Adaptive Patching Is Harder Than It Looks For Time-Series Forecasting

• URL: http://arxiv.org/abs/2606.04074v1
• Date: Tue, 02 Jun 2026 15:49:06 GMT
• Title: Adaptive Patching Is Harder Than It Looks For Time-Series Forecasting
• Abstract summary: Under conditions a content-adaptive patching operator should outperform a tuned uniform one.<n>We show that adaptive patching should be evaluated against a tuned uniform baseline.
• Score: 11.469701541304737
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Adaptive patching is a recent and compelling proposal for time-series Transformers: allocate finer patches where the sequence looks locally informative. This paper asks under what conditions a content-adaptive patching operator should outperform a tuned uniform one. Local heterogeneity alone is not enough: under pointwise forecasting losses, a complex-looking region is not automatically one where finer patching reduces the loss. We model patching as a budgeted bitrate allocation and derive an explicit threshold that a dynamic patching rule must satisfy to beat a well-tuned uniform baseline, then bound the achievable improvement both locally (a quadratic surrogate) and globally (a strong-convexity bound under the model's assumptions). Two structural results follow: without a coupling constraint, scalar local complexity cannot produce a non-uniform optimum under a common loss landscape; and once the backbone is trained to its representation-aware optimum, the alignment gain collapses around a well-tuned uniform patch size. To test these predictions, we run a controlled isolation study on three representative architectures, replacing each adaptive mechanism with a uniform patch-size sweep while keeping the backbone, data, and training protocol fixed. On standard long-horizon forecasting benchmarks, the validation-selected uniform baseline is competitive with the dynamic counterpart, with per-setting effects concentrated near zero and no consistent directional advantage once results are aggregated by dataset. The larger gains we do observe are method- and dataset-specific. Adaptive patching should therefore be evaluated against a tuned uniform baseline; its value depends on whether a cheap and reliable routing signal can identify where finer patches actually reduce forecasting loss.

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