arXiv subjects

Yi Liu

Publications and source records attributed to Yi Liu.

8 recordsLinked to original sources

arXiv2026

Numerical approximation to the invariant measure of McKean-Vlasov stochastic differential equations

Inspired by the stochastic particle method, this paper develops an easily implementable explicit scheme for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. We prove that the numerical solution of the interacting particle system (IPS) attains the optimal uniform-in-time strong convergence rate of order 1/2, and that it faithfully captures the long-term dynamics of MV-SDEs, including moment boundedness, stability, and ergodicity. In particular, the existence and uniqueness of an exchangeable numerical invariant probability measure for the IPS are established via an appropriately constructed operator semigroup. Concerning the approximation of the invariant measure, we derive a non-asymptotic error bound between the distribution of the one-particle numerical solution and the marginal distribution of the IPS's invariant measure; By the uniform-in-time propagation of chaos, we further obtain an asymptotic error bound between the one-particle marginal of the IPS's numerical invariant measure and the exact invariant measure of the MV-SDE. Numerical experiments are provided to validate the theoretical results.

math.PR↗

arXiv2026

Global to Local: Topology-Preserving Adaptive Graph Pooling via Granular-Ball

Graph pooling aims to compress the graph, including both node embeddings and their underlying topological patterns, into a more compact representation. Previous works focus primarily on the overly fine-grained representation of nodes, progressively coarsening the graph by removing nodes or merging them into clusters, thus neglecting the global-to-local patterns and adaptive granularity of the graph's topological structure. In the real scenario, graphs as a whole can be considered the coarsest level of granularity, encapsulating the global topological structure, with progressively finer-grained local topological structures represented from top to bottom. This process continues until the adaptive granularity for each subdomain is reached. To this end, we propose a novel Topology-Preserving Adaptive Graph Pooling (TPAGP) method that dynamically partitions graphs into granular balls by integrating node features and topological information, enabling the generation of multi-granularity representations that effectively capture both local and global structural patterns. Additionally, we design a multi-granularity graph network model that facilitates feature interaction and optimization across different granularities, significantly enhancing performance in graph classification tasks. Experimental results demonstrate that TPAGP outperforms existing pooling methods across various benchmark datasets, effectively mitigating information loss caused by fixed-granularity strategies.

cs.AI↗

arXiv2026

Multi-granularity Adaptive Hypergraph Representation Learning via Granular-ball

Hypergraph representation learning aims to capture high-order information in graphs by constructing hyperedges that simultaneously connect multiple nodes. These hyperedges adapt to the graph's topological features, facilitating the extraction of high-order relationships at multiple granularities. Most prior work relies on predefined definitions to generate hyperedges, overlooking the diversity in graph topological structures and the multi-granularity characteristics of hyperedges. As a result, this limits their ability to effectively and adaptively discover high-order relationships and efficiently process complex structural information. To address this limitation, we propose a novel framework called \underline{M}ulti-\underline{G}ranularity \underline{H}ypergraph \underline{R}epresentation \underline{L}earning (MGHRL). MGHRL introduces an Adaptive Granular Hypergraph Generation strategy, which generates hyperedges at multiple levels of granularity through the adaptive splitting of granular-ball, effectively capturing high-order relationships based on the graph's topological structure. Additionally, we propose a Multi-Granularity Hypergraph Network with multiple sub-networks, capturing features from hyperedges at different granularities and integrating them via hierarchical reversible connections. Experimental results show that MGHRL significantly outperforms baseline models on benchmark datasets.

cs.LG↗

arXiv2026

When Can Large Reasoning Models Save Thinking? Mechanistic Analysis of Behavioral Divergence in Reasoning

Large reasoning models (LRMs) have achieved remarkable success on complex tasks, yet their tendency to "overthink" leads to inefficiencies. Although "save-thinking" prompts are intended to mitigate this issue, we find that LRMs still frequently enter the "Still-thinking" mode instead of the expected "No-thinking" mode, especially on difficult queries. To analyze this behavioral divergence, we examine LRMs from three perspectives: confidence at the thinking-termination boundary, divergence in internal attention distributions, and attention allocation across prompt segments. We find that high perplexity is associated with later Still-thinking behavior, and that Still-thinking cases allocate more attention to the original question. Based on these observations, we propose an attention intervention method to regulate this behavior. While this intervention suppresses explicit thinking, it also causes a drop in accuracy, suggesting that the suppressed reasoning behavior is often useful for correctness. Our work provides confidence- and attention-level evidence for this behavior, highlighting the trade-off between instruction following, inference efficiency, and reasoning correctness.

