Lasting Effects of Abstract Pretraining Beyond Perplexity

Pre-pretraining language models (LMs) on symbolic data can accelerate and improve natural language acquisition. However, existing pre-pretraining tasks, such as Dyck and procedural algorithms, rely on narrow primitives that fail to capture the expressive capacity of natural language. Moreover, prior studies remain restricted to relatively small token budgets, offering limited insight into skill emergence and representational dynamics. To address these limitations, we propose logic pre-pretraining (Logic-PPT) as a principled initialization strategy, leveraging formal derivations to impart richer structural and linguistic biases. Formal derivations require abstract mechanisms that are central to natural language, simultaneously binding variables, connecting quantifiers and relational dependencies, and composing predicate-argument structures over long contexts. Scaling our evaluation to a 100B-token regime, logic pre-pretraining substantially accelerates skill acquisition in LMs, achieving 80% accuracy on linguistic tasks with 36B fewer tokens than standard initialization, and outperforming alternative pre-pretraining baselines. Mechanistically, formal derivations induce persistent structural reorganization, distinctively characterized by a lower-rank, spectrally concentrated representation space. Crucially, we show that this internal geometry enables improved model compressibility via pruning, matching the dense baseline performance even at $\approx$33% sparsity.

We show that pre-training a Transformer on music before language significantly accelerates language acquisition. Using piano performances (MAESTRO dataset), a developmental pipeline -- music $\to$ poetry $\to$ prose -- yields a $17.5\%$ perplexity improvement over random initialization ($p < 0.001$, 5 seeds), with music and poetry improving orthogonal model components (internal computation and embeddings, respectively). Convergence tests confirm that this is not a transient head start: at $d\!=\!64$, multi-seed validation (5 seeds) shows a persistent 5.5% gap at plateau ($p = 0.017$), with the pipeline converging faster and to a lower loss in every run. Real music matches the transfer ceiling of synthetic patterns with one-third the data, and scaling experiments reveal that optimal pre-training data volume shifts with model capacity ($-3\% \to +3\% \to +6\%$ advantage of larger datasets from $d\!=\!16$ to $d\!=\!64$). Across the scales we study ($d\!\in\!\{16,32,64\}$, up to ${\sim}400$K parameters), these results suggest a capacity-dependent data curation principle and indicate that structured human creative outputs can provide an efficient pre-training substrate for small language models; stronger conclusions at modern pre-training scale will require substantially larger experiments.

Reinforcement learning (RL) has become central to improving large language models (LLMs) on complex reasoning tasks, yet RL post-training is largely studied in isolation from the pretraining that precedes it. As a result, two basic questions remain open: (1) how do pretraining choices (model size, data) shape the returns to RL compute, and (2) what does RL actually do to the model? These questions are difficult to study in the standard LLM setting: pretraining corpora are vast and uncontrolled, making it hard to attribute behaviors to pretraining versus RL, and systematic compute sweeps across both stages are prohibitively expensive. To address these challenges, we use chess as a controlled testbed for studying reasoning across the full pretraining-to-post-training pipeline. We follow the standard LLM training pipeline by pretraining language models from 5M to 1B parameters on human chess games, supervised fine-tuning on synthetic reasoning traces, and running RL on chess puzzles with verifiable rewards. Using this framework, we find that the post-RL performance at given RL compute level is well-predicted from the pretraining loss, and slope of the RL reward curves improves approximately linearly with the pretraining tokens. Beyond scaling, we find that RL does not simply sharpen the SFT policy: on easy puzzles it amplifies correct moves the SFT policy already preferred, while on hard puzzles it surfaces correct moves that were nearly absent under SFT. We further test whether our findings transfer beyond chess by training a 1B language model on math-domain text, where the same predictive pattern emerges: longer-pretrained checkpoints reach higher post-RL performance and improve faster under RL. In sum, we provide a quantitative account of the pretraining-to-RL interface and a controlled testbed for studying the science of reasoning across the full pretraining-to-post-training pipeline.