ROMAN: A Multiscale Routing Operator for Convolutional Time Series Models

Gonzalo Uribarri

cs.LGApr 2, 2026

ROMAN: A Multiscale Routing Operator for Convolutional Time Series Models

Authors: Gonzalo Uribarri

Organizations: Department of Computer and Systems Sciences, Stockholm University

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

Figures & tables

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.

Panel of Figure 2 — 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 $S=4$ .

Panel of Figure 3 — 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 $S=4$ .

Model	Config.	Wins	Ties	Losses	Acc. diff.	Absolute acc. diff.	Train ratio	Infer. ratio
MiniRocket	S=2	35	22	26	+0.11 [-0.89, +2.09]	1.57 [0.43, 4.01]	$\times$ 0.88	$\times$ 0.84
MiniRocket	S=3	32	18	33	+0.00 [-2.12, +2.17]	2.29 [0.62, 4.01]	$\times$ 0.73	$\times$ 0.63
MiniRocket	S=4	23	20	40	-0.44 [-3.86, +0.70]	2.14 [0.61, 4.42]	$\times$ 0.59	$\times$ 0.40
MultiRocket	S=2	23	23	37	-0.33 [-1.48, +0.62]	1.00 [0.45, 2.32]	$\times$ 0.77	$\times$ 0.71
MultiRocket	S=3	22	21	40	-0.46 [-1.96, +0.59]	1.55 [0.49, 3.38]	$\times$ 0.64	$\times$ 0.47
MultiRocket	S=4	22	13	48	-0.84 [-3.87, +0.65]	2.31 [0.79, 4.98]	$\times$ 0.49	$\times$ 0.30

Table 1: Archive-level summary of ROMAN on the long-sequence UCR benchmark. For each backbone and each nontrivial ROMAN configuration

S\in\{2,3,4\}

, the table reports wins, ties, and losses against the corresponding

S=1

baseline. The accuracy-difference columns are reported across datasets in percentage points as median

[Q_{1},Q_{3}]

. The final two columns report median per-dataset training and inference time ratios relative to baseline.

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 $S$ .

Model	Config.	Wins	Ties	Losses	Acc. diff.	Absolute acc. diff.	Train ratio	Infer. ratio
MiniRocket	S=2	6	1	8	-0.81 [-2.94, +1.45]	2.40 [1.37, 3.72]	$\times$ 0.87	$\times$ 0.88
MiniRocket	S=3	10	1	4	+1.11 [-0.43, +2.07]	1.75 [0.95, 4.44]	$\times$ 0.67	$\times$ 0.57
MiniRocket	S=4	7	4	4	+0.28 [-0.70, +2.68]	1.35 [0.65, 5.72]	$\times$ 0.59	$\times$ 0.44
MultiRocket	S=2	5	5	5	+0.00 [-1.64, +1.20]	1.33 [0.31, 2.27]	$\times$ 0.78	$\times$ 0.77
MultiRocket	S=3	5	4	6	-0.27 [-2.44, +1.64]	1.95 [0.85, 4.69]	$\times$ 0.49	$\times$ 0.51
MultiRocket	S=4	5	0	10	-0.97 [-3.23, +2.10]	2.67 [1.28, 4.28]	$\times$ 0.34	$\times$ 0.35

Table 2: Archive-level summary of ROMAN on the long-sequence UEA benchmark.

Archive	Model	Wins	Ties	Losses	Acc. diff.
UCR	MiniRocket	37	23	23	0.00 [-0.65, 1.92]
UCR	MultiRocket	32	26	25	0.00 [-0.80, 1.29]
UCR	FCN	41	10	22	1.10 [-2.29, 7.47]
UCR	CNN	42	18	13	1.28 [0.00, 3.59]
UEA	MiniRocket	7	2	6	0.40 [-1.83, 2.37]
UEA	MultiRocket	6	5	4	0.00 [-0.84, 0.72]

Table 3: Illustrative five-model hard-voting ensemble study: Mixed-scale Roman ensemble vs. Baseline ensemble. Accuracy difference is reported as Median[

Q_{1},Q_{3}

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 5 — 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.

Dataset	MiniRocket
	S=1	S=2	S=3	S=4
ACSF1 (1460)	0.908 (0.008)	0.896 (0.011)	0.860 (0.010)	0.830 (0.012)
AllGestureWiimoteX (385)	0.643 (0.008)	0.691 (0.008)	0.707 (0.016)	0.667 (0.011)
AllGestureWiimoteY (385)	0.684 (0.004)	0.713 (0.008)	0.725 (0.007)	0.687 (0.009)
AllGestureWiimoteZ (385)	0.623 (0.011)	0.626 (0.010)	0.606 (0.007)	0.581 (0.008)
AsphaltObstacles (736)	0.856 (0.006)	0.883 (0.006)	0.887 (0.006)	0.886 (0.007)

Appendix

Table 4: Per-dataset UCR benchmark results for MiniRocket. Each cell reports the mean test accuracy with standard deviation in parentheses over the five seeds for the corresponding ROMAN setting. Dataset names are followed by the time-series length in parentheses.

Dataset	MultiRocket
	S=1	S=2	S=3	S=4
ACSF1 (1460)	0.884 (0.011)	0.838 (0.013)	0.836 (0.009)	0.788 (0.022)
AllGestureWiimoteX (385)	0.719 (0.006)	0.721 (0.006)	0.710 (0.019)	0.669 (0.019)
AllGestureWiimoteY (385)	0.745 (0.010)	0.757 (0.010)	0.745 (0.017)	0.705 (0.007)
AllGestureWiimoteZ (385)	0.682 (0.015)	0.661 (0.008)	0.665 (0.012)	0.623 (0.017)
AsphaltObstacles (736)	0.829 (0.012)	0.847 (0.019)	0.862 (0.009)	0.856 (0.019)

Appendix

Table 5: Per-dataset UCR benchmark results for MultiRocket.

