FAME通过动态注意力与专家路由，实现函数间回归的端到端建模。
FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regression
- 用神经微分方程和专家路由构建连续注意力，捕捉函数内连续性
- 在合成与真实数据上均达到当前最优性能，对离散采样点鲁棒
- 适合处理高维函数数据的回归任务，尤其适用于不规则采样场景
函数数据在科学与工程中至关重要，但其无限维特性使表征学习充满挑战。传统统计模型依赖预设基展开或核函数，限制了数据驱动的灵活性；许多深度学习方法将函数视为固定网格向量，忽视了内在连续性。本文提出功能注意力与专家混合（FAME），一种端到端、全数据驱动的功能-功能回归框架。FAME通过双向神经控制微分方程与MoE驱动的向量场结合，形成连续注意力以捕捉函数内连续性，并利用多头交叉注意力融合函数间的依赖关系。在合成与真实世界函数回归基准上的大量实验表明，FAME实现了最先进的准确率，且对函数的任意离散采样点具有强鲁棒性。
原文摘要 · Abstract (English)
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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