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Paper Summary (WIP)

Updated 2019-03-07

Reconciling deep learning with symbolic artificial intelligence

Link to article

I must admit that I discovered this article trying to build my original ideas, and I was pleasantly surprised on how it overlapped 80%-90% on what I had come to conclude even before reading this. It is reassuring that to know that people who are far more qualified, and who have spent way more time than I have on this topic have come to similar conclusion (albeit with more references). Self adulation aside, lets get to business.

Deep Learning

Shortcoming in Deep Learning

They categorize (with examples) which are fairly common and intuitive with current Deep Learning method.

  1. Data Inefficiency: Need no less than a simulator for Deep RL and millions of samples in old-fashioned DL.
  2. Poor Generalization: In ability to transfer or reuse learning to a (even slightly) different domain.
  3. Lack of Interpretability: Black box phenomenon.

Strengths of DL

  1. Data driven automatic representation (and compute) learning: Throw in huge amount of data, and a suitable optimizer and wait.

Symbolic AI

Most predominant until 1980s, in symbolic AI, representations are typically propositional in character, and assert that certain relations hold between certain objects, while each reasoning step computes a further set of relations that follow from those already established, according to a formally specified set of inference rules. As reminder (and mathematically speaking), a proposition is a statement that evaluates to either True or False. Predicate is a function or mapping that takes variables produce propositional output. A relation is a predicate of two variables.

Shortcoming of Symbolic AI

  1. Hand crafted representation: It is not clear how the representations can be learned from data and have traditionally been hand crafted to be used. This is known as symbol grounding problem. The contrast with DL is obvious.

Strengths of Symbolic AI

Strengths typically align with shortcomings of DL.

  1. Data efficiency: thanks to their declarative nature, symbolic representations lend themselves to re-use in multiple tasks, which promotes data efficiency. There is mostly no training needed, as the rules are often handcrafted.
  2. Cross-domain generalization: Symbolic representations tend to be high-level and abstract, which facilitates generalisation. As long as symbols are mapped to correct variables, and problem is correctly formulation in Symbolic AI language.
  3. Interpretable: Because of their language-like, propositional character, symbolic representations are amenable to human understanding. The predetermined rules of inference can be examined by humans.

WIP, more to follow.


Show that this can be done using Tensors

Relational Representation

Can be done using Tensors

It is easy to show that each layer of feed-forward network is than one function.