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Sea-Net: A Small and Inherently Interpretable Neural Network for Time Series Classification

Ubaid Ur Rehman, Tanmoy Mondal

arXiv:2610.17939v1cs.LGcs.CV

TL;DR

Time-series classification must provide accurate predictions and useful temporal explanations while fitting small device budgets. SEA-Net combines a compact encoder with selective MIL pooling, and its bottleneck model improves WebTraffic accuracy and NDCG@n over MILLET with fewer parameters.

  • Problem

    Time-series classification needs competitive accuracy, explanations identifying decision-driving time steps, and small parameter budgets; MILLET’s encoder exceeds the stated micro-controller memory budget.

    Source: §1 · pp. 1–2

  • Method

    SEA-Net pairs a smaller encoder that produces per-time-step embeddings with selective MIL pooling, including Top-k aggregation of the strongest evidence values.

    Source: §3.1 · p. 3, §3.3 · p. 7

  • Results

    0.931 ± 0.032 accuracy and 0.765 ± 0.013 NDCG@n with 41,324 parameters outperform MILLET’s 0.888 ± 0.007 accuracy and 0.681 ± 0.013 NDCG@n with 423,707 parameters on WebTraffic.

    Source: §4.1 · p. 8

  • Takeaways & Limitations

    SEA-Net’s 41 K parameters make it a candidate for micro-controller-class devices while preserving per-time-step interpretation, although deployment fitness is argued from size rather than demonstrated on hardware.

    Source: §5 · p. 9

    No model was quantized or run on a micro-controller, interpretation was scored only on WebTraffic—the design set—and AOPCR is budget-sensitive.

    Source: §5 · p. 9

Abstract

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Traditional time-series classification methods often operate as black boxes, providing a class prediction without indicating which time point or time interval within the series led to that prediction. To improve temporal interpretability, MILLET (Multiple Instance Learning with Temporal Explanation), which combines an InceptionTime encoder with Conjunctive Pooling, provides both classification and temporal explanations. However, MILLET contains approximately 424 K parameters, making it unsuitable for deployment on resource-constrained micro-controllers, and it achieves an overall time-series accuracy of 0.888 and an explanation score of 0.681 NDCG@n. We therefore propose SEA-Net, a lightweight architecture using small multi-scale depthwise-separable convolutional TSC encoders and improved Multiple Instance Learning (MIL) pooling heads. Our SEA-Net bottleneck encoder with Top-k pooling achieves 0.931 accuracy and 0.765 NDCG@n with only 41 K parameters. Another variant, using a gated encoder with Top-k pooling, achieves 0.955 accuracy and 0.750 NDCG@n with 62 K parameters. These results demonstrate that lightweight architectures can maintain strong classification performance and temporal explanations while substantially reducing model size. The proposed variants address specific limitations of the pooling strategy used by MILLET, providing a practical direction for interpretable time-series classification on resource-constrained edge devices.

1 INTRODUCTION

Time-series classification needs to balance accuracy, explanations tied to the prediction, and a small model size. SEA-Net combines a compact encoder with interpretable pooling; on WebTraffic, its bottleneck model improves accuracy and NDCG@n over MILLET with far fewer parameters.

1 INTRODUCTION

  • Time-series applications motivating this work require competitive accuracy, explanations that identify decision-driving time steps, and a small parameter budget for edge devices.The explanation must be part of the prediction computation rather than a separate post-hoc approximation.Source: §1 · p. 1
  • On WebTraffic, SEA-Net (41,324 parameters) achieved 0.931 accuracy and 0.765 NDCG@n, exceeding MILLET’s 0.888 accuracy and 0.681 NDCG@n; SEA-Net used 10.3× fewer parameters.Source: §1 · p. 2
  • MILLET provides classification and a built-in explanation, but its InceptionTime backbone needs 423,707 parameters and 848 MFLOPs for a length-1008 series.At 32-bit precision, its weights alone take about 1.6 MB, exceeding the memory budget described for micro-controller deployment.Source: §1 · p. 2
  • On the 85 UCR datasets, the paper reports 0.810 accuracy against 0.827 for its MILLET re-run, whose published figure is 0.845.The authors report that they received no reply to their query about the discrepancy.Source: §1 · p. 2

2 RELATED WORK

Prior work supplies strong convolutional TSC baselines, built-in interpretability approaches, and efficient architectures, but the related work describes them as addressing these concerns separately.

