循环Transformer训练难、部署贵的问题被Attractor Models用不动点求解优雅解决，做语言模型预训练或推理增强的团队值得关注——它用更少参数和成本实现了对更大模型的超越。
论文提出Attractor Models，用隐式微分求解不动点替代传统循环Transformer的显式迭代，训练内存不随有效深度增长，迭代次数由收敛自适应决定。在语言模型预训练中，770M参数模型超越1.3B Transformer（训练数据多一倍），困惑度降低46.6%，下游准确率提升19.7%。在推理任务中，27M参数模型在Sudoku-Extreme和Maze-Hard上分别达91.4%和93.1%准确率，而Claude和GPT o3完全失败。模型还展现出“平衡内化”现象：训练后可在推理时移除求解器而性能几乎不降。
Solve the Loop: Attractor Models for Language and Reasoning
Looped Transformers offer a promising alternative to purely feed-forward computation by iteratively refining latent representations, improving language modeling and reasoning. Yet recurrent architectures remain unstable to train, costly to optimize and deploy, and constrained to small, fixed recurrence depths. We introduce Attractor Models, in which a backbone module first proposes output embeddings, then an attractor module refines them by solving for the fixed point, with gradients obtained through implicit differentiation. Thus, training memory remains constant in effective depth, and iterations are chosen adaptively by convergence. Empirically, Attractor Models outperform existing models across two regimes, large-scale language-model pretraining and reasoning with tiny models. In language modeling, Attractor Models deliver a Pareto improvement over standard Transformers and stable looped models across sizes, improving perplexity by up to 46.6% and downstream accuracy by up to 19.7% while reducing training cost. Notably, a 770M Attractor Model outperforms a 1.3B Transformer trained on twice as many tokens. On challenging reasoning tasks, we show that our model with only 27M parameters and approximately 1000 examples achieves 91.4% accuracy on Sudoku-Extreme and 93.1% on Maze-Hard, scaling favorably where frontier models like Claude and GPT o3, fail completely, and specialized recursive reasoners collapse at larger sizes. Lastly, we show that Attractor Models exhibit a novel phenomenon, which we call equilibrium internalization: fixed-point training places the model's initial output embedding near equilibrium, allowing the solver to be removed at inference time with little degradation. Together, these results suggest that Attractor Models make iterative refinement scalable by turning recurrence into a computation the model can learn to internalize.