How Simple Can It Get? From Interpretable Equations to Readable Rules for Financial Decision Making

Scored Rule Sets for Interpretable Multiclass Classification

: Interpretable multiclass classification is studied across several research communities, but comparisons and conceptual integrations across rule sets, rule lists, decision trees, and evolutionary approaches are still limited. This paper addresses this gap by proposing scored rule sets as a unifying and interpretable hypothesis space. We first analyze structural relationships among established algorithms and identify indications of research siloing, especially between evolutionary and non-evolutionary lines of work. We then compare selected highly interpretable multiclass learners on UCI benchmark datasets. Beyond empirical comparison, we provide a formal definition of scored rule sets, show how they generalize classical rule-based models, and illustrate concrete transformations from logicGP, ExSTraCS, and CART representations. The resulting perspective clarifies when scored rule sets preserve interpretability while increasing modeling flexibility. Overall, the results support scored rule sets as a practically useful bridge between existing interpretable model families and as a basis for future cross-community method development.

Evidential Rule Learning for Interpretable Classification with Abstention

Interpretable classification often requires more than accurate predictions for real-life deployment: models should be transparent about the evidence behind their decisions and abstain when they cannot decide reliably. We introduce Fast Evidential Rule Learning (FERL), a method that learns interpretable, accurate fuzzy rule models whose outputs are evidential. Unlike post-hoc calibration, FERL's belief, plausibility, and abstention capabilities arise directly from the fuzzy memberships in a single deterministic pass, with no auxiliary head, held-out set, or repeated inference. Our theoretical analysis further shows that FERL is Lipschitz stable, which means that its evidential outputs vary smoothly with the input. Against state-of-the-art rule learners, FERL is statistically significantly more accurate across a 30 tabular-dataset benchmark ($+2.6\%$ average accuracy over the second best). Its native set predictions attain the best utility-discounted accuracy among credal classifiers ($u_{65}/u_{80}=0.80/0.83$ vs.\ $0.79/0.80$ for the naive credal classifier), at higher set coverage ($0.92$ vs.\ $\le0.82$). FERL also matches dedicated out-of-distribution detectors on tabular near-OOD detection ($77.7$ vs.\ $77.4$ AUROC for the strongest baseline). Under detector-class-disjoint concept-bottleneck evaluation, its it is within $2.3$ AUROC points of the strongest dedicated detector on both CUB and AwA2, while attaining the best AwA2 AUPR-Out ($68.3$) and novel-class rejection ($57.2$), while being able to name which attributes are anomalous.

Toward Defeasible Machine Learning: When Learned Rule Sets Become Defeasible Theories

Can LLM’s Pick Up Where GP Left off? Investigating LLM Mathematical Expression Simplification Capabilities

Symbolic regression seeks to discover interpretable mathematical expressions that describe the relationship between variables in a dataset. Genetic Programming remains the dominant approach for SR, however it is well established that GP is prone to producing complex expressions due to bloat. Post-hoc simplification of GP-derived mathematical expressions is therefore a practically important objective. In this work, we investigate the use of Large Language Models as a post-hoc simplification layer for GP-derived mathematical expressions, examining two prompting strategies; Few-Shot Prompting and In-Context Learning across two contemporary LLMs: GPT-5.4-mini and Nemotron-3-Super. We evaluate our approach across 91 datasets drawn from the Penn Machine Learning Benchmark, assessing simplification performance in terms of expression size, mean squared error (MSE), and coefficient of determination (R2). Our results demonstrate that LLMs are capable of reducing expression complexity without catastrophic accuracy loss in the majority of cases. All LLM approaches produce significantly shorter expressions than the GP baseline, with node count reductions ranging from approximately 1 to 7 nodes on average. The accuracy cost is statistically significant but small in practice, with rank-biserial effect sizes between 0.01 and 0.16. These findings suggest that LLMs represent a promising and complementary component within larger SR pipelines.

Confidence Estimation for Financial Vision-Language Models in Chart and Document Understanding

LVLMs are increasingly used to read financial charts, tables, and documents, where a single misread figure can move a decision and the most authoritative-looking answer is sometimes one the model produced without reading the exhibit. The operational question is therefore trust, not accuracy: which answers can be acted on, and which escalated to a reviewer. We evaluate seven confidence estimators, three inference-only and four trained internal probes, across five open-weight LVLMs and four conditions from three financial visual question-answering benchmarks, one bilingual; every probe is trained only on natural images and applied to finance without adaptation, so the results measure out-of-distribution transfer. Three findings hold. First, the scarce property is calibration, not ranking: the inference baselines rank correct above incorrect answers competitively but are badly overconfident, calibration error far above what a threshold can tolerate, and only the trained probes produce a thresholdable score. Second, reliability is structured rather than global, along two axes a practitioner can read directly: the best estimator shifts with both model and task, none leading more than eight of twenty (model, condition) cells, and a controlled bilingual contrast exposes an apparent language robustness as a composition artifact that dissolves once models are read one at a time. Third, cast as deferral under an error budget, how much can be safely automated is set first by the model's competence and only narrowed by its confidence, so deferral clears a real share of the easiest condition and almost none of the hardest, near zero at a strict 5% budget. Two trained probes carry the calibration a deferral policy needs, and among them only the grounding-aware one lowers its confidence on answers a model gives without using the figure, separating detected non-grounding from a fluent guess.

Explorations on Improving Interpretability of Decision Making Processes of Rule-Based Classifiers

Rule-based classifiers are often preferred over other types of learners due to the transparent mode in which decisions are made. Each decision rule includes in its premise conditions on attributes. When they are satisfied, the conclusion part of the rule comes into play and leads to assigning an object to a specific class. Following the classification process is relatively straightforward but can become more complex when the cardinality of rule set is high. Furthermore, when rules are induced from continuous data, the conditions listed belong to this domain as well, which makes them less general. This paper presents an illustrative example for the exploratory research methodology where the sets of rules are induced in the continuous input domain, but next, they are transformed by discretisation procedures, which results in a simplified representation of the data and knowledge patterns learnt. In addition, the rule sets are also filtered based on rankings obtained for variants of the transformed data. The processing results in reduced decision algorithms with categorical conditions. This simplification is advantageous in and of itself, but the experiments carried out on datasets in the stylometric domain show that it can also lead to enhanced performance of rule-based classifiers.