{"ID":2861939,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.00621","arxiv_id":"2510.00621","title":"FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regression","abstract":"Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting the flexibility of data-driven discovery, while many deep-learning pipelines treat functions as fixed-grid vectors, ignoring inherent continuity. In this paper, we introduce Functional Attention with a Mixture-of-Experts (FAME), an end-to-end, fully data-driven framework for function-on-function regression. FAME forms continuous attention by coupling a bidirectional neural controlled differential equation with MoE-driven vector fields to capture intra-functional continuity, and further fuses change to inter-functional dependencies via multi-head cross attention. Extensive experiments on synthetic and real-world functional-regression benchmarks show that FAME achieves state-of-the-art accuracy, strong robustness to arbitrarily sampled discrete observations of functions.","short_abstract":"Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting the flexibility of data-driven discovery, while many deep-learning pipelines tre...","url_abs":"https://arxiv.org/abs/2510.00621","url_pdf":"https://arxiv.org/pdf/2510.00621v1","authors":"[\"Yifei Gao\",\"Yong Chen\",\"Chen Zhang\"]","published":"2025-10-01T07:53:55Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}