Dataset	CNN
	S=1	S=2	S=3	S=4
ACSF1 (1460)	0.228 (0.057)	0.176 (0.058)	0.200 (0.067)	0.316 (0.141)
AllGestureWiimoteX (385)	0.342 (0.053)	0.426 (0.037)	0.424 (0.039)	0.388 (0.034)
AllGestureWiimoteY (385)	0.286 (0.112)	0.392 (0.059)	0.436 (0.052)	0.406 (0.051)
AllGestureWiimoteZ (385)	0.251 (0.121)	0.266 (0.059)	0.307 (0.067)	0.339 (0.037)
AsphaltObstacles (736)	0.756 (0.024)	0.765 (0.022)	0.760 (0.032)	0.753 (0.043)

Appendix

Table 6: Per-dataset UCR benchmark results for CNN.

Dataset	FCN
	S=1	S=2	S=3	S=4
ACSF1 (1460)	0.660 (0.062)	0.660 (0.060)	0.612 (0.043)	0.562 (0.060)
AllGestureWiimoteX (385)	0.649 (0.025)	0.638 (0.065)	0.655 (0.033)	0.561 (0.036)
AllGestureWiimoteY (385)	0.637 (0.018)	0.674 (0.026)	0.659 (0.046)	0.596 (0.059)
AllGestureWiimoteZ (385)	0.644 (0.021)	0.591 (0.022)	0.539 (0.051)	0.443 (0.059)
AsphaltObstacles (736)	0.867 (0.019)	0.854 (0.011)	0.840 (0.010)	0.828 (0.020)

Appendix

Table 7: Per-dataset UCR benchmark results for FCN.

Dataset	S=1	S=2	S=3	S=4
AsphObstCoord (736)	0.828 (0.008)	0.840 (0.003)	0.844 (0.008)	0.824 (0.005)
AsphPaveTypeCoord (2371)	0.924 (0.007)	0.935 (0.005)	0.941 (0.004)	0.932 (0.005)
AsphaltRegularityCoordinates (4201)	0.992 (0.002)	0.995 (0.001)	0.998 (0.001)	0.994 (0.001)
AtrialFibrillation (640)	0.093 (0.060)	0.053 (0.056)	0.053 (0.056)	0.133 (0.047)
Cricket (1197)	0.961 (0.006)	0.978 (0.008)	0.972 (0.010)	0.964 (0.008)
DuckDuckGeese (270)	0.644 (0.036)	0.568 (0.023)	0.500 (0.024)	0.464 (0.033)

Appendix

Table 8: Complete per-dataset UEA benchmark results for MiniRocket. Each cell reports the mean test accuracy with standard deviation in parentheses over the five seeds for the corresponding ROMAN setting. Dataset names are followed by the time-series length in parentheses.

Dataset	S=1	S=2	S=3	S=4
AsphObstCoord (736)	0.773 (0.015)	0.794 (0.014)	0.823 (0.013)	0.828 (0.016)
AsphPaveTypeCoord (2371)	0.895 (0.010)	0.875 (0.015)	0.878 (0.016)	0.885 (0.015)
AsphaltRegularityCoordinates (4201)	0.989 (0.002)	0.989 (0.003)	0.986 (0.004)	0.983 (0.005)
AtrialFibrillation (640)	0.187 (0.056)	0.173 (0.060)	0.120 (0.056)	0.147 (0.056)
Cricket (1197)	0.986 (0.010)	0.983 (0.006)	0.983 (0.006)	0.969 (0.012)
DuckDuckGeese (270)	0.500 (0.020)	0.436 (0.017)	0.432 (0.054)	0.472 (0.054)

Appendix

Table 9: Complete per-dataset UEA benchmark results for MultiRocket.

Dataset	S=1	S=2	S=3	S=4
AsphObstCoord (736)	0.633 (0.017)	0.604 (0.026)	0.477 (0.109)	0.275 (0.010)
AsphPaveTypeCoord (2371)	0.752 (0.212)	0.840 (0.060)	0.825 (0.022)	0.851 (0.070)
AsphaltRegularityCoordinates (4201)	0.988 (0.003)	0.989 (0.003)	0.991 (0.002)	0.987 (0.004)
AtrialFibrillation (640)	0.347 (0.119)	0.320 (0.119)	0.320 (0.056)	0.293 (0.076)
Cricket (1197)	0.739 (0.054)	0.764 (0.033)	0.822 (0.033)	0.825 (0.025)
DuckDuckGeese (270)	0.376 (0.036)	0.300 (0.089)	0.416 (0.046)	0.292 (0.067)

Appendix

Table 10: Complete per-dataset UEA benchmark results for CNN.

Dataset	S=1	S=2	S=3	S=4
AsphObstCoord (736)	0.808 (0.026)	0.788 (0.037)	0.739 (0.033)	0.765 (0.026)
AsphPaveTypeCoord (2371)	0.963 (0.009)	0.954 (0.004)	0.948 (0.004)	0.949 (0.003)
AsphaltRegularityCoordinates (4201)	0.994 (0.002)	0.991 (0.006)	0.990 (0.002)	0.990 (0.004)
AtrialFibrillation (640)	0.307 (0.060)	0.293 (0.060)	0.360 (0.037)	0.320 (0.030)
Cricket (1197)	0.989 (0.006)	0.983 (0.015)	0.969 (0.021)	0.942 (0.023)
DuckDuckGeese (270)	0.552 (0.039)	0.564 (0.033)	0.512 (0.036)	0.528 (0.039)

Appendix

Table 11: Complete per-dataset UEA benchmark results for FCN.

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