# FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting

arXiv: https://arxiv.org/abs/2302.00962 · HTML: https://mlsanity.com/paper/2302.00962/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Global Filter Networks for Image Classification](https://mlsanity.com/paper/2107.00645/) (2021)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [ETSformer: Exponential Smoothing Transformers for Time-series Forecasting](https://mlsanity.com/paper/2202.01381/) (2022)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Exploring Interpretable LSTM Neural Networks over Multi-Variable Data](https://mlsanity.com/paper/1905.12034/) (2019)
- [Approximation Properties of Deep ReLU CNNs](https://mlsanity.com/paper/2109.00190/) (2021)
- [Sliced Recurrent Neural Networks](https://mlsanity.com/paper/1807.02291/) (2018)
- [An Interpretive Constrained Linear Model for ResNet and MgNet](https://mlsanity.com/paper/2112.07441/) (2021)
- [Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space](https://mlsanity.com/paper/2203.00614/) (2022)

## Built on by (most cited first, 2 of 2)

- [Orthogonal greedy algorithm for linear operator learning with shallow neural network](https://mlsanity.com/paper/2501.02791/) (2025)
- [Self-composing neural operators for high-frequency and multiscale PDE surrogates](https://mlsanity.com/paper/2508.20650/) (2025)

## Abstract (arXiv)

By investigating iterative methods for a constrained linear model, we propose a new class of fully connected V-cycle MgNet for long-term time series forecasting, which is one of the most difficult tasks in forecasting. MgNet is a CNN model that was proposed for image classification based on the multigrid (MG) methods for solving discretized partial differential equations (PDEs). We replace the convolutional operations with fully connected operations in the existing MgNet and then apply them to forecasting problems. Motivated by the V-cycle structure in MG, we further propose the FV-MgNet, a V-cycle version of the fully connected MgNet, to extract features hierarchically. By evaluating the performance of FV-MgNet on popular data sets and comparing it with state-of-the-art models, we show that the FV-MgNet achieves better results with less memory usage and faster inference speed. In addition, we develop ablation experiments to demonstrate that the structure of FV-MgNet is the best choice among the many variants.