arXiv subjects
Publications and source records attributed to Xudong Chen.
We show that the Lie algebra of algebraic vector fields for any connected, semi-simple matrix group over $\mathbb{F}$, for $\mathbb{F}=\mathbb{R},\mathbb{C}$, can be generated by three $\mathbb{F}$-complete algebraic vector fields.
Large language models (LLMs) provide a flexible foundation for multi-agent systems, but their effectiveness and computational cost depend critically on orchestration design. Across different tasks, role design, capacity assignment, and dependency construction jointly affect both solution quality and execution efficiency. Existing approaches automate parts of this design process, yet they often optimize these decisions partially or sequentially, and rely on execution-level feedback that provides limited credit assignment for local orchestration decisions. We propose LEMON (Learning Executable Multi-Agent Orchestration via Counterfactual Reinforcement Learning), an LLM-based orchestrator that learns to design efficient multi-agent orchestration. Given a task, LEMON designs a unified orchestration specification that composes customized agent duties, capacity levels, and dependency relations. To train the orchestrator, we augment the orchestration-level Group Relative Policy Optimization (GRPO) objective with a localized counterfactual credit signal that edits role, capacity, or dependency fields and applies the resulting reward contrast only to the edited spans. Experiments on six reasoning and coding benchmarks, including MMLU, GSM8K, AQuA, MultiArith, SVAMP, and HumanEval, show that LEMON achieves the best average performance among evaluated multi-agent orchestration methods while improving the accuracy-token trade-off.
Exploring high-order correlations and long-range dependencies in brain networks holds significant value for both neuroscience research and clinical diagnosis. However, previous studies have lacked a unified integration of high-order and long-range dependency information in brain networks, and there is substantial redundancy behind various types of information. These issues limit their effectiveness in the diagnosis of brain diseases. To address this, we propose an Information Bottleneck-Guided Adaptive HyperGraph Transformer (IBAHGT). By incorporating the information bottleneck (IB) principle, this approach enables adaptive learning of high-order correlations and both short- and long-range dependencies within a unified framework for brain network analysis, achieving high-precision brain disease diagnosis. IBAHGT consists of three key components: an information bottleneck-guided adaptive hypergraph convolution, which introduces a novel hypergraph information bottleneck (HIB) principle to adaptively learn hypergraph message-passing weights between nodes and hyperedges, optimizes information flow and captures high-order information in brain networks that is maximally informative and minimally redundant (MIMR). The Transformer encoder captures global information within brain networks through the attention mechanism, specifically modeling short- and long-range dependencies. An information bottleneck-guided node-level adaptive fusion employs the IB principle to learn independent weights for each node, facilitating the fine-grained integration of high-order information and global information to obtain an efficient representation for downstream tasks. Extensive experiments demonstrate that the proposed method outperforms current state-of-the-art methods and can identify biomarkers for clinical applications.
We exhibit two vector fields on $S^2$, which generate the entire Lie algebra of algebraic vector fields. Compositions of the flows associated with these two vector fields enable us to approximate every diffeomorphism of $S^2$ isotopic to the identity in the $\mathrm{C}^r$-sense for any $r\geq 0$.
In this paper, we consider linear stochastic systems with control-linear noise and periodically sampled measurements. We address the problem of feedback stabilization in the mean-square sense. The main contribution of the paper is to provide a necessary and sufficient condition for feedback stabilization. In particular, we relate feedback stabilizability of the stochastic system to the existence of a fixed point of a Riccati-type algebraic equation and, further, to the existence of a solution to an infinite-horizon optimal control problem.
We consider in this paper complex Lie groups $\mathrm{SL}_n(\mathbb{C})$ for $n\geq 2$, $\mathrm{SO}_n(\mathbb{C})$ for $n\geq 5$, and $\mathrm{Sp}_{2n}(\mathbb{C})$ for $n\geq 1$. We show that for any such Lie group, the Lie algebra of polynomial vector fields can be generated by three $\mathbb{C}$-complete polynomial vector fields.
We show that for any real, connected, semi-simple matrix group, its Lie algebra of algebraic vector fields can be generated by three complete vector fields.
