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Neural Networks with a Redundant Representation: Detecting the Undetectable
Physical Review Letters ( IF 9.227 ) Pub Date : 2020-01-13 , DOI: 10.1103/physrevlett.124.028301
Elena Agliari, Francesco Alemanno, Adriano Barra, Martino Centonze, and Alberto Fachechi

We consider a three-layer Sejnowski machine and show that features learnt via contrastive divergence have a dual representation as patterns in a dense associative memory of order P=4. The latter is known to be able to Hebbian store an amount of patterns scaling as NP−1, where N denotes the number of constituting binary neurons interacting P wisely. We also prove that, by keeping the dense associative network far from the saturation regime (namely, allowing for a number of patterns scaling only linearly with N, while P>2) such a system is able to perform pattern recognition far below the standard signal-to-noise threshold. In particular, a network with P=4 is able to retrieve information whose intensity is O(1) even in the presence of a noise O(N) in the large N limit. This striking skill stems from a redundancy representation of patterns—which is afforded given the (relatively) low-load information storage—and it contributes to explain the impressive abilities in pattern recognition exhibited by new-generation neural networks. The whole theory is developed rigorously, at the replica symmetric level of approximation, and corroborated by signal-to-noise analysis and Monte Carlo simulations.
更新日期:2020-01-14

 

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