TSMixer: An all-MLP architecture for time series forecasting

Posted by Si-An Chen, Student Researcher, Cloud AI Team, and Chun-Liang Li, Research Scientist, Cloud AI Team Time series forecasting is critical to various real-world applications, from demand forecasting to pandemic spread prediction. In multivariate time series forecasting (forecasting multiple variants at the same time), one can split existing methods into two categories: univariate models and multivariate models. Univariate models focus on inter-series interactions or temporal patterns that encompass trends and seasonal patterns on a time series with a single variable. Examples of such trends and seasonal patterns might be the way mortgage rates increase due to inflation, and how traffic peaks during rush hour. In addition to inter-series patterns, multivariate models process intra-series features, known as cross-variate information, which is especially useful when one series is an advanced indicator of another series. For example, a rise in body weight may cause an increase in blood pressure, and increasing the price of a product may lead to a decrease in sales. Multivariate models have recently become popular solutions for multivariate forecasting as practitioners believe their capability of handling cross-variate information may lead to better performance. In recent years, deep learning Transformer-based architectures have become a popular choice for multivariate forecasting models due to their superior performance on sequence tasks. However, advanced multivariate models perform surprisingly worse than simple univariate linear models on commonly-used long-term forecasting benchmarks, such as Electricity Transformer Temperature (ETT), Electricity, Traffic, and Weather. These results raise two questions: Does cross-variate information benefit time series forecasting? When cross-variate information is not beneficial, can multivariate models still perform as well as univariate models? In “TSMixer: An All-MLP Architecture for Time Series Forecasting”, we analyze the advantages of univariate linear models and reveal their effectiveness. Insights from this analysis lead us to develop Time-Series Mixer (TSMixer), an advanced multivariate model that leverages linear model characteristics and performs well on long-term forecasting benchmarks. To the best of our knowledge, TSMixer is the first multivariate model that performs as well as state-of-the-art univariate models on long-term forecasting benchmarks, where we show that cross-variate information is less beneficial. To demonstrate the importance of cross-variate information, we evaluate a more challenging real-world application, M5. Finally, empirical results show that TSMixer outperforms state-of-the-art models, such as PatchTST, Fedformer, Autoformer, DeepAR and TFT. TSMixer architecture A key difference between linear models and Transformers is how they capture temporal patterns. On one hand, linear models apply fixed and time-step-dependent weights to capture static temporal patterns, and are unable to process cross-variate information. On the other hand, Transformers use attention mechanisms that apply dynamic and data-dependent weights at each time step, capturing dynamic temporal patterns and enabling them to process cross-variate information. In our analysis, we show that under common assumptions of temporal patterns, linear models have naïve solutions to perfectly recover the time series or place bounds on the error, which means they are great solutions for learning static temporal patterns of univariate time series more effectively. In contrast, it is non-trivial to find similar solutions for attention mechanisms, as the weights applied to each time step are dynamic. Consequently, we develop a new architecture by replacing Transformer attention layers with linear layers. The resulting TSMixer model, which is similar to the computer vision MLP-Mixer method, alternates between applications of the multi-layer perceptron in different directions, which we call time-mixing and feature-mixing, respectively. The TSMixer architecture efficiently captures both temporal patterns and cross-variate information, as shown in the figure below. The residual designs ensure that TSMixer retains the capacity of temporal linear models while still being able to exploit cross-variate information. Transformer block and TSMixer block architectures. TSMixer replaces the multi-head attention layer with time-mixing, a linear model applied on the time dimension. Comparison between data-dependent (attention mechanisms) and time-step-dependent (linear models). This is an example of forecasting the next time step by learning the weights of the previous three time steps. Evaluation on long-term forecasting benchmarks We evaluate TSMixer using seven popular long-term forecasting datasets (ETTm1, ETTm2, ETTh1, ETTh2, Electricity, Traffic, and Weather), where recent research has shown that univariate linear models outperform advanced multivariate models with large