Horizon Activation Mapping for Neural Networks in Time Series Forecasting

Neural networks for time series forecasting have relied on error metrics and architecture-specific interpretability approaches for model selection that don't apply across models of different families. To interpret forecasting models agnostic to the types of layers across state-of-the-art model families, we introduce Horizon Activation Mapping (HAM), a visual interpretability technique inspired by grad-CAM that uses gradient norm averages to study the horizon's subseries where grad-CAM studies attention maps over image data. We introduce causal and anti-causal modes to calculate gradient update norm averages across subseries at every timestep and lines of proportionality signifying uniform distributions of the norm averages. Optimization landscape studies with respect to changes in batch sizes, early stopping, train-val-test splits, univariate forecasting and dropouts are studied with respect to performances and subseries in HAM. Interestingly, batch size based differences in activities seem to indicate potential for existence of an exponential approximation across them per epoch relative to each other. Multivariate forecasting models including MLP-based CycleNet, N-Linear, N-HITS, self attention-based FEDformer, Pyraformer, SSM-based SpaceTime and diffusion-based Multi-Resolution DDPM over different horizon sizes trained over the ETTm2 dataset are used for HAM plots in this study. NHITS' neural approximation theorem and SpaceTime's exponential autoregressive activities have been attributed to trends in HAM plots over their training, validation and test sets. In general, HAM can be used for granular model selection, validation set choices and comparisons across different neural network model families.