# Explaining Process Control Optimisation Recommendations via GradientSHAP and Implicit Differentiation

arXiv: https://arxiv.org/abs/2607.14970 · HTML: https://mlsanity.com/paper/2607.14970/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Builds on (most cited first, 8 of 8)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Tell Me a Story! Narrative-Driven XAI with Large Language Models](https://mlsanity.com/paper/2309.17057/) (2023)
- [Revisiting Implicit Differentiation for Learning Problems in Optimal Control](https://mlsanity.com/paper/2310.14468/) (2023)

## Abstract (arXiv)

Automated optimisation is increasingly adopted in industrial processes, yet a trust gap persists between engineers who design these algorithms and operators who must act on their recommendations. Explainable AI methods like SHAP (SHapley Additive exPlanations) have transformed interpretability for machine learning predictions; optimisation outputs could benefit from similar techniques. We present an approach that integrates Implicit Function Theorem (IFT) based sensitivity analysis with SHAP attribution and narrative generation via Large Language Models (LLM), producing explanations tailored for operators. Our approach leverages IFT to compute exact parameter sensitivities partial p^*/partial x from the optimality conditions, enabling efficient GradientSHAP computation. For an industrial High Pressure Grinding Roll (HPGR) control optimisation problem with 22 features, we achieve equivalent SHAP attributions (correlation >0.99 with KernelSHAP) with over 40× speedup, enabling real-time natural language explanations. We validate on industrial scenarios and present feedback from domain experts on generated explanations.