用可学习激活函数实现高精度功能先验，提升神经网络的不确定性建模能力。
Hi-fi functional priors by learning activations
- 通过可训练激活函数设计灵活的功能空间先验
- 单个宽隐层网络即可逼近复杂目标函数分布
- 适合需要可靠置信度估计的决策系统
贝叶斯神经网络中的函数空间先验能更直观地将先验信念嵌入模型输出，从而增强正则化、不确定性量化和风险感知决策。然而在贝叶斯神经网络中施加函数空间先验仍具挑战性。本文通过优化技术探索可训练激活函数如何容纳更高复杂度的先验，并匹配复杂的目标函数分布。研究了包括佩德函数和分段线性函数在内的灵活激活模型，讨论了可辨识性、损失构造及对称性带来的学习难题。实证结果表明，即使仅使用单个宽隐层的贝叶斯神经网络，只要配备灵活的可训练激活函数，也能有效实现期望的功能空间先验。
原文摘要 · Abstract (English)
Function-space priors in Bayesian Neural Networks (BNNs) provide a more intuitive approach to embedding beliefs directly into the model's output, thereby enhancing regularization, uncertainty quantification, and risk-aware decision-making. However, imposing function-space priors on BNNs is challenging. We address this task through optimization techniques that explore how trainable activations can accommodate higher-complexity priors and match intricate target function distributions. We investigate flexible activation models, including Pade functions and piecewise linear functions, and discuss the learning challenges related to identifiability, loss construction, and symmetries. Our empirical findings indicate that even BNNs with a single wide hidden layer when equipped with flexible trainable activation, can effectively achieve desired function-space priors.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。