Think Twice: The Metis-1.6 Technical Report

AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered practical adoption: (i) unequal hyperparameter tuning and (ii) limited or misleading evaluation setups. To address these two issues, we conduct a systematic study of ten deep learning optimizers across four model scales (0.1B-1.2B parameters) and data-to-model ratios (1-8x the Chinchilla optimum). We find that fair and informative comparisons require rigorous hyperparameter tuning and evaluations across a range of model scales and data-to-model ratios, performed at the end of training. First, optimal hyperparameters for one optimizer may be suboptimal for another, making blind hyperparameter transfer unfair. Second, the actual speedup of many proposed optimizers over well-tuned baselines is lower than claimed and decreases with model size to only 1.1x for 1.2B parameter models. Thirdly, comparing intermediate checkpoints before reaching the target training budgets can be misleading, as rankings between two optimizers can flip during training due to learning rate decay. Through our thorough investigation, we find that all the fastest optimizers such as Muon and Soap, use matrices as preconditioners -- multiplying gradients with matrices rather than entry-wise scalars. However, the speedup of matrix-based optimizers is inversely proportional to model scale, decreasing from 1.4x over AdamW for 0.1B parameter models to merely 1.1x for 1.2B parameter models.

Training capable language models typically relies on web-scale pretraining followed by multi-stage post-training, creating substantial computational and data-governance barriers for settings in which training data must satisfy explicit permissibility constraints. We introduce Mimir, a 1.78B-parameter language model based on the Hierarchical Reasoning Model Text (HRM-Text) architecture, a recurrent-depth transformer whose layers are split into a low-level (L) and a high-level (H) stack that are applied repeatedly in an interleaved schedule. Mimir is trained from random initialization directly on a curated mixture of instruction, reasoning, tool-use, multilingual, and synthetic data: 161 datasets and 70.5B tokens per epoch for Mimir v1, extended to 103B tokens per epoch for its continued-training successor Mimir v1.5, with synthetic replacements for sources that do not satisfy permissibility criteria. Across 20 benchmarks in English, Danish (a low-resource language with ~6M speakers), and Math & Code, Mimir v1.5 attains the highest average score of all sub-2B models in every domain, outperforming both HRM-Text 1B and the looped transformers Ouro 1.4B and Ouro 2.6B, and Mimir matches or exceeds the performance of models of up to 9B parameters, such as Qwen 3.5 9B and Gemma 4 E4B, on the English and Danish averages. Two independent memorisation audits indicate low memorisation risk despite multi-epoch training. Inference-time ablations show that the number of L-stack applications can be changed with graceful degradation, whereas changing the number of H-stack applications breaks the model. Our results provide evidence that hierarchical recurrent language models can learn effectively from post-training-oriented, permissible data mixtures without conventional web-scale pretraining.

Mixture-of-Experts (MoE) architectures have become standard in large language models, yet many of their core design choices - expert count, granularity, shared experts, load balancing, token dropping - have only been studied one or two at a time over narrow configuration ranges. It remains an open question whether these choices can be optimized independently, without considering interactions. We present the first systematic study of over 2,000 pretraining runs spanning models up to 6.6B total parameters, in which we exhaustively vary total experts, expert dimension, heterogeneous expert sizing within a single layer, shared expert size and load-balancing mechanisms. We find that at every active-parameter scale that we study, performance consistently improves with total MoE parameters even at extreme active expert parameter ratios like 128.Further, the optimal expert size is nearly invariant to total parameter count and depends only on active parameter count. Third, we see that other choices like shared experts, heterogeneous experts and load-balancing settings have small effects relative to expert count and granularity, although dropless routing yields a consistent gain. Overall, our results suggest a simpler recipe: focus on expert count and granularity, other choices have minimal effect on final quality.