Understanding Transformers for Time Series: Rank Structure, Flow-of-ranks, and Compressibility

• URL: http://arxiv.org/abs/2510.03358v1
• Date: Thu, 02 Oct 2025 23:56:17 GMT
• Title: Understanding Transformers for Time Series: Rank Structure, Flow-of-ranks, and Compressibility
• Authors: Annan Yu, Danielle C. Maddix, Boran Han, Xiyuan Zhang, Abdul Fatir Ansari, Oleksandr Shchur, Christos Faloutsos, Andrew Gordon Wilson, Michael W. Mahoney, Yuyang Wang,
• Abstract summary: We analyze Transformers through the lens of rank structure.<n>We show that time-series embeddings exhibit sharply decaying singular value spectra.<n>We prove that the associated $Q/K/V$ projections admit accurate low-rank approximations.
• Score: 90.894232610821
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Transformers are widely used across data modalities, and yet the principles distilled from text models often transfer imperfectly to models trained to other modalities. In this paper, we analyze Transformers through the lens of rank structure. Our focus is on the time series setting, where the structural properties of the data differ remarkably from those of text or vision. We show that time-series embeddings, unlike text or vision, exhibit sharply decaying singular value spectra: small patch sizes and smooth continuous mappings concentrate the data into low-rank subspaces. From this, we prove that the associated $Q/K/V$ projections admit accurate low-rank approximations, and that attention layers become compressible in proportion to the decay of the embedding spectrum. We introduce the concept of flow-of-ranks, a phenomenon by which nonlinear mixing across depth inflates the rank, explaining why early layers are most amenable to compression and why ranks grow with depth. Guided by these theoretical and empirical results, we use these insights to compress Chronos, a large time series foundation model, achieving a reduction of $65\%$ in inference time and $81\%$ in memory, without loss of accuracy. Our findings provide principled guidance for allocating width, depth, and heads in time series foundation models, and for exploiting their inherent compressibility.

Related papers

• From Frames to Sequences: Temporally Consistent Human-Centric Dense Prediction [22.291273919939957]
  We develop a scalable synthetic data pipeline that generates human frames and motion-aligned sequences with pixel-accurate depth, normals, and masks.<n>We train a unified ViT-based dense predictor that injects an explicit geometric human prior via CSE embeddings.<n>Our two-stage training strategy, combining static pretraining with dynamic sequence supervision, enables the model first to acquire robust spatial representations and then refine temporal consistency across motion-aligned sequences.
  arXiv  Detail & Related papers  (2026-02-02T05:28:58Z)
• Token Pruning for In-Context Generation in Diffusion Transformers [20.121758465381053]
  In-context generation significantly enhances Diffusion Transformers (DiTs) by enabling controllable image-to-image generation through reference examples.<n>Existing token reduction techniques, primarily tailored for text-to-image synthesis, fall short in this paradigm.<n>We introduce ToPi, a training-free token pruning framework tailored for in-context generation in DiTs.
  arXiv  Detail & Related papers  (2026-02-02T03:54:32Z)
• TensorLens: End-to-End Transformer Analysis via High-Order Attention Tensors [53.891337639229285]
  We introduce attentionLens, a novel formulation that captures the entire transformer as a single, input-dependent linear operator expressed through a high-order attention-interaction connection.<n>Our experiments demonstrate that the attention tensor can serve as a powerful foundation for developing tools aimed at interpretability and model understanding.
  arXiv  Detail & Related papers  (2026-01-25T19:21:25Z)
• Edit2Perceive: Image Editing Diffusion Models Are Strong Dense Perceivers [55.15722080205737]
  Edit2Perceive is a unified diffusion framework that adapts editing models for depth, normal, and matting.<n>Our single-step deterministic inference yields up to faster runtime while training on relatively small datasets.
  arXiv  Detail & Related papers  (2025-11-24T01:13:51Z)
• Tracing the Representation Geometry of Language Models from Pretraining to Post-training [22.18942718274405]
  We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training.<n>We uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining.<n>Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data.
  arXiv  Detail & Related papers  (2025-09-27T00:46:29Z)
• A Two-Phase Perspective on Deep Learning Dynamics [0.0]
  We propose that learning in deep neural networks proceeds in two phases: a rapid curve fitting phase followed by a slower compression or coarse graining phase.<n>We empirically show that the associated timescales align in two rather different settings.<n>We argue that the second phase is not actively optimized by standard training algorithms and may be unnecessarily prolonged.
  arXiv  Detail & Related papers  (2025-04-17T06:57:37Z)
• Localized Gaussians as Self-Attention Weights for Point Clouds Correspondence [92.07601770031236]
  We investigate semantically meaningful patterns in the attention heads of an encoder-only Transformer architecture.<n>We find that fixing the attention weights not only accelerates the training process but also enhances the stability of the optimization.
  arXiv  Detail & Related papers  (2024-09-20T07:41:47Z)
• Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Data [39.41800375686212]
  Diffusion Transformer, the backbone of Sora for video generation, successfully scales the capacity of diffusion models.<n>We make the first theoretical step towards bridging diffusion transformers for capturing spatial-temporal dependencies.<n>We highlight how the spatial-temporal dependencies are captured and affect learning efficiency.
  arXiv  Detail & Related papers  (2024-07-23T02:42:43Z)
• Super Consistency of Neural Network Landscapes and Learning Rate Transfer [72.54450821671624]
  We study the landscape through the lens of the loss Hessian. We find that certain spectral properties under $mu$P are largely independent of the size of the network. We show that in the Neural Tangent Kernel (NTK) and other scaling regimes, the sharpness exhibits very different dynamics at different scales.
  arXiv  Detail & Related papers  (2024-02-27T12:28:01Z)
• DepthFormer: Exploiting Long-Range Correlation and Local Information for Accurate Monocular Depth Estimation [50.08080424613603]
  Long-range correlation is essential for accurate monocular depth estimation. We propose to leverage the Transformer to model this global context with an effective attention mechanism. Our proposed model, termed DepthFormer, surpasses state-of-the-art monocular depth estimation methods with prominent margins.
  arXiv  Detail & Related papers  (2022-03-27T05:03:56Z)
• A Differential Attention Fusion Model Based on Transformer for Time Series Forecasting [4.666618110838523]
  Time series forecasting is widely used in the fields of equipment life cycle forecasting, weather forecasting, traffic flow forecasting, and other fields. Some scholars have tried to apply Transformer to time series forecasting because of its powerful parallel training ability. The existing Transformer methods do not pay enough attention to the small time segments that play a decisive role in prediction.
  arXiv  Detail & Related papers  (2022-02-23T10:33:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.