Conformal prediction (CP) provides distribution-free coverage guarantees and has emerged as a principled tool for uncertainty quantification. In edge-level fraud detection on temporal interaction graphs, where false positives and false negatives both carry substantial cost, such coverage guarantees are particularly appealing for risk-aware decision making. However, directly applying existing graph conformal predictors yields inefficient prediction sets due to two recurring properties of fraud data. Fraudulent interactions are often embedded in benign-dominated neighborhoods that dilute calibration signals, while extreme class imbalance leaves scarce labeled-fraud support in the calibration split and leads to overly conservative class-conditional thresholds. To address these issues, we propose ProtoCP, a conformal prediction framework for edge-level fraud detection on temporal graphs. ProtoCP improves calibration efficiency by focusing calibration on fraud-relevant subgraph context and producing more stable nonconformity scores under class imbalance and temporal drift. Specifically, it leverages learned prototypes to suppress benign-dominated noise in the calibration context and introduces a neighborhood-relative scoring mechanism with temporal score diffusion for stable class-conditional calibration. Experiments on four fraud benchmarks (YelpChi, S-FFSD, FTFD, and BankSim) show that ProtoCP achieves the target coverage with consistently smaller prediction sets than state-of-the-art baselines. Our codes are available at https://github.com/Picard1701ent/ProtoCP.git
We consider a countably infinite collection of linear, scalar control systems, where each system is represented by the pair $(a_n,b_n)$ with $a_n>0$ for $n\in \mathbb{N}$, and all systems are forced by a common scalar control input. We refer to this collection of systems as a discrete linear ensemble system. The ensemble system is feedback stabilizable if there exists a common feedback control input that asymptotically stabilizes every system simultaneously. Unlike finite-dimensional linear systems, an infinite-dimensional linear system is not guaranteed to be stable if its poles lie in the open left half-plane. Stability is guaranteed, however, if (i) its poles are contained in the closed left half-plane and (ii) its infinitesimal generator is diagonalizable. In this paper, we provide necessary and sufficient conditions for the existence of a static, linear feedback control law that ensures the closed-loop ensemble system satisfies (i) and (ii). In particular, we show that the exponential decay of the sequences $(|b_n|)_{n\in \mathbb{N}}$ and $(a_n/|b_n|)_{n\in \mathbb{N}}$ is necessary and, under an assumption on the desired poles, sufficient.
In this paper, we study four-strategy conservative replicator dynamics induced by constant payoff matrices. We establish necessary and sufficient conditions for coexistence to occur by associating the payoff matrix with its digraph, revealing exactly five distinct digraph classes governing the global behavior. We further show that, whenever the dynamics is coexistent, every non-equilibrium trajectory in the relative interior of the simplex is a Lyapunov-stable periodic orbit. Together with the classification of the boundary phase portraits, these results provide a complete characterization of the global dynamics in the four-strategy case with coexistence.
We study structural averaged controllability for multi-input linear ensemble systems. In this problem, one asks whether a sparsity pattern admits a linear ensemble system that is averaged controllable. The single-input case has been characterized completely, while the general multi-input case has remained open. In this work, we give a complete characterization for the general multi-input case. In particular, we prove that in addition to accessibility, a necessary and sufficient condition for structural averaged controllability of ensemble systems is existence of a row-saturating matching for its \emph{core}, an acyclic subgraph associated with the system which plays a central role in the result for the single-input case.
Baichuan-M4 is Baichuan Intelligence's clinical-grade medical large model, designed for continuous care rather than single-turn medical question answering. It is built as a coordinated medical agent system around three pillars: Baichuan-Harness, a unified runtime that keeps reinforcement-learning training and real-world deployment consistent while enforcing action constraints, tool use, long-term patient memory, and multi-agent coordination; a core reasoning model trained with a continuous-care reinforcement-learning framework that integrates span-level reward modeling (SPAR++), reasoning-path compression, curriculum learning, and stabilized policy optimization; and a clinical tool layer for patient-memory management, authoritative evidence-based retrieval, and multimodal medical perception across documents, X-rays, and dermatology. On a cross-dimensional medical evaluation suite, Baichuan-M4 attains leading results in static medical knowledge and safety, dynamic OSCE-style consultation, long-context clinical memory, evidence-based retrieval, medical document OCR, and multimodal image understanding, while lowering the hallucination rate to 3.3%.
