Inference-time scaffolds can outperform students for fundamental reasons
A model wrapped in an inference-time harness can retain capabilities that a same-class student trained on the harness’s traces cannot recover, so distillation alone may not replace multi-call systems. The harness calls the model repeatedly while keeping state, letting even a trivial lookup primitive compute an NL-complete closure, while the paper argues no fixed-depth forward pass can match it under NL not being contained in TC^0. Experiments find the gap with simple scaffolds, small models, and an agentic competition-math harness.