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[Submitted on 27 Sep 2026] Title:Representational Simplicity and Circuit Size Dissociate in a Threshold-Dependent Way: A Controlled Test via Adversarial Training View a PDF of the paper titled Representational Simplicity and Circuit Size Dissociate in a Threshold-Dependent Way: A Controlled Test via Adversarial Training, by Adam Elimadi View PDF HTML (experimental) Abstract: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 decomposability, SAE feature engagement in task attribution, and the size of faithful circuits recovered from the raw computational graph. The robust model is more SAE-decomposable and engages fewer SAE features in task attribution. Circuit size is regime-dependent: on competence-matched IOI, standard leads or ties below 85% faithfulness, but robust needs substantially fewer edges at high faithfulness (90%, 95%), a pattern established on the primary pair while representational trends generalize across a seven-point sweep and a second corpus. Comments: Under review at ICLR 2027. 21 pages, 5 figures, 12 tables Subjects: Artificial Intelligence (cs.AI) ACM classes: I.2.7 Cite as: arXiv:2609.35890 [cs.AI] (or arXiv:2609.35890v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2609.35890 arXiv-issued DOI via DataCite (pending registration) Submission history From: Adam Elimadi [view email] [v1] Sun, 27 Sep 2026 07:35:31 UTC (476 KB) Full-text links: Access Paper: View a PDF of the paper titled Representational Simplicity and Circuit Size Dissociate in a Threshold-Dependent Way: A Controlled Test via Adversarial Training, by Adam Elimadi View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI new | recent | 2026-09 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)