DGNet: Discrete Green Networks for Data-Efficient Learning of Spatiotemporal PDEs

Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications. Neural PDE solvers offer a promising alternative to classical numerical methods. However, existing approaches typically require large numbers of training trajectories, while high-fidelity PDE data are expensive to generate. Under limited data, their performance degrades substantially, highlighting their low data efficiency. A key reason is that PDE dynamics embody strong structural inductive biases that are not explicitly encoded in neural architectures, forcing models to learn fundamental physical structure from data. A particularly salient manifestation of this inefficiency is poor generalization to unseen source terms. In this work, we revisit Green's function theory-a cornerstone of PDE theory-as a principled source of structural inductive bias for PDE learning. Based on this insight, we propose DGNet, a discrete Green network for data-efficient learning of spatiotemporal PDEs. The key idea is to transform the Green's function into a graph-based discrete formulation, and embed the superposition principle into the hybrid physics-neural architecture, which reduces the burden of learning physical priors from data, thereby improving sample efficiency. Across diverse spatiotemporal PDE scenarios, DGNet consistently achieves state-of-the-art accuracy using only tens of training trajectories. Moreover, it exhibits robust zero-shot generalization to unseen source terms, serving as a stress test that highlights its data-efficient structural design.

SELAUR: Self Evolving LLM Agent via Uncertainty-aware Rewards

Large language models (LLMs) are increasingly deployed as multi-step decision-making agents, where effective reward design is essential for guiding learning. Although recent work explores various forms of reward shaping and step-level credit assignment, a key signal remains largely overlooked: the intrinsic uncertainty of LLMs. Uncertainty reflects model confidence, reveals where exploration is needed, and offers valuable learning cues even in failed trajectories. We introduce SELAUR: Self Evolving LLM Agent via Uncertainty-aware Rewards, a reinforcement learning framework that incorporates uncertainty directly into the reward design. SELAUR integrates entropy-, least-confidence-, and margin-based metrics into a combined token-level uncertainty estimate, providing dense confidence-aligned supervision, and employs a failure-aware reward reshaping mechanism that injects these uncertainty signals into step- and trajectory-level rewards to improve exploration efficiency and learning stability. Experiments on two benchmarks, ALFWorld and WebShop, show that our method consistently improves success rates over strong baselines. Ablation studies further demonstrate how uncertainty signals enhance exploration and robustness.

Self-Generative Adversarial Fine-Tuning for Large Language Models

Fine-tuning large language models (LLMs) for alignment typically relies on supervised fine-tuning or reinforcement learning from human feedback, both limited by the cost and scarcity of high-quality annotations. Recent self-play and synthetic data approaches reduce this dependence but often rely on heuristic assumptions or ungrounded self-evaluation, which can cause bias accumulation and performance drift. In this paper, we propose Self-Generative Adversarial LLM (SGALM), a unified fine-tuning framework that formulates alignment as a generative adversarial game within a single LLM. SGALM jointly evolves generation and discrimination capabilities without external reward models. Theoretical and empirical results demonstrate that SGALM achieves state-of-the-art performance, serves as an effective alignment algorithm and a robust synthetic data engine.

Semantic Distance Measurement based on Multi-Kernel Gaussian Processes

Semantic distance measurement is a fundamental problem in computational linguistics, providing a quantitative characterization of similarity or relatedness between text segments, and underpinning tasks such as text retrieval and text classification. From a mathematical perspective, a semantic distance can be viewed as a metric defined on a space of texts or on a representation space derived from them. However, most classical semantic distance methods are essentially fixed, making them difficult to adapt to specific data distributions and task requirements. In this paper, a semantic distance measure based on multi-kernel Gaussian processes (MK-GP) was proposed. The latent semantic function associated with texts was modeled as a Gaussian process, with its covariance function given by a combined kernel combining Matérn and polynomial components. The kernel parameters were learned automatically from data under supervision, rather than being hand-crafted. This semantic distance was instantiated and evaluated in the context of fine-grained sentiment classification with large language models under an in-context learning (ICL) setup. The experimental results demonstrated the effectiveness of the proposed measure.

LLM-Empowered Representation Learning for Emerging Item Recommendation

In this work, we tackle the challenge of recommending emerging items, whose interactions gradually accumulate over time. Existing methods often overlook this dynamic process, typically assuming that emerging items have few or even no historical interactions. Such an assumption oversimplifies the problem, as a good model must preserve the uniqueness of emerging items while leveraging their shared patterns with established ones. To address this challenge, we propose EmerFlow, a novel LLM-empowered representation learning framework that generates distinctive embeddings for emerging items. It first enriches the raw features of emerging items through LLM reasoning, then aligns these representations with the embedding space of the existing recommendation model. Finally, new interactions are incorporated through meta-learning to refine the embeddings. This enables EmerFlow to learn expressive embeddings for emerging items from only limited interactions. Extensive experiments across diverse domains, including movies and pharmaceuticals, show that EmerFlow consistently outperforms existing methods.

