Selected work

Representative Papers

Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning

Jun 30, 2024arXiv.org

Existing operator learning methods for irregular geometric domains suffer from high memory consumption and poor geometric adaptability. Method: This paper proposes the Deep Integral Operator (DIO) framework, which employs learnable compactly supported kernel functions and a sparsity-aware parametrization scheme to jointly ensure smoothness and computational efficiency; it further incorporates adaptive numerical quadrature to achieve geometry-agnostic modeling, eliminating reliance on structured grids. Contribution/Results: On standard benchmarks, DIO achieves higher accuracy than state-of-the-art neural operators, with improved training and test accuracy. It reduces trainable parameters by over an order of magnitude, significantly enhancing memory efficiency, generalization capability, and geometric robustness.

4 citationsRead paper

Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients

Jun 10, 2024arXiv.org

In symbolic regression, jointly optimizing expression complexity and fitting accuracy remains challenging, while deep learning approaches suffer from inefficient policy updates due to gradient vanishing. To address these issues, we propose a complexity-aware reinforcement learning framework. Methodologically, we design an unbiased reward mechanism grounded in the Bayesian Information Criterion (BIC) to explicitly balance goodness-of-fit and model parsimony; further, we integrate a Transformer-driven breadth-first expression generation scheme with risk-seeking policy optimization to overcome tail-end gradient vanishing. Experiments across multiple benchmark datasets demonstrate substantial improvements: +12.3% in discovery accuracy, 28% reduction in average expression length (enhancing simplicity), and 37% fewer iterations to convergence (accelerating training). The framework also exhibits superior generalization. Overall, it establishes a robust and efficient new paradigm for interpretable mathematical modeling.

3 citationsRead paper

Training-Conditional Coverage Bounds under Covariate Shift

May 26, 2024arXiv.org

This work addresses the lack of theoretical guarantees on training-conditional coverage—i.e., coverage under the training data distribution—of conformal prediction under covariate shift. We first systematically investigate its upper-bound characterization and controllability. We derive a weighted Dvoretzky–Kiefer–Wolfowitz inequality to establish tight, provable training-conditional coverage bounds for split conformal prediction under nearly assumption-free conditions. Furthermore, leveraging algorithmic uniform stability, we provide the first training-conditional coverage guarantees for full conformal and jackknife+ methods. Our results demonstrate that all three mainstream conformal prediction frameworks achieve controllable training-conditional coverage under covariate shift, with split conformal yielding bounds that are both minimally assumption-dependent and tight. This work fills a critical theoretical gap in conditional coverage analysis of conformal prediction beyond the i.i.d. setting.

3 citationsRead paper

Improving Flow Matching by Aligning Flow Divergence

Jan 31, 2026International Conference on Machine Learning

This work addresses the challenge that conditional flow matching (CFM) struggles to accurately recover the true data distribution dynamics when modeling probability paths. To overcome this limitation, the authors propose a novel approach that introduces a partial differential equation characterizing the discrepancy between learned and ground-truth probability paths. They formulate a joint objective that simultaneously optimizes both the flow field and its divergence, and for the first time establish a theoretical upper bound linking the total variation error of the probability path to the CFM loss and the divergence loss. This method enables concurrent matching of the flow field and its divergence, achieving significant performance improvements over standard CFM on tasks including dynamical systems modeling, DNA sequence generation, and video synthesis, while preserving computational efficiency during generation.

2 citationsRead paper

Blue Noise as a Lattice Gibbs Ensemble

Aug 13, 2026

This work addresses the longstanding challenge in blue-noise sampling of simultaneously achieving high quality, locality, and parallelizability. The authors formulate blue-noise generation as a lattice-based Gibbs distribution with pairwise repulsive interactions and, for the first time, unify it within a parametric Gibbs ensemble framework that enables continuous control over spectral characteristics. By introducing bounded dependency regions and a haloed tiling strategy combined with the Coupling From The Past algorithm, they achieve communication-free exact sampling per tile, with memory consumption scaling only with tile size. Experiments demonstrate that the method faithfully reproduces standard blue-noise spectra, yields tilewise results bit-identical to global generation, and successfully scales to applications such as 14K adaptive stippling and multi-class extensions.

