THÔNG BÁO SEMINAR: BAYESIAN SPARSE KOLMOGOROV-ARNOLD NETWORKS (KAN) FOR REGRESSION IN ANISOTROPIC BESOV SPACES
Khoa Toán – Tin học, Trường Đại học Khoa học tự nhiên, ĐHQG-HCM trân trọng thông báo Seminar với các thông tin như sau:
Báo cáo viên:
GS. Lizhen Lin – University of Maryland, Hoa Kỳ
Tên báo cáo:
Bayesian Sparse Kolmogorov-Arnold Networks (KAN) for Regression in Anisotropic Besov Spaces
Thời gian: 10g00, Thứ Hai, ngày 24/8/2026
Địa điểm: Phòng C34, Trường Đại học Khoa học tự nhiên, ĐHQG-HCM – Cơ sở 1
(227 Nguyễn Văn Cừ, Phường Chợ Quán, Thành phố Hồ Chí Minh)
Link đăng ký: https://forms.gle/HP4psexsAZB45vtT6
Tóm tắt báo cáo:
We study posterior contraction rates for sparse Bayesian Kolmogorov-Arnold networks (KANs) over anisotropic Besov spaces, providing a statistical foundation of KANs from a Bayesian point of view. We show that sparse Bayesian KANs equipped with spike-and-slab-type sparsity priors attain the near-minimax posterior contraction. In particular, the contraction rate depends on the intrinsic anisotropic smoothness of the underlying function. Moreover, by placing a hyperprior on a single model-size parameter, the resulting posterior adapts to unknown anisotropic smoothness and still achieves the corresponding near-minimax rate. A distinctive feature of our results, compared with those for standard sparse MLP-based models, is that the KAN depth can be kept fixed: owing to the flexibility of learnable spline edge functions, the required approximation complexity is controlled through the network width, spline-grid range and size, and parameter sparsity. We then extend the analysis to compositional Besov spaces and show that the contraction rates depend on layerwise smoothness and effective dimension of the underlying compositional structure, thereby effectively avoiding the curse of dimensionality. Together, the developed tools and findings advance the theoretical understanding of Bayesian neural networks and provide rigorous statistical foundations for KANs. This is a joint work with Jeunghun Oh, Kyeongwon Lee, and Jaeyong Lee.
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