Beyond Similarity: Temporal Operator Attention for Time Series Analysis

• URL: http://arxiv.org/abs/2605.11287v1
• Date: Mon, 11 May 2026 22:13:53 GMT
• Title: Beyond Similarity: Temporal Operator Attention for Time Series Analysis
• Abstract summary: A persistent paradox in time-series forecasting is that structurally simple and linear models often outperform high-capacity Transformers.<n>We propose $textbf Operator Attention (TOA)$, a framework that augments attention with explicit learnable sequence-space operators.<n>To make dense $N times operators practical, we introduce a high-variance dropout mechanism that stabilizes training and prevents trivial memorization.
• Score: 5.084091872064936
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A persistent paradox in time-series forecasting is that structurally simple MLP and linear models often outperform high-capacity Transformers. We argue that this gap arises from a mismatch in the sequence-modeling primitive: while many time-series dynamics are governed by global temporal operators (e.g., filtering and harmonic structure), standard attention forms each output as a convex combination of inputs. This restricts its ability to represent signed and oscillatory transformations that are fundamental to temporal signal processing. We formalize this limitation as a simplex-constrained mixing bottleneck in softmax attention, which becomes especially restrictive for operator-driven time-series tasks. To address this, we propose $\textbf{Temporal Operator Attention (TOA)}$, a framework that augments attention with explicit, learnable sequence-space operators, enabling direct signed mixing across time while preserving input-dependent adaptivity. To make dense $N \times N$ operators practical, we introduce Stochastic Operator Regularization, a high-variance dropout mechanism that stabilizes training and prevents trivial memorization. Across forecasting, anomaly detection, and classification benchmarks, TOA consistently improves performance when integrated into standard backbones such as PatchTST and iTransformer, with particularly strong gains in reconstruction-heavy tasks. These results suggest that explicit operator learning is a key ingredient for effective time-series modeling.

Related papers

• Stabilizing Extrapolation in Looped Transformers via Learned Stochastic Stopping [56.14767235650558]
  Looped Transformers, which repeatedly apply a shared transformer block, are an architecturally natural fit for variable-length computation tasks.<n>We trace this variance to the spurious correlation in simple algorithmic tasks between sequence length and number of loops.<n>Our work suggests that "when to stop" should be treated as a training design choice, not merely an inference-time-allocation rule.
  arXiv  Detail & Related papers  (2026-06-29T08:58:09Z)
• Preserving Temporal Dynamics in Time Series Generation [0.2099922236065961]
  Time-series data augmentation plays a crucial role in regression-oriented forecasting tasks.<n>Existing approaches primarily focus on matching marginal data distributions.<n>We propose a model-agnostic Markov Chain Monte Carlo framework to mitigate distribution shift and preserve temporal dynamics.
  arXiv  Detail & Related papers  (2026-04-29T20:32:45Z)
• The Phasor Transformer: Resolving Attention Bottlenecks on the Unit Circle [0.09229852843814058]
  We introduce the textbfPhasor Transformer block, a phase-native alternative representing sequence states on the unit-circle manifold $S1$.<n> Stacking these blocks defines the textbfLarge Phasor Model (LPM), which learns stable global dynamics and achieves competitive forecasting behavior.<n>Our results establish an explicit efficiency-performance frontier, demonstrating that large-model scaling for time-series can emerge from geometry-constrained phase with deterministic global coupling.
  arXiv  Detail & Related papers  (2026-03-18T07:18:41Z)
• Patch-Level Tokenization with CNN Encoders and Attention for Improved Transformer Time-Series Forecasting [0.0]
  This paper proposes a two-stage forecasting framework that separates local temporal representation learning from global dependency modelling.<n>A convolutional neural network operates on fixed-length temporal patches to extract short-range temporal dynamics and non-linear feature interactions.<n> Token-level self-attention is applied during representation learning to refine these embeddings, after which a Transformer encoder models inter-patch temporal dependencies to generate forecasts.
  arXiv  Detail & Related papers  (2026-01-18T16:16:01Z)
• Provable In-Context Learning of Nonlinear Regression with Transformers [66.99048542127768]
  In-context learning (ICL) is the ability to perform unseen tasks using task specific prompts without updating parameters.<n>Recent research has actively explored the training dynamics behind ICL, with much of the focus on relatively simple tasks.<n>This paper investigates more complex nonlinear regression tasks, aiming to uncover how transformers acquire in-context learning capabilities.
  arXiv  Detail & Related papers  (2025-07-28T00:09:28Z)
• Sequence Complementor: Complementing Transformers For Time Series Forecasting with Learnable Sequences [5.244482076690776]
  We find that expressive capability of sequence representation is a key factor influencing Transformer performance in time forecasting.<n>We propose a novel attention mechanism with Sequence Complementors and prove feasible from an information theory perspective.
  arXiv  Detail & Related papers  (2025-01-06T03:08:39Z)
• Timer-XL: Long-Context Transformers for Unified Time Series Forecasting [67.83502953961505]
  We present Timer-XL, a causal Transformer for unified time series forecasting.<n>Based on large-scale pre-training, Timer-XL achieves state-of-the-art zero-shot performance.
  arXiv  Detail & Related papers  (2024-10-07T07:27:39Z)
• PRformer: Pyramidal Recurrent Transformer for Multivariate Time Series Forecasting [82.03373838627606]
  Self-attention mechanism in Transformer architecture requires positional embeddings to encode temporal order in time series prediction. We argue that this reliance on positional embeddings restricts the Transformer's ability to effectively represent temporal sequences. We present a model integrating PRE with a standard Transformer encoder, demonstrating state-of-the-art performance on various real-world datasets.
  arXiv  Detail & Related papers  (2024-08-20T01:56:07Z)
• Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patching [46.58170057001437]
  We introduce the Rough Transformer, a variation of the Transformer model that operates on continuous-time representations of input sequences.<n>We find that, on a variety of time-series-related tasks, Rough Transformers consistently outperform their vanilla attention counterparts.
  arXiv  Detail & Related papers  (2024-05-31T14:00:44Z)
• A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics [51.147876395589925]
  A non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time. A fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance.
  arXiv  Detail & Related papers  (2024-02-26T04:39:01Z)
• Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting [46.63798583414426]
  Long-term time series forecasting (LTSF) represents a critical frontier in time series analysis. Our study demonstrates, through both analytical and empirical evidence, that decomposition is key to containing excessive model inflation. Remarkably, by tailoring decomposition to the intrinsic dynamics of time series data, our proposed model outperforms existing benchmarks.
  arXiv  Detail & Related papers  (2024-01-22T13:15:40Z)
• Towards Long-Term Time-Series Forecasting: Feature, Pattern, and Distribution [57.71199089609161]
  Long-term time-series forecasting (LTTF) has become a pressing demand in many applications, such as wind power supply planning. Transformer models have been adopted to deliver high prediction capacity because of the high computational self-attention mechanism. We propose an efficient Transformerbased model, named Conformer, which differentiates itself from existing methods for LTTF in three aspects.
  arXiv  Detail & Related papers  (2023-01-05T13:59:29Z)

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.