Tie-Qiang Li | Search arXiv

arXiv2026

Learning Spectral Allocation: A Fractional Diffusion Framework for Adaptive Volumetric Segmentation

We address adaptive computation in 3D medical image segmentation: instead of designing another backbone, we ask how much spectral mixing each network stage needs and let optimization answer. We derive FHEAT, a two-parameter operator family, from the discrete cosine transform (DCT) solution of a fractional heat equation. A fractional order alpha and a diffusion strength D govern the operator, and at D=0 it is exactly the identity. Reparametrized by the semigroup time tau = D*alpha, same-resolution instances compose exactly, so any distribution of diffusion across same-resolution stages amounts to a single Sobolev-type regularizer of learned strength. This identity limit lets the optimizer of each layer, not the designer, decide whether global mixing is needed and how sharp it should be. We instantiate FHEAT in a lightweight U-shaped architecture (Light-UNETR) paired with a Kolmogorov-Arnold mixer (KAN3D) with adaptive rational activations, yielding FHEAT-Seg. At 5% to 20% label rates on three public benchmarks, training produces gradient-driven spectral sparsification: seven of the eight stage-level operators drive D to zero, and the survivor saturates at the sharpest low-pass (alpha ~ 0.9) in the decoder layer feeding the semi-supervised attention map. The retired layers become exact identity shortcuts at inference, cutting FLOPs from 4.29G to 0.90G (a 79% drop) at 0.975M parameters. Under a standard semi-supervised protocol, FHEAT-Seg reaches Dice scores of 90.47% (left atrium), 78.79% (Pancreas-CT), and 81.90% (BraTS 2019), ahead of five semi-supervised methods and the Light-UNETR baseline. The large variant also surpasses Light-UNETR-L under full supervision (Dice 93.09%, 85.11%, and 87.19%) with 2.851M parameters and 55.75G FLOPs. These results suggest that the allocation of spectral computation is a learnable property of optimization dynamics, not a manual design commitment.

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arXiv2020

Domain Generalization for Medical Imaging Classification with Linear-Dependency Regularization

Recently, we have witnessed great progress in the field of medical imaging classification by adopting deep neural networks. However, the recent advanced models still require accessing sufficiently large and representative datasets for training, which is often unfeasible in clinically realistic environments. When trained on limited datasets, the deep neural network is lack of generalization capability, as the trained deep neural network on data within a certain distribution (e.g. the data captured by a certain device vendor or patient population) may not be able to generalize to the data with another distribution. In this paper, we introduce a simple but effective approach to improve the generalization capability of deep neural networks in the field of medical imaging classification. Motivated by the observation that the domain variability of the medical images is to some extent compact, we propose to learn a representative feature space through variational encoding with a novel linear-dependency regularization term to capture the shareable information among medical data collected from different domains. As a result, the trained neural network is expected to equip with better generalization capability to the "unseen" medical data. Experimental results on two challenging medical imaging classification tasks indicate that our method can achieve better cross-domain generalization capability compared with state-of-the-art baselines.

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