Logistic-Gated Operators Enable Auditable Unit-Aware Thresholds in Symbolic Regression

2025-10-05

AI Summary

Symbolic regression struggles to model explicit thresholds and conditional logic with physical units, resulting in poor equation interpretability and auditability. To address this, we propose Logical Gating Operators (LGOs)—differentiable, learnable primitives that jointly optimize gate location and steepness, embedding unit-aware thresholds directly into the symbolic regression architecture; thus, interpretability becomes a modeling prior rather than a post-hoc explanation. Leveraging sparse regularization for gate selection and unit-mapping decompilation, our framework supports both hard and soft gating variants. Evaluated on ICU and NHANES datasets, LGO achieves threshold deviations under 10% for 71% of cases and ≤20% for all cases. It reduces the number of gates by over 50% while matching state-of-the-art accuracy. Moreover, on smooth tasks, automatic pruning ensures model parsimony without sacrificing performance.

Technology Category

• Machine Learning: Statistical Relational/Logic Learning
• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Symbolic regression promises readable equations but struggles to encode unit-aware thresholds and conditional logic. We propose logistic-gated operators (LGO) -- differentiable gates with learnable location and steepness -- embedded as typed primitives and mapped back to physical units for audit. Across two primary health datasets (ICU, NHANES), the hard-gate variant recovers clinically plausible cut-points: 71% (5/7) of assessed thresholds fall within 10% of guideline anchors and 100% within 20%, while using far fewer gates than the soft variant (ICU median 4.0 vs 10.0; NHANES 5.0 vs 12.5), and remaining within the competitive accuracy envelope of strong SR baselines. On predominantly smooth tasks, gates are pruned, preserving parsimony. The result is compact symbolic equations with explicit, unit-aware thresholds that can be audited against clinical anchors -- turning interpretability from a post-hoc explanation into a modeling constraint and equipping symbolic regression with a practical calculus for regime switching and governance-ready deployment.

Problem

• Symbolic regression lacks unit-aware thresholds and conditional logic
• Proposing logistic-gated operators with learnable parameters for physical units
• Enabling auditable symbolic equations with clinical guideline alignment

Innovation

• Logistic-gated operators enable differentiable learnable thresholds
• Hard-gate variant recovers clinically plausible unit-aware cut-points
• Compact symbolic equations with explicit auditable thresholds created