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arxiv: 2605.18534 · v1 · pith:XX367GU5new · submitted 2026-05-18 · 💻 cs.LG

XCTFormer: Leveraging Cross-Channel and Cross-Time Dependencies for Enhanced Time-Series Analysis

Israel Zexer , Omri Azencot This is my paper

Pith reviewed 2026-05-20 11:52 UTC · model grok-4.3

classification 💻 cs.LG
keywords multivariate time serieschannel-dependent modelingtransformer attentionimputationcross-channel dependenciesforecastinganomaly detection
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The pith

XCTFormer improves multivariate time-series modeling by using direct pairwise attention across both channels and time steps.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents XCTFormer as a channel-dependent transformer that addresses shortcomings in prior models by explicitly modeling dependencies between every pair of tokens from different variables and time points. It claims that earlier channel-dependent approaches relied on indirect strategies that missed key relationships, while channel-independent methods succeeded partly because of those modeling gaps. The new architecture adds a Cross-Relational Attention Block to increase the model's ability to express cross-channel and cross-temporal links, plus an optional compression step for efficiency. Experiments across three benchmarks show competitive or superior results on forecasting, imputation, and anomaly detection, with the largest gains on imputation. If correct, this suggests that careful direct attention can make channel-dependent designs reliably better than both indirect alternatives and independent baselines.

Core claim

XCTFormer operates in a token-to-token manner to capture pairwise dependencies across time and channels through its Cross-Relational Attention Block, combined with a data processing module and optional Dependency Compression Plugin, delivering state-of-the-art imputation accuracy that exceeds the second-best method by an average of 20.8 percent in MSE and 15.3 percent in MAE on standard benchmarks.

What carries the argument

The Cross-Relational Attention Block (CRAB), which computes explicit pairwise attention between all tokens spanning both temporal and channel dimensions to directly represent inter-variable and cross-time relationships.

If this is right

  • The model attains state-of-the-art results on imputation while remaining competitive on forecasting and anomaly detection.
  • Direct pairwise modeling across channels and time increases model capacity and expressiveness compared with indirect channel-dependent strategies.
  • The optional Dependency Compression Plugin allows the approach to scale without prohibitive compute demands on the evaluated tasks.
  • Explicit cross-relational attention can be added to transformer pipelines for multivariate sequences without assuming independence between variables.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same explicit pairwise token modeling could be tested on sequence tasks outside time series, such as video frames or sensor networks, where variables share a common physical context.
  • If the performance edge holds on larger or noisier datasets, practitioners might shift away from channel-independent defaults toward lightweight cross-channel attention layers.
  • The gap between indirect and direct dependency modeling suggests a broader design principle: when variables arise from a shared process, explicit cross terms should be the default starting point rather than an add-on.

Load-bearing premise

That an explicit token-to-token attention mechanism will capture the true underlying dependencies without introducing noise, overfitting, or computational costs that outweigh the gains on typical time-series benchmarks.

What would settle it

A new time-series dataset or benchmark in which XCTFormer fails to match or exceed the imputation accuracy of the current second-best method while also showing no clear advantage over strong channel-independent baselines.

Figures

Figures reproduced from arXiv: 2605.18534 by Israel Zexer, Omri Azencot.

Figure 1
Figure 1. Figure 1: XCTFormer model overview. Multivariate inputs are divided into patches per channel, tokenized, [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Potential cross-channel and temporal dependencies for token at channel 3 at time [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Interpretable Learned Mask Structure: The data permutation step places the patch sequence [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Analysis of learnable attention masks on ETTm1 dataset. Top row: 96 [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: DeCoP k sensitivity on Traffic (forecasting). Average MAE/MSE across horizons {96, 192, 336, 720} for different compressed representation sizes k. C.2 DeCoP compression size analysis As recalled, DeCoP compresses token-to-token interactions into a low-dimensional representation; the choice of k directly controls the expressive capacity of this bottleneck and thus can affect both accuracy and efficiency. In… view at source ↗
Figure 6
Figure 6. Figure 6: DeCoP k sensitivity on ECL (forecasting). Average MAE/MSE across horizons {96, 192, 336, 720} for different compressed representation sizes k. 0 50 100 150 200 250 k 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 Test MSE imputation - Electricity Test Validation 0 50 100 150 200 250 k 0.14 0.15 0.16 0.17 0.18 0.19 0.20 Test MAE imputation - Electricity 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085… view at source ↗
Figure 7
Figure 7. Figure 7: DeCoP k sensitivity on ECL (imputation). Average MAE/MSE across mask ratios {0.125, 0.25, 0.375, 0.5} for different compressed representation sizes k. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Patch length sensitivity on ETTm1 (forecasting). Average validation and test losses across horizons {96, 192, 336, 720} for different patch_len values with stride = patch_len/2. Following PatchTST’s (Nie et al., 2023) best practice, we kept the patching configuration fixed in most of our main experiments. For forecasting and anomaly detection, we used patch_len= 16 and stride= 8. For imputation, where the … view at source ↗
Figure 9
Figure 9. Figure 9: Patch length sensitivity on Weather (forecasting). Average validation and test losses across horizons {96, 192, 336, 720} for different patch_len values with stride = patch_len/2. 0.6 0.4 0.2 0.0 0.2 0.4 0.6 Value 0 1 2 Density Mask: Layer 1 [-0.618, 0.636] Mean=-0.0001 0.75 0.50 0.25 0.00 0.25 0.50 0.75 Value 0 1 2 Density Mask: Layer 2 [-0.708, 0.696] Mean=0.0018 0.050 0.025 0.000 0.025 0.050 0.075 Value… view at source ↗
Figure 10
Figure 10. Figure 10: Distributions of mask and signed-attention weights. Histograms of the learnable mask values M and the resulting activated attention weights. Results are shown for the forecasting task upon the ETTm1 dataset with lookback L=96 and horizon H=192. The left panel shows the distributions after the first training epoch, and the right panel after the final (10th) epoch. The distributions remain approximately Gau… view at source ↗
Figure 11
Figure 11. Figure 11: Scalability with respect to channel dimensionality ( [PITH_FULL_IMAGE:figures/full_fig_p030_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Scalability with respect to sequence length ( [PITH_FULL_IMAGE:figures/full_fig_p031_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Synthetic dataset visualization: source signals (var_1 through var_6) and the constructed target [PITH_FULL_IMAGE:figures/full_fig_p034_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Prediction examples on the synthetic dataset: ground-truth target vs. model forecasts for selected [PITH_FULL_IMAGE:figures/full_fig_p035_14.png] view at source ↗
read the original abstract

Multivariate time-series analysis involves extracting informative representations from sequences of multiple interdependent variables, supporting tasks such as forecasting, imputation, and anomaly detection. In real-world scenarios, these variables are typically collected from a shared context or underlying phenomenon, suggesting the presence of latent dependencies across time and channels that can be leveraged to improve performance. However, recent findings show that channel-independent (CI) models, which assume no inter-variable dependencies, often outperform channel-dependent (CD) models that explicitly model such relationships. This surprising result indicates that current CD models may not fully exploit their potential due to limitations in how dependencies are captured. Recent studies have revisited channel dependence modeling with various approaches; however, these methods often employ indirect modeling strategies, which can lead to meaningful dependencies being overlooked. To address this issue, we introduce XCTFormer, a transformer-based channel-dependent (CD) model that explicitly captures cross-temporal and cross-channel dependencies via an enhanced attention mechanism. The model operates in a token-to-token fashion, modeling pairwise dependencies between every pair of tokens across time and channels. The architecture comprises (i) a data processing module, (ii) a novel Cross-Relational Attention Block (CRAB) that increases capacity and expressiveness, and (iii) an optional Dependency Compression Plugin (DeCoP) that improves scalability. Through extensive experiments on three time-series benchmarks, we show that XCTFormer achieves strong results compared to widely recognized baselines; in particular, it attains state-of-the-art performance on the imputation task, outperforming the second-best method by an average of 20.8% in MSE and 15.3% in MAE.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces XCTFormer, a channel-dependent Transformer for multivariate time-series analysis. It uses a data-processing module, a Cross-Relational Attention Block (CRAB) that performs explicit token-to-token pairwise attention over cross-channel and cross-time tokens, and an optional Dependency Compression Plugin (DeCoP) for scalability. The central claim is that this explicit modeling overcomes limitations of prior indirect CD strategies and yields state-of-the-art imputation performance on three public benchmarks, outperforming the second-best method by 20.8% MSE and 15.3% MAE on average.

Significance. If the reported gains can be shown to stem specifically from the uncompressed token-to-token attention in CRAB rather than from the data-processing module, residual connections, or DeCoP, the work would supply concrete empirical counter-evidence to the recent preference for channel-independent models. It would also demonstrate that direct pairwise dependency modeling is feasible on standard benchmarks without prohibitive cost, potentially guiding future CD architectures.