2 RELATED WORK

  • FCN, ResNet, and InceptionTime are convolutional TSC baselines; TCN dilation broadens temporal context without significantly increasing parameters.Convolutional models commonly end with global average pooling, which removes explicit temporal resolution.Source: §2 · p. 3
  • Interpretability approaches include post-hoc attribution, shapelets, and MIL; MILLET adapts attention-based MIL to time-series classification.The paper follows the MIL direction, where explanations are incorporated into prediction rather than applied afterward.Source: §2 · p. 3
  • Depthwise separable convolutions and bottlenecks reduce model cost, while ATCN and optimized TCNs target efficient inference or edge constraints.The cited efficient approaches focus on efficiency rather than explicitly identifying the temporal regions behind predictions.Source: §2 · p. 3
  • MCUNet, MicroNets, and MLPerf Tiny address micro-controller constraints such as flash, SRAM, and computation, but not interpretability under those constraints.Source: §2 · p. 3

3 METHOD

SEA-Net treats each time point as an instance, encodes the ordered series into per-time-step embeddings, and pools those embeddings into class predictions and temporal interpretations. Its method combines a lightweight multi-scale encoder with selective MIL pooling heads.

3.1 PROBLEM SETUP AND NOTATION

  • Each series is a MIL bag with a single observed label, while its ordered time points are unannotated instances whose evidence must be recovered from that label.SEA-Net preserves instance order through its layers.Source: §3.1 · p. 3
  • The encoder produces one embedding per time point, and the pooling head returns both class probabilities and per-time-step interpretation scores.The stem expands the input into d channels before the multi-scale residual blocks.Source: §3.1 · p. 3, §3.2 · p. 4

3.2 SEA-NET ENCODER

  • Six residual blocks combine depthwise filters at kernel sizes 5, 11, and 23, examining short, medium, and long patterns in parallel.Dilation grows geometrically and is capped at 16; stride-one same padding keeps the temporal length unchanged.Source: §3.2 · pp. 4–5
  • At d = 64, bottlenecked pointwise mixing reduces the model from 57,580 to 41,324 parameters, a 28% reduction, while preserving its output shape.The squeeze and expansion convolutions are equivalent to a rank-r mixing matrix and halve pointwise cost when r = d/4.Source: §3.2 · p. 5
  • Channel reweighting can use one series-level set of weights or time-varying weights computed from the raw input.The input-gated variant uses a kernel-7 convolution, allowing weights to respond to local events; the mean-based variant applies the same weights at every time point.Source: §3.2 · p. 5
  • The spike/trend variant adds a parallel branch that subtracts a five-point moving average from the input to highlight discontinuities before pooling.It concatenates these spike features with encoder trend features and projects them back to d channels.Source: §3.2 · pp. 5–6

3.3 MIL POOLING HEAD

  • The pooling variants address shared class attention, length-dependent aggregation, and dilution of informative time points by background regions.Class-wise attention assigns class-specific importance, while soft-max pooling normalizes attention across time and learns its concentration.Source: §3.3 · pp. 6–7
  • Top-k pooling retains the largest evidence values per class, and κ controls the retained fraction without adding learnable parameters.At κ = 1 it reduces to class-wise pooling; for κ < 1, it focuses aggregation on a subset of time points.Source: §3.3 · p. 7

4 EXPERIMENTAL SETUP AND RESULTS

Experiments evaluate classification, temporal interpretation, and model cost on synthetic WebTraffic and UCR datasets. On WebTraffic, the bottleneck Top-k model improves accuracy and NDCG@n over MILLET with about one-tenth the parameters; UCR results show a size-related trade-off.

