FDN让模型根据输入动态调整不确定性，更适应分布外数据。
Functional Distribution Networks (FDN)
- 用输入条件分布建模网络权重，生成自适应预测混合
- 在1D任务和UCI回归上精度媲美贝叶斯/集成等方法
- 能感知分布偏移，适合需要可靠不确定性的场景
现代概率回归器在分布偏移下仍易过度自信。功能性分布网络（FDN）将输入条件分布置于网络权重上，生成随输入变化的预测混合分布；采用蒙特卡洛β-ELBO目标进行训练。我们结合一种评估协议，区分内插与外推，并强调简单的分布外（OOD）合理性检查。在控制的1维任务以及小型/中型的UCI风格回归基准上，FDN在准确率上与强贝叶斯、集成、丢弃和超网络基线相当，同时在匹配参数量和更新预算下，提供强输入依赖的、对分布偏移敏感的不确定性，并实现良好校准。
原文摘要 · Abstract (English)
Modern probabilistic regressors often remain overconfident under distribution shift. Functional Distribution Networks (FDN) place input-conditioned distributions over network weights, producing predictive mixtures whose dispersion adapts to the input; we train them with a Monte Carlo beta-ELBO objective. We pair FDN with an evaluation protocol that separates interpolation from extrapolation and emphasizes simple OOD sanity checks. On controlled 1D tasks and small/medium UCI-style regression benchmarks, FDN remains competitive in accuracy with strong Bayesian, ensemble, dropout, and hypernetwork baselines, while providing strongly input-dependent, shift-aware uncertainty and competitive calibration under matched parameter and update budgets.
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