# Noise-robust Contrastive Learning for Critical Transition Detection in Dynamical Systems

arXiv: https://arxiv.org/abs/2512.12523 · HTML: https://mlsanity.com/paper/2512.12523/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 57 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 24 of 24)

- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [Selective-Supervised Contrastive Learning with Noisy Labels](https://mlsanity.com/paper/2203.04181/) (2022)
- [Multi-Objective Interpolation Training for Robustness to Label Noise](https://mlsanity.com/paper/2012.04462/) (2020)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Robust Contrastive Learning against Noisy Views](https://mlsanity.com/paper/2201.04309/) (2022)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [The loss landscape of overparameterized neural networks](https://mlsanity.com/paper/1804.10200/) (2018)
- [Symmetry Induces Structure and Constraint of Learning](https://mlsanity.com/paper/2309.16932/) (2023)
- [From Manifold to Manifold: Geometry-Aware Dimensionality Reduction for SPD Matrices](https://mlsanity.com/paper/1407.1120/) (2014)
- [Deep Learning of Causal Structures in High Dimensions](https://mlsanity.com/paper/2212.04866/) (2022)
- [An overview of condensation phenomenon in deep learning](https://mlsanity.com/paper/2504.09484/) (2025)
- [Parameter Symmetry Potentially Unifies Deep Learning Theory](https://mlsanity.com/paper/2502.05300/) (2025)
- [Deep Causal Learning: Representation, Discovery and Inference](https://mlsanity.com/paper/2211.03374/) (2022)
- [Universal Early Warning Signals of Phase Transitions in Climate Systems](https://mlsanity.com/paper/2206.00060/) (2022)
- [SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification](https://mlsanity.com/paper/2408.16698/) (2024)
- [A simple framework for contrastive learning phases of matter](https://mlsanity.com/paper/2205.05607/) (2022)
- [A predictive physics-aware hybrid reduced order model for reacting flows](https://mlsanity.com/paper/2301.09860/) (2023)
- [Regularized Gauss-Newton for Optimizing Overparameterized Neural Networks](https://mlsanity.com/paper/2404.14875/) (2024)
- [Low-Rank Matrix Approximation for Neural Network Compression](https://mlsanity.com/paper/2504.20078/) (2025)
- [An Inclusive Theoretical Framework of Robust Supervised Contrastive Loss against Label Noise](https://mlsanity.com/paper/2501.01130/) (2025)
- [Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA](https://mlsanity.com/paper/2501.12582/) (2025)
- [Low-Rank Tensor Decompositions for the Theory of Neural Networks](https://mlsanity.com/paper/2508.18408/) (2025)
- [How Does Overparameterization Affect Machine Unlearning of Deep Neural Networks?](https://mlsanity.com/paper/2503.08633/) (2025)

## Abstract (arXiv)

Detecting critical transitions in complex, noisy time-series data is a fundamental challenge across science and engineering. Such transitions may be anticipated by the emergence of a low-dimensional order parameter, whose signature is often masked by high-amplitude stochastic variability. Standard contrastive learning approaches based on deep neural networks, while promising for detecting critical transitions, are often overparameterized and sensitive to irrelevant noise, leading to inaccurate identification of critical points. To address these limitations, we propose a neural network architecture, constructed using singular value decomposition technique, together with a strictly semi-orthogonality-constrained training algorithm, to enhance the performance of traditional contrastive learning. Extensive experiments demonstrate that the proposed method matches the performance of traditional contrastive learning techniques in identifying critical transitions, yet is considerably more lightweight and markedly more resistant to noise.