Stable Solutions from Chaos: Learning to Solve Inverse Problems
A novel learned optimization framework improves the stability and convergence of solutions for ill-posed inverse problems, offering a significant advancement in fields like brain imaging.



![The projection of model capabilities-ranging from baseline performance [latex] (orange curves) [/latex] to enhanced reasoning with an advanced base model [latex] (gpt-5.1-codex-max, green curve) [/latex]-reveals an overall trajectory [latex] (blue curve) [/latex] predictably limited by the estimated 50% model horizon as defined by METR.](https://arxiv.org/html/2602.04836v1/fig/extrapolation_spline.png)
![The Deep Rational-ANOVA Network (RAN) employs a deep residual backbone facilitating sparse pairwise interactions and node-wise updates, coupled with learnable rational units-initialized for identity and stabilized with positive denominators [latex]1 + \text{softplus}(\cdot)[/latex]-to enable pole-free composition and robust signal processing.](https://arxiv.org/html/2602.04006v1/x2.png)
![Despite achieving high predictive accuracy on observed neural activity, unconstrained model exploration failed to uncover the underlying mechanisms of a simulated neuromechanical system, while a structure-constrained search - guided by prior knowledge of potential connections - successfully identified the correct signs and magnitudes of interactions within the neural circuit, demonstrating that mechanistic discovery requires incorporating structural priors beyond mere predictive performance-even when working with [latex]in\thinspace silico[/latex] testbeds.](https://arxiv.org/html/2602.04492v1/x1.png)
![Machine learning frameworks exhibit vulnerabilities stemming from diverse sources, including adversarial attacks targeting model robustness - often formulated as finding perturbations δ such that [latex] f(x + \delta) \neq f(x) [/latex] - and data poisoning which compromises training data integrity, alongside issues related to model privacy and security concerning sensitive information leakage or manipulation.](https://arxiv.org/html/2602.04753v1/img/study1codebook1.png)