cs.AI↗

arXiv2026

UniACE: A Unified Framework for Evaluating LLM Agentic Capabilities

Agent benchmarks are increasingly used to compare large language models (LLMs) across domains, yet a reported score reflects a complete model--harness--environment configuration rather than the model alone. Benchmark packages couple native tasks with specific prompts, tool protocols, orchestration logic, and sometimes dynamic external resources, making cross-benchmark comparisons sensitive to implementation and resource conditions. We present UniACE, a unified framework for model-centric evaluation under an explicit, common execution condition. UniACE represents each benchmark as an instruction--tool--environment triplet, executes LLMs through a shared, task-agnostic harness in isolated per-task runtimes, and preserves native success criteria. For tasks that rely on dynamic resources, an optional offline mode replaces live access with fixed, pre-collected snapshots. Its evaluation protocol further standardizes efficiency measurement, execution records, and trace-based failure attribution. We migrate 7 benchmarks spanning 24 domains and evaluate 15 models in more than 400K rollouts consuming 5B tokens. Comparisons with source implementations show large bidirectional score changes and model-ranking reversals, while matched online and offline runs reveal substantial sensitivity to accessible evidence and its representation. Under the shared UniACE configuration, efficiency and failure profiles expose task-dependent model behaviors hidden by task-success scores alone. These findings motivate reporting agent benchmark outcomes as properties of an explicit evaluation configuration, enabling more interpretable and reproducible cross-benchmark comparisons. Codes and benchmarks at are available at https://github.com/whfeLingYu/A-Unified-Framework-for-the-Evaluation-of-LLM-Agentic-Capabilities, https://huggingface.co/datasets/whfeLingYu/Unified_Agent_Framework.

cs.AI↗

arXiv2026

Polished but Unresolved: Identifying Late-Stage Pressure States in Long-Horizon Tool-Use Agents

Long-horizon tool-use agents need not only to search and plan, but also to decide when to finalize. We study late-stage pressure states, in which an agent is biased toward submitting a final answer that appears complete and polished while key constraints remain unresolved. We first train a linear probe to show that this pressure state is identifiable from the agent's hidden states. Then, we use activation interventions along this pressure direction and find that shifting the hidden states changes both the pressure score and whether the agent continues tool use or submits early. Through controlled context manipulations, we further see that the pressure is mitigated by constraint clarity and action mapping. Based on these findings, we propose Probe-Sensed Pressure Relief (PSPR), a plugin that applies lightweight pressure relief direction under moderate pressure and moves to structured organization under high pressure risk. Experiments on multiple long-horizon benchmarks show that our method consistently strengthens existing agent methods.

cs.AI↗

arXiv2026

Dense Process Supervision for Search Agents via Fact Utility Estimation

Reinforcement learning (RL) for search agents typically relies on outcome rewards. However, it often fails to achieve effective credit assignment, due to the unclear value of intermediate steps. It is hard to separate their contributions from the final result. In this paper, we propose a dense process supervision method based on fact utility estimation, which models the reasoning process as the accumulation of discrete evidence facts. We first extract structured facts from raw observations and organize them into an explicit fact store. To support credit assignment, we then cluster semantically equivalent facts and infer the posterior utility of each fact cluster using Bayesian estimation over group rollouts. Finally, we convert the estimated fact utilities into dense step-level rewards to guide RL training. Experiments on seven single-hop and multi-hop QA benchmarks show that our method consistently outperforms existing baselines. Ablation studies validate clear relative improvements on multi-hop QA compared to outcome reward-only training.

cs.CL↗

arXiv2026

On the Complexity of Bayesian Signal Processing

We develop a computational framework for Bayesian decision-making. We show that as long as no action is optimal in every state, Bayes-optimal choice is intractable. This hardness need not arise from large action, state, or signal spaces, nor from a complicated represented utility function: extracting enough information from a hard-to-interpret signal to act optimally can itself be computationally hard. We also characterize tractability across approximation notions and identify their sources of difficulty. Under the probably approximately correct criterion, sample-based Bayesian learning is tractable if and only if the signal support is bounded. Our results provide justifications for bounded rationality, costly Bayesian inference, and sample-based Bayesian learning.

econ.TH↗