The argument, associated with Chomsky and generative grammar, starts from an asymmetry: children receive a finite, noisy corpus with almost no negative evidence (nobody tells them which sentences are ungrammatical), and yet they converge quickly on the same grammar. If the data are compatible with many hypotheses and children always pick the right one, something must constrain the search: an innate Universal Grammar. The classic example is yes/no questions. From The man who is tired is eating English speakers form Is the man who is tired eating?, not *Is the man who tired is eating?: children apply the hierarchical rule (front the main-clause auxiliary) rather than the linear one (front the first auxiliary), even though they rarely hear cases that tell the two apart.
Millière & Buckner (2024a) separate two claims that are often conflated (2024a, sec. 3.2). The strong learnability claim says that no amount of data suffices without grammatical priors; LLMs, which acquire sophisticated syntax without them, are an "empiricist existence proof" against it. The developmental claim, the poverty of the stimulus proper, says that the data children actually receive are insufficient; and large models see at least a few thousand times more text (Piantadosi, 2024, p. 366). Piantadosi (2024) holds that LLMs settle the issue, though he grants that it remains to be seen how they do on human-sized datasets (2024, pp. 371–372).
That is the empirical frontier. Yedetore et al. (2023) trained LSTMs and transformers on child-directed speech of roughly realistic size: they captured the surface statistics well, but generalized yes/no questions with the linear rule; the authors conclude that stronger biases than those of these architectures are needed (2023, p. 9370). Meanwhile, Kallini et al. (2024) showed that GPT-2 learns "impossible" languages worse than English, against Chomsky's claim that LLMs would learn both equally well, and Kallini & Potts (2026) propose using models to isolate which inductive biases separate the possible from the impossible. The question is no longer whether a statistical learner can learn grammar, but with which biases and how much data (see empiricism and nativism).