Can length generalization transfer between different related tasks?

The "Extrapolation by Association" paper demonstrates a specific mechanism for out-of-distribution generalization: length generalization — the ability to handle longer inputs than seen during training — can transfer from one task to another.

The setup: train multiple related tasks jointly, where an "auxiliary task" uses longer inputs and a "main task" uses shorter inputs. The finding: the main task generalizes to the length of the longer auxiliary task, even though it was never trained at that length. This works across arithmetic operations, string transformations, and maze navigation — diverse algorithmic domains sharing an underlying structural similarity.

The mechanistic evidence is precise: length generalization transfer correlates with the reuse of the same attention heads between tasks. The model doesn't learn separate length-handling circuitry per task. Instead, it develops shared computational infrastructure that handles the length dimension, and this infrastructure transfers because the related tasks route through the same attention heads.

The pretrained-model finding extends this further: pretrained language models already exhibit similar transfer effects, suggesting that pretraining equips models with "reusable computational scaffolding" that facilitates extrapolation in downstream settings. The scaffolding is not task-specific — it is a general capability for processing longer sequences that was acquired during pretraining and can be activated by fine-tuning on related tasks.

This connects to Do base models already contain hidden reasoning ability? through a shared principle: pretraining installs capabilities that later training surfaces rather than creates. The base model already has the computational scaffolding for length handling; the auxiliary task merely activates it for the main task.

The connection to Do neural networks naturally learn modular compositional structure? is direct: attention head reuse across tasks is a specific instance of modular subnetwork sharing. The decomposition into reusable modules happens naturally, and pretraining encourages it — exactly the compositional generalization thesis applied to the length dimension.

Since Can neural networks learn compositional skills without symbolic mechanisms?, length generalization may follow the same scaling trajectory — more data and larger models produce more transferable attention head circuits. The practical implication: training on a diverse set of related tasks at varying lengths may be more efficient than training each task independently at the target length.