[论文解读] The Inevitability of Probability: Probabilistic Inference in Generic Neural Networks Trained with Non-Probabilistic Feedback

A. Emin Orhan, Wei Ji|arXiv (Cornell University)|Jan 12, 2016

Neural Networks and Applications被引用 5

一句话总结

该论文表明，通过在非概率性反馈上使用简单的基于误差的学习方法训练的通用前馈和循环神经网络，能够在心理物理任务中自然发展出接近最优的概率推理能力。关键发现是，隐藏层形成了基于稀疏性的概率种群编码，从而在极小的网络规模下实现稳健的推理并具备强大的泛化能力，即使没有显式的概率监督。

ABSTRACT

Humans and other animals have been shown to perform near-optimal probabilistic inference in a wide range of psychophysical tasks. On the face of it, this is surprising because optimal probabilistic inference in each case is associated with highly non-trivial behavioral strategies. Yet, typically subjects receive little to no feedback during most of these tasks and the received feedback is not explicitly probabilistic in nature. How can subjects learn such non-trivial behavioral strategies from scarce non-probabilistic feedback? We show that generic feed-forward and recurrent neural networks trained with a relatively small number of non-probabilistic examples using simple error-based learning rules can perform near-optimal probabilistic inference in standard psychophysical tasks. The hidden layers of the trained networks develop a novel sparsity-based probabilistic population code. In all tasks, performance asymptotes at very small network sizes, usually on the order of tens of hidden units, due to the low computational complexity of the typical psychophysical tasks. For the same reason, the trained networks also display remarkable generalization to stimulus conditions not seen during training. We further show that in a probabilistic binary categorization task involving arbitrary categories where both human and monkey subjects have been shown to perform probabilistic inference, a monkey subject's performance (but not human subjects' performance) is consistent with an error-based learning rule. Our results suggest that near-optimal probabilistic inference in standard psychophysical tasks emerges naturally and robustly in generic neural networks trained with error-based learning rules, even when neither the training objective nor the training examples are explicitly probabilistic, and that these types of networks can be used as simple plausible neural models of probabilistic inference.

研究动机与目标

• 研究神经网络如何在使用非概率性反馈训练的情况下实现接近最优的概率推理。
• 确定基于误差的学习规则是否能在通用神经架构中引发概率推理。
• 探索训练网络隐藏层中基于稀疏性的概率种群编码的出现机制。
• 评估训练网络在未见刺激条件下的泛化性能。
• 将模型预测与灵长类动物（猴子）和人类在概率分类任务中的行为数据进行比较。

提出的方法

• 使用标准基于误差的学习规则在非概率性示例上训练前馈和循环神经网络。
• 在隐藏层中采用基于稀疏性的编码方案来表示概率不确定性。
• 在标准心理物理任务上评估网络在需要概率推理任务中的表现。
• 通过分析不同网络规模下的网络行为，评估计算效率。
• 测试网络在训练期间未出现的新颖刺激条件下的泛化能力。
• 将模型预测与人类和猴子受试者在二元分类任务中的行为数据进行比较。

实验结果

研究问题

• RQ1 使用非概率性反馈训练的通用神经网络能否实现接近最优的概率推理？
• RQ2 支持概率推理的隐藏层中会涌现出何种内部表征（编码）？
• RQ3 此类网络在保持最优性能的前提下，最小可小到何种程度？
• RQ4 这些网络在多大程度上能泛化到未见过的刺激？
• RQ5 观察到的行为是否与非人灵长类动物中的基于误差的学习规则一致？

主要发现

• 尽管使用非概率性反馈和训练目标，训练后的网络在心理物理任务中仍能达到接近最优的概率推理。
• 由于任务复杂度较低，性能在极小的网络规模下趋于稳定，通常仅需数十个隐藏单元。
• 基于稀疏性的概率种群编码在隐藏层中自发涌现，用于编码不确定性。
• 网络在训练期间未见的刺激条件下表现出强大的泛化能力。
• 猴子在概率分类任务中的表现与所提出的基于误差的学习规则一致，而人类表现则不一致。
• 结果表明，在生物上合理的学习规则下，概率推理可在神经网络中自然涌现。