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Functional Complexity-adaptive Temporal Tensor Decomposition
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Proposes CATTE, a Bayesian functional temporal tensor decomposition that encodes continuous indexes of all modes as Fourier features, models factor trajectories with a neural ODE, and automatically learns rank via a Gaussian-Gamma sparsity prior with an analytical ELBO.
Problem
Temporal tensor decomposition typically handles continuous timestamps only in the time mode and requires manual rank selection; there is no rank-adaptive method for tensors with continuous indexes across all modes.
Approach
Combine Fourier-feature encoding of continuous non-temporal indexes with neural-ODE latent trajectories for each factor, and place a sparsity-inducing Gaussian-Gamma prior over whole factor trajectories (functional automatic rank determination), optimized via a sampling-free analytical ELBO.
Key results
- On CA traffic, Server Room and SSF at R=7 baselines, CATTE achieves RMSE 0.284, 0.078 and 0.373 versus best baselines around 0.365-0.389, 0.094-0.156 and 0.502-0.595 (LRTFR/DEMOTE); CATTE learns ranks 5, 7, 7.
- On synthetic data with true rank 1, CATTE recovers rank 1 by pruning four of five components.
- Under noise variance 0.5 and 1 on CA traffic, CATTE RMSE is 0.305 and 0.406 versus 0.356 and 0.461 for CATTE without FARD.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Catte rather than the strongest listed baseline | CA Traffic · CA Traffic | RMSE: 0.365 ± 0.042 -> 0.284 ± 0.016 | Helped |
| use Catte rather than the strongest listed baseline | CA Traffic · CA Traffic | MAE: 0.091 ± 0.001 -> 0.085 ± 0.004 | Helped |
| use Catte rather than the strongest listed baseline | Server Room · Server Room | RMSE: 0.094 ± 0.006 -> 0.078 ± 0.001 | Helped |
| use Catte rather than the strongest listed baseline | Server Room · Server Room | MAE: 0.062 ± 0.006 -> 0.047 ± 0.003 | Helped |
| use Catte rather than the strongest listed baseline | SSF · SSF | RMSE: 0.502 ± 0.033 -> 0.373 ± 0.003 | Helped |
| use Catte rather than the strongest listed baseline | SSF · SSF | MAE: 0.392 ± 0.028 -> 0.288 ± 0.003 | Helped |
| add FARD (ablation) | Catte on CA Traffic · CA Traffic | RMSE: 0.301 ± 0.020 -> 0.284 ± 0.016 | Helped |
| add FARD (ablation) | Catte on CA Traffic · CA Traffic | MAE: 0.094 ± 0.010 -> 0.085 ± 0.004 | Helped |
| add FARD (ablation) | Catte on Server Room · Server Room | RMSE: 0.091 ± 0.008 -> 0.078 ± 0.001 | Helped |
| add FARD (ablation) | Catte on Server Room · Server Room | MAE: 0.0657 ± 0.005 -> 0.047 ± 0.003 | Helped |
| add FARD (ablation) | Catte on SSF · SSF | RMSE: 0.402 ± 0.013 -> 0.373 ± 0.003 | Helped |
| add FARD (ablation) | Catte on SSF · SSF | MAE: 0.310 ± 0.010 -> 0.288 ± 0.003 | Helped |
Surprising findings
- Methods that ignore continuity of non-temporal modes (NONFAT, DEMOTE, THIS-ODE) perform very poorly on the SSF dataset.
Limitations
- No explicit incorporation of physical laws into the model.
- Baseline ranks are fixed at R in {3,5,7} while CATTE's rank is learned, so comparisons depend on baseline rank choice.
- Several results (e.g., ODE state dimension, prior hyperparameter sensitivity) are only briefly reported.
Experimental setup
Datasets: CA traffic (lane-blocked records) Server Room (Poznan temperature logs) SSF (HYCOM ocean temperature/salinity) synthetic two-mode temporal tensor
Benchmarks: CA traffic Server Room SSF
Metrics: RMSE MAE
Baselines: THIS-ODE NONFAT DEMOTE FunBaT-CP FunBaT-Tucker LRTFR
Builds on: CANDECOMP/PARAFAC decomposition Bayesian CP rank learning (Gaussian-Gamma prior) neural ODE NONFAT LRTFR
Closest papers by meaning
- Streaming Factor Trajectory Learning for Temporal Tensor Decomposition (NeurIPS 2023 · similarity 0.88)
- Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data (ICLR 2024 · similarity 0.88)
- Online Functional Tensor Decomposition via Continual Learning for Streaming Data Completion (NeurIPS 2025 · similarity 0.88)
- Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition (ICML 2022 · similarity 0.88)
- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs (NeurIPS 2025 · similarity 0.86)
- Deep Rank-One Tensor Functional Factorization for Multi-Dimensional Data Recovery (AAAI 2025 · similarity 0.85)
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