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

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.

PRISM: Lightweight Multivariate Time-Series Classification through Symmetric Multi-Resolution Convolutional Layers

Multivariate time-series classification is pivotal in domains ranging from wearable sensing to biomedical monitoring. Despite recent advances, Transformer- and CNN-based models often remain computationally heavy, offer limited frequency diversity, and require extensive parameter budgets. We propose PRISM (Per-channel Resolution-Informed Symmetric Module), a convolutional-based feature extractor that applies symmetric finite-impulse-response (FIR) filters at multiple temporal scales, independently per channel. This multi-resolution, per-channel design yields highly frequency-selective embeddings without any inter-channel convolutions, greatly reducing model size and complexity. Across human-activity, sleep-stage and biomedical benchmarks, PRISM, paired with lightweight classification heads, matches or outperforms leading CNN and Transformer baselines, while using roughly an order of magnitude fewer parameters and FLOPs. By uniting classical signal processing insights with modern deep learning, PRISM offers an accurate, resource-efficient solution for multivariate time-series classification.