Holographic Reduced Representations: Convolution Algebra for Compositional Distributed Representations

By Tony A. Plate. 1991

Subfields: Representation & Self-Supervised Learning, Knowledge Graphs & Representation

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Citations in the corpus

Learning to Relate Images (2011, methodology): “Like an auto-encoder, this model can be trained with gradient based optimization.”
Lightweight and Efficient Neural Natural Language Processing with Quaternion Networks (2019, background): “On the other hand, complex spaces are also intuitively linked to associative composition, along with holographic reduced representations (Plate, 1991; Nickel et al., 2016; Tay et al., 2017a).”
Dimensions of Neural-symbolic Integration - A Structured Survey (2005, methodology): “The related approach on Holographic reduced representations (HRRs) [Plate, 1991, Plate, 1995] also uses ﬁxed-length representations of variable-sized data, but using diﬀerent methods.”
Unsupervised learning of invariant representations with low sample complexity: the magic of sensory cortex or a new framework for machine learning? (2013, background): “[45] since it gives a Lipschitz bound for a diﬀeomorphic transformation at each layer of the scattering representation.”
A Solution to the Binding Problem for Compositional Connectionism (2004, background): “, Halford et al, 1998; Smolensky, 1990), and related schemes (e.g., Kanerva, 1998; Plate, 1991).”
Unsupervised learning of invariant representations (2016, background): “Interestingly the sparsity condition under the group is related to associative memories for instance of the holographic type[44],[45].”
Composition in Distributional Models of Semantics (2010, background): “Holographic reduced representations (Plate, 1991) are one implementation of this idea where the tensor product is projected onto the space of the original vectors, thus avoiding any dimensionality increase.”
Compositional Operators in Distributional Semantics (2014, methodology): “Using a concept from signal processing, Plate [35] suggests the replacement of tensor product by circular convolution.”
Resonator Networks, 1: An Efficient Solution for Factoring High-Dimensional, Distributed Representations of Data Structures (2020, background): “Here we show how this may be accomplished within the framework of vector symbolic architectures (VSA) (Plate, 1991; Gayler, 1998; Kanerva, 1996), whereby data structures are encoded by combining high-dimensional vectors with operations that together form an algebra on the space of distributed repres”
Category-theoretic quantitative compositional distributional models of natural language semantics (2013, methodology): “One notable method by which these dimensionality problems can be solved in general are the holographic reduced representations proposed by [67].”
Connectionist sentence processing in perspective (1999, background): “Associative devices more closely related to Willshaw nets, such as the Holographic Reduced Representations (HRR) proposed by Plate (1991, 1994, 1997) are a promising alternative for both recursive structure building and grammar represen- tation.”
Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors (2009, methodology): “This problem was solved by Plate in the holographic reduced representation (HRR) [13].”
Darwin's mistake: Explaining the discontinuity between human and nonhuman minds (2008, unknown): “…connectionist architectures that are functionally discrete, particular-involving, and syntactically structured without being concatenatively compositional in the sense postulated by the PSS hypothesis (e.g., Plate 1991; Pollack 1990; Smolensky 1990; van Gelder 1990; Wilson et al. 2001).”