PaperlayerView exact revision on arXiv

Source-linked AI summary

AliO: Output Alignment Matters in Long-Term Time Series Forecasing

Kwangryeol Park, Jaeho Kim, Seulki Lee

arXiv:2610.11213v1cs.AI

TL;DR

LTSF models can disagree on overlapping timestamps despite their forecasting accuracy, a consistency gap with practical costs. AliO aligns overlapping predictions in time and frequency domains; the paper reports improvements in both TAM and MSE.

  • Problem

    LTSF models may produce inconsistent predictions for the same timestamps across lagged inputs, although minimizing prediction error alone does not ensure alignment.

    Source: §1 · p. 2

  • Method

    AliO uses regression pulling with stop-gradient and aligns overlapping predictions in time and frequency domains.

    Source: §4 · p. 5

  • Results

    Up to 27.5% improvement in MSE and 58.2% improvement in TAM are reported across LTSF models and datasets.

    Source: §8 · p. 10

  • Takeaways & Limitations

    AliO improves forecast reliability through better output alignment while maintaining or improving overall forecasting performance.

    Source: §1 · p. 2

    TAM should be used cautiously on highly volatile datasets outside typical LTSF tasks; more robust metrics for inherently volatile data remain future work.

    Source: §7 · p. 10

Abstract

from arXiv · show

Long-term Time Series Forecasting (LTSF) tasks, which leverage the current data sequence as input to predict the future sequence, have become increasingly crucial in real-world applications such as weather forecasting and planning of electricity consumption. However, state-of-the-art LTSF models often fail to achieve prediction output alignment for the same timestamps across lagged input sequences. Instead, these models exhibit low output alignment, resulting in fluctuation in prediction outputs for the same timestamps, undermining the model's reliability. To address this, we propose AliO (Align Outputs), a novel approach designed to improve the output alignment of LTSF models by reducing the discrepancies between prediction outputs for the same timestamps in both the time and frequency domains. To measure output alignment, we introduce a new metric, TAM (Time Alignment Metric), which quantifies the alignment between prediction outputs, whereas existing metrics such as MSE only capture the distance between prediction outputs and ground truths. Experimental results show that AliO effectively improves the output alignment, i.e., up to 58.2% in TAM, while maintaining or enhancing the forecasting performance (up to 27.5%). This improved output alignment increases the reliability of the LTSF models, making them more applicable in real-world scenarios.

1 Introduction

LTSF models can produce inconsistent forecasts for the same timestamps across lagged inputs, a gap with practical consequences. AliO aligns overlapping predictions, and the reported results include improved TAM while maintaining or enhancing forecasting performance.

1 Introduction

  • LTSF forecasts can disagree for the same timestamps across lagged inputs, potentially undermining reliability and increasing electricity-budget rescheduling costs.The introduction illustrates this with forecasts whose periods overlap from May to November.Source: §1 · p. 2, Figure 1 · p. 2
  • AliO reduces discrepancies between overlapping predictions in time and frequency domains while directing predictions toward ground truth.It can integrate with forecasting objectives such as MSE without requiring model modifications.Source: §1 · p. 2
  • Existing LTSF methods focus on forecasting objectives without considering prediction output alignment.Source: §1 · p. 2
  • AliO improves TAM by up to 58.2% while maintaining or enhancing forecasting performance.The method targets discrepancies between predictions for overlapping timestamps.Source: §1 · p. 2

2 Motivation

The motivation section contrasts models' high forecasting accuracy with insufficient consistency across predictions. AliO is presented as addressing both goals, while TAM measures consistency separately from regression accuracy.

2 Motivation

  • Inconsistent forecasts can prompt replanning and resource reallocation, consuming organizational time and resources.The section connects these costs to fluctuating predictions and lost opportunity costs.Source: §2 · p. 3
  • Modern LTSF models can have high accuracy but low consistency across predictions.The section illustrates this contrast with DLinear forecasts on ILI and notes it across other models and datasets.Source: §2 · p. 3
  • Regression metrics such as MSE, MAE, and DTW measure prediction distance from ground truth, whereas TAM measures distance between predictions.The section treats these as measures of accuracy and consistency, respectively.Source: §2 · p. 3
  • AliO is reported to improve or maintain accuracy while enhancing consistency, with experiments also examining how initial TAM relates to MSE improvement.The section presents these as dual goals for the method.Source: §2 · p. 3

3 Time alignment metric (TAM)

Output alignment means consistent prediction patterns at overlapping timestamps across lagged inputs. TAM quantifies this consistency by averaging distances between overlapping predictions, unlike regression metrics that compare predictions with ground truth.

