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Dan Lee

Publications and source records attributed to Dan Lee.

2 recordsLinked to original sources

Training Language Models via Neural Cellular Automata

Pre-training is crucial for large language models (LLMs), as it is when most representations and capabilities are acquired. However, natural language pre-training has problems: high-quality text is finite, it contains human biases, and it entangles knowledge with reasoning. This raises a fundamental question: is natural language the only path to intelligence? We propose using neural cellular automata (NCA) to generate synthetic, non-linguistic data for pre-pre-training LLMs--training on synthetic-then-natural language. NCA data exhibits rich spatiotemporal structure and statistics resembling natural language while being controllable and cheap to generate at scale. We find that pre-pre-training on only 164M NCA tokens improves downstream language modeling by up to 6% and accelerates convergence by up to 1.6x. Surprisingly, this even outperforms pre-pre-training on 1.6B tokens of natural language from Common Crawl with more compute. These gains also transfer to reasoning benchmarks, including GSM8K, HumanEval, and BigBench-Lite. Investigating what drives transfer, we find that attention layers are the most transferable, and that optimal NCA complexity varies by domain: code benefits from simpler dynamics, while math and web text favor more complex ones. These results enable systematic tuning of the synthetic distribution to target domains. More broadly, our work opens a path toward more efficient models with fully synthetic pre-training.

cs.LG

Stability of the positive mass theorem under Ricci curvature lower bounds

We establish Gromov-Hausdorff stability of the Riemannian positive mass theorem under the assumption of a Ricci curvature lower bound. More precisely, consider a class of orientable complete uniformly asymptotically flat Riemannian 3-manifolds with nonnegative scalar curvature, vanishing second homology, and a uniform lower bound on Ricci curvature. We prove that if a sequence of such manifolds has ADM mass approaching zero, then it must converge to Euclidean 3-space in the pointed Gromov-Hausdorff sense. In particular, this confirms Huisken and Ilmanen's conjecture on stability of the positive mass theorem under the assumptions described above. The proof is based on the harmonic level set approach to proving the positive mass theorem, combined with techniques used in the proof of Cheeger and Colding's almost splitting theorem. Furthermore, we show that the same results hold under a more general lower bound on scalar curvature.

math.DG