margins. We compare TSMixer with state-of-the-art multivariate models (TFT, FEDformer, Autoformer, Informer), and univariate models, including linear models and PatchTST. The figure below shows the average improvement of mean squared error (MSE) by TSMixer compared with others. The average is calculated across datasets and multiple forecasting horizons. We demonstrate that TSMixer significantly outperforms other multivariate models and performs on par with state-of-the-art univariate models. These results show that multivariate models are capable of performing as well as univariate models. The average MSE improvement of TSMixer compared with other baselines. The red bars show multivariate methods and the blue bars show univariate methods. TSMixer achieves significant improvement over other multivariate models and achieves comparable results to univariate models. Ablation study We performed an ablation study to compare TSMixer with TMix-Only, a TSMixer variant that consists of time mixing layers only. The results show that TMix-Only performs almost the same as TSMixer, which means the additional feature mixing layers do not improve the performance and confirms that cross-variate information is less beneficial on popular benchmarks. The results validate the superior univariate model performance shown in previous research. However, existing long-term forecasting benchmarks are not well representative of the need for cross-variate information in some real-world applications where time series may be intermittent or sparse, hence temporal patterns may not be sufficient for forecasting. Therefore, it may be inappropriate to evaluate multivariate forecasting models solely on these benchmarks. Evaluation on M5: Effectiveness of cross-variate information To further demonstrate the benefit of multivariate models, we evaluate TSMixer on the challenging M5 benchmark, a large-scale retail dataset containing crucial cross-variate interactions. M5 contains the information of 30,490 products collected over 5 years. Each product description includes time series data, like daily sales, sell price, promotional event information, and static (non-time-series) features, such as store location and product category. The goal is to forecast the daily sales of each product for the next 28 days, evaluated using the weighted root mean square scaled error (WRMSSE) from the M5 competition. The complicated nature of retail makes it more challenging to forecast solely using univariate models that focus on temporal patterns, so multivariate models with cross-variate information and even auxiliary features are more essential. First, we compare TSMixer to other methods only considering the historical data, such as daily sales and historical sell prices. The results show that multivariate models outperforms univariate models significantly, indicating the usefulness of cross-variate information. And among all compared methods, TSMixer effectively leverages the cross-variate information and achieves the best performance. Additionally, to leverage more information, such as static features (e.g., store location, product category) and future time series (e.g., a promotional event scheduled in coming days) provided in M5, we propose a principle design to extend TSMixer. The extended TSMixer aligns different types of features into the same length, and then applies multiple mixing layers to the concatenated features to make predictions. The extended TSMixer architecture outperforms models popular in industrial applications, including DeepAR and TFT, showcasing its strong potential for real-world impact. The architecture of the extended TSMixer. In the first stage (align stage), it aligns the different types of features into the same length before concatenating them. In the second stage (mixing stage) it applies multiple mixing layers conditioned with static features. The WRMSSE on M5. The first three methods (blue) are univariate models. The middle three methods (orange) are multivariate models that consider only historical features. The last three methods (red) are multivariate models that consider historical, future, and static features. Conclusion We present TSMixer, an advanced multivariate model that leverages linear model characteristics and performs as well as state-of-the-art univariate models on long-term forecasting benchmarks. TSMixer creates new possibilities for the development of time series forecasting architectures by providing insights into the importance of cross-variate and auxiliary information in real-world scenarios. The empirical results highlight the need to consider more realistic benchmarks for multivariate forecasting models in future research. We hope that this work will inspire further exploration in the field of time series forecasting, and lead to the development of more powerful and effective models that can be applied to real-world applications. Acknowledgements This research was conducted by Si-An Chen, Chun-Liang Li, Nate Yoder, Sercan O. Arik, and Tomas Pfister.

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Posted by Si-An Chen, Student Researcher, Cloud AI Team, and Chun-Liang Li, Research Scientist, Cloud AI Team

Time series forecasting is critical to various real-world applications, from demand forecasting to pandemic spread prediction. In multivariate time series forecasting (forecasting multiple variants at the same time), one can split existing methods into two categories: univariate models and multivariate models. Univariate models focus on inter-series interactions or temporal patterns that encompass trends and seasonal patterns on a time series with a single variable. Examples of such trends and seasonal patterns might be the way mortgage rates increase due to inflation, and how traffic peaks during rush hour. In addition to inter-series patterns, multivariate models process intra-series features, known as cross-variate information, which is especially useful when one series is an advanced indicator of another series. For example, a rise in body weight may cause an increase in blood pressure, and increasing the price of a product may lead to a decrease in sales. Multivariate models have recently become popular solutions for multivariate forecasting as practitioners believe their capability of handling cross-variate information may lead to better performance.

In recent years, deep learning Transformer-based architectures have become a popular choice for multivariate forecasting models due to their superior performance on sequence tasks. However, advanced multivariate models perform surprisingly worse than simple univariate linear models on commonly-used long-term forecasting benchmarks, such as Electricity Transformer Temperature (ETT), Electricity, Traffic, and Weather. These results raise two questions:

  • Does cross-variate information benefit time series forecasting?
  • When cross-variate information is not beneficial, can multivariate models still perform as well as univariate models?

In “TSMixer: An All-MLP Architecture for Time Series Forecasting”, we analyze the advantages of univariate linear models and reveal their effectiveness. Insights from this analysis lead us to develop Time-Series Mixer (TSMixer), an advanced multivariate model that leverages linear model characteristics and performs well on long-term forecasting benchmarks. To the best of our knowledge, TSMixer is the first multivariate model that performs as well as state-of-the-art univariate models on long-term forecasting benchmarks, where we show that cross-variate information is less beneficial. To demonstrate the importance of cross-variate information, we evaluate a more challenging real-world application, M5. Finally, empirical results show that TSMixer outperforms state-of-the-art models, such as PatchTST, Fedformer, Autoformer, DeepAR and TFT.

TSMixer architecture

A key difference between linear models and Transformers is how they capture temporal patterns. On one hand, linear models apply fixed and time-step-dependent weights to capture static temporal patterns, and are unable to process cross-variate information. On the other hand, Transformers use attention mechanisms that apply dynamic and data-dependent weights at each time step, capturing dynamic temporal patterns and enabling them to process cross-variate information.

In our analysis, we show that under common assumptions of temporal patterns, linear models have naïve solutions to perfectly recover the time series or place bounds on the error, which means they are great solutions for learning static temporal patterns of univariate time series more effectively. In contrast, it is non-trivial to find similar solutions for attention mechanisms, as the weights applied to each time step are dynamic. Consequently, we develop a new architecture by replacing Transformer attention layers with linear layers. The resulting TSMixer model, which is similar to the computer vision MLP-Mixer method, alternates between applications of the multi-layer perceptron in different directions, which we call time-mixing and feature-mixing, respectively. The TSMixer architecture efficiently captures both temporal patterns and cross-variate information, as shown in the figure below. The residual designs ensure that TSMixer retains the capacity of temporal linear models while still being able to exploit cross-variate information.

Transformer block and TSMixer block architectures. TSMixer replaces the multi-head attention layer with time-mixing, a linear model applied on the time dimension.

Comparison between data-dependent (attention mechanisms) and time-step-dependent (linear models). This is an example of forecasting the next time step by learning the weights of the previous three time steps.

Evaluation on long-term forecasting benchmarks

We evaluate TSMixer using seven popular long-term forecasting datasets (ETTm1, ETTm2, ETTh1, ETTh2, Electricity, Traffic, and Weather), where recent research has shown that univariate linear models outperform advanced multivariate models with large margins. We compare TSMixer with state-of-the-art multivariate models (TFT, FEDformer, Autoformer, Informer), and univariate models, including linear models and PatchTST. The figure below shows the average improvement of mean squared error (MSE) by TSMixer compared with others. The average is calculated across datasets and multiple forecasting horizons. We demonstrate that TSMixer significantly outperforms other multivariate models and performs on par with state-of-the-art univariate models. These results show that multivariate models are capable of performing as well as univariate models.

The average MSE improvement of TSMixer compared with other baselines. The red bars show multivariate methods and the blue bars show univariate methods. TSMixer achieves significant improvement over other multivariate models and achieves comparable results to univariate models.

Ablation study

We performed an ablation study to compare TSMixer with TMix-Only, a TSMixer variant that consists of time mixing layers only. The results show that TMix-Only performs almost the same as TSMixer, which means the additional feature mixing layers do not improve the performance and confirms that cross-variate information is less beneficial on popular benchmarks. The results validate the superior univariate model performance shown in previous research. However, existing long-term forecasting benchmarks are not well representative of the need for cross-variate information in some real-world applications where time series may be intermittent or sparse, hence temporal patterns may not be sufficient for forecasting. Therefore, it may be inappropriate to evaluate multivariate forecasting models solely on these benchmarks.

Evaluation on M5: Effectiveness of cross-variate information

To further demonstrate the benefit of multivariate models, we evaluate TSMixer on the challenging M5 benchmark, a large-scale retail dataset containing crucial cross-variate interactions. M5 contains the information of 30,490 products collected over 5 years. Each product description includes time series data, like daily sales, sell price, promotional event information, and static (non-time-series) features, such as store location and product category. The goal is to forecast the daily sales of each product for the next 28 days, evaluated using the weighted root mean square scaled error (WRMSSE) from the M5 competition. The complicated nature of retail makes it more challenging to forecast solely using univariate models that focus on temporal patterns, so multivariate models with cross-variate information and even auxiliary features are more essential.

First, we compare TSMixer to other methods only considering the historical data, such as daily sales and historical sell prices. The results show that multivariate models outperforms univariate models significantly, indicating the usefulness of cross-variate information. And among all compared methods, TSMixer effectively leverages the cross-variate information and achieves the best performance.

Additionally, to leverage more information, such as static features (e.g., store location, product category) and future time series (e.g., a promotional event scheduled in coming days) provided in M5, we propose a principle design to extend TSMixer. The extended TSMixer aligns different types of features into the same length, and then applies multiple mixing layers to the concatenated features to make predictions. The extended TSMixer architecture outperforms models popular in industrial applications, including DeepAR and TFT, showcasing its strong potential for real-world impact.

The architecture of the extended TSMixer. In the first stage (align stage), it aligns the different types of features into the same length before concatenating them. In the second stage (mixing stage) it applies multiple mixing layers conditioned with static features.

The WRMSSE on M5. The first three methods (blue) are univariate models. The middle three methods (orange) are multivariate models that consider only historical features. The last three methods (red) are multivariate models that consider historical, future, and static features.

Conclusion

We present TSMixer, an advanced multivariate model that leverages linear model characteristics and performs as well as state-of-the-art univariate models on long-term forecasting benchmarks. TSMixer creates new possibilities for the development of time series forecasting architectures by providing insights into the importance of cross-variate and auxiliary information in real-world scenarios. The empirical results highlight the need to consider more realistic benchmarks for multivariate forecasting models in future research. We hope that this work will inspire further exploration in the field of time series forecasting, and lead to the development of more powerful and effective models that can be applied to real-world applications.

Acknowledgements

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

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Distilling step-by-step: Outperforming larger language models with less training data and smaller model sizes

Posted by Cheng-Yu Hsieh, Student Researcher, and Chen-Yu Lee, Research Scientist, Cloud AI Team

Large language models (LLMs) have enabled a new data-efficient learning paradigm wherein they can be used to solve unseen new tasks via zero-shot or few-shot prompting. However, LLMs are challenging to deploy for real-world applications due to their sheer size. For instance, serving a single 175 billion LLM requires at least 350GB of GPU memory using specialized infrastructure, not to mention that today’s state-of-the-art LLMs are composed of over 500 billion parameters. Such computational requirements are inaccessible for many research teams, especially for applications that require low latency performance.

To circumvent these deployment challenges, practitioners often choose to deploy smaller specialized models instead. These smaller models are trained using one of two common paradigms: fine-tuning or distillation. Fine-tuning updates a pre-trained smaller model (e.g., BERT or T5) using downstream manually-annotated data. Distillation trains the same smaller models with labels generated by a larger LLM. Unfortunately, to achieve comparable performance to LLMs, fine-tuning methods require human-generated labels, which are expensive and tedious to obtain, while distillation requires large amounts of unlabeled data, which can also be hard to collect.

In “Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes”, presented at ACL2023, we set out to tackle this trade-off between model size and training data collection cost. We introduce distilling step-by-step, a new simple mechanism that allows us to train smaller task-specific models with much less training data than required by standard fine-tuning or distillation approaches that outperform few-shot prompted LLMs’ performance. We demonstrate that the distilling step-by-step mechanism enables a 770M parameter T5 model to outperform the few-shot prompted 540B PaLM model using only 80% of examples in a benchmark dataset, which demonstrates a more than 700x model size reduction with much less training data required by standard approaches.

While LLMs offer strong zero and few-shot performance, they are challenging to serve in practice. On the other hand, traditional ways of training small task-specific models require a large amount of training data. Distilling step-by-step provides a new paradigm that reduces both the deployed model size as well as the number of data required for training.

Distilling step-by-step

The key idea of distilling step-by-step is to extract informative natural language rationales (i.e., intermediate reasoning steps) from LLMs, which can in turn be used to train small models in a more data-efficient way. Specifically, natural language rationales explain the connections between the input questions and their corresponding outputs. For example, when asked, “Jesse’s room is 11 feet long and 15 feet wide. If she already has 16 square feet of carpet, how much more carpet does she need to cover the whole floor?”, an LLM can be prompted by the few-shot chain-of-thought (CoT) prompting technique to provide intermediate rationales, such as, “Area = length * width. Jesse’s room has 11 * 15 square feet.” That better explains the connection from the input to the final answer, “(11 * 15 ) – 16”. These rationales can contain relevant task knowledge, such as “Area = length * width”, that may originally require many data for small models to learn. We utilize these extracted rationales as additional, richer supervision to train small models, in addition to the standard task labels.

Overview on distilling step-by-step: First, we utilize CoT prompting to extract rationales from an LLM. We then use the generated rationales to train small task-specific models within a multi-task learning framework, where we prepend task prefixes to the input examples and train the model to output differently based on the given task prefix.

Distilling step-by-step consists of two main stages. In the first stage, we leverage few-shot CoT prompting to extract rationales from LLMs. Specifically, given a task, we prepare few-shot exemplars in the LLM input prompt where each example is composed of a triplet containing: (1) input, (2) rationale, and (3) output. Given the prompt, an LLM is able to mimic the triplet demonstration to generate the rationale for any new input. For instance, in a commonsense question answering task, given the input question “Sammy wanted to go to where the people are. Where might he go? Answer Choices: (a) populated areas, (b) race track, (c) desert, (d) apartment, (e) roadblock”, distilling step-by-step provides the correct answer to the question, “(a) populated areas”, paired with the rationale that provides better connection from the question to the answer, “The answer must be a place with a lot of people. Of the above choices, only populated areas have a lot of people.” By providing CoT examples paired with rationales in the prompt, the in-context learning ability allows LLMs to output corresponding rationales for future unseen inputs.

We use the few-shot CoT prompting, which contains both an example rationale (highlighted in green) and a label (highlighted in blue), to elicit rationales from an LLM on new input examples. The example is from a commonsense question answering task.

After the rationales are extracted, in the second stage, we incorporate the rationales in training small models by framing the training process as a multi-task problem. Specifically, we train the small model with a novel rationale generation task in addition to the standard label prediction task. The rationale generation task enables the model to learn to generate the intermediate reasoning steps for the prediction, and guides the model to better predict the resultant label. We prepend task prefixes (i.e., [label] and [rationale] for label prediction and rationale generation, respectively) to the input examples for the model to differentiate the two tasks.