4 EXPERIMENTAL SETUP AND RESULTS

  • The evaluation asks whether small models retain classification accuracy and useful interpretation, and assesses cost and the contributions of the bottleneck and Top-k pooling.WebTraffic provides per-time-point ground truth for interpretation scoring; UCR lacks such annotations, so interpretation there is assessed only with AOPCR.Source: §4 · p. 7

4.1 CLASSIFICATION AND INTERPRETATION RESULTS

  • 0.931 accuracy and 0.765 NDCG@n with 41,324 parameters exceed MILLET’s 0.888 accuracy and 0.681 NDCG@n with 423,707 parameters on WebTraffic.The gated (mean) + Top-k variant reaches 0.955 ± 0.002 accuracy and 0.750 ± 0.018 NDCG@n with 61,740 parameters.Source: Table 1 · p. 8, §4.1 · p. 8
  • On UCR, the 41 K model reaches 0.810 mean accuracy, below matched-budget MILLET at 0.827 and published MILLET at 0.845; widening SEA-Net reaches 0.829.The wider configuration has mean rank 11.53 versus 12.60 for matched-budget MILLET; the reported gap is attributed to size, not design.Source: §4.1 · p. 8
  • Replacing the plain encoder with the bottleneck removes 16,256 parameters, or 28%, with no measurable accuracy or interpretation cost in the single-seed ablation.Accuracy and NDCG@n changes remain within the reported run spreads.Source: §4.1 · p. 8
  • Top-k raises NDCG@n by 0.059 on the plain encoder and 0.032 on the bottleneck encoder; its accuracy changes are within the ±0.032 spread.The authors claim an interpretation-ranking gain, not an accuracy gain.Source: §4.1 · pp. 8–9
  • The selection fraction κ has a non-monotone effect, and AOPCR can rise with longer training even as NDCG@n falls, so AOPCR comparisons require a fixed training budget.The one-seed ablations also report that removing the attention-entropy penalty raises accuracy and NDCG@n while lowering AOPCR.Source: §4.1 · p. 9

5 DISCUSSION AND CONCLUSION

SEA-Net’s parameter savings come with a UCR accuracy trade-off, while keeping per-time-step interpretation. The discussion argues deployment suitability from model size, but reports that deployment was not tested on micro-controllers.

5 DISCUSSION AND CONCLUSION

  • Saving 10.3× in parameters costs 1.8 accuracy points on UCR, while retaining per-time-step interpretation.The discussion frames a 41 K model as a candidate for micro-controller-class devices where a 424 K model may not fit.Source: §5 · p. 9
  • No model was quantized or run on a micro-controller, so deployment fitness is argued from size rather than demonstrated.Activation memory exceeds the baseline’s, and SRAM may bind instead of flash.Source: §5 · pp. 9–10
  • Interpretation is scored only on WebTraffic, which is also the design set, and its backup metric AOPCR is budget-sensitive.Training is slower, as GPU kernels favor dense over depthwise convolutions; the stated saving is at inference.Source: §5 · p. 10

REPRODUCIBILITY STATEMENT

The paper and anonymous code release contain the information needed to reproduce the reported results.

REPRODUCIBILITY STATEMENT

ETHICS STATEMENT

The work uses public UCR data and synthetic data, and reports no new data collection or human subjects. It cautions that explanation scores and user trust require care in decision-making contexts.

ETHICS STATEMENT

  • The work collects no new data and involves no human subjects.Source: ETHICS STATEMENT · p. 11
  • The study uses the public UCR archive and a synthetic benchmark generated by released code.Source: ETHICS STATEMENT · p. 11
  • The authors caution that explanations may increase trust and that a common faithfulness score can rise with longer training rather than better explanations.They recommend checking interpretations on the target domain before using them to support decisions about people.Source: ETHICS STATEMENT · p. 11

AI USE STATEMENT

The appendix expands on SEA-Net’s MIL interpretation, encoder designs, and pooling heads, and reports the authors’ use of generative AI tools. It explains how per-time-point evidence supports both predictions and interpretations.

A WHY MIL MAKES SEA-NET INTERPRETABLE

  • MIL pooling scores each time point before aggregation, so the evidence used for prediction also forms the interpretation; the interpretation is part of the forward pass, not post hoc.The series is the bag, each time point an instance, and only the bag label is observed.Source: A WHY MIL MAKES SEA-NET INTERPRETABLE · p. 14

B.1 MULTI-SCALE SEPARABLE BLOCKS

  • The multi-scale separable blocks use depthwise convolutions at three kernel sizes, while pointwise convolution mixes channels and holds most of the parameters.Dilation widens the receptive field without adding weights, and its cap keeps each embedding local.Source: §B.1 · p. 15, Figure 4 · p. 15

