Greedy Grammar Induction Algorithm Achieves Weak Equivalence on Benchmark Languages
A new paper on arXiv introduces a non-lexicalized grammar-induction procedure that uses indirect negative evidence to prevent overgeneralization in learned grammars. The method centers on a rule-coverage bound that defines a comparison universe of short strings unsupported by observed data, guiding a greedy search over rule sets. The work offers a theoretically grounded approach to unsupervised grammar learning with proven weak-recovery guarantees across 31 benchmark tests.
The paper, submitted to arXiv under computational linguistics (cs.CL), proposes a grammar-induction algorithm that separates two distinct tasks: recognizing strings in a finite training presentation and rejecting short strings generated by a hypothesis but absent from the evidence. The key theoretical construct is the rule-coverage bound ℓ*(G), which determines the maximum length of the shortest preterminal string derivable by any rule in a grammar G, thereby defining a comparison universe for evaluating overgenerating hypotheses. A greedy search algorithm operates over this rule universe, and the authors prove a conditional weak-recovery theorem showing that under explicit reachability and saturation conditions, the learner converges to a grammar weakly equivalent to the unknown target. Complexity is analyzed in a slice-wise fashion: for each fixed incrementality radius k, the algorithm explores only polynomially many rule-set extensions. Empirical validation spans 31 benchmark runs covering Dyck-k languages (k=1–4), palindromes, the classic a^n b^n language, English-like recursive fragments, and an inherently ambiguous union language, with grammar-level analysis confirming weak equivalence in every case. The paper is 29 pages including appendices and has undergone three revisions since its initial submission in December 2023.
What's missing
The study's own limitations include the conditionality of the weak-recovery theorem, which depends on explicit reachability conditions and sufficient saturation of the training presentation — conditions that may not hold in practice for natural language corpora. The benchmarks used are formal or semi-formal languages; generalization to large-scale, noisy natural language data remains undemonstrated. The non-lexicalized nature of the approach may limit applicability to tasks requiring lexical sensitivity.
What different sources said
- arXiv cs.CLCenter
Greedy Grammar Induction with Indirect Negative Evidence
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