{"paper":{"title":"Local Inverse Geometry Can Be Amortized","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A learned reverse operator amortizes local inverse geometry so first-order methods match damped Gauss-Newton on nonlinear inverse problems.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aaditya L. Kachhadiya","submitted_at":"2026-05-13T06:41:57Z","abstract_excerpt":"Nonlinear inverse problems often trade inexpensive but fragile first-order updates against curvature-aware methods such as Gauss-Newton and Levenberg-Marquardt, which obtain stronger directions by repeatedly solving Jacobian-based linearized systems. We propose a learned alternative: amortize local inverse geometry into a reusable reverse operator. Our framework learns a bidirectional surrogate, Deceptron, and deploys it through D-IPG (Deceptron Inverse-Preconditioned Gradient), an iterative solver that pulls residual-corrected measurement-space proposals back to latent space. The key mechanis"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that D-IPG is first-order equivalent to damped Gauss-Newton under local pseudoinverse consistency, with deviation controlled by composition error and conditioning.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The learned reverse Jacobian maintains local pseudoinverse consistency with the forward Jacobian along optimization trajectories, which is enforced only by the Jacobian Composition Penalty during training.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"D-IPG uses a trained Deceptron and Jacobian Composition Penalty to deliver first-order equivalent performance to damped Gauss-Newton on nonlinear inverse problems at up to 77x lower inference cost.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A learned reverse operator amortizes local inverse geometry so first-order methods match damped Gauss-Newton on nonlinear inverse problems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2cdb3b04a26adb6dd97115e2424b6a23a0751c2b8e5e3db8f92731f12cea34e6"},"source":{"id":"2605.13068","kind":"arxiv","version":1},"verdict":{"id":"3abd5316-c062-49d7-95d0-d7075863bcec","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:57:27.540664Z","strongest_claim":"We prove that D-IPG is first-order equivalent to damped Gauss-Newton under local pseudoinverse consistency, with deviation controlled by composition error and conditioning.","one_line_summary":"D-IPG uses a trained Deceptron and Jacobian Composition Penalty to deliver first-order equivalent performance to damped Gauss-Newton on nonlinear inverse problems at up to 77x lower inference cost.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The learned reverse Jacobian maintains local pseudoinverse consistency with the forward Jacobian along optimization trajectories, which is enforced only by the Jacobian Composition Penalty during training.","pith_extraction_headline":"A learned reverse operator amortizes local inverse geometry so first-order methods match damped Gauss-Newton on nonlinear inverse problems."},"references":{"count":14,"sample":[{"doi":"","year":1944,"title":"A method for the solution of certain non-linear problems in least squares","work_id":"a4647f73-6981-4bd5-aabe-9c92749dfae1","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1963,"title":"Donald W. Marquardt. An algorithm for least-squares estimation of nonlinear parameters. 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