The Steering Budget: Examples beat Knobs

Generative models are steered by turning knobs — prompts, guidance scales — but every knob saturates: push it far enough and it stops moving the property you care about. This ceiling is a budget fixed by the training data before the model exists — no knob can push past it. We introduce showing, which reaches any value the whole budget allows, not just what a knob can reach, by partitioning outputs into easy-to-compute bins, auditing each, and combining bins in the proportions needed. This audit makes the split exact: a target property's variance divides into a within-bin part (telling's reach) and a between-bin part (showing's reach), both computable from data alone, before a model exists. A second, model-facing diagnostic then confirms this split carries over to a trained model: on crystals, it correctly forecasts the carry-over order of three properties before the model was ever audited. Across two unrelated domains — image and crystal-structure generation — showing out-reaches the strongest knob baselines we could build by 4.8-26x on crystal properties and 3x on image targets, with no fine-tuning: only a different choice of examples. The same two numbers also say, in advance, when telling remains the better choice. Given showing wins, a property's curvature determines the shape of the fix: concentrate on one bin for an average goal, spread across bins for coverage. Showing further brings expressiveness a knob cannot: because the specification lives in the examples, it can steer toward a target recognized but never named.