Where We Have Arrived in Proving the Emergence of Sparse Symbolic Concepts in AI Models

Fuente: arXiv
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Main Authors: Ren, Qihan, Gao, Jiayang, Shen, Wen, Zhang, Quanshi
Format: Preprint
Published: 2023
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author Ren, Qihan
Gao, Jiayang
Shen, Wen
Zhang, Quanshi
author_facet Ren, Qihan
Gao, Jiayang
Shen, Wen
Zhang, Quanshi
contents This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i) The high-order derivatives of the network output with respect to the input variables are all zero. (ii) The DNN can be used on occluded samples and when the input sample is less occluded, the DNN will yield higher confidence. (iii) The confidence of the DNN does not significantly degrade on occluded samples. These conditions are quite common, and we prove that under these conditions, the DNN will only encode a relatively small number of sparse interactions between input variables. Moreover, we can consider such interactions as symbolic primitive inference patterns encoded by a DNN, because we show that inference scores of the DNN on an exponentially large number of randomly masked samples can always be well mimicked by numerical effects of just a few interactions.
format Preprint
id arxiv_https___arxiv_org_abs_2305_01939
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Where We Have Arrived in Proving the Emergence of Sparse Symbolic Concepts in AI Models
Ren, Qihan
Gao, Jiayang
Shen, Wen
Zhang, Quanshi
Machine Learning
Artificial Intelligence
Computer Vision and Pattern Recognition
This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i) The high-order derivatives of the network output with respect to the input variables are all zero. (ii) The DNN can be used on occluded samples and when the input sample is less occluded, the DNN will yield higher confidence. (iii) The confidence of the DNN does not significantly degrade on occluded samples. These conditions are quite common, and we prove that under these conditions, the DNN will only encode a relatively small number of sparse interactions between input variables. Moreover, we can consider such interactions as symbolic primitive inference patterns encoded by a DNN, because we show that inference scores of the DNN on an exponentially large number of randomly masked samples can always be well mimicked by numerical effects of just a few interactions.
title Where We Have Arrived in Proving the Emergence of Sparse Symbolic Concepts in AI Models
topic Machine Learning
Artificial Intelligence
Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2305.01939