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

arXiv: https://arxiv.org/abs/2606.04074 · HTML: https://mlsanity.com/paper/2606.04074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 32 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Token Merging: Your ViT But Faster](https://mlsanity.com/paper/2210.09461/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [AdaViT: Adaptive Tokens for Efficient Vision Transformer](https://mlsanity.com/paper/2112.07658/) (2021)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Mixture-of-Depths: Dynamically allocating compute in transformer-based language models](https://mlsanity.com/paper/2404.02258/) (2024)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Patch n' Pack: NaViT, a Vision Transformer for any Aspect Ratio and Resolution](https://mlsanity.com/paper/2307.06304/) (2023)
- [PonderNet: Learning to Ponder](https://mlsanity.com/paper/2107.05407/) (2021)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting](https://mlsanity.com/paper/2501.13041/) (2025)
- [Vision Transformers with Mixed-Resolution Tokenization](https://mlsanity.com/paper/2304.00287/) (2023)
- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [TimeMosaic: Temporal Heterogeneity Guided Time Series Forecasting via Adaptive Granularity Patch and Segment-wise Decoding](https://mlsanity.com/paper/2509.19406/) (2025)
- [Kairos: Toward Adaptive and Parameter-Efficient Time Series Foundation Models](https://mlsanity.com/paper/2509.25826/) (2025)
- [DualSG: A Dual-Stream Explicit Semantic-Guided Multivariate Time Series Forecasting Framework](https://mlsanity.com/paper/2507.21830/) (2025)
- [DART: Differentiable Dynamic Adaptive Region Tokenizer for Vision Foundation Models](https://mlsanity.com/paper/2506.10390/) (2025)
- [TimeSqueeze: Dynamic Patching for Efficient Time Series Forecasting](https://mlsanity.com/paper/2603.11352/) (2026)
- [Dynamic Tokenization via Reinforcement Patching: End-to-end Training and Zero-shot Transfer](https://mlsanity.com/paper/2603.26097/) (2026)

## Abstract (arXiv)

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.