0 citationsRead paper

Recent publications

Latest Papers

Blue Noise as a Lattice Gibbs Ensemble

Aug 13, 2026

This work addresses the longstanding challenge in blue-noise sampling of simultaneously achieving high quality, locality, and parallelizability. The authors formulate blue-noise generation as a lattice-based Gibbs distribution with pairwise repulsive interactions and, for the first time, unify it within a parametric Gibbs ensemble framework that enables continuous control over spectral characteristics. By introducing bounded dependency regions and a haloed tiling strategy combined with the Coupling From The Past algorithm, they achieve communication-free exact sampling per tile, with memory consumption scaling only with tile size. Experiments demonstrate that the method faithfully reproduces standard blue-noise spectra, yields tilewise results bit-identical to global generation, and successfully scales to applications such as 14K adaptive stippling and multi-class extensions.

0 citationsRead paper

AaLLM: An End-to-End Analog Circuit Design Framework from Topology Generation to Sizing Using Large Language Models

Aug 13, 2026

This work addresses the inefficiency and heavy reliance on expert knowledge in analog circuit design, particularly within the nonlinear, high-dimensional search space where existing large language model (LLM) approaches struggle to jointly handle topology generation and sizing optimization. To overcome these limitations, the authors propose AaLLM, an end-to-end multi-agent framework featuring a Designer–Critic–Evaluator triad that integrates retrieval-augmented generation (RAG) with automated knowledge base construction to directly translate user specifications into complete netlists. The approach significantly enhances both innovation and efficiency: generated circuits achieve figures of merit (FoMs) comparable to or exceeding those of human-designed counterparts—by up to threefold—while reducing SPICE simulation calls by 3–4.5× and accelerating overall runtime by 40×.

0 citationsRead paper

Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size

Aug 12, 2026

This work addresses the challenges of stepsize sensitivity, unstable curvature estimation, and high computational cost of line search in composite stochastic optimization over non-Euclidean geometries. The authors propose Ada-BPSG, a novel method that integrates a stabilized Barzilai–Borwein (BB) stepsize with Bregman proximal stochastic gradient, incorporating SAGA variance reduction, weighted median aggregation of secant information, and explicit stepsize constraints to enable adaptive stepsize selection without line search. The approach establishes a direct analytical framework linking relative smoothness to convergence, guaranteeing an $O(n/K)$ ergodic convergence rate under convexity, linear convergence with restarts under quadratic growth, and an $O(1/K)$ bound on proximal residuals in the non-convex setting. Experiments demonstrate superior performance in logistic regression and sparse non-negative matrix factorization, achieving lower objective values, robustness to initial stepsize choices, and elimination of line search overhead.

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Topology-Preserving Meshing of Implicit Scalar Fields via Monotonicity Constraints

Aug 12, 2026

Existing approaches to extracting topological structures—such as Morse–Smale complexes—from implicit two-dimensional scalar fields rely on explicit field representations, which limits their applicability. This work proposes a topology-preserving meshing method that requires only pointwise evaluations of the scalar field. By constructing a piecewise-linear (PL) triangulation and enforcing monotonicity of mesh edges with respect to the scalar field, the method accurately recovers critical points and their connectivity without access to an explicit field representation. An adaptive refinement strategy, incorporating monotonicity violation detection and correction, ensures topological correctness while significantly enhancing the geometric fidelity of separatrices. Experimental results demonstrate that the approach reliably reconstructs the Morse–Smale complex and achieves high-quality geometric approximation through targeted refinement.

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Inference-Time Orthogonal Seeding Enables Geometry-Aligned 3D Organ Segmentation for Slice-Propagation Methods

Aug 12, 2026

This work addresses the geometric error accumulation in existing single-slice propagation methods, which propagate annotations along only one axis and neglect information from coronal and sagittal planes, severely degrading surface distance metrics far from the seed slice. To overcome this limitation, the authors propose an orthogonal seed configuration strategy at inference time that leverages seed slices from all three orthogonal anatomical planes—axial, coronal, and sagittal—without requiring multi-axis training. By integrating unlabeled multi-planar registration and a label fusion rule, the method effectively exploits full 3D geometric structure. Experiments on multi-organ CT datasets demonstrate substantial improvements over single-axis baselines: Dice coefficient increases by 21.9%, normalized surface Dice by 25.5%, and mean Hausdorff distance decreases by 53.5%, confirming that orthogonal geometric layout is more critical than the number of seed slices.

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