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He Lyu

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3works
7topics
4close collaborators

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3 publications

preprint2026arXiv

Disentangling Shared and Task-Specific Representations from Multi-Modal Clinical Data

Real-world clinical data is inherently multimodal, providing complementary evidence that mirrors the practical necessity of jointly assessing multiple related outcomes. Although multi-task learning can improve efficiency by sharing information across outcomes, existing approaches often fail to balance shared representation learning with outcome-specific modeling. Hard parameter sharing can trigger negative transfer when task gradients conflict, while flexible sharing may still entangle shared and task-specific signals. To address this, we propose a multi-task framework built on a unified Transformer for multimodal fusion, augmented with Orthogonal Task Decomposition (OrthTD) to split patient representations into shared and task-specific subspaces and impose a geometric orthogonality constraint to reduce redundancy and isolate task-specific signals. We evaluated OrthTD on a real-world cohort of 12,430 surgical patients for predicting four outcomes. OrthTD achieved average AUC (area under the receiver operating characteristic curve) of 87.5% and average AUPRC (area under the precision-recall curve) of 37.2%, consistently outperformed advanced tabular and multi-task methods. Notably, OrthTD achieves substantial gains in AUPRC, indicating superior performance in identifying rare events within imbalanced clinical data. These results suggest that enforcing non-redundant shared and task-specific representations can improve multi-outcome prediction from multimodal clinical data.

preprint2022arXiv

Perturbation of invariant subspaces for ill-conditioned eigensystem

Given a diagonalizable matrix AA, we study the stability of its invariant subspaces when its matrix of eigenvectors is ill-conditioned. Let X1\mathcal{X}_1 be some invariant subspace of AA and X1X_1 be the matrix storing the right eigenvectors that spanned X1\mathcal{X}_1. It is generally believed that when the condition number κ2(X1)κ_2(X_1) gets large, the corresponding invariant subspace X1\mathcal{X}_1 will become unstable to perturbation. This paper proves that this is not always the case. Specifically, we show that the growth of κ2(X1)κ_2(X_1) alone is not enough to destroy the stability. As a direct application, our result ensures that when AA gets closer to a Jordan form, one may still estimate its invariant subspaces from the noisy data stably.

preprint2022arXiv

Sigma Delta quantization for images

In signal quantization, it is well-known that introducing adaptivity to quantization schemes can improve their stability and accuracy in quantizing bandlimited signals. However, adaptive quantization has only been designed for one-dimensional signals. The contribution of this paper is two-fold: i). we propose the first family of two-dimensional adaptive quantization schemes that maintain the same mathematical and practical merits as their one-dimensional counterparts, and ii). we show that both the traditional 1-dimensional and the new 2-dimensional quantization schemes can effectively quantize signals with jump discontinuities. These results immediately enable the usage of adaptive quantization on images. Under mild conditions, we show that the adaptivity is able to reduce the reconstruction error of images from the presently best O(P)O(\sqrt P) to the much smaller O(s)O(\sqrt s), where ss is the number of jump discontinuities in the image and PP (P≫sP\gg s) is the total number of samples. This P/s\sqrt{P/s}-fold error reduction is achieved via applying a total variation norm regularized decoder, whose formulation is inspired by the mathematical super-resolution theory in the field of compressed sensing. Compared to the super-resolution setting, our error reduction is achieved without requiring adjacent spikes/discontinuities to be well-separated, which ensures its broad scope of application. We numerically demonstrate the efficacy of the new scheme on medical and natural images. We observe that for images with small pixel intensity values, the new method can significantly increase image quality over the state-of-the-art method.

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