Lookahead brittleness and the gradient-reward/task-requirement gap

Determine whether the size of the gap between the information directly rewarded by next-token training and the information required by a task predicts where lookahead-dependent tasks become brittle in autoregressive language models.

Background

The paper distinguishes gradient reward—the information directly supervised for the current output token—from task requirement—the information that must be resolved to produce that token correctly. In big-endian addition, future result digits may need to be represented because carry propagation requires lookahead, even though those future digits are not directly rewarded at the current position.

The authors identify the gap between these two notions as potentially relevant to the systematic lookahead limitations observed in LLMs. They specifically propose testing whether the magnitude of this gap predicts the point at which tasks that depend on lookahead become fragile.