Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Emergence of Compositional Representations in Restricted Boltzmann
  Machines   Extracting automatically the complex set of features composing real
high-dimensional data is crucial for achieving high performance in
machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically
known to be efficient for this purpose, and to be able to generate distributed
and graded representations of the data. We characterize the structural
conditions (sparsity of the weights, low effective temperature, nonlinearities
in the activation functions of hidden units, and adaptation of fields
maintaining the activity in the visible layer) allowing RBM to operate in such
a compositional phase. Evidence is provided by the replica analysis of an
adequate statistical ensemble of random RBMs and by RBM trained on the
handwritten digits dataset MNIST.

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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci