An all-MLP structure for time collection forecasting – Google Analysis Weblog

Time series forecasting is vital to varied real-world purposes, from demand forecasting to pandemic spread prediction. In multivariate time series forecasting (forecasting a number of variants on the similar time), one can break up present strategies into two classes: univariate fashions and multivariate fashions. Univariate fashions deal with inter-series interactions or temporal patterns that embody developments and seasonal patterns on a time collection with a single variable. Examples of such developments and seasonal patterns is perhaps the way in which mortgage charges enhance attributable to inflation, and the way site visitors peaks throughout rush hour. Along with inter-series patterns, multivariate fashions course of intra-series options, generally known as cross-variate data, which is particularly helpful when one collection is a sophisticated indicator of one other collection. For instance, an increase in physique weight might trigger a rise in blood stress, and rising the value of a product might result in a lower in gross sales. Multivariate fashions have recently become popular solutions for multivariate forecasting as practitioners consider their functionality of dealing with cross-variate data might result in higher efficiency.

Lately, deep studying Transformer-based architectures have turn out to be a well-liked selection for multivariate forecasting fashions attributable to their superior efficiency on sequence duties. Nevertheless, superior multivariate fashions perform surprisingly worse than easy univariate linear fashions on commonly-used long-term forecasting benchmarks, similar to Electricity Transformer Temperature (ETT), Electricity, Traffic, and Weather. These outcomes elevate two questions:

  • Does cross-variate data profit time collection forecasting?
  • When cross-variate data isn’t helpful, can multivariate fashions nonetheless carry out in addition to univariate fashions?

In “TSMixer: An All-MLP Architecture for Time Series Forecasting”, we analyze some great benefits of univariate linear fashions and reveal their effectiveness. Insights from this evaluation lead us to develop Time-Collection Mixer (TSMixer), a sophisticated multivariate mannequin that leverages linear mannequin traits and performs nicely on long-term forecasting benchmarks. To the most effective of our data, TSMixer is the primary multivariate mannequin that performs in addition to state-of-the-art univariate fashions on long-term forecasting benchmarks, the place we present that cross-variate data is much less helpful. To exhibit the significance of cross-variate data, we consider a tougher real-world utility, M5. Lastly, empirical outcomes present that TSMixer outperforms state-of-the-art fashions, similar to PatchTST, Fedformer, Autoformer, DeepAR and TFT.

TSMixer structure

A key distinction between linear fashions and Transformers is how they seize temporal patterns. On one hand, linear fashions apply fastened and time-step-dependent weights to seize static temporal patterns, and are unable to course of cross-variate data. However, Transformers use attention mechanisms that apply dynamic and data-dependent weights at every time step, capturing dynamic temporal patterns and enabling them to course of cross-variate data.

In our evaluation, we present that below widespread assumptions of temporal patterns, linear fashions have naïve options to completely recuperate the time collection or place bounds on the error, which implies they’re nice options for studying static temporal patterns of univariate time collection extra successfully. In distinction, it’s non-trivial to search out comparable options for consideration mechanisms, because the weights utilized to every time step are dynamic. Consequently, we develop a brand new structure by changing Transformer consideration layers with linear layers. The ensuing TSMixer mannequin, which has similarities to the pc imaginative and prescient MLP-Mixer technique, alternates between purposes of the multi-layer perceptron in numerous instructions, which we name time-mixing and feature-mixing, respectively. The TSMixer structure effectively captures each temporal patterns and cross-variate data, as proven within the determine beneath. The residual designs make sure that TSMixer retains the capability of temporal linear fashions whereas nonetheless with the ability to exploit cross-variate data.

Transformer block and TSMixer block architectures. TSMixer replaces the multi-head consideration layer with time-mixing, a linear mannequin utilized on the time dimension.

Comparability between data-dependent (consideration mechanisms) and time-step-dependent (linear fashions). That is an instance of forecasting the subsequent time step by studying the weights of the earlier three time steps.

