ArXiv-to-Model: A Practical Study of Scientific LM Training

Scientific foundation models increasingly operate on continuous phenomena, yet still use discrete residual computation. We ask whether pretrained residual transformations can support additional latent computation without expanding the backbone. To test this possibility, we introduce Continuum-LM, which reuses these transformations as dynamical operators in a continuous-depth language model. Its hidden states evolve through an ordinary differential equation evaluated by higher-order numerical integration, with solver order and step size controlling computation. Across eight scientific tasks, Continuum-LM trains stably and improves mean exact-match accuracy by 7.77 and 10.96 percentage points over discrete counterparts at the 0.6B and 1.7B scales, respectively. At 0.6B, it also outperforms an Ouro-style recurrent control under matched parameter and residual-function evaluation budgets. Together, these results support extensible computational depth through parameter reuse, identifying continuous hidden-state evolution as a practical design dimension for scientific language models beyond parameter scaling.

In this report, we present LOGOS (Language Of Generative Objects in Science), a scientific generative language model that unifies heterogeneous tasks across the natural sciences within a single autoregressive framework based on a shared scientific grammar. It encodes diverse scientific objects and their spatial interactions as token sequences over a common vocabulary. By representing spatial contact and constraint patterns as discrete tokens, the model captures complex structural interactions in a purely sequential manner, without relying on explicit coordinates or geometric neural networks. This unified representation enables a wide range of downstream tasks to be formulated consistently as next-token prediction in the same grammar space, creating strong alignment between continued multi-domain pre-training and downstream objectives. Across diverse tasks, LOGOS consistently matches or outperforms domain-specific baselines, providing preliminary evidence for the feasibility of "one model fits all" in the natural sciences. We train LOGOS models at different scales (1B, 3B, and 8B parameters) and find a consistent positive correlation between model size and performance. This suggests that the future of AI for Science (AI4S) may not lie in building an independent technical stack that is separated from large language models (LLMs). Instead, it may depend on deeply aligning scientific foundation models with LLMs through shared architectures, shared training paradigms, and shared inference infrastructure, so that LLMs can truly become a new entry point for AI4S. We release the model weights and associated resources to facilitate further research.

Looped language models increase effective depth by repeatedly applying a shared block of layers, but existing large-scale recipes require multi-stage training over trillions of tokens, while the benefits of recurrence remain difficult to separate from differences in data and training. In this work, we establish practical training recipes for looped language models, with three main results. (1) We develop a compute-efficient from-scratch pipeline that reduces the training budget from 7.7T tokens in Ouro to 310B tokens while retaining strong reasoning performance. Pretraining followed by high-quality mid-training, together with learning-rate warmup and stronger exit-gate regularization, enables stable recurrent training without prior multi-stage schedules. (2) Under controlled comparisons, our 1.4B LoopLM outperforms a parameter-matched dense model trained on the same data and token budget on all 12 evaluated benchmarks, including +14 points on GSM8K, +10 on MATH, and +22 on DROP. At matched inference compute, it approaches a 3.9B dense model on mathematical reasoning and reading comprehension while using only 36% as many parameters. (3) We introduce a minimal recipe for converting pretrained dense models into looped ones: a single learned input-mixing scalar and a smoothed exit loss, with no step-specific parameters. Applied to Qwen3-1.7B-Base, Looped Qwen improves over an identically continued dense baseline on every evaluated benchmark across two data regimes, with statistically clear gains on GSM8K, MATH, and MMLU-Pro on the curated mixture. Together, these results make looped language models substantially cheaper to train from scratch and practical to introduce into existing pretrained checkpoints, while isolating the gains due to recurrence itself.