Probabilistic computation and uncertainty quantification with emerging covariance

Fuente: arXiv
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Main Authors: Ma, Hengyuan, Qi, Yang, Zhang, Li, Lu, Wenlian, Feng, Jianfeng
Format: Preprint
Published: 2023
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author Ma, Hengyuan
Qi, Yang
Zhang, Li
Lu, Wenlian
Feng, Jianfeng
author_facet Ma, Hengyuan
Qi, Yang
Zhang, Li
Lu, Wenlian
Feng, Jianfeng
contents Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges for most conventional artificial neural network, as they are essentially implemented in a deterministic manner. In this paper, we develop an efficient probabilistic computation framework by truncating the probabilistic representation of neural activation up to its mean and covariance and construct a moment neural network that encapsulates the nonlinear coupling between the mean and covariance of the underlying stochastic network. We reveal that when only the mean but not the covariance is supervised during gradient-based learning, the unsupervised covariance spontaneously emerges from its nonlinear coupling with the mean and faithfully captures the uncertainty associated with model predictions. Our findings highlight the inherent simplicity of probabilistic computation by seamlessly incorporating uncertainty into model prediction, paving the way for integrating it into large-scale AI systems.
format Preprint
id arxiv_https___arxiv_org_abs_2305_19265
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Probabilistic computation and uncertainty quantification with emerging covariance
Ma, Hengyuan
Qi, Yang
Zhang, Li
Lu, Wenlian
Feng, Jianfeng
Machine Learning
Neural and Evolutionary Computing
Statistics Theory
Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges for most conventional artificial neural network, as they are essentially implemented in a deterministic manner. In this paper, we develop an efficient probabilistic computation framework by truncating the probabilistic representation of neural activation up to its mean and covariance and construct a moment neural network that encapsulates the nonlinear coupling between the mean and covariance of the underlying stochastic network. We reveal that when only the mean but not the covariance is supervised during gradient-based learning, the unsupervised covariance spontaneously emerges from its nonlinear coupling with the mean and faithfully captures the uncertainty associated with model predictions. Our findings highlight the inherent simplicity of probabilistic computation by seamlessly incorporating uncertainty into model prediction, paving the way for integrating it into large-scale AI systems.
title Probabilistic computation and uncertainty quantification with emerging covariance
topic Machine Learning
Neural and Evolutionary Computing
Statistics Theory
url https://arxiv.org/abs/2305.19265