Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variable Binding for Sparse Distributed Representations: Theory and
  Applications   Symbolic reasoning and neural networks are often considered incompatible
approaches. Connectionist models known as Vector Symbolic Architectures (VSAs)
can potentially bridge this gap. However, classical VSAs and neural networks
are still considered incompatible. VSAs encode symbols by dense pseudo-random
vectors, where information is distributed throughout the entire neuron
population. Neural networks encode features locally, often forming sparse
vectors of neural activation. Following Rachkovskij (2001); Laiho et al.
(2015), we explore symbolic reasoning with sparse distributed representations.
The core operations in VSAs are dyadic operations between vectors to express
variable binding and the representation of sets. Thus, algebraic manipulations
enable VSAs to represent and process data structures in a vector space of fixed
dimensionality. Using techniques from compressed sensing, we first show that
variable binding between dense vectors in VSAs is mathematically equivalent to
tensor product binding between sparse vectors, an operation which increases
dimensionality. This result implies that dimensionality-preserving binding for
general sparse vectors must include a reduction of the tensor matrix into a
single sparse vector. Two options for sparsity-preserving variable binding are
investigated. One binding method for general sparse vectors extends earlier
proposals to reduce the tensor product into a vector, such as circular
convolution. The other method is only defined for sparse block-codes,
block-wise circular convolution. Our experiments reveal that variable binding
for block-codes has ideal properties, whereas binding for general sparse
vectors also works, but is lossy, similar to previous proposals. We demonstrate
a VSA with sparse block-codes in example applications, cognitive reasoning and
classification, and discuss its relevance for neuroscience and neural networks.

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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an