STRIDE: State-Transition Representation via Increment Dynamics and Evolution

We introduce STRIDE (State-Transition Representation via Increment Dynamics and Evolution), which defines states through derivative fingerprints and learns local functions for state transitions (qpairs), recasting continuous forecasting as transition prediction. Trailing convolution windows estimate local joint-transition frequencies, whose lagged differences form a high-dimensional increment trajectory. Proper orthogonal decomposition (POD) gives coordinate paths, jointly forecast by sparse dynamics with memory. Recombining their forecasts and applying history-anchored inversion recovers future transition distributions; sampled state paths select local functions to generate continuous forecasts. Three-seed experiments compare STRIDE against fourteen baselines across nine benchmark families. Five independent Markov and hidden-state baselines cover all 230 evaluated tasks, with 220 complete whole-horizon pairs. Against these comparators, system-weighted late-Energy win fractions range from 73.6% to 78.5% on 190 multi-step pairs; against DLinear, the fraction is 77.3% on 72 paired multi-step tasks. Matched controls examine the intermediate representation. On 64 independently initialized Aizawa trajectories, late-Energy reductions against four matched controls range from approximately 24% to 56%, with all four prespecified contrasts passing Holm correction. These results connect transition-statistic prediction to continuous probabilistic forecasting, with substantial long-horizon gains in the matched Aizawa study.