Kinematic Tokenization: Optimization-Based Continuous-Time Tokens for Learnable Decision Policies in Noisy Time Series

Abstract: Transformers are designed for discrete tokens, yet many real-world signals are continuous processes observed through noisy sampling. Discrete tokenizations (raw values, patches, finite differences) can be brittle in low signal-to-noise regimes, especially when downstream objectives impose asymmetric penalties that rationally encourage abstention. We introduce Kinematic Tokenization, an optimization-based continuous-time representation that reconstructs an explicit spline from noisy measurements and tokenizes local spline coefficients (position, velocity, acceleration, jerk). This is applied to financial time series data in the form of asset prices in conjunction with trading volume profiles. Across a multi-asset daily-equity testbed, we use a risk-averse asymmetric classification objective as a stress test for learnability. Under this objective, several discrete baselines collapse to an absorbing cash policy (the Liquidation Equilibrium), whereas the continuous spline tokens sustain calibrated, non-trivial action distributions and stable policies. These results suggest that explicit continuous-time tokens can improve the learnability and calibration of selective decision policies in noisy time series under abstention-inducing losses.