Making Every Bit MATTER: Scale-Aware Forecasting on a Fixed Budget

As the volume of time-series data continues to grow, efficient data storage is becoming increasingly important, particularly for signals captured and processed at the edge. A fixed bits-per-value (BPV) representation provides a predictable storage footprint, allowing the representation to be matched to a fixed storage or communication budget. Existing lossless compression methods exploit redundancies in the signal, but make compression signal-dependent. At the same time, lossy compression methods that allow for setting a fixed BPV budget focus on reconstruction fidelity rather than on preserving useful information for downstream tasks. Meanwhile, modern time-series modeling pipelines are designed primarily for predictive performance and computational efficiency and generally assume access to the underlying raw signal rather than providing a compact representation for storage. To bridge this gap, we introduce MATTER, a time-series architecture that separates lightweight signal encoding from downstream modeling. A causal hierarchical tokenizer can run directly at the edge to convert the raw signal into a compact, fixed-rate discrete representation, producing a payload of approximately $4.39$ BPV in the default setting. A decoder-only Transformer then operates directly on these stored tokens without requiring access to the original full-precision signal. Under a shared downstream forecaster, MATTER's tokenizer yields a favorable forecasting-storage trade-off relative to generic lossy compression methods, isolating the utility of the representation itself. The complete $6.6$M-parameter MATTER model achieves competitive zero-shot forecasting while operating natively on the discrete representation.