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How (and when) can you fit examples to logic-based hypothesis classes over infinite structures?

arXiv CS Tuesday 02 June 2026, 04:00 UTC By Michael Benedikt, Alessio Mansutti 1 min read
Key Points

arXiv:2606.01107v1 Announce Type: new Abstract: We study fitting problems, sometimes called ``training problems'', where we have a finite sample consisting of inputs and outputs, and we want to know whether there is a function in a certain class that could produce these outputs, exactly or approximately, on the given inputs. We focus on the computational and descriptive complexity of fitting for logically-defined classes in common decidable structures, like the real ordered field and...

arXiv:2606.01107v1 Announce Type: new Abstract: We study fitting problems, sometimes called ``training problems'', where we have a finite sample consisting of inputs and outputs, and we want to know whether there is a function in a certain class that could produce these outputs, exactly or approximately, on the given inputs. We focus on the computational and descriptive complexity of fitting for logically-defined classes in common decidable structures, like the real ordered field and Presburger arithmetic, and also for broader classes defined via combinatorial or model-theoretic properties. We isolate the complexity of these fitting problems, with particular attention to cases where we can use queries in a natural query language over the sample to determine whether a sample is fittable.
arXiv:2606.01107v1 Announce Type: (ORG) Presburger (ORG)
Originally published by arXiv CS Read original →

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