Accurate forecasting of multivariate time series data remains a formidable challenge, particularly due to the growing complexity of temporal dependencies in real-world scenarios. While neural network-based models have achieved notable success in this domain, complex channel-dependent models often suffer from performance degradation compared to channel-independent models that do not consider the relationship between components but provide high robustness due to small capacity. In this work, we propose HN-MVTS, a novel architecture that integrates the hypernetwork-based generative prior with an arbitrary neural network forecasting model. The input of this hypernetwork is a learnable embedding matrix of time series components. To restrict the number of new parameters, the hypernetwork learns to generate the weights of the last layer of the target forecasting networks, serving as a data-adaptive regularizer that improves generalization and long-range predictive accuracy. The hypernetwork is only used during training, so it does not increase the inference time compared to the base forecasting model. Extensive experiments on eight benchmark datasets demonstrate that application of HN-MVTS to the state-of-the-art models (DLinear, PatchTST, TSMixer, etc.) typically improves their performance. Our findings suggest that hypernetwork-driven parameterization offers a promising direction for enhancing existing forecasting techniques in complex scenarios.

The paper will provide examples of computer vision tasks in which topological data analysis gave new effective solutions. Ideas underlying topological data analysis and its basic methods will be briefly described and illustrated with examples of computer vision problems. No prior knowledge in topological data analysis and computational geometry is assumed, a brief introduction to subject is given throughout the text.