3 Time alignment metric (TAM)

  • Output alignment is consistency across overlapping timestamps in predictions generated from lagged inputs.The paper illustrates the distinction with overlapping forecasts that show either similar or divergent patterns.Source: §3 · p. 4
  • Lagged inputs are shifted by a lag, producing prediction sequences whose overlapping segments are compared to assess alignment.The overlap length is h′ = h − l.Source: §3 · p. 4
  • TAM averages the MAE between all pairs of overlapping output sequences, with lower values indicating better alignment.The metric is defined over N overlapping predictions.Source: §3 · p. 4
  • Unlike MSE or MAE against ground truth, TAM measures distances between overlapping predictions and captures their fluctuations across forecasts.The paper describes lower TAM as reflecting improved alignment and data-model robustness.Source: §3 · p. 4

4 Improving output alignment (AliO)

AliO aligns overlapping predictions in the time and frequency domains while maintaining their direction toward ground truth. Its components combine temporal alignment, regression pulling, frequency alignment, and a weighted alignment loss added to the forecasting regression loss.

4 Improving output alignment (AliO)

  • AliO reduces discrepancies between overlapping predictions in time and frequency domains while maintaining forecasting regression performance by aligning predictions with ground truth.Regression pulling with stop-gradient is used to pursue both objectives.Source: §4 · p. 5

4.1 Time domain alignment

  • Time-domain alignment minimizes distances between overlapping predictions, but doing so alone may move both predictions away from ground truth and degrade forecasting performance.The distance function may be MSE or Dynamic Time Warping.Source: §4.1 · p. 5

4.2 Regression pulling (RegPull)

  • Regression pulling uses stop-gradient on selected prediction points to align overlaps while keeping the alignment-loss direction consistent with forecasting regression.Points farther from ground truth are pulled toward it, aligning optimization with regression loss.Source: §4.2 · pp. 5–6

4.3 Frequency domain alignment

  • Frequency-domain alignment complements temporal alignment by aligning phase and amplitude components to improve consistency in time.Theorems connect frequency-domain MSE to phase alignment and, once phases align, reduced amplitude differences.Source: §4.3 · pp. 6–7

4.4 AliO loss

  • The AliO loss weights time- and frequency-domain alignment losses and adds their combination to the forecasting regression loss.λT and λF control the respective alignment contributions.Source: §4.4 · p. 7

5 Experiment

Experiments evaluate AliO across LTSF models and datasets, comparing forecasting accuracy and output alignment. They also examine how results vary with alignment coefficients, overlapping predictions, lag size, and initial alignment.

5 Experiment

  • The experiments cover seven LTSF model families and representative datasets, using AliO settings N = 2 and l = 1 and averaging results across prediction lengths.The models span Transformer-, linear-, CNN-, and LLM-based approaches; datasets include ETT, Electricity, Traffic, Weather, and ILI.Source: §5 · p. 7

5.1 Output alignment and forecasting performance

  • AliO improves TAM by up to 70.5% for CycleNet and MSE by up to 11.5% across seven datasets.Table 1 compares baseline and AliO models using MSE and TAM2, averaged over three seeds and prediction lengths.Source: §5.1 · p. 7, Table 1 · p. 8

5.2 How AliO maintains or improves regression performance

  • On ILI, AliO improves MSE by 17.4% and TAM by 58.1%, where baseline output alignment is poor.The paper reports comparatively smaller MSE improvements on datasets with better initial alignment.Source: §5.2 · p. 8, Table 2 · p. 8
  • With AliO, DLinear predictions on ILI align better in both time and frequency domains, reducing TAM and improving MSE.Figure 5 shows alignment of both phase and amplitude in the frequency domain.Source: §5.2 · p. 8, Figure 5 · p. 9

