# Explainable AI via Learning to Optimize

arXiv: https://arxiv.org/abs/2204.14174 · HTML: https://mlsanity.com/paper/2204.14174/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 73 references that are in the map.
- First posted on arXiv 29 Apr 2022.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Model Cards for Model Reporting](https://mlsanity.com/paper/1810.03993/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Towards Explainable Artificial Intelligence](https://mlsanity.com/paper/1909.12072/) (2019)
- [A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems](https://mlsanity.com/paper/1912.01825/) (2019)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [A survey of sparse representation: algorithms and applications](https://mlsanity.com/paper/1602.07017/) (2016)
- [Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators](https://mlsanity.com/paper/1903.01014/) (2019)
- [Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games](https://mlsanity.com/paper/2002.10113/) (2020)
- [A Three-Operator Splitting Scheme and its Optimization Applications](https://mlsanity.com/paper/1504.01032/) (2015)
- [FactSheets: Increasing Trust in AI Services through Supplier's Declarations of Conformity](https://mlsanity.com/paper/1808.07261/) (2018)
- [SoK: Decentralized Finance (DeFi)](https://mlsanity.com/paper/2101.08778/) (2021)
- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [The LoDoPaB-CT Dataset: A Benchmark Dataset for Low-Dose CT Reconstruction Methods](https://mlsanity.com/paper/1910.01113/) (2019)
- [Improved Price Oracles: Constant Function Market Makers](https://mlsanity.com/paper/2003.10001/) (2020)
- [Flash Boys 2.0: Frontrunning, Transaction Reordering, and Consensus Instability in Decentralized Exchanges](https://mlsanity.com/paper/1904.05234/) (2019)
- [Yes We Care! -- Certification for Machine Learning Methods through the Care Label Framework](https://mlsanity.com/paper/2105.10197/) (2021)
- [Music Source Separation with Deep Equilibrium Models](https://mlsanity.com/paper/2110.06494/) (2021)

## Built on by (most cited first, 14 of 14)

- [Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splitting](https://mlsanity.com/paper/2301.13395/) (2023)
- [On Logical Extrapolation for Mazes with Recurrent and Implicit Networks](https://mlsanity.com/paper/2410.03020/) (2024)
- [A Generalization Bound for a Family of Implicit Networks](https://mlsanity.com/paper/2410.07427/) (2024)
- [Recovering implicit physics model under real-world constraints](https://mlsanity.com/paper/2412.02215/) (2024)
- [Explainable AI: Learning from the Learners](https://mlsanity.com/paper/2601.05525/) (2026)
- [End-to-End Training of High-Dimensional Optimal Control with Implicit Hamiltonians via Jacobian-Free Backpropagation](https://mlsanity.com/paper/2510.00359/) (2025)
- [Estimating a potential without the agony of the partition function](https://mlsanity.com/paper/2208.09433/) (2022)
- [On the Convergence of Jacobian-Free Backpropagation for Optimal Control Problems with Implicit Hamiltonians](https://mlsanity.com/paper/2602.00921/) (2026)
- [Training Implicit Networks for Image Deblurring using Jacobian-Free Backpropagation](https://mlsanity.com/paper/2402.02065/) (2024)
- [Bridging the Communication Gap: Evaluating AI Labeling Practices for Trustworthy AI Development](https://mlsanity.com/paper/2501.11909/) (2025)
- [Thinking Out of the Box: Hybrid SAT Solving by Unconstrained Continuous Optimization](https://mlsanity.com/paper/2506.00674/) (2025)
- [xInv: Explainable Optimization of Inverse Problems](https://mlsanity.com/paper/2506.11056/) (2025)
- [Hierarchical Causal Abduction: A Foundation Framework for Explainable Model Predictive Control](https://mlsanity.com/paper/2605.10624/) (2026)
- [End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers](https://mlsanity.com/paper/2607.20674/) (2026)

## Abstract (arXiv)

Indecipherable black boxes are common in machine learning (ML), but applications increasingly require explainable artificial intelligence (XAI). The core of XAI is to establish transparent and interpretable data-driven algorithms. This work provides concrete tools for XAI in situations where prior knowledge must be encoded and untrustworthy inferences flagged. We use the "learn to optimize" (L2O) methodology wherein each inference solves a data-driven optimization problem. Our L2O models are straightforward to implement, directly encode prior knowledge, and yield theoretical guarantees (e.g. satisfaction of constraints). We also propose use of interpretable certificates to verify whether model inferences are trustworthy. Numerical examples are provided in the applications of dictionary-based signal recovery, CT imaging, and arbitrage trading of cryptoassets. Code and additional documentation can be found at https://xai-l2o.research.typal.academy.