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Omni-Scale CNNs: a simple and effective kernel size configuration for time series classification

Wensi Tang, Guodong Long, Lu Liu, Tianyi Zhou, Michael Blumenstein, Jing Jiang

arXiv:2002.10061v3cs.LGstat.ML

TL;DR

Time-series classifiers need suitable receptive-field sizes, but the best size varies across datasets and conventional scale search is costly. The paper introduces the prime-kernel OS-block to cover receptive-field sizes automatically, and reports state-of-the-art performance across four benchmarks while matching models with searched optimal scales.

  • Problem

    Receptive-field size strongly affects 1D-CNN performance, yet its optimal value varies across datasets and finding it requires costly scale search.

  • Method

    The OS-block uses prime-number kernel sizes, with a final 1-and-2 kernel layer, to cover receptive-field sizes according to the time-series length.

  • Results

    The OS-block achieved consistent state-of-the-art performance on four time-series classification benchmarks and matched models using the best receptive-field size.

  • Takeaways & Limitations

    A simple 1D-CNN using the OS-block can capture optimal time scales without feature-extraction scale tuning across datasets from multiple domains.

  • Takeaways & Limitations

    The paper mainly targets classic one-dimensional time-series classification, while its extension to time-series vision tasks is presented as future scope.

Abstract

from arXiv · show

The Receptive Field (RF) size has been one of the most important factors for One Dimensional Convolutional Neural Networks (1D-CNNs) on time series classification tasks. Large efforts have been taken to choose the appropriate size because it has a huge influence on the performance and differs significantly for each dataset. In this paper, we propose an Omni-Scale block (OS-block) for 1D-CNNs, where the kernel sizes are decided by a simple and universal rule. Particularly, it is a set of kernel sizes that can efficiently cover the best RF size across different datasets via consisting of multiple prime numbers according to the length of the time series. The experiment result shows that models with the OS-block can achieve a similar performance as models with the searched optimal RF size and due to the strong optimal RF size capture ability, simple 1D-CNN models with OS-block achieves the state-of-the-art performance on four time series benchmarks, including both univariate and multivariate data from multiple domains. Comprehensive analysis and discussions shed light on why the OS-block can capture optimal RF sizes across different datasets. Code available [https://github.com/Wensi-Tang/OS-CNN]

1 INTRODUCTION

Time-series classifiers must capture dataset-dependent time scales, yet receptive-field choices strongly affect accuracy and no single size works consistently. The OS-block addresses this by automatically covering receptive fields with a universal prime-kernel rule, achieving strong results across diverse benchmarks.

  • Time-series data contains signals at varied time scales because sources and recording settings differ.
  • Traditional methods expend substantial computation searching for appropriate feature-extraction scales, such as subsequence lengths.For a dataset of length 512, one shapelet method tried 71 subsequence lengths.
  • Changing receptive-field size can alter accuracy by more than 5% on many UCR 85 datasets, while no size consistently performs best.
  • The OS-block automatically selects prime-based kernels to cover receptive fields across scales without complicated searching.Its maximum prime is chosen according to the time-series length.
  • OS-block models achieved consistent state-of-the-art performance on four benchmarks spanning healthcare, human activity, speech, and spectrum domains.The models used unified training hyperparameters and matched the performance of models using the best receptive-field size.

2 MOTIVATIONS

The motivation rests on two observations: performance depends mainly on receptive-field size, while the exact kernel configuration used to realize that size matters less. Therefore, covering many receptive-field sizes can substitute for dataset-specific scale search.

  • 1D-CNNs are relatively insensitive to the specific kernel configuration used to compose a given receptive-field size.
  • 1D-CNN performance is mainly determined by the best receptive-field size available in the model.
  • A multi-receptive-field model can achieve accuracy similar to the highest accuracy among corresponding single-receptive-field models.
  • Covering all receptive-field sizes can produce performance similar to using the best size, avoiding explicit time-scale search.
  • Candidate all-scale designs still differ in characteristics such as model size and expandability for long time series.

3 METHOD

The OS-block is a three-layer multi-kernel CNN structure whose prime-sized kernels cover a range of receptive fields efficiently. It supports univariate and multivariate classification and can be integrated with other deep-learning structures.