Most existing secure neural network inference protocols based on secure multi-party computation (MPC) typically support at most four participants, demonstrating severely limited scalability. Liu et al. (USENIX Security'24) presented the first relatively practical approach by utilizing Shamir secret sharing with Mersenne prime fields. However, when processing deeper neural networks such as VGG16, their protocols incur substantial communication overhead, resulting in particularly significant latency in wide-area network (WAN) environments. In this paper, we propose a high-throughput and scalable MPC protocol for neural network inference against semi-honest adversaries in the honest-majority setting. The core of our approach lies in leveraging packed Shamir secret sharing (PSS) to enable parallel computation and reduce communication complexity. The main contributions are three-fold: i) We present a communication-efficient protocol for vector-matrix multiplication, based on our newly defined notion of vector-matrix multiplication-friendly random share tuples. ii) We design the filter packing approach that enables parallel convolution. iii) We further extend all non-linear protocols based on Shamir secret sharing to the PSS-based protocols for achieving parallel non-linear operations. Extensive experiments across various datasets and neural networks demonstrate the superiority of our approach in WAN. Compared to Liu et al. (USENIX Security'24), our scheme reduces the communication upto 5.85x, 11.17x, and 6.83x in offline, online and total communication overhead, respectively. In addition, our scheme is upto 1.59x, 2.61x, and 1.75x faster in offline, online and total running time, respectively.
In this paper, we focus on the class of complete $S$-partite graphs, for $S$ an undirected graph possibly with self-loops, and address the problem of finding largest $2$-regular subgraphs of these graphs, which can be formulated as an integer linear program. Roughly speaking, a complete $S$-partite graph is obtained by replacing every single node of $S$ with a number of nodes, preserving the edge/non-edge relations of $S$. Our motivation in finding largest $2$-regular subgraphs is rooted in the structural systems theory, particularly in the problem of finding largest subnetworks that can sustain controllability or asymptotic stability of the corresponding subsystems. A main contribution of the paper is to show that the integer linear problem can be solved efficiently in $O(|V(S)|^3)$, independent of the order/size of the $S$-partite graph itself. Furthermore, we demonstrate through simulations that with high probability, a random $S$-partite graph contains a largest $2$-regular subgraph of the same order as its complete counterpart does.
A graphon is said to have the $H$-property if a random undirected graph $G_n$ on $n$ nodes sampled from it has a node-wise disjoint cycle cover almost surely as $n\to\infty$. It has been shown in the earlier work that the $H$-property obeys the zero-one law, i.e., the probability that the random graph has a cycle cover tends to either one or zero. In this paper, we sharpen the result by characterizing the convergence rate of the probability. Specifically, we show that there are two different types of rates, with one being exponential and the other being root $n$. We provide a rigorous proof and numerical validation.
This paper introduces and solves a structural controllability problem for ensembles of switched linear systems. All individual systems in the ensemble are sparse and governed by the same sparsity pattern, and undergo switching among subsystems by following the same switching sequence. The controllability of an ensemble system describes the ability to use a common control input to simultaneously steer every individual system. A sparsity pattern is called structurally controllable for pair \((k,q)\) if it admits a controllable ensemble of \(q\) individual systems with at most \(k\) subsystems. We derive a necessary and sufficient condition for a sparsity pattern to be structurally controllable for a given \((k,q)\), and characterize when a sparsity pattern admits a finite \(k\) that guarantees structural controllability for \((k,q)\) for arbitrary $q$. Compared with the linear time-invariant ensemble case, this second condition is strictly weaker. We further show that these conditions have natural connections with maximum flow, and hence can be checked by polynomial algorithms. Specifically, the time complexity of deciding structural controllability is \(O(n^3)\) and the complexity of computing the smallest number of subsystems needed is \(O(n^3 \log n)\), with \(n\) the dimension of each individual system.
A step-graphon has the strong (resp., weak) $H$-property if a directed, random graph sampled from it has a Hamilton cycle (resp., a node-wise disjoint cycle cover) asymptotically almost surely. The weak/strong $H$-property is essentially a zero-one property. We identify key objects associated with the step-graphon that matter for the zero-one law and provide a complete characterization.
Replicator dynamics have been widely used in evolutionary game theory to model how strategy frequencies evolve over time in large populations. The so-called payoff matrix encodes the pairwise fitness that each strategy obtains when interacting with every other strategy, and it solely determines the replicator dynamics. If the payoff matrix is unknown, we show in this paper that it cannot be inferred from observed strategy frequencies alone -- distinct payoff matrices can induce the same replicator dynamics. We thus look for a canonical representative of the payoff matrix in the equivalence class. The main result of the paper is to show that for every polynomial replicator dynamics (i.e., the vector field is a polynomial), there always exists a skew-symmetric, polynomial payoff matrix that can induce the given dynamics.