Representational Simplicity and Circuit Size Dissociate in a Threshold-Dependent Way: A Controlled Test via Adversarial Training

Adam Elimadi

Sparse-autoencoder decomposability and concentrated feature attribution are increasingly treated as evidence that a model's computation is easier to reverse-engineer. Whether this representational and attributional cleanliness actually predicts a smaller or more tractable causal circuit remains an open question. We test this directly using adversarial training as a controlled instrument: it reliably reshapes internal representations, but this alone does not constitute a test of circuit size. We investigate this question through reverse-engineering complexity: the causal structure required to recover a model's behavior at a fixed level of faithfulness. To our knowledge, this is the first controlled empirical test of whether representational or attributional simplicity translates into causal simplicity at the circuit level. Starting from the same pretrained GPT-2 Small checkpoint, we apply matched standard and adversarial continual training, requiring both conditions to retain competence on indirect object identification and pass independent robustness verification before comparing mechanisms. We then compare the models along three complementary axes: sparse-autoencoder…