MrCoM: A Meta-Regularized World-Model Generalizing Across Multi-Scenarios

Model-based reinforcement learning (MBRL) is a crucial approach to enhance the generalization capabilities and improve the sample efficiency of RL algorithms. However, current MBRL methods focus primarily on building world models for single tasks and rarely address generalization across different scenarios. Building on the insight that dynamics within the same simulation engine share inherent properties, we attempt to construct a unified world model capable of generalizing across different scenarios, named Meta-Regularized Contextual World-Model (MrCoM). This method first decomposes the latent state space into various components based on the dynamic characteristics, thereby enhancing the accuracy of world-model prediction. Further, MrCoM adopts meta-state regularization to extract unified representation of scenario-relevant information, and meta-value regularization to align world-model optimization with policy learning across diverse scenario objectives. We theoretically analyze the generalization error upper bound of MrCoM in multi-scenario settings. We systematically evaluate our algorithm's generalization ability across diverse scenarios, demonstrating significantly better performance than previous state-of-the-art methods.

SC2Arena and StarEvolve: Benchmark and Self-Improvement Framework for LLMs in Complex Decision-Making Tasks

Evaluating large language models (LLMs) in complex decision-making is essential for advancing AI's ability for strategic planning and real-time adaptation. However, existing benchmarks for tasks like StarCraft II fail to capture the game's full complexity, such as its complete game context, diverse action spaces, and all playable races. To address this gap, we present SC2Arena, a benchmark that fully supports all playable races, low-level action spaces, and optimizes text-based observations to tackle spatial reasoning challenges. Complementing this, we introduce StarEvolve, a hierarchical framework that integrates strategic planning with tactical execution, featuring iterative self-correction and continuous improvement via fine-tuning on high-quality gameplay data. Its key components include a Planner-Executor-Verifier structure to break down gameplay, and a scoring system for selecting high-quality training samples. Comprehensive analysis using SC2Arena provides valuable insights into developing generalist agents that were not possible with previous benchmarks. Experimental results also demonstrate that our proposed StarEvolve achieves superior performance in strategic planning. Our code, environment, and algorithms are publicly available.

Beyond Markovian: Reflective Exploration via Bayes-Adaptive RL for LLM Reasoning

Large Language Models (LLMs) trained via Reinforcement Learning (RL) have exhibited strong reasoning capabilities and emergent reflective behaviors, such as backtracking and error correction. However, conventional Markovian RL confines exploration to the training phase to learn an optimal deterministic policy and depends on the history contexts only through the current state. Therefore, it remains unclear whether reflective reasoning will emerge during Markovian RL training, or why they are beneficial at test time. To remedy this, we recast reflective exploration within the Bayes-Adaptive RL framework, which explicitly optimizes the expected return under a posterior distribution over Markov decision processes. This Bayesian formulation inherently incentivizes both reward-maximizing exploitation and information-gathering exploration via belief updates. Our resulting algorithm, BARL, instructs the LLM to stitch and switch strategies based on the observed outcomes, offering principled guidance on when and how the model should reflectively explore. Empirical results on both synthetic and mathematical reasoning tasks demonstrate that BARL outperforms standard Markovian RL approaches at test time, achieving superior token efficiency with improved exploration effectiveness. Our code is available at https://github.com/shenao-zhang/BARL.

Dense Communication between Language Models

As higher-level intelligence emerges from the combination of modular components with lower-level intelligence, many works combines Large Language Models (LLMs) for collective intelligence. Such combination is achieved by building communications among LLMs. While current systems primarily facilitate such communication through natural language, this paper proposes a novel paradigm of direct dense vector communication between LLMs. Our approach eliminates the unnecessary embedding and de-embedding steps when LLM interact with another, enabling more efficient information transfer, fully differentiable optimization pathways, and exploration of capabilities beyond human heuristics. We use such stripped LLMs as vertexes and optimizable seq2seq modules as edges to construct LMNet, with similar structure as MLPs. By utilizing smaller pre-trained LLMs as vertexes, we train a LMNet that achieves comparable performance with LLMs in similar size with only less than 0.1% training cost. This offers a new perspective on scaling for general intelligence rather than training a monolithic LLM from scratch. Besides, the proposed method can be used for other applications, like customizing LLM with limited data, showing its versatility.

Understanding the Uncertainty of LLM Explanations: A Perspective Based on Reasoning Topology

Understanding the uncertainty in large language model (LLM) explanations is important for evaluating their faithfulness and reasoning consistency, and thus provides insights into the reliability of LLM's output regarding a question. In this work, we propose a novel framework that quantifies uncertainty in LLM explanations through a reasoning topology perspective. By designing a structural elicitation strategy, we guide the LLMs to frame the explanations of an answer into a graph topology. This process decomposes the explanations into the knowledge related sub-questions and topology-based reasoning structures, which allows us to quantify uncertainty not only at the semantic level but also from the reasoning path. It further brings convenience to assess knowledge redundancy and provide interpretable insights into the reasoning process. Our method offers a systematic way to interpret the LLM reasoning, analyze limitations, and provide guidance for enhancing robustness and faithfulness. This work pioneers the use of graph-structured uncertainty measurement in LLM explanations and demonstrates the potential of topology-based quantification.