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Animation — distinguishers that see the model's output

The BOOST procedure with ε = 0.05 on the same target as the companion animation, but the class of tests now also contains functions of the model's output: the level-set indicators 1{p(x) ∈ B} for buckets B partitioning [−1, 1] (purple bars), alongside the five tests that depend only on x (blue bars). At each step the orange bar is the test selected for the update; the procedure halts when every test in the larger class is inside the ±ε band.

Boosting animation with tests of x and the model's output, per-test error, and L2 error — Left: target p^* and model *p_t*. Middle: the indistinguishability error of each test, Right: the l2 distance between the truth and the model across iterations

Because we've enriched the set of functions in ways that caught previous errors, the final l2 error is now smaller.