Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems

By Paul Smolensky. 1990

Subfields: Natural Language Processing, Model Architectures

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Citations in the corpus

Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving (2019, methodology): “hidden representation at each cell to approximate the vector embedding of a symbolic structure built from the relations generated by that cell. This embedding is a Tensor-Product Representation (TPR; Smolensky, 1990) in an end-to-end-differentiable TPR system (Schlag & Schmidhuber, 2018; Schmidh”
A Structured Vector Space Model for Word Meaning in Context (2008, methodology): “Smolensky (1990) uses tensor product to combine two word vectors a and b into a vector c representing the expression a+b.”
Holographic Reduced Representations: Convolution Algebra for Compositional Distributed Representations (1991, methodology): “Frames can be represented using convolution encoding in an manner analogous to cross products of roles and llers in Hinton 1981] or the frames of DUCS Touretzky and Geva, 1987].”
Resonator Networks, 1: An Efficient Solution for Factoring High-Dimensional, Distributed Representations of Data Structures (2020, background): “In the domain of language, it has been argued that a factorization of sentence structure into “roles” and “fillers” is required for robust and flexible processing (Smolensky, 1990; Jackendoff, 2002).”
Nouns are Vectors, Adjectives are Matrices: Representing Adjective-Noun Constructions in Semantic Space (2010, unknown): “…2007; Sahlgren et al., 2008) or sophisticated composition methods based on tensor products, quantum logic, etc., that have not yet been empirically tested on large-scale corpus-based semantic space tasks (Clark and Pulman, 2007; Rudolph and Giesbrecht, 2010; Smolensky, 1990; Widdows, 2008).”
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).”