Synapse: Adaptive Arbitration of Complementary Expertise in Time Series Foundational Models

TL;DR

This work addresses the challenge that a single Time Series Foundational Model (TSFM) cannot universally forecast diverse, non-stationary time series. It formalizes a dynamic arbitration problem over a pool of TSFMs and introduces Synapse, which combines predictive sampling with forward-simulation-based weight adaptation to produce an arbitrated predictive distribution at each timestamp. An empirical Oracle demonstrates substantial potential gains from dynamic arbitration, and extensive experiments on the GIFT-Eval benchmark show that Synapse consistently outperforms individual TSFMs and strong ensemble baselines, with advantages growing at longer horizons. The results suggest a paradigm shift toward adaptive ensembles of specialized TSFMs, where arbitration, not a single strong model, drives real-world robustness and performance.

Abstract

Pre-trained Time Series Foundational Models (TSFMs) represent a significant advance, capable of forecasting diverse time series with complex characteristics, including varied seasonalities, trends, and long-range dependencies. Despite their primary goal of universal time series forecasting, their efficacy is far from uniform; divergent training protocols and data sources cause individual TSFMs to exhibit highly variable performance across different forecasting tasks, domains, and horizons. Leveraging this complementary expertise by arbitrating existing TSFM outputs presents a compelling strategy, yet this remains a largely unexplored area of research. In this paper, we conduct a thorough examination of how different TSFMs exhibit specialized performance profiles across various forecasting settings, and how we can effectively leverage this behavior in arbitration between different time series models. We specifically analyze how factors such as model selection and forecast horizon distribution can influence the efficacy of arbitration strategies. Based on this analysis, we propose Synapse, a novel arbitration framework for TSFMs. Synapse is designed to dynamically leverage a pool of TSFMs, assign and adjust predictive weights based on their relative, context-dependent performance, and construct a robust forecast distribution by adaptively sampling from the output quantiles of constituent models. Experimental results demonstrate that Synapse consistently outperforms other popular ensembling techniques as well as individual TSFMs, demonstrating Synapse's efficacy in time series forecasting.

Figures (9)

• Figure 1: (Left) Oracle arbitrator's model selection frequency across seven different domains of GIFT-Eval aksu2024gift. These values represent the percentage of timestamps each model was selected by Oracle as the optimal predictor across different domains. (Right) Oracle model switching frequency by domain and forecast horizon, expressed as an average percentage of the total prediction length. These demonstrate the dynamic nature of model performance, showing that different TSFMs provide the optimal prediction at different timestamps - highlighting the necessity of an arbitration approach.
• Figure 2: GIFT-Eval Performance comparison (MASE | CRPS) of the Oracle Arbitrator against individual constituent TSFMs. Oracle selector can outperform all other constituent models by a large margin, demonstrating the efficacy of a strong arbitrator.
• Figure 3: Overview of Synapse. It takes a Historical Context Input (left), which is then fed into a pool of $N$ diverse Time Series Foundational Models (TSFMs). Each model produces its probabilistic forecast. These individual forecasts are then fed into the core arbitration mechanism. At each timestep $t$, a set of Dynamic Weights$\{w_1, \ldots, w_N\}$ is applied to the corresponding model forecasts, which is leveraged in the predictive sampling and in subsequent construction of the final Arbitrated Forecast Distribution for that timestep. This entire process is governed by a Dynamic Weight Adaptation via Forward Simulation loop: the arbitrator's own forecast from step previous step is used as a simulated observation, which is then used to update a rolling performance window, which recalculates the CRPS for all models to determine the dynamic weights $\{w_{i, t+1}\}$ for the next timestep.
• Figure 4: Pairwise Win/Loss performance comparison of Synapse against constituent individual models and Quantile Median/Mean ensemble baselines. Besides strong overall performance, comparative analysis demonstrates the overall consistency of Synapse.
• Figure 5: Performance of all models across different forecast horizons (Short, Medium, Long). Synapse consistently shows strong and often superior performance for both CRPS and MASE, particularly as the forecast horizon increases.