We formalize and instantiate four primitives, translating abstract transition dynamics into concrete interactive environments. Building upon this, we establish OdysseyArena-Lite for standardized benchmarking, providing a set of 120 tasks to measure an agent's inductive efficiency and long-horizon discovery. Pushing further, we introduce OdysseyArena-Challenge to stress-test agent stability across extreme interaction horizons (e.g., > 200 steps). Extensive experiments on 15+ leading LLMs reveal that even frontier models exhibit a deficiency in inductive scenarios, identifying a critical bottleneck in the pursuit of autonomous discovery in complex environments. Our code and data are available at https://github.com/xufangzhi/Odyssey-Arena

AERO: Autonomous Evolutionary Reasoning Optimization via Endogenous Dual-Loop Feedback

Large Language Models (LLMs) have achieved significant success in complex reasoning but remain bottlenecked by reliance on expert-annotated data and external verifiers. While existing self-evolution paradigms aim to bypass these constraints, they often fail to identify the optimal learning zone and risk reinforcing collective hallucinations and incorrect priors through flawed internal feedback. To address these challenges, we propose \underline{A}utonomous \underline{E}volutionary \underline{R}easoning \underline{O}ptimization (AERO), an unsupervised framework that achieves autonomous reasoning evolution by internalizing self-questioning, answering, and criticism within a synergistic dual-loop system. Inspired by the \textit{Zone of Proximal Development (ZPD)} theory, AERO utilizes entropy-based positioning to target the ``solvability gap'' and employs Independent Counterfactual Correction for robust verification. Furthermore, we introduce a Staggered Training Strategy to synchronize capability growth across functional roles and prevent curriculum collapse. Extensive evaluations across nine benchmarks spanning three domains demonstrate that AERO achieves average performance improvements of 4.57\% on Qwen3-4B-Base and 5.10\% on Qwen3-8B-Base, outperforming competitive baselines. Code is available at https://github.com/mira-ai-lab/AERO.

Multimodal Generative Recommendation for Fusing Semantic and Collaborative Signals

Sequential recommender systems rank relevant items by modeling a user's interaction history and computing the inner product between the resulting user representation and stored item embeddings. To avoid the significant memory overhead of storing large item sets, the generative recommendation paradigm instead models each item as a series of discrete semantic codes. Here, the next item is predicted by an autoregressive model that generates the code sequence corresponding to the predicted item. However, despite promising ranking capabilities on small datasets, these methods have yet to surpass traditional sequential recommenders on large item sets, limiting their adoption in the very scenarios they were designed to address. To resolve this, we propose MSCGRec, a Multimodal Semantic and Collaborative Generative Recommender. MSCGRec incorporates multiple semantic modalities and introduces a novel self-supervised quantization learning approach for images based on the DINO framework. Additionally, MSCGRec fuses collaborative and semantic signals by extracting collaborative features from sequential recommenders and treating them as a separate modality. Finally, we propose constrained sequence learning that restricts the large output space during training to the set of permissible tokens. We empirically demonstrate on three large real-world datasets that MSCGRec outperforms both sequential and generative recommendation baselines and provide an extensive ablation study to validate the impact of each component.

ConsistentRFT: Reducing Visual Hallucinations in Flow-based Reinforcement Fine-Tuning

Reinforcement Fine-Tuning (RFT) on flow-based models is crucial for preference alignment. However, they often introduce visual hallucinations like over-optimized details and semantic misalignment. This work preliminarily explores why visual hallucinations arise and how to reduce them. We first investigate RFT methods from a unified perspective, and reveal the core problems stemming from two aspects, exploration and exploitation: (1) limited exploration during stochastic differential equation (SDE) rollouts, leading to an over-emphasis on local details at the expense of global semantics, and (2) trajectory imitation process inherent in policy gradient methods, distorting the model's foundational vector field and its cross-step consistency. Building on this, we propose ConsistentRFT, a general framework to mitigate these hallucinations. Specifically, we design a Dynamic Granularity Rollout (DGR) mechanism to balance exploration between global semantics and local details by dynamically scheduling different noise sources. We then introduce a Consistent Policy Gradient Optimization (CPGO) that preserves the model's consistency by aligning the current policy with a more stable prior. Extensive experiments demonstrate that ConsistentRFT significantly mitigates visual hallucinations, achieving average reductions of 49\% for low-level and 38\% for high-level perceptual hallucinations. Furthermore, ConsistentRFT outperforms other RFT methods on out-of-domain metrics, showing an improvement of 5.1\% (v.s. the baseline's decrease of -0.4\%) over FLUX1.dev. This is \href{https://xiaofeng-tan.github.io/projects/ConsistentRFT}{Project Page}.