title: Simple deductive reasoning tests and numerical data sets for exposing limitation of today's deep neural networks
abstract: Learning for Deductive Reasoning is an open problem in the machine learning world today. 
  Deductive reasoning involves storing facts in memory and generation of newer facts over time. 
  The concept of memory, processor and code in deduction systems is fundamentally different from the purpose and formulation of weights in a deep neural network. 
  A majority of the machine learning models are inductive reasoning models including state of the art deep neural networks which are effectively tensor interpolation based models.
  A step towards realization of memory is through recurrent neural networks and its variants, however the formal representation is not sufficient enough to capture a complex mapping function between input and output patterns.
  Deep neural networks are positioned to do away with feature engineering which is essentially deductive reasoning methodology.
  There are existing works in deductive reasoning in neural networks that require learning of syntax, unification and deduction and operate on text data as sequence of tokens.
  However the performance of deductive reasoning networks is far from perfection which may be either due to syntax or deduction aspects.
  In this context, we have proposed a suite of completely numeric data sets which do not require parsing as with text data.
  The 10 data sets are for - (a) selection (3 data sets) - minimum, maximum and top 2nd element in an array of numbers; (b) matching (3 data sets) - duplicate detection, counting and histogram learning; (c) divisibility tests (2 data sets) - divisibility of two numbers and divisibility by 3; (d) representation (2 data sets) - binary representation and parity. 
  Though extremely simple in terms of feature engineering, in all of these tests, simple deep neural networks, random forest and recurrent neural networks have failed with very low accuracies. 
  We propose these as numerical test-bed for testing learning models for deductive reasoning.
authors: Kalidas Yeturu Manish Kumar Srivastava
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