B.2 WHERE THE BOTTLENECK SAVING COMES FROM

  • The bottleneck factorizes pointwise mixing, reducing measured parameters from 57,580 to 41,324, a saving of 16,256.The depthwise filters remain unchanged because they are not where the cost is.Source: §B.2 · p. 15

B.3 THE TWO GATED VARIANTS, WRITTEN OUT

  • Gated (mean) shares one time-constant channel gate, while Input Gated computes a separate gate at each time point from the raw series.Input Gated costs 7d weights, less than the mean gate, and its gradient reaches the input directly.Source: §B.3 · p. 16

B.4 SEA-NET SPIKE/TREND ENCODER

  • The Spike/Trend variant adds a moving-average-based spike branch, but it was the weakest of the five encoders, contrary to the expected advantage on sharp-spike datasets.The reconstruction-residual variant instead learns residual features end to end without a separate reconstruction loss and was the second strongest encoder.Source: §B.4 · p. 16, §B.5 · p. 16

B.6 SEA-NET MULTI-SCALE CHANNELS (WRAPPER)

  • The multi-scale channels wrapper adds rolling maximum, minimum, standard deviation, and first-difference sign; the pyramid wrapper shares encoder weights across downsampled scales but adds about 1.9× compute.The pyramid was the weakest variant built and requires a shallow enough encoder to avoid nearly constant signals at the coarsest scales.Source: §B.6 · p. 17, §B.7 · p. 17

C POOLING HEADS COMPARED

  • Conjunctive pooling forms per-time-point class evidence before aggregation; class-wise, Soft-Max, and Top-k variants target shared gates, unnormalized weights, and diluted decisive points, respectively.Top-k is exactly class-wise pooling at κ = 1; for κ < 1, gradients reach only selected time points.Source: C POOLING HEADS COMPARED · p. 20, §C.1 · p. 20, §C.2 · p. 20

C.5 ADAPTIVE CLASS-WISE POOLING

  • Adaptive class-wise pooling learns per-class soft-argmax sharpness, attention-max learns a per-class mean–maximum blend, and per-class gated attention adds a second layer to select attention features.Attention-max serves as a hard-selection control; per-class gated attention is the most expensive head here and cannot recover conjunctive pooling through a setting of its weights.Source: §C.5 · p. 22, §C.6 · p. 22, §C.7 · p. 23

C.8 DUAL-STREAM CONJUNCTIVE POOLING

Dual-stream conjunctive pooling blends class-wise aggregation with a stream centered on each class’s most supporting time point. Despite its baseline fallback, it was the worst tested head.

C.8 DUAL-STREAM CONJUNCTIVE POOLING

  • A learned scalar blends the class-wise mean stream with a stream that reweights time points by similarity to each class’s most supporting point.The second stream targets scattered evidence, where one decisive time point should dominate without discarding the rest.Source: §C.8 · pp. 23–24, Figure 13 · p. 24
  • The dual-stream head was the worst tested: its four pairings scored 0.860, 0.824, 0.736, and 0.556.Although it can return to the baseline, training does not push its learned blend back toward that baseline.Source: §C.8 · p. 24

C.9 THE EIGHT HEADS TOGETHER

  • The eight pooling heads are defined by two choices: the attention head and the aggregation over time.The accompanying tables give each head’s layer-by-layer operations and input and output shapes; d is 64 for SEA-Net and 128 for MILLET.Source: §C.9 · p. 24

D REPRODUCING THE EXPERIMENTS

  • The experiment appendix documents WebTraffic and the 85 UCR datasets, baselines, shared training configuration, interpretation metrics, hyperparameters, and model sizes.It also includes full results and seed-level results.Source: D REPRODUCING THE EXPERIMENTS · p. 27

D.1 DATASETS

WebTraffic is the only dataset with per-time-point labels, enabling NDCG@n evaluation; the study also uses the 85 UCR datasets published by MILLET. Baselines are retrained under a shared training setup.

