# ToTMNet: FFT-Accelerated Toeplitz Temporal Mixing Network for Lightweight Remote Photoplethysmography

arXiv: https://arxiv.org/abs/2601.04159 · HTML: https://mlsanity.com/paper/2601.04159/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 40 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Builds on (most cited first, 30 of 32)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [DeepPhys: Video-Based Physiological Measurement Using Convolutional Attention Networks](https://mlsanity.com/paper/1805.07888/) (2018)
- [Multi-Task Temporal Shift Attention Networks for On-Device Contactless Vitals Measurement](https://mlsanity.com/paper/2006.03790/) (2020)
- [Remote Photoplethysmograph Signal Measurement from Facial Videos Using Spatio-Temporal Networks](https://mlsanity.com/paper/1905.02419/) (2019)
- [PhysFormer: Facial Video-based Physiological Measurement with Temporal Difference Transformer](https://mlsanity.com/paper/2111.12082/) (2021)
- [Learning Fast Algorithms for Linear Transforms Using Butterfly Factorizations](https://mlsanity.com/paper/1903.05895/) (2019)
- [Fastfood: Approximate Kernel Expansions in Loglinear Time](https://mlsanity.com/paper/1408.3060/) (2014)
- [EfficientPhys: Enabling Simple, Fast and Accurate Camera-Based Vitals Measurement](https://mlsanity.com/paper/2110.04447/) (2021)
- [The Way to my Heart is through Contrastive Learning: Remote Photoplethysmography from Unlabelled Video](https://mlsanity.com/paper/2111.09748/) (2021)
- [rPPG-Toolbox: Deep Remote PPG Toolbox](https://mlsanity.com/paper/2210.00716/) (2022)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [CirCNN: Accelerating and Compressing Deep Neural Networks Using Block-CirculantWeight Matrices](https://mlsanity.com/paper/1708.08917/) (2017)
- [Camera Measurement of Physiological Vital Signs](https://mlsanity.com/paper/2111.11547/) (2021)
- [Contrast-Phys: Unsupervised Video-based Remote Physiological Measurement via Spatiotemporal Contrast](https://mlsanity.com/paper/2208.04378/) (2022)
- [PhysFormer++: Facial Video-based Physiological Measurement with SlowFast Temporal Difference Transformer](https://mlsanity.com/paper/2302.03548/) (2023)
- [Toeplitz Neural Network for Sequence Modeling](https://mlsanity.com/paper/2305.04749/) (2023)
- [Structured Transforms for Small-Footprint Deep Learning](https://mlsanity.com/paper/1510.01722/) (2015)
- [From block-Toeplitz matrices to differential equations on graphs: towards a general theory for scalable masked Transformers](https://mlsanity.com/paper/2107.07999/) (2021)
- [RhythmFormer: Extracting Patterned rPPG Signals based on Periodic Sparse Attention](https://mlsanity.com/paper/2402.12788/) (2024)
- [SCAMPS: Synthetics for Camera Measurement of Physiological Signals](https://mlsanity.com/paper/2206.04197/) (2022)
- [PHNNs: Lightweight Neural Networks via Parameterized Hypercomplex Convolutions](https://mlsanity.com/paper/2110.04176/) (2021)

## Built on by (most cited first, 1 of 1)

- [Template Collapse and Information-Theoretic Limits in Camera rPPG Pulse Morphology Restoration](https://mlsanity.com/paper/2606.03802/) (2026)

## Abstract (arXiv)

Remote photoplethysmography (rPPG) estimates a blood volume pulse (BVP) waveform from facial videos captured by commodity cameras. Although recent deep models improve robustness compared to classical signal-processing approaches, many methods increase computational cost and parameter count, and attention-based temporal modeling introduces quadratic scaling with respect to the temporal length. This paper proposes ToTMNet, a lightweight rPPG architecture that replaces temporal attention with an FFT-accelerated Toeplitz temporal mixing layer. The Toeplitz operator provides full-sequence temporal receptive field using a linear number of parameters in the clip length and can be applied in near-linear time using circulant embedding and FFT-based convolution. ToTMNet integrates the global Toeplitz temporal operator into a compact gated temporal mixer that combines a local depthwise temporal convolution branch with gated global Toeplitz mixing, enabling efficient long-range temporal filtering while only having 63k parameters. Experiments on two datasets, UBFC-rPPG (real videos) and SCAMPS (synthetic videos), show that ToTMNet achieves strong heart-rate estimation accuracy with a compact design. On UBFC-rPPG intra-dataset evaluation, ToTMNet reaches 1.055 bpm MAE with Pearson correlation 0.996. In a synthetic-to-real setting (SCAMPS to UBFC-rPPG), ToTMNet reaches 1.582 bpm MAE with Pearson correlation 0.994. Ablation results confirm that the gating mechanism is important for effectively using global Toeplitz mixing, especially under domain shift. The main limitation of this preprint study is the use of only two datasets; nevertheless, the results indicate that Toeplitz-structured temporal mixing is a practical and efficient alternative to attention for rPPG.