Resonator Networks, 2: Factorization Performance and Capacity Compared to Optimization-Based Methods.

Abstract:

:We develop theoretical foundations of resonator networks, a new type of recurrent neural network introduced in Frady, Kent, Olshausen, and Sommer (2020), a companion article in this issue, to solve a high-dimensional vector factorization problem arising in Vector Symbolic Architectures. Given a composite vector formed by the Hadamard product between a discrete set of high-dimensional vectors, a resonator network can efficiently decompose the composite into these factors. We compare the performance of resonator networks against optimization-based methods, including Alternating Least Squares and several gradient-based algorithms, showing that resonator networks are superior in several important ways. This advantage is achieved by leveraging a combination of nonlinear dynamics and searching in superposition, by which estimates of the correct solution are formed from a weighted superposition of all possible solutions. While the alternative methods also search in superposition, the dynamics of resonator networks allow them to strike a more effective balance between exploring the solution space and exploiting local information to drive the network toward probable solutions. Resonator networks are not guaranteed to converge, but within a particular regime they almost always do. In exchange for relaxing the guarantee of global convergence, resonator networks are dramatically more effective at finding factorizations than all alternative approaches considered.

journal_name

Neural Comput

journal_title

Neural computation

authors

Kent SJ,Frady EP,Sommer FT,Olshausen BA

doi

10.1162/neco_a_01329

subject

Has Abstract

pub_date

2020-12-01 00:00:00

pages

2332-2388

issue

12

eissn

0899-7667

issn

1530-888X

journal_volume

32

pub_type

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