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Researcher profile

Kang Liu

Kang Liu contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Artificial Intelligencemath.NANumerical AnalysisComputer VisionMachine Learningmath.APmath.OC

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Published work

5 published item(s)

preprint2026arXiv

Learning How to Remember: A Meta-Cognitive Management Method for Structured and Transferable Agent Memory

Large language model (LLM) agents increasingly rely on accumulated memory to solve long-horizon decision-making tasks. However, most existing approaches store memory in fixed representations and reuse it at a single or implicit level of abstraction, which limits generalization and often leads to negative transfer when distribution shift. This paper proposes the Meta-Cognitive Memory Abstraction method (MCMA), which treats memory abstraction as a learnable cognitive skill rather than a fixed design choice. MCMA decouples task execution from memory management by combining a frozen task model with a learned memory copilot. The memory copilot is trained using direct preference optimization, it determines how memories should be structured, abstracted, and reused. Memories are further organized into a hierarchy of abstraction levels, enabling selective reuse based on task similarity. When no memory is transferable, MCMA transfers the ability to abstract and manage memory by transferring the memory copilot. Experiments on ALFWorld, ScienceWorld, and BabyAI demonstrate substantial improvements in performance, out-of-distribution generalization, and cross-task transfer over several baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Moments, Time-Inversion and Source Identification for the Heat Equation

We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on moment analysis of the heat flow, transforming the problem into a more stable inverse moment formulation. By evolving the measured terminal time moments backward through their governing ODE system, we recover the moments of the initial distribution. We then reconstruct the source by solving a convex optimization problem that minimizes the total variation of a measure subject to these moment constraints. This formulation naturally promotes sparsity, yielding atomic solutions that are sums of Dirac measures. Compared to existing methods, our moment-based approach reduces exponential error growth to polynomial growth with respect to the terminal time. We provide explicit error estimates on the recovered initial distributions in terms of moment order, terminal time, and measurement errors. In addition, we develop efficient numerical discretization schemes and demonstrate significant stability improvements of our approach through comprehensive numerical experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

PriorRG: Prior-Guided Contrastive Pre-training and Coarse-to-Fine Decoding for Chest X-ray Report Generation

Chest X-ray report generation aims to reduce radiologists' workload by automatically producing high-quality preliminary reports. A critical yet underexplored aspect of this task is the effective use of patient-specific prior knowledge -- including clinical context (e.g., symptoms, medical history) and the most recent prior image -- which radiologists routinely rely on for diagnostic reasoning. Most existing methods generate reports from single images, neglecting this essential prior information and thus failing to capture diagnostic intent or disease progression. To bridge this gap, we propose PriorRG, a novel chest X-ray report generation framework that emulates real-world clinical workflows via a two-stage training pipeline. In Stage 1, we introduce a prior-guided contrastive pre-training scheme that leverages clinical context to guide spatiotemporal feature extraction, allowing the model to align more closely with the intrinsic spatiotemporal semantics in radiology reports. In Stage 2, we present a prior-aware coarse-to-fine decoding for report generation that progressively integrates patient-specific prior knowledge with the vision encoder's hidden states. This decoding allows the model to align with diagnostic focus and track disease progression, thereby enhancing the clinical accuracy and fluency of the generated reports. Extensive experiments on MIMIC-CXR and MIMIC-ABN datasets demonstrate that PriorRG outperforms state-of-the-art methods, achieving a 3.6% BLEU-4 and 3.8% F1 score improvement on MIMIC-CXR, and a 5.9% BLEU-1 gain on MIMIC-ABN. Code and checkpoints will be released upon acceptance.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Theory-optimal Quantization Based on Flatness

Post-training quantization has emerged as a widely adopted technique for compressing and accelerating the inference of Large Language Models (LLMs). The primary challenges in LLMs quantization stem from activation outliers, which significantly degrade model performance especially at lower bit precision. While recent approaches attempt to mitigate outliers through linear transformations across feature dimensions, our analysis reveals that the transformed weights and activations still exhibit persistent outlier patterns with concentrated magnitude distributions. In this paper, we first model the mathematical relationship between quantization error and outliers, and then introduce a new metric Flatness to quantify the distribution of outliers. Based on this, we derive the theoretical optimal solution with respect to Flatness. Building on these insights, we propose Bidirectional Diagonal Quantization (BDQ), a novel post-training quantization framework that effectively disperses outlier patterns through optimized matrix transformations. BDQ strategically distributes outlier magnitudes across matrix dimensions via learned diagonal operations. Extensive experiments demonstrate that BDQ establishes a new quantization benchmark. It achieves less than 1\% accuracy drop in W4A4 quantization on the LLaMA-3-8B model. In the more challenging W2A4KV16 experiment, compared to state-of-the-art approaches, BDQ reduces the performance gap by 39.1\% on the DeepSeek-R1-Distill-LLaMA-70B model.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications

In this paper, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. We investigate the universal approximation properties of SA-NODEs for dynamical systems from both a theoretical and a numerical perspective. Within the assumption of a finite-time horizon, under general hypotheses we establish an asymptotic approximation result, demonstrating that the error vanishes as the number of parameters goes to infinity. Under additional regularity assumptions, we further specify this convergence rate in relation to the number of parameters, utilizing quantitative approximation results in the Barron space. Based on the previous result, we prove an approximation rate for transport equations by their neural counterparts. Our numerical experiments validate the effectiveness of SA-NODEs in capturing the dynamics of various ODE systems and transport equations. Additionally, we compare SA-NODEs with vanilla NODEs, highlighting the superior performance and reduced complexity of our approach.

0 citations0 reviewsNo code linkedOpen access