Transformers struggle to generalize to tasks they were not explicitly trained on. Instead, we propose in 2026 that it is the job of the harness to generalize through composition. We observe a powerful property when training RLMs: for tasks with shared structure that look different, the root model naturally learns the same trajectory, meaning it views the two task trajectories as the same! In other words, the Transformer does not need additional generalization capabilities to transfer capabilities from one task to the other, the harness induces it. We find that well-designed harnesses form a quotient set over task trajectories, meaning their individual LLM calls can see structurally “similar” tasks as near-identical, token-for-token! Harnesses can effectively generalize for the Transformer during training, without relying on any intrinsic generalization capability from the model. For example, RLMs can see problems of different lengths as the same: we show that RLMs can train exclusively on short tasks, and fully generalize to similar but unseen tasks 8-32x longer because it produces near identical trajectories for both. Taking this further, we show that tasks across different domains (e.g. math solutions vs. essay writing) that share a decomposition strategy exhibit the same generalization effect. RLMs can train on the problem of finding which essays belong to the same author and improve performance on finding math problems that share similar solutions. The full blogpost, experiments, and discussion are in the thread below.