Analysis on long-term forecasting benchmarks

We consider TSMixer utilizing seven standard long-term forecasting datasets (ETTm1, ETTm2, ETTh1, ETTh2, Electricity, Traffic, and Weather), the place recent research has proven that univariate linear fashions outperform superior multivariate fashions with giant margins. We examine TSMixer with state-of-the-art multivariate fashions (TFT, FEDformer, Autoformer, Informer), and univariate fashions, together with linear models and PatchTST. The determine beneath exhibits the typical enchancment of mean squared error (MSE) by TSMixer in contrast with others. The typical is calculated throughout datasets and a number of forecasting horizons. We exhibit that TSMixer considerably outperforms different multivariate fashions and performs on par with state-of-the-art univariate fashions. These outcomes present that multivariate fashions are able to performing in addition to univariate fashions.

The typical MSE enchancment of TSMixer in contrast with different baselines. The pink bars present multivariate strategies and the blue bars present univariate strategies. TSMixer achieves important enchancment over different multivariate fashions and achieves comparable outcomes to univariate fashions.

Ablation research

We carried out an ablation research to check TSMixer with TMix-Solely, a TSMixer variant that consists of time mixing layers solely. The outcomes present that TMix-Solely performs nearly the identical as TSMixer, which implies the extra function mixing layers don’t enhance the efficiency and confirms that cross-variate data is much less helpful on standard benchmarks. The outcomes validate the superior univariate mannequin efficiency proven in previous research. Nevertheless, present long-term forecasting benchmarks will not be nicely consultant of the necessity for cross-variate data in some real-world purposes the place time collection could also be intermittent or sparse, therefore temporal patterns might not be adequate for forecasting. Due to this fact, it could be inappropriate to guage multivariate forecasting fashions solely on these benchmarks.

Analysis on M5: Effectiveness of cross-variate data

To additional exhibit the good thing about multivariate fashions, we consider TSMixer on the difficult M5 benchmark, a large-scale retail dataset containing essential cross-variate interactions. M5 incorporates the knowledge of 30,490 merchandise collected over 5 years. Every product description contains time collection knowledge, like each day gross sales, promote worth, promotional occasion data, and static (non-time-series) options, similar to retailer location and product class. The purpose is to forecast the each day gross sales of every product for the subsequent 28 days, evaluated utilizing the weighted root mean square scaled error (WRMSSE) from the M5 competitors. The difficult nature of retail makes it tougher to forecast solely utilizing univariate fashions that target temporal patterns, so multivariate fashions with cross-variate data and even auxiliary options are extra important.

First, we examine TSMixer to different strategies solely contemplating the historic knowledge, similar to each day gross sales and historic promote costs. The outcomes present that multivariate fashions outperforms univariate fashions considerably, indicating the usefulness of cross-variate data. And amongst all in contrast strategies, TSMixer successfully leverages the cross-variate data and achieves the most effective efficiency.

Moreover, to leverage extra data, similar to static options (e.g., retailer location, product class) and future time collection (e.g., a promotional occasion scheduled in coming days) supplied in M5, we suggest a precept design to increase TSMixer. The prolonged TSMixer aligns various kinds of options into the identical size, after which applies a number of mixing layers to the concatenated options to make predictions. The prolonged TSMixer structure outperforms fashions standard in industrial purposes, together with DeepAR and TFT, showcasing its robust potential for real-world impression.

The structure of the prolonged TSMixer. Within the first stage (align stage), it aligns the various kinds of options into the identical size earlier than concatenating them. Within the second stage (mixing stage) it applies a number of mixing layers conditioned with static options.

The WRMSSE on M5. The primary three strategies (blue) are univariate fashions. The center three strategies (orange) are multivariate fashions that contemplate solely historic options. The final three strategies (pink) are multivariate fashions that contemplate historic, future, and static options.


We current TSMixer, a sophisticated multivariate mannequin that leverages linear mannequin traits and performs in addition to state-of-the-art univariate fashions on long-term forecasting benchmarks. TSMixer creates new potentialities for the event of time collection forecasting architectures by offering insights into the significance of cross-variate and auxiliary data in real-world situations. The empirical outcomes spotlight the necessity to contemplate extra reasonable benchmarks for multivariate forecasting fashions in future analysis. We hope that this work will encourage additional exploration within the subject of time collection forecasting, and result in the event of extra highly effective and efficient fashions that may be utilized to real-world purposes.


This analysis was carried out by Si-An Chen, Chun-Liang Li, Nate Yoder, Sercan O. Arik, and Tomas Pfister.

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