Dynamic Tokenization via Reinforcement Patching: End-to-end Training and Zero-shot Transfer

Transformer-based time series foundation models face a fundamental trade-off in choice of tokenization: point-wise embeddings preserve temporal fidelity but scale poorly with sequence length, whereas fixed-length patching improves efficiency by imposing uniform boundaries that may disrupt natural transitions and blur informative local dynamics. In order to address these limitations, we introduce TimeSqueeze, a dynamic patching mechanism that adaptively selects patch boundaries within each sequence based on local signal complexity. TimeSqueeze first applies a lightweight state-space encoder to extract full-resolution point-wise features, then performs content-aware segmentation by allocating short patches to information-dense regions and long patches to smooth or redundant segments. This variable-resolution compression preserves critical temporal structure while substantially reducing the token sequence presented to the Transformer backbone. Specifically for large-scale pretraining, TimeSqueeze attains up to 20x faster convergence and 8x higher data efficiency compared to equivalent point-token baselines. Experiments across long-horizon forecasting benchmarks show that TimeSqueeze consistently outperforms comparable architectures that use either point-wise tokenization or fixed-size patching.

Adaptive patching has been proposed for time-series forecasting: allocate finer patches where the sequence looks locally informative. We compare three adaptive patching methods with tuned uniform counterparts that use one fixed patch size throughout the input, while preserving each method's backbone family and shared training protocol. Across the evaluated long-horizon benchmarks, we observe mostly small accuracy differences and no consistent advantage for adaptive patching; uniform variants generally train faster and avoid adaptive routing at inference. Motivated by these observations, we develop a theoretical framework for budgeted patch allocation through a common resolution-density representation of uniform, nonuniform, and overlapping layouts, independently of the patching rule. Within a separable shared-loss model, we derive an exact criterion for when nonuniform allocation improves on uniform allocation at the same budget. We characterize modeled gains locally through a quadratic surrogate and bound them globally under strong convexity and a bounded loss derivative. The analysis distinguishes where resolution is placed from how much it is redistributed: even an allocation that correctly ranks regions by their weights can redistribute too much resolution and increase modeled loss. Without coupling across time, positive regional weights preserve the minimizers of the shared loss. When the shared loss has a common minimizing rate, the remaining absolute headroom for improvement tends to zero as the uniform rate approaches it. These results characterize the roles of regional weighting, placement, and redistribution strength under the stated model. The empirical findings support evaluating adaptive patching against a tuned uniform baseline and weighing any accuracy gain against the additional training and inference cost of adaptive routing.

Accurate forecasting of multivariate time series remains challenging due to the need to capture both short-term fluctuations and long-range temporal dependencies. Transformer-based models have emerged as a powerful approach, but their performance depends critically on the representation of temporal data. Traditional point-wise representations preserve individual time-step information, enabling fine-grained modeling, yet they tend to be computationally expensive and less effective at modeling broader contextual dependencies, limiting their scalability to long sequences. Patch-wise representations aggregate consecutive steps into compact tokens to improve efficiency and model local temporal dynamics, but they often discard fine-grained temporal details that are critical for accurate predictions in volatile or complex time series. We propose IPatch, a multi-resolution Transformer architecture that integrates both point-wise and patch-wise tokens, modeling temporal information at multiple resolutions. Experiments on 7 benchmark datasets demonstrate that IPatch consistently improves forecasting accuracy, robustness to noise, and generalization across various prediction horizons compared to single-representation baselines.