Selective Associative Memory: Rethinking the Representation Learner in Continuous-Time Time Series Forecasting

We identify selective associative memory as the unifying principle behind gated RNNs, attention, gated CNNs/MLPs, selective SSMs, and MoE architectures. These models differ not in their fundamental operation, but in four distinct, largely independent design dimensions: operating space, branch count, gating function type, and fusion method. Based on this framework, we derive the minimal gating requirements for time series forecasting: feature and time dimension gating only. We instantiate this minimal design in Alterum, a lightweight continuous-time model with about 10K trainable parameters, combining an exponential-scale Fourier Feature Embedding with a Temporal Decomposition Gated Network and a closed-form ridge regression head. Across multivariate, univariate, and few-shot forecasting, Alterum attains average MSE of 0.276, 0.094, and 0.330, respectively, and remains competitive under 15% random input masking. These results indicate that a framework-driven minimal design can substantially reduce parameter count and improve inference efficiency while maintaining competitive accuracy. Code is available at https://anonymous.4open.science/r/ALTERUM-E23B/.