Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition

XAI can translate ML insights into human-understandable rules: The researchers used SHAP (a tool for explaining AI decisions) to understand why machine learning models made good choices about variable ordering in mathematical computations, then converted those insights into traditional algorithmic heuristics that don't require AI at all—demonstrating that explainability tools can bridge the gap between "black box" ML and interpretable human logic.

Responsible AI in mathematics means avoiding unnecessary complexity: Rather than deploying ML models directly into computer algebra systems, the team showed that XAI can extract the underlying decision patterns and encode them as simple, human-designed rules of comparable complexity to existing methods—suggesting that responsible AI adoption means using ML as a research tool rather than as a permanent system component when simpler alternatives suffice.

Explainability enables verification and trust in specialized domains: By making the ML model's reasoning transparent through SHAP analysis, the researchers could verify that the model was learning sensible mathematical principles rather than exploiting spurious patterns, which is particularly important in symbolic computation where correctness is critical and domain experts need confidence in algorithmic choices.

XAI can inspire innovation in established fields: The paper demonstrates that explainable AI isn't just about auditing existing systems—it can actively generate new insights and heuristics in mature mathematical fields, suggesting that XAI techniques have value as research instruments for responsible innovation, not merely as compliance or safety tools.