# Functional Complexity-adaptive Temporal Tensor Decomposition

arXiv: https://arxiv.org/abs/2502.06164 · HTML: https://mlsanity.com/paper/2502.06164/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Distributed Flexible Nonlinear Tensor Factorization](https://mlsanity.com/paper/1604.07928/) (2016)
- [Spatiotemporal Data Mining: A Survey on Challenges and Open Problems](https://mlsanity.com/paper/2103.17128/) (2021)
- [Dynamic Tensor Recommender Systems](https://mlsanity.com/paper/2003.05568/) (2020)
- [Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data](https://mlsanity.com/paper/2311.04829/) (2023)
- [Towards Flexible Sparsity-Aware Modeling: Automatic Tensor Rank Learning Using The Generalized Hyperbolic Prior](https://mlsanity.com/paper/2009.02472/) (2020)
- [Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition](https://mlsanity.com/paper/2207.02446/) (2022)
- [Optimization of Functions Given in the Tensor Train Format](https://mlsanity.com/paper/2209.14808/) (2022)
- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes](https://mlsanity.com/paper/2310.19666/) (2023)

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

- [Subspace Kernel Learning on Tensor Sequences](https://mlsanity.com/paper/2603.19546/) (2026)
- [StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Models](https://mlsanity.com/paper/2605.07384/) (2026)

## Abstract (arXiv)

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by incorporating continuous timestamps in latent factors, they still struggle with general tensor data with continuous indexes not only in the temporal mode but also in other modes, such as spatial coordinates in climate data. Moreover, the challenge of self-adapting model complexity is largely unexplored in functional temporal tensor models, with existing methods being inapplicable in this setting. To address these limitations, we propose functional underlineComplexity-underlineAdaptive underlineTemporal underlineTensor dunderlineEcomposition (textscCatte). Our approach encodes continuous spatial indexes as learnable Fourier features and employs neural ODEs in latent space to learn the temporal trajectories of factors. To enable automatic adaptation of model complexity, we introduce a sparsity-inducing prior over the factor trajectories. We develop an efficient variational inference scheme with an analytical evidence lower bound, enabling sampling-free optimization. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that textscCatte not only reveals the underlying ranks of functional temporal tensors but also significantly outperforms existing methods in prediction performance and robustness against noise.