Preprint
FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regression
ArXiv.org
Cornell University
10/01/2025
DOI: 10.48550/arxiv.2510.00621
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.
Details
- Title: Subtitle
- FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regression
- Creators
- Yifei Gao - Tsinghua UniversityYong Chen - University of IowaChen Zhang - Tsinghua University
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2510.00621
- ISSN
- 2331-8422
- Publisher
- Cornell University; ithaca, New York
- Language
- English
- Date posted
- 10/01/2025
- Academic Unit
- Industrial and Systems Engineering
- Record Identifier
- 9984969241802771
Metrics
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