Experimental setup

In the experiments, we consider a 540B PaLM model as the LLM. For task-specific downstream models, we use T5 models. For CoT prompting, we use the original CoT prompts when available and curate our own examples for new datasets. We conduct the experiments on four benchmark datasets across three different NLP tasks: e-SNLI and ANLI for natural language inference; CQA for commonsense question answering; and SVAMP for arithmetic math word problems. We include two sets of baseline methods. For comparison to few-shot prompted LLMs, we compare to few-shot CoT prompting with a 540B PaLM model. In the paper, we also compare standard task-specific model training to both standard fine-tuning and standard distillation. In this blogpost, we will focus on the comparisons to standard fine-tuning for illustration purposes.

Less training data

Compared to standard fine-tuning, the distilling step-by-step method achieves better performance using much less training data. For instance, on the e-SNLI dataset, we achieve better performance than standard fine-tuning when using only 12.5% of the full dataset (shown in the upper left quadrant below). Similarly, we achieve a dataset size reduction of 75%, 25% and 20% on ANLI, CQA, and SVAMP.

Distilling step-by-step compared to standard fine-tuning using 220M T5 models on varying sizes of human-labeled datasets. On all datasets, distilling step-by-step is able to outperform standard fine-tuning, trained on the full dataset, by using much less training examples.

Smaller deployed model size

Compared to few-shot CoT prompted LLMs, distilling step-by-step achieves better performance using much smaller model sizes. For instance, on the e-SNLI dataset, we achieve better performance than 540B PaLM by using a 220M T5 model. On ANLI, we achieve better performance than 540B PaLM by using a 770M T5 model, which is over 700X smaller. Note that on ANLI, the same 770M T5 model struggles to match PaLM’s performance using standard fine-tuning.

We perform distilling step-by-step and standard fine-tuning on varying sizes of T5 models and compare their performance to LLM baselines, i.e., Few-shot CoT and PINTO Tuning. Distilling step-by-step is able to outperform LLM baselines by using much smaller models, e.g., over 700× smaller models on ANLI. Standard fine-tuning fails to match LLM’s performance using the same model size.

Distilling step-by-step outperforms few-shot LLMs with smaller models using less data

Finally, we explore the smallest model sizes and the least amount of data for distilling step-by-step to outperform PaLM’s few-shot performance. For instance, on ANLI, we surpass the performance of the 540B PaLM using a 770M T5 model. This smaller model only uses 80% of the full dataset. Meanwhile, we observe that standard fine-tuning cannot catch up with PaLM’s performance even using 100% of the full dataset. This suggests that distilling step-by-step simultaneously reduces the model size as well as the amount of data required to outperform LLMs.

We show the minimum size of T5 models and the least amount of human-labeled examples required for distilling step-by-step to outperform LLM’s few-shot CoT by a coarse-grained search. Distilling step-by-step is able to outperform few-shot CoT using not only much smaller models, but it also achieves so with much less training examples compared to standard fine-tuning.

Conclusion

We propose distilling step-by-step, a novel mechanism that extracts rationales from LLMs as informative supervision in training small, task-specific models. We show that distilling step-by-step reduces both the training dataset required to curate task-specific smaller models and the model size required to achieve, and even surpass, a few-shot prompted LLM’s performance. Overall, distilling step-by-step presents a resource-efficient paradigm that tackles the trade-off between model size and training data required.

Availability on Google Cloud Platform

Distilling step-by-step is available for private preview on Vertex AI. If you are interested in trying it out, please contact vertex-llm-tuning-preview@google.com with your Google Cloud Project number and a summary of your use case.

Acknowledgements

This research was conducted by Cheng-Yu Hsieh, Chun-Liang Li, Chih-Kuan Yeh, Hootan Nakhost, Yasuhisa Fujii, Alexander Ratner, Ranjay Krishna, Chen-Yu Lee, and Tomas Pfister. Thanks to Xiang Zhang and Sergey Ioffe for their valuable feedback.

douglas.campbell@wellstar360.com September 21, 2023

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