major comments (2)
  1. [Abstract / §3 (Architecture)] Abstract and architecture description: the central claim attributes the 20.8% MSE / 15.3% MAE imputation gains to the explicit token-to-token pairwise attention inside the CRAB block. However, DeCoP is introduced as an optional plugin that improves scalability (implying reduction of the O((T·C)^2) cost). The manuscript does not state which configuration—full pairwise CRAB or the compressed DeCoP variant—was used to obtain the reported SOTA numbers. This distinction is load-bearing: if DeCoP was active, the results cannot be read as direct validation that explicit pairwise attention resolves the shortcomings of indirect CD modeling.
  2. [Experimental evaluation] Experimental section: the abstract asserts strong results and SOTA imputation performance, yet supplies no information on the exact baselines, ablation studies isolating CRAB, statistical significance tests, train/validation/test splits, or error bars across random seeds. These omissions prevent attribution of the quoted percentage improvements to the proposed mechanism and therefore undermine the empirical support for the main thesis.
minor comments (2)
  1. [§2 (Preliminaries)] The tokenization scheme that flattens time and channel dimensions into a single sequence could be illustrated with a small diagram or explicit indexing equations to aid readability.
  2. [Introduction] A few sentences in the introduction are overly long; splitting them would improve clarity without changing content.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us clarify key aspects of the work. We address each major comment below and have revised the manuscript accordingly to strengthen the presentation of our results and experimental details.

read point-by-point responses

  1. Referee: [Abstract / §3 (Architecture)] Abstract and architecture description: the central claim attributes the 20.8% MSE / 15.3% MAE imputation gains to the explicit token-to-token pairwise attention inside the CRAB block. However, DeCoP is introduced as an optional plugin that improves scalability (implying reduction of the O((T·C)^2) cost). The manuscript does not state which configuration—full pairwise CRAB or the compressed DeCoP variant—was used to obtain the reported SOTA numbers. This distinction is load-bearing: if DeCoP was active, the results cannot be read as direct validation that explicit pairwise attention resolves the shortcomings of indirect CD modeling.

    Authors: We thank the referee for identifying this critical point of clarification. The reported SOTA imputation results were obtained using the full CRAB block with uncompressed token-to-token pairwise attention; the DeCoP plugin was not activated. This choice was made because the three standard benchmarks have moderate dimensions (T and C) for which the quadratic complexity remains computationally feasible. DeCoP is presented as an optional module specifically for larger-scale settings. We have revised the abstract and Section 3 to explicitly state the configuration used for the main results and have added a brief discussion of DeCoP's role and when it would be applied. revision: yes

  2. Referee: [Experimental evaluation] Experimental section: the abstract asserts strong results and SOTA imputation performance, yet supplies no information on the exact baselines, ablation studies isolating CRAB, statistical significance tests, train/validation/test splits, or error bars across random seeds. These omissions prevent attribution of the quoted percentage improvements to the proposed mechanism and therefore undermine the empirical support for the main thesis.

    Authors: We agree that these details are essential for reproducibility and for rigorously attributing performance gains to the proposed mechanisms. In the revised version we have substantially expanded the experimental section to include: (i) the complete list of baselines with full citations, (ii) dedicated ablation studies that isolate the CRAB block (including variants with and without cross-relational attention), (iii) statistical significance tests (paired t-tests and Wilcoxon signed-rank tests across runs), (iv) explicit descriptions of the train/validation/test splits, and (v) error bars showing mean and standard deviation over five random seeds. These additions directly support the claim that the observed improvements stem from the explicit modeling in CRAB. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical architecture proposal with independent benchmark evaluation

full rationale

The paper introduces an architectural design (CRAB block for explicit token-to-token attention plus optional DeCoP) and supports its claims solely through experimental results on public time-series benchmarks. No derivation, equation, or first-principles argument reduces the reported performance gains to a quantity defined by the model's own fitted parameters or to a self-citation chain. The central performance numbers (20.8% MSE / 15.3% MAE on imputation) are presented as measured outcomes rather than as algebraic consequences of the model definition itself. Self-citations, if present, are not load-bearing for the empirical claims.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 2 invented entities

The central claim rests on the empirical superiority of explicit pairwise token modeling; the architecture introduces two new components whose effectiveness is demonstrated only through benchmark comparisons rather than theoretical guarantees.

free parameters (1)
  • Transformer hyperparameters (layers, heads, embedding size, etc.)
    Standard architectural choices that are tuned on the evaluation benchmarks to achieve the reported performance.
axioms (1)
  • domain assumption Multivariate time-series variables collected from a shared context exhibit latent cross-channel and cross-time dependencies that explicit modeling can exploit.
    Invoked in the opening paragraphs of the abstract as the motivation for moving beyond channel-independent baselines.
invented entities (2)
  • Cross-Relational Attention Block (CRAB) no independent evidence
    purpose: To increase model capacity by computing pairwise dependencies between every pair of tokens across time and channels.
    New architectural component introduced to address limitations of prior indirect dependency modeling.
  • Dependency Compression Plugin (DeCoP) no independent evidence
    purpose: To improve scalability of the full pairwise attention computation.
    Optional module proposed to mitigate computational cost of the token-to-token design.

pith-pipeline@v0.9.0 · 5829 in / 1566 out tokens · 50996 ms · 2026-05-20T11:52:13.003004+00:00 · methodology

discussion (0)

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