Twisted Convolutional Networks (TCNs): Enhancing Feature Interactions for Non-Spatial Data Classification

TL;DR

The paper introduces Twisted Convolutional Networks (TCNs), a framework for classifying non-spatial, unordered data by explicitly forming feature interactions through twisted convolution. By operating on subsets of features and using either full multiplicative products or sums of pairwise products, TCNs simulate polynomial-like expansions within a trainable neural architecture, enabling higher-order interactions without relying on feature order. Empirical results across five diverse datasets show that TCNs outperform standard CNNs, ResNets, GNNs, DeepSets, and SVM in most settings, with notable gains in robustness and interpretability via interaction attributions. The authors also provide practical guidance on hyperparameter choices (notably the interaction order C) and demonstrate a projection-based residual design that improves efficiency while preserving accuracy, making TCNs a compelling option for tabular and other non-spatial data tasks.

Abstract

Twisted Convolutional Networks (TCNs) are proposed as a novel deep learning architecture for classifying one-dimensional data with arbitrary feature order and minimal spatial relationships. Unlike conventional Convolutional Neural Networks (CNNs) that rely on structured feature sequences, TCNs explicitly combine subsets of input features through theoretically grounded multiplicative and pairwise interaction mechanisms to create enriched representations. This feature combination strategy, formalized through polynomial feature expansions, captures high-order feature interactions that traditional convolutional approaches miss. We provide a comprehensive mathematical framework for TCNs, demonstrating how the twisted convolution operation generalizes standard convolutions while maintaining computational tractability. Through extensive experiments on five benchmark datasets from diverse domains (medical diagnostics, political science, synthetic data, chemometrics, and healthcare), we show that TCNs achieve statistically significant improvements over CNNs, Residual Networks (ResNet), Graph Neural Networks (GNNs), DeepSets, and Support Vector Machine (SVM). The performance gains are validated through statistical testing. TCNs also exhibit superior training stability and generalization capabilities, highlighting their robustness for non-spatial data classification tasks.

Figures (3)

• Figure 1: Comparison of feature–interaction mechanisms. Left: Twisted Convolutional Network (TCN) forms high‑order feature interactions by explicitly combining arbitrary feature subsets (illustrated with a pairwise combination size $k=2$). Right: In a standard CNN, a convolutional kernel of the same size $k=2$ slides across an ordered feature map, capturing only local patterns. TCN therefore dispenses with any assumption of spatial locality or feature order.
• Figure 2: Overall pipeline of the proposed Twisted Convolutional Network (TCN). The model first generates explicit feature combinations in the feature combination layer, refines them via the feature interaction and transformation modules, and finally feeds the transformed representations through batch‑normalized dense blocks with residual connections, dropout, and softmax classification.
• Figure 3: Training and validation accuracy over epochs for TCN, GNN, CNN, and ResNet on the Breast Cancer dataset. TCN exhibits minimal oscillation and a small train–validation gap, demonstrating robust generalization.