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It is shown theoretically that the task's algebraic structure controls its effective memory: compressible regimes support late-bottleneck reasoning, while incompressible regimes preserve full-history dependence and destabilize latent rollouts.
It is shown that length generalization need not rely on faithful step-by-step reasoning, as Looped Transformers can exploit task structure without explicitly representing every intermediate state.
Tail subtraction is introduced, which removes shared prompt and continuation semantics from boundary states and yields cleaner, more stable steering signals, and suggests that steering depends on representations of what the model is about to do, not merely on what has already appeared.
Activation Steering Adapter (ASA), a training-free, inference-time controller that performs a single-shot mid-layer intervention and targets tool domains via a router-conditioned mixture of steering vectors with a probe-guided signed gate to amplify true intent while suppressing spurious triggers is proposed.
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