Synthesizing DSLs for Few-Shot Learning

TL;DR

This paper introduces a method for synthesizing domain-specific languages (DSLs) tailored for few-shot learning tasks in symbolic domains, ensuring small expressions generalize from training to testing samples.

Contribution

It proves the decidability of DSL synthesis for certain classes of languages and grammars, advancing automated language generation for symbolic learning.

Findings

Decidability established for DSL synthesis with tree automata semantics.

Grammar solutions form a regular set of trees.

Decidability results extend to macro grammar variants.

Abstract

We study the problem of synthesizing domain-specific languages (DSLs) for few-shot learning in symbolic domains. Given a base language and instances of few-shot learning problems, where each instance is split into training and testing samples, the DSL synthesis problem asks for a grammar over the base language that guarantees that small expressions solving training samples also solve corresponding testing samples. We prove that the problem is decidable for a class of languages whose semantics over fixed structures can be evaluated by tree automata and when expression size corresponds to parse tree depth in the grammar, and, furthermore, the grammars solving the problem correspond to a regular set of trees. We also prove decidability results for variants of the problem where DSLs are only required to express solutions for input learning problems and where DSLs are defined using macro grammars.