5.3 Hyper-parameter Analysis

  • Increasing λT from 1.0 to 5.0 consistently improves TAM; λF has a less pronounced, context-dependent effect on MSE and TAM.When λT alone cannot improve performance, λF can affect both metrics; the heatmaps show normalized MSE and TAM across coefficient settings.Source: §5.3 · pp. 8–9, Figure 6 · p. 9
  • Higher initial TAM, indicating poorer alignment, is positively associated with greater MSE improvement; the reported correlation coefficient is 0.33.The passage describes this as a positive trend.Source: Figure 4 · p. 9
  • Increasing the number of overlapping predictions N improves TAM, while increasing lag l degrades it; MSE has no clear overall trend.When both N and l are large, MSE tends to increase; balanced settings such as (l, N) = (1, 8), (2, 4), and (8, 2) have lower MSE values.Source: §5.3 · p. 9, Figure 7 · p. 9

6 Related works

The paper frames output alignment as data-model robustness, distinct from robustness to model initialization. It contrasts AliO with existing work on initialization robustness and contrastive learning.

6 Related works

  • The paper states that prior work had not adequately identified the output alignment problem and offered a solution.It describes AliO as addressing that gap.Source: §6 · p. 9
  • Output alignment concerns consistent predictions for lagged inputs, which the paper terms data-model robustness, rather than consistency across randomly initialized weights.The paper presents TAM as a way to quantify this aspect of robustness.Source: §6 · pp. 9–10
  • Unlike AliO, contrastive learning aligns representations or whole vectors, not overlapping output timestamps, and does not use regression pulling.The paper says AliO operates independently of existing methods and can be integrated with them.Source: §6 · p. 10

7 Limitations and discussions

The discussion identifies volatile datasets as a caution for TAM and points to alternative distance functions as a direction for improving regression performance.

7 Limitations and discussions

  • TAM should be used cautiously on highly volatile datasets outside typical LTSF tasks, although the Exchange Rate results suggest potential applicability in volatile settings.The paper identifies more robust metrics for inherently volatile data as future work.Source: §7 · p. 10
  • AliO’s MSE distance may help under high initial TAM because it matches the training regression loss; shape-sensitive alternatives remain a future direction.The paper presents alternative distance functions as promising directions for exploration, not established improvements.Source: §7 · p. 10

8 Conclusion

The conclusion presents AliO as a time- and frequency-domain approach to output alignment, with reported improvements in both MSE and TAM. An electricity-demand example illustrates the practical stakes of inconsistent forecasts.

8 Conclusion

  • AliO addresses output alignment with TAM as its quantitative measure and reports up to 27.5% MSE improvement and up to 58.2% TAM improvement.The approach aligns predictions in both time and frequency domains.Source: §8 · p. 10

A Exemplar illustrations on importance of output alignment

  • In the electricity-demand example, differing forecasts lead people to view the March budget as wasted.The example illustrates why differing predictions for the same forecasting scenario can matter in practice.Source: Figure 8 · p. 13

B.1 Proof of Theorem 4.1

The appendix proofs connect frequency-domain discrepancies to phase and amplitude alignment, while visualizations illustrate improved alignment. It also states when TAM may be unreliable and describes a figure relating initial TAM to MSE improvement.

B.1 Proof of Theorem 4.1

  • Minimizing the frequency-domain discrepancy increases the cosine between prediction phases, aligning them because one prediction is fixed by stop-gradient.The proof identifies the stop-gradient prediction as the constant reference.Source: §B.1 · p. 14

B.2 Proof of Theorem 4.2

  • With one prediction fixed by stop-gradient, reducing the frequency-domain discrepancy also reduces the amplitude difference.The passages frame this as the result proved in Theorem 4.2.Source: §B.2 · p. 14

C Visualization of alignment

  • AliO improves alignment for overlapping timestamps in visualizations of DLinear, PatchTST, TimesNet, and iTransformer.The figures compare regression loss alone with regression loss plus AliO on ECL, ETTm1, ETTm2, and Solar, respectively.Source: Figure 9 · p. 14, Figure 10 · p. 15, Figure 11 · p. 15

D On sudden event

  • TAM assumes predictable, stable outputs; sudden events or OOD inputs may violate that assumption, although precursor signals can preserve its validity when outputs remain predictable.The paper advises caution in perturbed settings.Source: D On sudden event · p. 17

E Initial TAM vs. MSE improvement

F Zero coefficient of time domain alignment (λT)

The appendix examines AliO with a zero time-domain coefficient and illustrates normalized MSE and TAM across time- and frequency-domain coefficient settings. It reports that nonzero time alignment is important, while coefficients that are too large can degrade performance.