  • OS-block architecture: The OS-block uses three same-padding, multi-kernel convolutional layers to generate multiple receptive-field paths.
  • OS-block architecture: Prime kernel sizes in the first two layers, followed by kernels of sizes 1 and 2, cover integer receptive-field sizes in a selected range.
  • OS-block architecture: The maximum prime is chosen to cover receptive fields from 1 to the time-series length, or another range based on prior knowledge.
  • Assumption: The construction relies on Goldbach’s conjecture, whose relevant cases have been computationally validated up to 4 × 10^14 although the conjecture remains theoretically unproven.
  • Efficiency: For receptive fields up to r, prime-sized kernels have model-size complexity O(r^2/log(r)), compared with O(r^2) for even- or odd-number pairs.
  • Integration: The OS-block can process univariate and multivariate time series and can be combined with pooling, fully connected classification, parallel convolution, dilation, and other structures.

4 EXPERIMENT

Experiments evaluate OS-block across four benchmarks and compare it with models using varied receptive-field sizes. OS-CNN achieves strong benchmark performance and generally matches models using the best time scale.

  • 4.1 BENCHMARKS: The evaluation covers four benchmarks containing univariate and multivariate time-series datasets from multiple domains.The benchmarks include MEG-TLE, UEA 30, UCR 85, and UCR 128 archives.
  • 4.1 BENCHMARKS: The experiments use benchmark-specific evaluation criteria, unified training hyperparameters, and comparisons with leading baseline methods.The setup includes accuracy, F1 score, win counts, critical-difference diagrams, model size, and fixed learning rate, batch size, and optimizer choices.
  • 4.4 STATE-OF-THE-ART PERFORMANCE ON BENCHMARKS: OS-CNN achieves consistent state-of-the-art performance across four benchmarks and the best average rank across all dataset archives.On MEG-TLE, OS-CNN also outperforms baselines with a ten-times-smaller model size.
  • 4.5 OS-BLOCK CAN CAPTURE THE BEST TIME SCALE: Across most datasets, OS-CNN achieves accuracy close to the models with the best receptive-field scale among 20 tested FCN variants.The comparison varies receptive-field sizes from 10 to 200 and proportionally adjusts layer kernel sizes while controlling model size.
  • 4.6 DISCUSSION ABOUT BEST TIME SCALE CAPTURE ABILITY: The comparison suggests that covering receptive-field scales matters more than the particular kernel configuration used to compose them.The OS-block covers important and redundant scales without reducing performance in the reported comparisons.
  • 4.7 CASE STUDY FOR THE BEST TIME SCALE CAPTURE ABILITY: Class activation maps show OS-CNN resembling the better-performing receptive-field model on both ScreenType and InsectWingbeatSound.The comparisons favor FCN(10) for ScreenType and FCN(200) for InsectWingbeatSound.

5 RELATED WORKS

Related work frames time-scale selection as a central challenge in time-series classification. Existing approaches search, tune, dilate, or adapt receptive fields, whereas OS-block uses a prime-based multi-kernel design to cover scales.

  • BACKGROUND: Time-series classification must extract features from multiple time scales because signals vary across sources and may contain information at different scales.This challenge applies to data such as medical sensors, economic indicators, and logs.
  • 1D-CNNs FOR TSC: For 1D-CNNs, feature-extraction scale remains an unresolved kernel-size selection problem handled through grid search or empirical tuning.The literature does not establish a consensus on the best kernel-size approach.
  • DILATED CONVOLUTION: Dilated convolutions improve scale coverage but require prior knowledge or search to set dilation sizes that determine filtering thresholds.The dilation choice controls the effective sampling frequency relative to the raw signal.
  • INCEPTION STRUCTURE: Inception-style methods use multiple kernels, while OS-block distinguishes itself by avoiding complicated procedures to assign greater weight to important scales.The OS-block’s multi-kernel design is inspired by Inception but uses a different scale-selection rule.
  • ADAPTIVE RECEPTIVE FIELD: Adaptive receptive-field methods learn kernel masks during training, whereas OS-block composes receptive fields by linking kernels of different sizes.OS-block targets coverage of all receptive-field sizes while assigning larger weight to important sizes.
  • EXTENSION AND SCOPE: The prime-size design may extend to time-series vision tasks, although this paper focuses on classic one-dimensional time-series classification.The stated extension concerns applying prime-sized kernels along the time dimension.

