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arXiv · 2510.00621

FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regression

Yifei Gao·Yong Chen·Chen Zhang
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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.

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Yifei Gao, Yong Chen, Chen Zhang. 2025-10-01. FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regression. https://arxiv.org/abs/2510.00621

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