Neural Network Models for Contextual Regression

Neural networks are a commonly used prediction tool in computer science and statistics. However, the barrier to entry of this interesting field remains high, particularly for classical statisticians trained in a frequentist perspective. In this letter, we demystify neural networks by describing networks that approximate a linear regression and describe common customizations that provide a foundation for further study.

Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed Differentiable Logic Networks (DLNs) to address these issues for tabular classification based on relaxing discrete logic into a differentiable form, thereby enabling gradient-based learning of networks built from binary logic operations. DLNs offer interpretable reasoning and substantially lower inference cost. We extend the DLN framework to supervised tabular regression. We first redesign the final output layer (the SumLayer) to support continuous targets. More critically, we find the original two-phase training procedure used for classification is suboptimal for regression, and thus develop a unified, single-stage optimization procedure. We also demonstrate that temperature annealing of the network's differentiable relaxations is decisive for achieving stable convergence and high accuracy. We evaluate the resulting model on 15 public regression benchmarks, comparing it with modern neural networks and classical regression baselines. Regression DLNs match or exceed baseline accuracy while preserving interpretability and fast inference. Our results show that DLNs are a viable, cost-effective alternative for regression tasks, especially where model transparency and computational efficiency are important.

Real-world time-series regression often involves non-stationarity, heteroscedasticity, and regime changes, under which recent prediction errors may contain structured information about local temporal mismatch between model predictions and observations. Learning how to represent and reuse these errors can therefore provide useful information for subsequent prediction. We introduce the Variability-Aware Recursive Neural Network (VARNN), a residual-aware architecture for supervised time-series regression that learns an explicit residual-memory state from recent prediction errors and uses it to condition subsequent predictions. Specifically, VARNN maps scalar prediction innovations into a learned nonlinear, vector-valued residual representation over a short context. Across nine datasets spanning energy, healthcare, and environmental domains, VARNN achieves lower test MSE than the compared static, lag-based, and sequence-model baselines. Targeted ablations further show that learned projected residual memory improves predictive accuracy over direct scalar residual feedback, supporting the benefit of a learned nonlinear representation of prediction deviations.