# RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems

arXiv: https://arxiv.org/abs/2510.17396 · HTML: https://mlsanity.com/paper/2510.17396/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 71 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Builds on (most cited first, 30 of 33)

- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)
- [An Alternative Probabilistic Interpretation of the Huber Loss](https://mlsanity.com/paper/1911.02088/) (2019)
- [WINNet: Wavelet-inspired Invertible Network for Image Denoising](https://mlsanity.com/paper/2109.06381/) (2021)
- [Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series](https://mlsanity.com/paper/2105.00899/) (2021)
- [Learning the optimal Tikhonov regularizer for inverse problems](https://mlsanity.com/paper/2106.06513/) (2021)
- [A Survey on Nonconvex Regularization Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning](https://mlsanity.com/paper/1808.05403/) (2018)
- [Adjusting for Autocorrelated Errors in Neural Networks for Time Series](https://mlsanity.com/paper/2101.12578/) (2021)
- [Sparse Regularization via Convex Analysis](https://mlsanity.com/paper/1803.06765/) (2018)
- [Untrained Graph Neural Networks for Denoising](https://mlsanity.com/paper/2109.11700/) (2021)
- [Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation](https://mlsanity.com/paper/2402.01052/) (2024)
- [Outlier-Robust Sparse Mean Estimation for Heavy-Tailed Distributions](https://mlsanity.com/paper/2211.16333/) (2022)
- [Robust Time Series Denoising with Learnable Wavelet Packet Transform](https://mlsanity.com/paper/2206.06126/) (2022)
- [The Neural Tangent Link Between CNN Denoisers and Non-Local Filters](https://mlsanity.com/paper/2006.02379/) (2020)
- [Learning Provably Robust Estimators for Inverse Problems via Jittering](https://mlsanity.com/paper/2307.12822/) (2023)
- [One-dimensional Deep Image Prior for Time Series Inverse Problems](https://mlsanity.com/paper/1904.08594/) (2019)
- [Near-Optimal Algorithms for Gaussians with Huber Contamination: Mean Estimation and Linear Regression](https://mlsanity.com/paper/2312.01547/) (2023)
- [LINN: Lifting Inspired Invertible Neural Network for Image Denoising](https://mlsanity.com/paper/2105.03303/) (2021)
- [Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery](https://mlsanity.com/paper/2306.11498/) (2023)
- [Physics-Enhanced Graph Neural Networks For Soft Sensing in Industrial Internet of Things](https://mlsanity.com/paper/2404.08061/) (2024)
- [Contrastive Blind Denoising Autoencoder for Real-Time Denoising of Industrial IoT Sensor Data](https://mlsanity.com/paper/2004.06806/) (2020)
- [Learnable Wavelet Packet Transform for Data-Adapted Spectrograms](https://mlsanity.com/paper/2201.11069/) (2022)
- [Robust Dominant Periodicity Detection for Time Series with Missing Data](https://mlsanity.com/paper/2303.03553/) (2023)

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

- [WaveGraphNet: Physics-Consistent Guided-Wave Damage Localization through Coupled Inverse-Forward Graph Learning](https://mlsanity.com/paper/2605.20311/) (2026)

## Abstract (arXiv)

Time series data are often affected by various forms of corruption, such as missing values, noise, and outliers, which pose significant challenges for tasks such as forecasting and anomaly detection. To address these issues, inverse problems focus on reconstructing the original signal from corrupted data by leveraging prior knowledge about its underlying structure. While deep learning methods have demonstrated potential in this domain, they often require extensive pretraining and struggle to generalize under distribution shifts. In this work, we propose RINS-T (Robust Implicit Neural Solvers for Time Series Linear Inverse Problems), a novel deep prior framework that achieves high recovery performance without requiring pretraining data. RINS-T leverages neural networks as implicit priors and integrates robust optimization techniques, making it resilient to outliers while relaxing the reliance on Gaussian noise assumptions. To further improve optimization stability and robustness, we introduce three key innovations: guided input initialization, input perturbation, and convex output combination techniques. Each of these contributions strengthens the framework's optimization stability and robustness. These advancements make RINS-T a flexible and effective solution for addressing complex real-world time series challenges. Our code is available at https://github.com/EPFL-IMOS/RINS-T.