{"paper":{"title":"Undetectable Backdoors in Model Parameters: Hiding Sparse Secrets in High Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A sparse perturbation masked by Gaussian dither embeds backdoors whose detection reduces to the hard Sparse PCA problem.","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.CR","authors_text":"Ashish Hooda, Atharv Singh Patlan, Kassem Fawaz, Nils Palumbo, Sarthak Choudhary, Somesh Jha","submitted_at":"2026-05-05T18:48:09Z","abstract_excerpt":"We present Sparse Backdoor, a supply-chain attack that plants a provably undetectable backdoor in pre-trained image classifiers, including convolutional networks and Vision Transformers. The attack injects a structured sparse perturbation along a randomly chosen direction into a small subset of columns at each fully connected layer, propagating a trigger signal to an adversary-chosen target class, and masks the perturbation with an independent isotropic Gaussian dither. The dither serves a single technical purpose: it induces a clean reference distribution anchored at the pre-trained weights, "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that distinguishing the backdoor-injected model from this reference is at least as hard as Sparse PCA detection, which is computationally infeasible under standard hardness assumptions. The guarantee holds against any probabilistic polynomial-time distinguisher with white-box access to the parameters.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Under a mild margin condition on the pre-trained classifier, we show that the dithered reference is functionally equivalent to the original classifier.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Sparse Backdoor plants a provably undetectable backdoor in neural network weights via structured sparse perturbations and isotropic Gaussian dithering, with detection hardness reduced to Sparse PCA.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A sparse perturbation masked by Gaussian dither embeds backdoors whose detection reduces to the hard Sparse PCA problem.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4abf5a0048e9af099c8f815670b13a585c52cba3679462b0359f0ec9967571ba"},"source":{"id":"2605.04209","kind":"arxiv","version":2},"verdict":{"id":"d5f04a65-83af-45f4-ace9-2a199959f977","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T17:46:52.224990Z","strongest_claim":"We prove that distinguishing the backdoor-injected model from this reference is at least as hard as Sparse PCA detection, which is computationally infeasible under standard hardness assumptions. The guarantee holds against any probabilistic polynomial-time distinguisher with white-box access to the parameters.","one_line_summary":"Sparse Backdoor plants a provably undetectable backdoor in neural network weights via structured sparse perturbations and isotropic Gaussian dithering, with detection hardness reduced to Sparse PCA.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Under a mild margin condition on the pre-trained classifier, we show that the dithered reference is functionally equivalent to the original classifier.","pith_extraction_headline":"A sparse perturbation masked by Gaussian dither embeds backdoors whose detection reduces to the hard Sparse PCA problem."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.04209/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T12:36:29.502660Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:21.106278Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:42:12.068385Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8bfe0ea30b0c8efd3dea90410b7bf352ab53d4d5b4b3b87a22774ab37e819647"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":3,"snapshot_sha256":"2da0535982af8a43209d79cace1004967f5ad8af61d552cf59704771c860b437"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}