How Simple Can It Get? From Interpretable Equations to Readable Rules for Financial Decision Making
Authors: Adia Lumadjeng, Ilker Birbil, Erman Acar
Organizations: University of Amsterdam Amsterdam, the Netherlands
Abstract
In regulated domains such as finance, a model that cannot be explained cannot be deployed, yet many interpretable classifiers defeat their own purpose by producing formulas with dozens of features that no regulator could read. We take the reverse direction. Starting from an interpretable classifier expressed as a single equation over the input features, we progressively simplify it into more readable forms, including a pruned monomial, a directional if--then rule, and the integer scorecards and tallies that finance already deploys. Because the equation is itself the predictive model rather than a post-hoc explanation we can directly quantify what is lost under each simplification. Across four financial datasets, we find that pruning is nearly free and that fidelity can erode faster than predictive performance, allowing simpler rules to remain effective classifiers without faithfully reproducing the original model. A human assessment shows that simplification improves perceived readability, while preferences for different representations vary by professional background. Beyond measuring these losses empirically, we show that some can be anticipated from the original model: we derive a bound on the change caused by pruning and predict how faithfully a rule retaining only the direction of each feature's effect preserves the original ranking.
Reinforcement learning policies are difficult to inspect, but interpreting them is a prerequisite for trustworthiness. Converting a trained policy into explicit decision-tree rules improves transparency and the resulting artifacts often remain too complex for human understanding. We present a pruning process that simplifies such rule-based policies while preserving task performance and making edits to the policy auditable. The process defines a small set of structural and usage-aware operators and evaluates candidate edits by re-executing the policy to measure return and interpretability proxies. This exposes an transformation process from complex to compact policy structures. We investigate this approach on classic control and MuJoCo benchmarks, where pruning traces reveal consistent interpretability improvements while maintaining high performance.
Inherently interpretable classifiers for tabular data typically rely on sparse features, rules, or patterns that users can inspect directly. The marginal feature-screening step common to these methods can discard variables whose predictive value emerges only through joint configurations with other variables. We present Interaction Aware Interpretable Machine Learning (IAIML), a framework that addresses this limitation through three coordinated mechanisms: adaptive per-feature discretization, finite-grid pairwise interaction scoring, and a partitioned explanation budget. Detected interactions are routed through one of two strategies: relaxing the screening filter so that interaction-supported variables enter the pattern search, or constructing explicit pair terms for a sparse downstream classifier. On a 40-dataset panel comprising 24 real-world tabular benchmarks and 16 synthetic interaction stress tests, evaluated under nested cross-validation, IAIML achieves mean AUC within 1.4 points of tuned gradient-boosted ensembles while requiring roughly 14--28 times fewer fitted explanation components. On datasets with strong pairwise interaction structure and low marginal signal, IAIML outperforms all baselines. Among compact interpretable methods, IAIML is comparable to RuleFit in AUC and component count and is less expensive to tune. EBM obtains a small but significant AUC advantage across the full panel, with a substantially larger lookup-table footprint. Performance degrades on datasets requiring higher-order interactions beyond the pairwise scope. Component-isolated ablations confirm that adaptive discretization and interaction-aware admission each contribute incrementally. These results support IAIML as a compact, interaction-aware framework appropriate for settings where bounded explanation size and controlled treatment of feature interactions are design requirements.
Interpretable machine learning is essential in high-stakes domains where decision-making requires accountability, transparency, and trust. While rule-based models offer global and exact interpretability, learning rule sets that simultaneously achieve high predictive performance and low, human-understandable complexity remains challenging. To address this, we introduce TT-Sparse, a flexible neural building block that leverages differentiable truth tables as nodes to learn sparse, effective connections. A key contribution of our approach is a new soft TopK operator with straight-through estimation for learning discrete, cardinality-constrained feature selection in an end-to-end differentiable manner. Crucially, the forward pass remains sparse, enabling efficient computation and exact symbolic rule extraction. As a result, each node (and the entire model) can be transformed exactly into compact, globally interpretable DNF/CNF Boolean formulas via Quine-McCluskey minimization. Extensive empirical results across 28 datasets spanning binary, multiclass, and regression tasks show that the learned sparse rules exhibit superior predictive performance with lower complexity compared to existing state-of-the-art methods.
Hans Farrell Soegeng, Sarthak Ketanbhai Modi, Thomas Peyrin