6 CONCLUSION

The conclusion presents OS-block as a simple 1D-CNN component that avoids feature-scale tuning while retaining performance comparable to models using the best scales. It reports robust scale capture across domains and identifies future design and theoretical directions.

  • CONCLUSION: OS-block avoids feature-extraction-scale tuning while achieving performance similar to models with the best feature-extraction scales.Its core design uses prime numbers to cover receptive-field sizes efficiently.
  • CONCLUSION: Experiments show that OS-block robustly captures the best time scale across datasets from multiple domains.The paper links this scale-capture ability to state-of-the-art performance on multiple time-series-classification benchmarks.
  • FUTURE WORK: Future work includes finding more efficient designs, identifying structures better suited to OS-block, and developing theoretical explanations for its empirical characteristics.The conclusion presents these as open directions rather than established results.

A.1 STATISTIC OF THE COMPARISON (FIX MODEL SIZE)

The appendix evaluates OS-block against receptive-field-scale baselines using percentile-based dataset statistics. The reported distributions indicate that OS-block frequently approaches or exceeds the strongest candidate-scale results.

  • PERCENTILE STATISTICS: For more than 56% of 85 datasets, OS-block exceeds the 0.95 percentile of results from 20 candidate scales.The caption reports this as 8+40 out of 85 datasets.
  • PERCENTILE STATISTICS: OS-block has more than a 56% chance of outperforming grid search over 20 candidate scales for an unknown dataset under the reported statistic.This interpretation is stated directly in the figure description.
  • PERCENTILE STATISTICS: OS-block has more than a 96% chance of outperforming a randomly selected scale under the reported percentile comparison.The comparison uses the count of datasets above the 0.5 percentile.
  • SCALE-CAPTURE ANALYSIS: Across most datasets, the highest accuracy range of FCN models is lower than OS-CNN accuracy, supporting OS-block’s best-scale capture ability.The datasets are sorted for the comparison, and the consistency is reported across dataset types.

A.2 STATISTIC OF THE COMPARISON (FIX CHANNEL NUMBER)

With channel count fixed, OS-CNN achieves performance similar to a model using the best receptive-field scales. The comparison is presented alongside figures reporting the same static metric across additional settings.

  • OS-CNN still achieves similar performance to a model with the best receptive-field scales when FCN channel numbers are fixed.
  • Figures 10–12 report the same static metric used in Figures 5, 7, 8, and 9.

A.3 THE CD-DIAGRAM RESULT

The section uses critical-difference analysis and reports state-of-the-art comparisons across the UEA multivariate archive and two UCR dataset collections.

  • The critical-difference diagram reports average method ranks using Wilcoxon-Holm posthoc analysis between each series.
  • Figure 13 presents state-of-the-art results for the UEA 30 multivariate dataset archive.
  • Figures 14 and 15 present state-of-the-art results on the UCR 85 and UCR 128 datasets, respectively.

A.4 EXAMPLES OF THE TWO PHENOMENA

The experiments illustrate receptive-field behavior, OS-block extensibility, and the efficiency of prime-sized kernels. They also report improvements from combining OS-blocks with residual, ensemble, and multi-channel structures.

  • Examples of the two phenomena: For Google SpeechCommands, performance is proportional to receptive-field size, making it suitable for illustrating the paper’s two phenomena.
  • Examples of the two phenomena: Models sharing similar receptive-field sizes show similar performance, while the best receptive-field size mainly determines performance across configurations.
  • OS-block extensions: OS-block layers can be viewed as parallel masked convolutions and combined with dilation, supporting extension with more complex structures.
  • OS-block with other structures: Applying OS-blocks with residual connections, ensembles, or multi-channel architectures can further improve performance on UCR 85 and UEA 30 archives.
  • Comparison with other designs: The paper frames optimal kernel configuration as an exponential constrained combinatorial search and proposes a simple design that avoids it while achieving state-of-the-art performance.
  • Comparison with other designs: Prime-sized kernels reduce model-size complexity to O(r^2/log(r)) for receptive-field range r, versus O(r^2) for even- or odd-number sequences.
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