Neural models excel at extracting statistical patterns from large amounts of data, but struggle to learn patterns or reason about language from only a few examples. In this paper, we ask: Can we learn explicit rules that generalize well from only a few examples? We explore this question using program synthesis. We develop a synthesis model to learn phonology rules as programs in a domain-specific language. We test the ability of our models to generalize from few training examples using our new dataset of problems from the Linguistics Olympiad, a challenging set of tasks that require strong linguistic reasoning ability. In addition to being highly sample-efficient, our approach generates human-readable programs, and allows control over the generalizability of the learnt programs.
Providing examples is one of the most common way for end-users to interact with program synthesizers. However, program synthesis systems assume that examples consistent with the program are chosen at random, and do not exploit the fact that users choose examples pragmatically. Prior work [1] modeled program synthesis as pragmatic communication, but required an inefficient enumeration of the entire program space. In this paper, we show that it is possible to build a program synthesizer that is both pragmatic and efficient by approximating the joint distribution of programs with a product of independent factors, and performing pragmatic inference on each factor separately. This factored distribution approximates the exact joint distribution well when the examples are given pragmatically, and is compatible with a basic neuro-symbolic program synthesis algorithm. Surprisingly, we find that the synthesizer assuming a factored approximation performs better than a synthesizer assuming an exact joint distribution when evaluated on natural human inputs. This suggests that humans may be assuming a factored distribution while communicating programs.
Neural models excel at extracting statistical patterns from large amounts of data, but struggle to learn patterns or reason about language from only a few examples. In this paper, we ask: Can we learn explicit rules that generalize well from only a few examples? We explore this question using program synthesis. We develop a synthesis model to learn phonology rules as programs in a domain-specific language. We test the ability of our models to generalize from few training examples using our new dataset of problems from the Linguistics Olympiad, a challenging set of tasks that require strong linguistic reasoning ability. In addition to being highly sample-efficient, our approach generates human-readable programs, and allows control over the generalizability of the learnt programs.
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