Language Model Scaling Laws

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset. We provide the first such theory in the case of data-limited scaling laws. We isolate two key statistical properties of language that alone can predict neural scaling exponents: (i) the decay of pairwise token correlations with time separation between token pairs, and (ii) the decay of the next-token conditional entropy with the length of the conditioning context. We further derive a simple formula in terms of these statistics that predicts data-limited neural scaling exponents from first principles without any free parameters or synthetic data models. Our theory exhibits a remarkable match with experimentally measured neural scaling laws obtained from training GPT-2 and LLaMA style models from scratch on two qualitatively different benchmarks, TinyStories and WikiText.

Evaluating the real-world capabilities of AI systems requires grounding benchmark performance in human-interpretable measures of task difficulty. Existing approaches that rely on direct human task completion time annotations are costly, noisy, and difficult to scale across benchmarks. In this work, we propose BRIDGE, a unified psychometric framework that learns a latent difficulty scale from model responses and anchors it to human task completion time. Using a two-parameter logistic Item Response Theory model, we jointly estimate latent task difficulty and model capability from model performance data across multiple benchmarks. We demonstrate that latent task difficulty varies linearly with the logarithm of human completion time, allowing human task completion time to be inferred for new benchmarks from model performance alone. Leveraging this alignment, we forecast frontier model capabilities in terms of human task length and independently reproduce METR's exponential scaling results, with the 50% solvable task horizon doubling approximately every 6 months.

While Mixture-of-Experts (MoE) scales capacity via conditional computation, Transformers lack a native primitive for knowledge lookup, forcing them to inefficiently simulate retrieval through computation. To address this, we introduce conditional memory as a complementary sparsity axis, instantiated via Engram, a module that modernizes classic $N$-gram embedding for O(1) lookup. By formulating the Sparsity Allocation problem, we uncover a U-shaped scaling law that optimizes the trade-off between neural computation (MoE) and static memory (Engram). Guided by this law, we scale Engram to 27B parameters, achieving superior performance over a strictly iso-parameter and iso-FLOPs MoE baseline. Most notably, while the memory module is expected to aid knowledge retrieval (e.g., MMLU +3.4; CMMLU +4.0), we observe even larger gains in general reasoning (e.g., BBH +5.0; ARC-Challenge +3.7) and code/math domains~(HumanEval +3.0; MATH +2.4). Mechanistic analyses reveal that Engram relieves the backbone's early layers from static reconstruction, effectively deepening the network for complex reasoning. Furthermore, by delegating local dependencies to lookups, it frees up attention capacity for global context, substantially boosting long-context retrieval (e.g., Multi-Query NIAH: 84.2 to 97.0). Finally, Engram establishes infrastructure-aware efficiency: its deterministic addressing enables runtime prefetching from host memory, incurring negligible overhead. We envision conditional memory as an indispensable modeling primitive for next-generation sparse models.

Chemical Language Models (CLMs) are increasingly used in de novo drug design, driven by recent growth in model scale, compute, and dataset size. However, the relationship between design choices, training dynamics, and downstream generation quality remains poorly understood. We present a compute-controlled scaling study of CLMs comprising more than 30,000 experiments across molecular representations (SMILES, SELFIES, SAFE), tokenizations (atom-level and byte-pair encoding), model scales (0.5M-1B parameters), leakage-controlled datasets (MOSES, ChEMBL, PubChem, ZINC-22), and architectures (decoder-only and encoder-decoder). By fitting IsoFLOP profiles, we establish clear scaling trends in pretraining loss, but find that these improvements do not translate into comparable gains in goal-directed molecular design. Layer-wise probing and sparse autoencoder analysis reveal continued development of chemical representations: chemical syntax saturates early, while semantic properties emerge more slowly and become increasingly accessible with further training and model scale. These representational gains coexist with diminishing improvements in goal-directed generation under the evaluated protocols and oracle budgets. Our resulting suite of models, NovoMolGen, achieves state-of-the-art results, outperforming prior CLMs and specialized generative models in goal-directed molecular generation across drug discovery tasks. These findings expose a disconnect between chemical representation learning and downstream molecular design, motivating the development of pretraining paradigms that more directly learn chemical semantics.

Looped Transformers increase effective depth by iterating a shared block of layers, but most evaluations compare at fixed model size, conflating architectural advantage with extra FLOPs. We study looping on Mixture-of-Experts Transformers while closely matching per-token FLOPs, total non-embedding parameters, and KV cache. Through a series of ablations, we arrive at a recipe we call SMELT (Sparse MoE Transformer, middle layers Loop Twice), which loops the middle half of layers twice while matching the unlooped Baseline on all three budgets. We scale SMELT across four sizes up to 54B non-embedding parameters and fit a separate Chinchilla-style scaling law for each architecture. SMELT's loss drops faster with compute, saving 6.8--18.0% of training FLOPs on the compute-optimal frontier. The advantage transfers to downstream benchmarks beyond what validation loss predicts, is largest on Code, and grows with sample length and the number of in-context examples. Mechanistic analysis shows that the second visit reduces the attention sink and redirects mass toward content-relevant tokens, an inductive bias that may underlie the observed performance gains. These results show that looping can improve Transformers even under budget matching, offering a practical recipe that turns depth reuse into measurable gains.