Selected work

Representative Papers

The nature of mathematical models

Feb 11, 2025

Existing mathematical modeling lacks a rigorous, unambiguous ontological foundation, hindering a unified characterization of the mapping between models and real-world phenomena. This paper introduces, for the first time, an axiomatic definition of mathematical models grounded in Hilbert-space operator theory: a model is formalized as a computable operator acting on random variables, systematically unifying theoretical derivation, experimental implementation, and statistical identification. We further establish a geometric correspondence between the model manifold and the prediction surface, exposing intrinsic structural properties and the fundamental nature of model computability. This framework fills a critical gap in the formal ontology of modeling, providing a unified mathematical foundation for interdisciplinary model construction. It significantly enhances the logical rigor of theoretical inference and the reliability of empirical validation.

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An Iterative Geometric Approach to Optimizing Separating Hyperplanes

Jul 19, 2026

This work addresses the hard-margin support vector machine (SVM) problem on linearly separable datasets by proposing a geometrically motivated iterative optimization method. Starting from an arbitrary initial separating hyperplane, the algorithm employs an active-set strategy that leverages only local sample information at each iteration to progressively reorient the hyperplane. This process monotonically increases the margin while preserving correct classification, ultimately converging to the global optimum. The key innovation lies in decomposing the original convex quadratic program into a sequence of small-scale subproblems, thereby circumventing the need to solve a large-scale optimization problem directly. Experimental results demonstrate that, given a feasible initial solution, the proposed method is competitive on large-scale datasets and outperforms mainstream solvers in certain scenarios.

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Trainable Smooth-Rotation Transforms with Learned Channel Scales for LLM Quantization

Jun 07, 2026

This work addresses the issue of activation quantization error in post-training quantization of large language models, where outlier-dominated channels lead to excessive weight migration under conventional max-based scaling strategies. To mitigate this, the authors propose a joint optimization approach that replaces maximum-value statistics with robust high-percentile scaling and learns channel-wise scaling factors through constrained gradient-based optimization, all within the SmoothQuant-equivalent transformation framework. Experiments on LLaMA-3.2-1B demonstrate that the method reduces quantization error by 18.5% in selected layers and lowers the average error across all layers from 97.51 to 78.08—a 19.9% improvement—significantly enhancing the accuracy of W4A4 post-training quantization.

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On Linear Separability of the MNIST Handwritten Digits Dataset

Mar 13, 2026

This study systematically investigates the linear separability of the MNIST handwritten digit dataset, resolving a long-standing debate in the literature. By exhaustively examining all class combinations under both binary and one-versus-rest classification settings, the authors conduct empirical evaluations on the training set, test set, and their union, integrating theoretical insights from linear separability with modern optimization tools. The work presents the first complete characterization of MNIST’s separability boundaries under linear classification, uncovering its structural properties across different data partitions and classification strategies. These findings fill a critical gap in the foundational understanding of this benchmark dataset and provide a rigorous basis for informed model selection and theoretical analysis in machine learning research.

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Diffusion-Based Feature Denoising and Using NNMF for Robust Brain Tumor Classification

Mar 13, 2026

This work proposes a novel approach to enhance the robustness of brain tumor classification models against adversarial perturbations by integrating non-negative matrix factorization (NMF), a lightweight convolutional neural network, and a diffusion-based denoising mechanism. The method leverages NMF in the feature space to extract interpretable representations and employs diffusion denoising to purify adversarial inputs, thereby significantly improving model robustness. Experimental results demonstrate that the proposed framework achieves competitive classification accuracy while substantially outperforming existing methods under strong adversarial attacks, as evaluated by AutoAttack. This approach effectively realizes a synergistic optimization of both accuracy and robustness in brain tumor MRI classification.

