Z. Xiao
Publications
Freeze, Then Select: Structured Field Adapters and Stability-Validated Weak Selection for PDE Discovery from Sparse Observations
PDE discovery from sparse observations requires reconstructing a continuous field and selecting the correct differential terms. Our analysis of optimization paths in coupled neural PDE discovery reveals three behaviors: the exact support can persist to the end of training, appear only transiently, or fail to emerge. To decouple equation selection from neural optimization, we develop a freeze-then-select method combining a structured field adapter with Stability-Validated Weak Selection (SVWS). Trained from observations without a PDE residual, the adapter factorizes the field into learned spatial features and temporal coefficients represented by cubic splines. After freezing the field, SVWS identifies recurrent terms across independent weak-form systems, refits candidate supports, and selects the final equation on held-out weak-form systems. Beyond fixed libraries, we apply the same principle to expressions generated by genetic programming and recover the power-law form of an unknown nonlinear diffusion function from sparse, noisy observations. Across all six sparse MDBench regimes, our method attains the highest exact support recovery rate, with its clearest gains over classical and neural baselines on challenging Kuramoto-Sivashinsky dynamics.
AutoVSR: Automatic Visual-to-Symbolic Reasoning for Symbolic Expression Generation from Circuit Schematic
Symbolic expressions can effectively characterize and predict circuit behavior, but deriving them directly from circuit schematics is challenging. This process requires accurate visual-to-symbolic construction of circuit structure from images and correct multi-step symbolic derivation, both of which impose strict correctness requirements. This work proposes AutoVSR, an automated framework for visual-to-symbolic generation of circuit expressions using Vision Language Models (VLMs). By reconstructing circuit diagrams into an executable intermediate representation (Executable IR) and leveraging a symbolic solver for reasoning, AutoVSR significantly improves the accuracy of symbolic expression generation. AutoVSR introduces two key innovations: an IR construction method guided by component rule retrieval and verification-based feedback, and a symbolic solver implemented as a planning agent equipped with a symbolic tool library for reliable multi-step derivation. Compared with end-to-end VLM approaches and specialized methods on the main symbolic expression generation task, AutoVSR achieves accuracy improvements of 30.01--59.45% and 41.96--51.84%, respectively. Moreover, AutoVSR surpasses closed-source state-of-the-art VLMs in inference cost and computational efficiency. Code is available at https://github.com/LongfeiLi1/AutoVSR.
CirrusBench: Evaluating LLM-based Agents Beyond Correctness in Real-World Cloud Service Environments
The increasing agentic capabilities of Large Language Models (LLMs) have enabled their deployment in real-world applications, such as cloud services, where customer-assistant interactions exhibit high technical complexity and long-horizon dependencies, making robustness and resolution efficiency critical for customer satisfaction. However, existing benchmarks for LLM-based agents largely rely on synthetic environments that fail to capture the diversity and unpredictability of authentic customer inputs, often ignoring the resolution efficiency essential for real-world deployment. To bridge this gap, we introduce CirrusBench, a novel evaluation framework distinguished by its foundation in real-world data from authentic cloud service tickets. CirrusBench preserves the intricate multi-turn logical chains and realistic tool dependencies inherent to technical service environments. Moving beyond execution correctness, we introduce novel Customer-Centric metrics to define agent success, quantifying service quality through metrics such as the Normalized Efficiency Index and Multi-Turn Latency to explicitly measure resolution efficiency. Experiments utilizing our framework reveal that while state-of-the-art models demonstrate strong reasoning capabilities, they frequently struggle in complex, realistic multi-turn tasks and fail to meet the high-efficiency standards required for customer service, highlighting critical directions for the future development of LLM-based agents in practical technical service applications. CirrusBench evaluation framework is released at: https://github.com/CirrusAI