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 along the POD directions gives future increments; history-anchored inverse differencing recovers frequency windows. Learned causal deconvolution gives joint-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 tasks. Against these comparators, STRIDE wins 139-158 of 220 complete whole-horizon pairs and achieves system-weighted late-Energy win fractions of 73.6-78.5% on 190 multi-step pairs. Against DLinear, its system-weighted late-Energy win fraction is 77.3% across 72 paired multi-step tasks. Matched controls examine the contribution of the intermediate representation. On 64 independently initialized Aizawa trajectories, STRIDE lowers late Energy by 51.5%, 55.6%, 52.0%, and 24.2% against No-$D$, same-$q$ Markov, history-direct, and duration controls; all four prespecified comparisons pass Holm correction. These results connect transition-statistic prediction to continuous probabilistic forecasting, with substantial long-horizon gains in the matched Aizawa study.