Computer Science > Machine Learning
[Submitted on 30 Jun 2020 (v1), last revised 14 Aug 2020 (this version, v2)]
Title:Associative Memory in Iterated Overparameterized Sigmoid Autoencoders
View PDFAbstract:Recent work showed that overparameterized autoencoders can be trained to implement associative memory via iterative maps, when the trained input-output Jacobian of the network has all of its eigenvalue norms strictly below one. Here, we theoretically analyze this phenomenon for sigmoid networks by leveraging recent developments in deep learning theory, especially the correspondence between training neural networks in the infinite-width limit and performing kernel regression with the Neural Tangent Kernel (NTK). We find that overparameterized sigmoid autoencoders can have attractors in the NTK limit for both training with a single example and multiple examples under certain conditions. In particular, for multiple training examples, we find that the norm of the largest Jacobian eigenvalue drops below one with increasing input norm, leading to associative memory.
Submission history
From: Yibo Jiang [view email][v1] Tue, 30 Jun 2020 05:38:28 UTC (1,190 KB)
[v2] Fri, 14 Aug 2020 02:25:57 UTC (1,190 KB)
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