# TpopT: Efficient Trainable Template Optimization on Low-Dimensional Manifolds

arXiv: https://arxiv.org/abs/2310.10039 · HTML: https://mlsanity.com/paper/2310.10039/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 57 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Oriented Response Networks](https://mlsanity.com/paper/1701.01833/) (2017)
- [Unrolled Optimization with Deep Priors](https://mlsanity.com/paper/1705.08041/) (2017)
- [Locally Scale-Invariant Convolutional Neural Networks](https://mlsanity.com/paper/1412.5104/) (2014)
- [Maximal Sparsity with Deep Networks?](https://mlsanity.com/paper/1605.01636/) (2016)
- [Deep MRI Reconstruction: Unrolled Optimization Algorithms Meet Neural Networks](https://mlsanity.com/paper/1907.11711/) (2019)
- [Generalized Approach to Matched Filtering using Neural Networks](https://mlsanity.com/paper/2104.03961/) (2021)
- [Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization](https://mlsanity.com/paper/2203.05006/) (2022)
- [Principal Component Pursuit for Pattern Identification in Environmental Mixtures](https://mlsanity.com/paper/2111.00104/) (2021)
- [Boosting the Efficiency of Parametric Detection with Hierarchical Neural Networks](https://mlsanity.com/paper/2207.11583/) (2022)

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

- [Fast, Accurate Manifold Denoising by Tunneling Riemannian Optimization](https://mlsanity.com/paper/2502.16819/) (2025)
- [Local Averaging Accurately Distills Manifold Structure From Noisy Data](https://mlsanity.com/paper/2506.18761/) (2025)

## Abstract (arXiv)

In scientific and engineering scenarios, a recurring task is the detection of low-dimensional families of signals or patterns. A classic family of approaches, exemplified by template matching, aims to cover the search space with a dense template bank. While simple and highly interpretable, it suffers from poor computational efficiency due to unfavorable scaling in the signal space dimensionality. In this work, we study TpopT (TemPlate OPTimization) as an alternative scalable framework for detecting low-dimensional families of signals which maintains high interpretability. We provide a theoretical analysis of the convergence of Riemannian gradient descent for TpopT, and prove that it has a superior dimension scaling to covering. We also propose a practical TpopT framework for nonparametric signal sets, which incorporates techniques of embedding and kernel interpolation, and is further configurable into a trainable network architecture by unrolled optimization. The proposed trainable TpopT exhibits significantly improved efficiency-accuracy tradeoffs for gravitational wave detection, where matched filtering is currently a method of choice. We further illustrate the general applicability of this approach with experiments on handwritten digit data.