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Structural Compositional Function Networks: Interpretable Functional Compositions for Tabular Discovery

Fang Li

TL;DR

StructuralCFN presents a principled, interpretable approach to tabular discovery by imposing a Structural Prior that treats each feature as contextually derived from others. It uses Manifold-Adaptive Structural Gating to learn both additive and inhibitory interaction physics, via a Dependency Layer and a Hybrid Functional Committee that yields a compact, symbolic representation of learned relations. Across extensive cross-validation and OpenML benchmarks, CFN achieves competitive performance with dramatically smaller parameter counts (roughly 300–2,500 parameters) and intrinsic symbolic interpretability, including recovery of governing laws in human-readable form. The work highlights a new Pareto frontier for Resource-Efficient Scientific AI, suitable for low-power IoT and clinical contexts, while noting limitations in high-entropy or boundary-discrete manifolds and suggesting hybrid extensions for broader applicability.

Abstract

Despite the ubiquity of tabular data in high-stakes domains, traditional deep learning architectures often struggle to match the performance of gradient-boosted decision trees while maintaining scientific interpretability. Standard neural networks typically treat features as independent entities, failing to exploit the inherent manifold structural dependencies that define tabular distributions. We propose Structural Compositional Function Networks (StructuralCFN), a novel architecture that imposes a Relation-Aware Inductive Bias via a differentiable structural prior. StructuralCFN explicitly models each feature as a mathematical composition of its counterparts through Differentiable Adaptive Gating, which automatically discovers the optimal activation physics (e.g., attention-style filtering vs. inhibitory polarity) for each relationship. Our framework enables Structured Knowledge Integration, allowing domain-specific relational priors to be injected directly into the architecture to guide discovery. We evaluate StructuralCFN across a rigorous 10-fold cross-validation suite on 18 benchmarks, demonstrating statistically significant improvements (p < 0.05) on scientific and clinical datasets (e.g., Blood Transfusion, Ozone, WDBC). Furthermore, StructuralCFN provides Intrinsic Symbolic Interpretability: it recovers the governing "laws" of the data manifold as human-readable mathematical expressions while maintaining a compact parameter footprint (300--2,500 parameters) that is over an order of magnitude (10x--20x) smaller than standard deep baselines.

Structural Compositional Function Networks: Interpretable Functional Compositions for Tabular Discovery

TL;DR

StructuralCFN presents a principled, interpretable approach to tabular discovery by imposing a Structural Prior that treats each feature as contextually derived from others. It uses Manifold-Adaptive Structural Gating to learn both additive and inhibitory interaction physics, via a Dependency Layer and a Hybrid Functional Committee that yields a compact, symbolic representation of learned relations. Across extensive cross-validation and OpenML benchmarks, CFN achieves competitive performance with dramatically smaller parameter counts (roughly 300–2,500 parameters) and intrinsic symbolic interpretability, including recovery of governing laws in human-readable form. The work highlights a new Pareto frontier for Resource-Efficient Scientific AI, suitable for low-power IoT and clinical contexts, while noting limitations in high-entropy or boundary-discrete manifolds and suggesting hybrid extensions for broader applicability.

Abstract

Despite the ubiquity of tabular data in high-stakes domains, traditional deep learning architectures often struggle to match the performance of gradient-boosted decision trees while maintaining scientific interpretability. Standard neural networks typically treat features as independent entities, failing to exploit the inherent manifold structural dependencies that define tabular distributions. We propose Structural Compositional Function Networks (StructuralCFN), a novel architecture that imposes a Relation-Aware Inductive Bias via a differentiable structural prior. StructuralCFN explicitly models each feature as a mathematical composition of its counterparts through Differentiable Adaptive Gating, which automatically discovers the optimal activation physics (e.g., attention-style filtering vs. inhibitory polarity) for each relationship. Our framework enables Structured Knowledge Integration, allowing domain-specific relational priors to be injected directly into the architecture to guide discovery. We evaluate StructuralCFN across a rigorous 10-fold cross-validation suite on 18 benchmarks, demonstrating statistically significant improvements (p < 0.05) on scientific and clinical datasets (e.g., Blood Transfusion, Ozone, WDBC). Furthermore, StructuralCFN provides Intrinsic Symbolic Interpretability: it recovers the governing "laws" of the data manifold as human-readable mathematical expressions while maintaining a compact parameter footprint (300--2,500 parameters) that is over an order of magnitude (10x--20x) smaller than standard deep baselines.
Paper Structure (35 sections, 10 equations, 2 figures, 6 tables)

This paper contains 35 sections, 10 equations, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Methodology
  4. The Structural Prior
  5. Manifold-Adaptive Structural Gating
  6. Stage 1: The Dependency Layer
  7. Stage 2: Hybrid Functional Committee Aggregation
  8. Structure Sparsity via $L_1$ Penalty
  9. Experiments
  10. Experimental Setup
  11. Performance and Efficiency Analysis
  12. Extended OpenML Benchmarking
  13. Computational Efficiency and Parameter Counting
  14. Scientific Scalability & Discovery Potential
  15. Scale vs. Transparency: Comparison with High-Capacity SOTA
  16. ...and 20 more sections

Figures (2)

  • Figure 1: StructuralCFN Architecture. The model learns relational contexts $Z$ through Adaptive Gated nodes (left) and performs final prediction via a Hybrid Functional Committee with a Residual Linear Bypass (right).
  • Figure 2: Learned Dependency Matrix for the Diabetes dataset. Brighter cells indicate stronger directed influence ($M_{ij}$). The matrix reveals that S2 (LDL Cholesterol) acts as a primary structural driver for S5 (Triglycerides) and S6 (Glucose), a finding that aligns with clinical metabolic models.