A Computability Perspective on (Verified) Machine Learning

Abstract

There is a strong consensus that combining the versatility of machine learning with the assurances given by formal verification is highly desirable. It is much less clear what verified machine learning should mean exactly. We consider this question from the (unexpected?) perspective of computable analysis. This allows us to define the computational tasks underlying verified ML in a model-agnostic way, and show that they are in principle computable.

Computable PAC Learning of Continuous Features

“…It is also reasonable to consider settings in which there is a particular value signaling non-halting, which the computable function may never identify. This approach is explored by Crook et al [10], where nonhalting of a learner's output is signaled by the value ⊥. A related approach is considered by Calvert [9], who studies PAC learning for concepts that are Π 0 1 classes on 2 N , which can be thought of as equivalent to working with computable functions from 2 N to Sierpiński space S (i.e., the space {⊥, ⊤} with open sets {∅, {⊤}, {⊥, ⊤}}), where the inverse image of ⊤ is the Π 0 1 class in question.…”