D.1 DATASETS

  • WebTraffic is the only dataset with per-time-point ground truth, making it the only dataset where interpretation is scored with NDCG@n.Its generated class signature appears within a single window, except class 0, which has no signature; these labels are not used in training.Source: §D.1 · p. 27, Figure 14 · p. 27
  • The experiments use WebTraffic and the 85 UCR datasets used by MILLET.Table 14 reports dataset sizes, series lengths, class counts, and class imbalance.Source: §D.1 · p. 27, Table 14 · p. 28

D.2 BASELINES

  • MILLET is the baseline; FCN and ResNet are additional reference models trained with the same pooling head.The authors retrain baselines with their own training budget because faithfulness values from different training recipes cannot be compared; published MILLET numbers are included for reference.Source: §D.2 · p. 29

D.3 TRAINING CONFIGURATION

  • Optuna-selected hyperparameters are shared across models, so result-table differences reflect models rather than different training setups.Table 15 gives the shared settings, and Table 16 lists remaining hyperparameters by model.Source: §D.3 · p. 30, Table 15 · p. 30

D.4 INTERPRETATION METRICS

The appendix defines interpretation metrics and reports full model, leaderboard, and cost results. It notes that AOPCR scales depend on logits, while NDCG@n supports comparisons across models and datasets.

D.4 INTERPRETATION METRICS

  • AOPCR measures predicted-class logit drops as the model-ranked time points are replaced by the series mean, but differing logit scales make cross-model values incomparable.The evaluation removes the top-ranked points in steps of 1% up to 10% of series length.Source: §D.4 · p. 30
  • NDCG@n compares the model’s ranking of time points with the ground-truth signature window, using n equal to the number of signature points.Its normalization places scores in [0, 1], allowing comparisons across models, datasets, and papers.Source: §D.4 · pp. 30–31

D.5 FULL HYPERPARAMETERS

  • Every attention head adds well under 1% of encoder parameters, so encoder choice largely determines model size.Table 17 reports parameter counts for encoder–pooling-head pairs on WebTraffic with 10 classes.Source: Table 17 · p. 32

E COMPLETE RESULTS

  • The bottleneck + Top-k model is more accurate than MILLET and has better NDCG@n on WebTraffic, but stays slightly behind on the 85 UCR datasets.The reported UCR gap is attributed to reduced capacity rather than design; AOPCR comparisons are valid only within one training recipe.Source: E COMPLETE RESULTS · p. 34

E.1 COMPLETE WEBTRAFFIC RESULTS

  • MILLET wins AOPCR on three of four WebTraffic examples, while SEA-Net’s heatmaps are more concentrated.The figure compares deletion curves under each model’s own ranking against random deletion, with changes shown as fractions of original logits.Source: §E.1 · p. 34, Figure 15 · p. 34

E.2 MODEL COST

  • 10.3× smaller and 11.1× less computation than MILLET, the model’s weights fall from about 1.6 MB to 161 KB, but peak memory is higher: 179.0 MB versus 112.3 MB.The unchanged time dimension keeps activations large; latency improves only 1.6× despite the FLOPs reduction.Source: §E.2 · p. 40, Table 22 · p. 40
  • Model compute grows linearly with series length and depends little on class count; SEA-Net needs about ten times fewer operations across tested lengths.The comparison varies length at 10 classes and class count at length 463.Source: §E.2 · p. 40
  • No pooling head adds a multiplication term that grows faster than Conjunctive pooling, so the compute savings come from the encoder.The head-cost comparison counts multiplications as a function of series length, class count, and embedding size.Source: §E.2 · p. 40

E.3 ABLATION STUDIES

The ablations show that both pooling-head and encoder choices strongly affect WebTraffic accuracy, and that Top-k selection outperforms full conjunctive pooling. Across repeated runs, SEA-Net also shows dataset-level instability and substantially greater spread in AOPCR than in accuracy.

