Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

ROMAN: A Multiscale Routing Operator for Convolutional Time Series Models

Gonzalo Uribarri

Abstract

We introduce ROMAN (ROuting Multiscale representAtioN), a deterministic operator for time series that maps temporal scale and coarse temporal position into an explicit channel structure while reducing sequence length. ROMAN builds an anti-aliased multiscale pyramid, extracts fixed-length windows from each scale, and stacks them as pseudochannels, yielding a compact representation on which standard convolutional classifiers can operate. In this way, ROMAN provides a simple mechanism to control the inductive bias of downstream models: it can reduce temporal invariance, make temporal pooling implicitly coarse-position-aware, and expose multiscale interactions through channel mixing, while often improving computational efficiency by shortening the processed time axis. We formally analyze the ROMAN operator and then evaluate it in two complementary ways by measuring its impact as a preprocessing step for four representative convolutional classifiers: MiniRocket, MultiRocket, a standard CNN-based classifier, and a fully convolutional network (FCN) classifier. First, we design synthetic time series classification tasks that isolate coarse position awareness, long-range correlation, multiscale interaction, and full positional invariance, showing that ROMAN behaves consistently with its intended mechanism and is most useful when class information depends on temporal structure that standard pooled convolution tends to suppress. Second, we benchmark the same models with and without ROMAN on long-sequence subsets of the UCR and UEA archives, showing that ROMAN provides a practically useful alternative representation whose effect on accuracy is task-dependent, but whose effect on efficiency is often favorable. Code is available at https://github.com/gon-uri/ROMAN

ROMAN: A Multiscale Routing Operator for Convolutional Time Series Models

Abstract

We introduce ROMAN (ROuting Multiscale representAtioN), a deterministic operator for time series that maps temporal scale and coarse temporal position into an explicit channel structure while reducing sequence length. ROMAN builds an anti-aliased multiscale pyramid, extracts fixed-length windows from each scale, and stacks them as pseudochannels, yielding a compact representation on which standard convolutional classifiers can operate. In this way, ROMAN provides a simple mechanism to control the inductive bias of downstream models: it can reduce temporal invariance, make temporal pooling implicitly coarse-position-aware, and expose multiscale interactions through channel mixing, while often improving computational efficiency by shortening the processed time axis. We formally analyze the ROMAN operator and then evaluate it in two complementary ways by measuring its impact as a preprocessing step for four representative convolutional classifiers: MiniRocket, MultiRocket, a standard CNN-based classifier, and a fully convolutional network (FCN) classifier. First, we design synthetic time series classification tasks that isolate coarse position awareness, long-range correlation, multiscale interaction, and full positional invariance, showing that ROMAN behaves consistently with its intended mechanism and is most useful when class information depends on temporal structure that standard pooled convolution tends to suppress. Second, we benchmark the same models with and without ROMAN on long-sequence subsets of the UCR and UEA archives, showing that ROMAN provides a practically useful alternative representation whose effect on accuracy is task-dependent, but whose effect on efficiency is often favorable. Code is available at https://github.com/gon-uri/ROMAN

Paper Structure

This paper contains 56 sections, 21 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Related Work and Positioning
  4. Convolutional Backbones and Inductive Bias.
  5. Positioning of ROMAN.
  6. ROMAN: Definition and Properties
  7. Definition and Basic Property
  8. Roles of $S$ and $\alpha$.
  9. Representation and Inductive Bias
  10. Representation Size and Computational Implications
  11. Experimental Design
  12. Choice of Downstream Backbones.
  13. Synthetic Mechanism Studies.
  14. Archive Evaluation.
  15. Synthetic Mechanism Studies
  16. ...and 41 more sections

Figures (5)

  • Figure 1: Overview of the ROMAN transformation. Left: schematic multiscale construction. Each scale $s$ is partitioned into windows of common length $L_{\mathrm{base}}$, and the window index $w$ records coarse temporal position within that scale. Right: Example of the stacked pseudochannels generated by applying ROMAN (S=2) to a real time series.
  • Figure 2: Synthetic mechanism studies for (a) coarse position awareness and (b) long-range correlation. Left: representative examples. Right: mean test accuracy over ten realizations, comparing the baseline representation with ROMAN at $S=4$.
  • Figure 3: Synthetic mechanism studies for (c) multiscale interaction and (d) full positional invariance. Left: representative examples. Right: mean test accuracy over ten realizations, comparing the baseline representation with ROMAN at $S=4$.
  • Figure 4: Baseline ($S = 1$) vs. ROMAN-transformed data ($S \in \{2,3,4\}$) results for the MiniRocket and FCN Classifier models. We present the per-dataset UCR accuracies and the scaling of computational times with respect to $S$.
  • Figure 5: Critical-difference diagrams for the five-model hard-voting ensemble study on UCR and UEA. Each diagram compares the eight ensemble variants within the corresponding archive: the four baseline-only ensembles and their four mixed-scale ROMAN counterparts. Lower average rank is better.