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ref: -0 tags: inductive logic programming deepmind formal propositions prolog date: 11-21-2020 04:07 gmt revision:0 [head]

Learning Explanatory Rules from Noisy Data

  • From a dense background of inductive logic programming (ILP): given a set of statements, and rules for transformation and substitution, generate clauses that satisfy a set of 'background knowledge'.
  • Programs like Metagol can do this using search and simplify logic built into Prolog.
    • Actually kinda surprising how very dense this program is -- only 330 lines!
  • This task can be transformed into a SAT problem via rules of logic, for which there are many fast solvers.
  • The trick here (instead) is that a neural network is used to turn 'on' or 'off' clauses that fit the background knowledge
    • BK is typically very small, a few examples, consistent with the small size of the learned networks.
  • These weight matrices are represented as the outer product of composed or combined clauses, which makes the weight matrix very large!
  • They then do gradient descent, while passing the cross-entropy errors through nonlinearities (including clauses themselves? I think this is how recursion is handled.) to update the weights.
    • Hence, SGD is used as a means of heuristic search.
  • Compare this to Metagol, which is brittle to any noise in the input; unsurprisingly, due to SGD, this is much more robust.
  • Way too many words and symbols in this paper for what it seems to be doing. Just seems to be obfuscating the work (which is perfectly good). Again: Metagol is only 330 lines!