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Recent publications

Latest Papers

An Iterative Geometric Approach to Optimizing Separating Hyperplanes

Jul 19, 2026

This work addresses the hard-margin support vector machine (SVM) problem on linearly separable datasets by proposing a geometrically motivated iterative optimization method. Starting from an arbitrary initial separating hyperplane, the algorithm employs an active-set strategy that leverages only local sample information at each iteration to progressively reorient the hyperplane. This process monotonically increases the margin while preserving correct classification, ultimately converging to the global optimum. The key innovation lies in decomposing the original convex quadratic program into a sequence of small-scale subproblems, thereby circumventing the need to solve a large-scale optimization problem directly. Experimental results demonstrate that, given a feasible initial solution, the proposed method is competitive on large-scale datasets and outperforms mainstream solvers in certain scenarios.

0 citationsRead paper

Trainable Smooth-Rotation Transforms with Learned Channel Scales for LLM Quantization

Jun 07, 2026

This work addresses the issue of activation quantization error in post-training quantization of large language models, where outlier-dominated channels lead to excessive weight migration under conventional max-based scaling strategies. To mitigate this, the authors propose a joint optimization approach that replaces maximum-value statistics with robust high-percentile scaling and learns channel-wise scaling factors through constrained gradient-based optimization, all within the SmoothQuant-equivalent transformation framework. Experiments on LLaMA-3.2-1B demonstrate that the method reduces quantization error by 18.5% in selected layers and lowers the average error across all layers from 97.51 to 78.08—a 19.9% improvement—significantly enhancing the accuracy of W4A4 post-training quantization.

0 citationsRead paper

On Linear Separability of the MNIST Handwritten Digits Dataset

Mar 13, 2026

This study systematically investigates the linear separability of the MNIST handwritten digit dataset, resolving a long-standing debate in the literature. By exhaustively examining all class combinations under both binary and one-versus-rest classification settings, the authors conduct empirical evaluations on the training set, test set, and their union, integrating theoretical insights from linear separability with modern optimization tools. The work presents the first complete characterization of MNIST’s separability boundaries under linear classification, uncovering its structural properties across different data partitions and classification strategies. These findings fill a critical gap in the foundational understanding of this benchmark dataset and provide a rigorous basis for informed model selection and theoretical analysis in machine learning research.

0 citationsRead paper

Diffusion-Based Feature Denoising and Using NNMF for Robust Brain Tumor Classification

Mar 13, 2026

This work proposes a novel approach to enhance the robustness of brain tumor classification models against adversarial perturbations by integrating non-negative matrix factorization (NMF), a lightweight convolutional neural network, and a diffusion-based denoising mechanism. The method leverages NMF in the feature space to extract interpretable representations and employs diffusion denoising to purify adversarial inputs, thereby significantly improving model robustness. Experimental results demonstrate that the proposed framework achieves competitive classification accuracy while substantially outperforming existing methods under strong adversarial attacks, as evaluated by AutoAttack. This approach effectively realizes a synergistic optimization of both accuracy and robustness in brain tumor MRI classification.

0 citationsRead paper

A Scalable Pipeline Combining Procedural 3D Graphics and Guided Diffusion for Photorealistic Synthetic Training Data Generation in White Button Mushroom Segmentation

Dec 09, 2025

To address the scarcity of high-quality annotated data and the prohibitive cost of manual annotation in industrial white mushroom cultivation, this paper proposes a scalable synthetic data generation framework that integrates procedural 3D modeling (Blender) with constraint-guided diffusion models. The framework enables fully automated generation of photorealistic mushroom images with pixel-accurate, instance-level semantic annotations—without requiring expertise in computer graphics. It achieves a unique balance among full controllability, annotation fidelity, and photographic realism, while supporting zero-shot domain transfer. Leveraging this pipeline, we construct two synthetic datasets, each containing 6,000 images (totaling over 250,000 mushroom instances). Training Mask R-CNN on these datasets yields state-of-the-art zero-shot segmentation performance on the real-world M18K benchmark (F1 = 0.859), significantly outperforming existing synthetic-data approaches.

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