E.3 ABLATION STUDIES

  • Figure 16 compares prediction compute cost as series length or class count grows, with dashed lines marking the corresponding means across 85 UCR datasets.The comparisons are SEA-Net bottleneck + Top-k versus the MILLET baseline.Source: Figure 16 · p. 41
  • Nearly 18 points of WebTraffic accuracy separate pooling heads when averaged across paired encoders, making the head a consequential design choice.The authors caution that some head groups contain few pairings, so the full Table 19 grid is more reliable.Source: §E.3 · p. 41, Table 24 · p. 42
  • Wrong predictions on the hardest WebTraffic class arise either from identifying the right window but the wrong class, or from missing a weak signature near a seasonal pattern.Figures 17 and 18 show the SEA-Net and MILLET cases, respectively.Source: §E.3 · p. 42, Figure 17 · p. 44, Figure 18 · p. 44
  • The encoder spread, from 0.937 down to 0.771, is close to the pooling-head spread, indicating that encoder and head choices are about equally important.The means average across paired heads; the bottleneck encoder's 0.884 mean is pulled down by weak heads.Source: §E.3 · pp. 41–42, Table 25 · p. 43
  • 0.908 for κ = 1 is below the 0.938–0.940 obtained at κ = 0.1 and κ = 0.25, supporting selection of only a fraction of time points.κ = 1 recovers class-wise conjunctive pooling; the ablation changes only κ across five seed-0 runs.Source: §E.3 · p. 42, Table 26 · p. 43
  • Switching off the attention-entropy term gives 0.950 accuracy and 0.765 NDCG@n on seed 0, but the authors interpret the matched pair as showing no measurable effect.Seed 0 is the weakest of three default-model runs; the no-term run lies within one standard deviation of the three-run accuracy mean and matches its NDCG@n mean.Source: §E.3 · p. 42, Table 27 · p. 43

E.4 PER-SEED RESULTS

  • SEA-Net is the least stable of four models across 85 UCR datasets, with a long lower tail caused by occasional seeds far below their peers on particular datasets.WebTraffic run-to-run spreads are also much larger for AOPCR than accuracy, so differences of a few tenths in AOPCR are not treated as wins.Source: §E.4 · p. 45, Table 28 · p. 45, Figure 19 · p. 46

E.5 COMPLETE UCR RESULTS

On the UCR archive, SEA-Net bottleneck + Top-k reaches 0.810 mean accuracy, below both matched-budget and published MILLET results; the wide variant closes the gap. Most middle-table differences are not statistically significant, while the model ranking remains stable across dataset imbalance, series length, and training-set size.

E.5 COMPLETE UCR RESULTS

  • 0.810 mean accuracy for SEA-Net trails matched-budget MILLET at 0.827 and published MILLET at 0.8445; the wide variant closes the gap.With training budget fixed, changing the backbone at similar size moves mean rank from 12.60 to 11.53, suggesting reduced capacity—not the design—is associated with the accuracy loss.Source: Table 29 · p. 46, §E.5 · p. 46
  • Most differences in the middle of Table 30 are not significant at α = 0.05 under a Wilcoxon–Holm test, so mean-rank ordering alone is not relied upon.The authors also report win/tie/loss counts against published per-dataset MILLET results.Source: §E.5 · p. 46, Table 30 · p. 48, Table 31 · p. 49
  • 15 / 17 / 52 is SEA-Net's win/tie/loss count against published MILLET accuracy across the 85 UCR datasets.Ties are differences below 0.005; Figure 20 identifies the datasets with the largest positive and negative differences.Source: Figure 20 · p. 47
  • The model ranking remains stable on imbalanced datasets and across series-length and training-set-size bins; SEA-Net does not fall further behind in those subsets.The imbalance comparison is restricted to UCR datasets with normalized class entropy below one.Source: §E.5 · p. 46, Figure 21 · p. 47, Figure 22 · p. 48
  • Tables 30–33 provide archive-wide model summaries and per-dataset accuracy and AOPCR, but published MILLET AOPCR is on a different scale and is not comparable.The per-dataset tables distinguish published MILLET and models retrained under the paper's recipe.Source: Table 30 · p. 48, Table 32 · p. 50, Table 33 · p. 52

E.6 RELATION TO THE PUBLISHED MILLET RESULTS

The paper distinguishes published MILLET results from its own retrained baseline because the training recipes differ. On WebTraffic, the published accuracy is higher, while the large AOPCR discrepancy across recipes does not correspond to a better time-point ranking.

E.6 RELATION TO THE PUBLISHED MILLET RESULTS

  • 0.924 published WebTraffic accuracy for MILLET exceeds the 0.888 accuracy of the retrained baseline using the same architecture but a different training recipe.Only the retrained MILLET row is used in the paper's main comparisons.Source: Table 34 · p. 54, §E.6 · p. 54
  • 12.768 published WebTraffic AOPCR versus 2.457 for retrained MILLET is not evidence of better time-point ranking, given their similar NDCG@n values of 0.674 and 0.681.The authors compare AOPCR only within a training recipe, not across papers.Source: §E.6 · p. 54, Table 34 · p. 54

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