Abstract: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 mechanism is a Jacobian Composition Penalty (JCP), which trains the reverse Jacobian to act as a local left inverse of the forward Jacobian; its runtime counterpart, RJCP, measures the same inverse-consistency error along optimization trajectories. 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. Across seven PDE inverse-problem benchmarks, D-IPG outperforms standard baselines, achieves 94.8% mean success across the six-problem reliability suite, and reaches comparable or better recovery quality at up to 77x lower inference-time solve cost on the main benchmarks.
| Comments: | Preprint. 21 pages, 8 figures, 8 tables. Code available at this https URL |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.13068 [cs.LG] |
| (or arXiv:2605.13068v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13068 arXiv-issued DOI via DataCite (pending registration) |
From: Aaditya Kachhadiya [view email]
[v1]
Wed, 13 May 2026 06:41:57 UTC (680 KB)
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