F Zero coefficient of time domain alignment (λT)

  • Fig. 6 shows increasing λT consistently improves TAM; an excessively large coefficient can dominate regression loss and degrade performance, while an appropriate non-zero coefficient improves performance.The reported tables use lag 1 and two sequences (default).Source: F Zero coefficient of time domain… · p. 18
  • The figures compare normalized MSE on the left and TAM on the right across λF on the x-axis and λT on the y-axis.The supplied figures cover CycleNet, iTransformer, and TimesNet on several datasets.Source: Figure 14 · p. 18, Figure 16 · p. 18, Figure 18 · p. 18

G Dataset explanation

The appendix describes the datasets and evaluation settings used in the experiments. The collection spans electricity, exchange-rate, health, traffic, and solar-energy series, with dataset-specific sampling and forecasting configurations.

G Dataset explanation

  • The ETT subsets provide hourly or 15-minute records, Exchange contains daily exchange rates, and ECL contains minute-sampled household electricity consumption.ETT covers two years of data from two counties in China; Exchange spans 1990–2016, and ECL covers four years.Source: G Dataset explanation · p. 19
  • ILI contains weekly influenza-like-illness records, PEMS records highway traffic every five minutes, Solar-Energy covers 137 plants, and Traffic tracks hourly freeway congestion.The passages specify ILI records from 2002–2021, Solar-Energy in 2006, and Traffic data from 2015–2016.Source: G Dataset explanation · p. 20
  • For fair evaluation, experiments adopted sequence, prediction, and label length settings from recent LTSF models; for Autoformer, they followed its official implementation’s prediction lengths of 24, 48, 168, 336, and 720.Source: G Dataset explanation · p. 20

H Experiment configurations

The experiments preserve benchmark models’ original architectures and official configurations, while specifying AliO coefficients, evaluation metrics, and robustness procedures. AliO’s time and frequency losses use MSE, with the frequency-domain term optional by default.

H Experiment configurations

  • The experiments use official benchmark code and retain each model’s original architecture and official sequence, prediction, and label lengths.The models include Autoformer, DLinear, PatchTST, TimesNet, iTransformer, GPT4TS, and CycleNet.Source: H Experiment configurations · p. 20
  • Context lengths are 96 for CycleNet, Autoformer, and iTransformer; 96 for TimesNet except 36 on ILI; and 336 for PatchTST and DLinear except 104 on ILI.The listed context lengths follow the cited model papers.Source: H Experiment configurations · p. 20
  • Most prediction lengths are {96, 192, 336, 720}; ILI uses {24, 36, 48, 60}, and ETT lengths differ for Autoformer versus other models.Autoformer uses {24, 48, 168, 336, 720} on ETT; other models use {96, 192, 336, 720}.Source: H Experiment configurations · p. 21
  • AliO uses N = 2 samples and lag l = 1 by default, MSE distances in both domains, and optional frequency alignment with default λF = 0.λT and λF are selected from {1.0, 2.0, 5.0} and {0.0, 0.5, 1.0, 2.0}; AWL tunes coefficients automatically.Source: H Experiment configurations · p. 21
  • The evaluation reports MSE, MAE, MAPE, RMSE, and TAM, with lower values indicating better performance; robustness uses three random seeds.The seeds are 2023, 2024, and 2025, and baseline and AliO comparisons use the same GPU.Source: H Experiment configurations · p. 21

I Full experimental results

This section presents AliO’s full comparisons with seven LTSF baselines on forecasting and alignment metrics, alongside checklist statements about potential costs of improved stability, risks and ethical concerns, and LLM use.

I Full experimental results

NeurIPS Paper Checklist

  • The authors state that their open-source data and models pose no potential risks, adverse outcomes, or ethical concerns.They also report that the paper poses no risks requiring responsible-release safeguards.Source: NeurIPS Paper Checklist · pp. 43–44
  • The authors say improved predictive stability can reduce social time and resource costs associated with potential budget reallocations.They identify this as a positive societal impact of the technology.Source: NeurIPS Paper Checklist · p. 43
Loading 2610.11213v1…