# Geometry-Conditioned Fixed-Scaffold Encoders for Time-Warp Robust Sequence Retrieval

arXiv: https://arxiv.org/abs/2609.36809 · HTML: https://mlsanity.com/paper/2609.36809/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [ColBERT: Efficient and Effective Passage Search via Contextualized Late Interaction over BERT](https://mlsanity.com/paper/2004.12832/) (2020)
- [AST: Audio Spectrogram Transformer](https://mlsanity.com/paper/2104.01778/) (2021)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [Attention-Based Models for Speech Recognition](https://mlsanity.com/paper/1506.07503/) (2015)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [Time-Series Representation Learning via Temporal and Contextual Contrasting](https://mlsanity.com/paper/2106.14112/) (2021)
- [ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels](https://mlsanity.com/paper/1910.13051/) (2019)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding](https://mlsanity.com/paper/2106.00750/) (2021)
- [MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification](https://mlsanity.com/paper/2012.08791/) (2020)
- [CLOCS: Contrastive Learning of Cardiac Signals Across Space, Time, and Patients](https://mlsanity.com/paper/2005.13249/) (2020)
- [SSAST: Self-Supervised Audio Spectrogram Transformer](https://mlsanity.com/paper/2110.09784/) (2021)
- [CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecasting](https://mlsanity.com/paper/2202.01575/) (2022)
- [Monotonic Chunkwise Attention](https://mlsanity.com/paper/1712.05382/) (2017)
- [D3TW: Discriminative Differentiable Dynamic Time Warping for Weakly Supervised Action Alignment and Segmentation](https://mlsanity.com/paper/1901.02598/) (2019)
- [Soft Contrastive Learning for Time Series](https://mlsanity.com/paper/2312.16424/) (2023)
- [Learning Soft-Attention Models for Tempo-invariant Audio-Sheet Music Retrieval](https://mlsanity.com/paper/1906.10996/) (2019)
- [Deep Declarative Dynamic Time Warping for End-to-End Learning of Alignment Paths](https://mlsanity.com/paper/2303.10778/) (2023)
- [Dynamic Dynamic Time Warping](https://mlsanity.com/paper/2310.18128/) (2023)
- [FlexiAST: Flexibility is What AST Needs](https://mlsanity.com/paper/2307.09286/) (2023)
- [Diffeomorphic Temporal Alignment Nets for Time-series Joint Alignment and Averaging](https://mlsanity.com/paper/2502.06591/) (2025)

## Abstract (arXiv)

Embedding-based retrieval is attractive for long sequence collections because each item can be encoded once and searched by nearest-neighbor ranking. The difficulty is that the objects being indexed are often observed under a noncanonical clock: cardiac cycles stretch with rate, speech changes with tempo, and sensor traces reach comparable states at different speeds. This paper studies a specific source of instability in patch-based encoders for this regime. If patch boundaries are chosen from signal geometry, then the tokenization can change under the same temporal deformation that the representation is expected to tolerate. We propose GeoPatch, a fixed-scaffold patch encoder that keeps token support independent of geometry and uses slope, curvature, acceleration, affine-residual, and confidence descriptors only as continuous conditioning variables. The design turns boundary variation into feature modulation: geometry can change the embedding through a controlled pathway, but it cannot change the number, order, or support of local tokens. We formalize this distinction through a mechanism-level stability analysis that separates boundary drift, affine timing variation, confidence-weighted geometry perturbation, and retrieval-margin effects. The same local tokens support global embedding retrieval and late-interaction scoring, so the scoring rule can be matched to the evaluation protocol. Across ECG, speech, and multivariate time-series retrieval tasks, GeoPatch improves early-rank retrieval under timing variation while exposing a clear trade-off between local surface matching and strict non-overlap retrieval.