Evaluating the relationship between regularity and learnability in recursive numeral systems using Reinforcement Learning

Referee: [Methods] Methods: the RL reward function and training regime are not described in sufficient detail to confirm that the setup enforces generalization from limited data to exact representation of all integers (rather than finite-set memorization). Without explicit specification of training-set size, recursion depth, and how exactness is rewarded, the reported regularity advantage cannot be isolated from architectural or reward artifacts.

Authors: We agree that the current methods description is insufficiently detailed. In the revised manuscript we will add an expanded Methods subsection that explicitly states: training occurs on integers 1-100 only; the reward is +1 only if the agent produces the exact correct numeral string for every integer from 1 to 10^6 (and 0 otherwise), thereby enforcing exact generalization rather than memorization; recursion depth is implicitly handled by the policy network's ability to apply the learned recursive rules to arbitrary depth within the tested range. These specifications will make clear that the regularity advantage is measured under the generalization-to-exactness regime described in the abstract. revision: yes

Referee: [Results] Results: no quantitative validation is provided against empirical child numeral-acquisition data (error patterns, sample efficiency, or recursive-rule extraction). The central claim equates RL performance with an explanation for human cross-linguistic prevalence, yet the manuscript contains no direct test that the agent's behavior matches attested acquisition trajectories.

Authors: Our central claim is that, within an RL model of sequential production, regular recursive systems exhibit a learnability advantage under the generalization-to-exactness objective; this computational result supplies one possible mechanism that could contribute to the cross-linguistic dominance of regular systems. We do not equate RL performance with a full model of child acquisition and therefore did not perform quantitative comparisons to child error patterns or sample-efficiency data. Such validation would require a separate human-experiment study. We will add a clarifying paragraph in the Discussion stating the intended scope of the RL simulation and noting qualitative consistency with known regularization tendencies in children, but we maintain that the absence of direct empirical matching does not undermine the reported computational asymmetry. revision: no

Referee: [Discussion] Discussion: the claim that regularity facilitates learning is load-bearing for the prevalence explanation, but the paper does not test whether the observed asymmetry persists under alternative RL architectures or reward formulations that more explicitly penalize non-compositional solutions.

Authors: We selected a standard policy-gradient RL agent because it naturally models the incremental, sequential nature of numeral production. While we agree that robustness checks across architectures (e.g., transformer-based agents) or more compositionality-penalizing rewards would be valuable, performing those experiments lies outside the scope of the present study. In the revised Discussion we will explicitly acknowledge this limitation, state that the reported regularity advantage holds for the chosen RL formulation, and outline how future work could test alternative architectures. This keeps the current results as an existence proof rather than a universal claim. revision: no