Adaptive Quantization in Generative Flow Networks for Probabilistic Sequential Prediction

Probabilistic time series forecasting, essential in domains like healthcare and neuroscience, requires models capable of capturing uncertainty and intricate temporal dependencies. While deep learning has advanced forecasting, generating calibrated probability distributions over continuous future values remains challenging. We introduce Temporal Generative Flow Networks (Temporal GFNs), adapting Generative Flow Networks (GFNs) – a powerful framework for generating compositional objects – to this sequential prediction task. GFNs learn policies to construct objects (eg. forecast trajectories) step-by-step, sampling final objects proportionally to a reward signal. However, applying GFNs directly to continuous time series necessitates addressing their inherently discrete action spaces and ensuring differentiability. Our framework tackles this by representing time series segments as states and sequentially generating future values via quantized actions chosen by a forward policy. We introduce two key innovations: (1) An adaptive, curriculum-based quantization strategy that dynamically adjusts the number of discretization bins based on reward improvement and policy entropy, balancing precision and exploration throughout training. (2) A straight-through estimator mechanism enabling the forward policy to output both discrete (hard) samples for trajectory construction and continuous (soft) samples for stable gradient propagation. Training utilizes a trajectory balance loss objective, ensuring flow consistency, augmented by an entropy regularizer. We provide rigorous theoretical bounds on the quantization error's impact and the adaptive factor's range. We demonstrate how Temporal GFNs offer a principled way to leverage the structured generation capabilities of GFNs for probabilistic forecasting in continuous domains.