PBEBench: A Multi-Step Programming by Examples Reasoning Benchmark inspired by Historical Linguistics

Recently, long chain of thought (LCoT), Large Language Models (LLMs), have taken the machine learning world by storm with their breathtaking reasoning capabilities. However, are the abstract reasoning abilities of these models general enough for problems of practical importance? Unlike past work, which has focused mainly on math, coding, and data wrangling, we focus on a historical linguistics-inspired inductive reasoning problem, formulated as Programming by Examples. We develop a fully automated pipeline for dynamically generating a benchmark for this task with controllable difficulty in order to tackle scalability and contamination issues to which many reasoning benchmarks are subject. Using our pipeline, we generate a test set with nearly 1k instances that is challenging for all state-of-the-art reasoning LLMs, with the best model (Claude-3.7-Sonnet) achieving a mere 54% pass rate, demonstrating that LCoT LLMs still struggle with a class or reasoning that is ubiquitous in historical linguistics as well as many other domains.

Programming by Examples Meets Historical Linguistics: A Large Language Model Based Approach to Sound Law Induction

Historical linguists have long written "programs" that convert reconstructed words in an ancestor language into their attested descendants via ordered string rewrite functions (called sound laws) However, writing these programs is time-consuming, motivating the development of automated Sound Law Induction (SLI) which we formulate as Programming by Examples (PBE) with Large Language Models (LLMs) in this paper. While LLMs have been effective for code generation, recent work has shown that PBE is challenging but improvable by fine-tuning, especially with training data drawn from the same distribution as evaluation data. In this paper, we create a conceptual framework of what constitutes a "similar distribution" for SLI and propose four kinds of synthetic data generation methods with varying amounts of inductive bias to investigate what leads to the best performance. Based on the results we create a SOTA open-source model for SLI as PBE (+6% pass rate with a third of the parameters of the second-best LLM) and also highlight exciting future directions for PBE research.