# Time-series attribution maps with regularized contrastive learning

arXiv: https://arxiv.org/abs/2502.12977 · HTML: https://mlsanity.com/paper/2502.12977/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 46 references that are in the map.
- First posted on arXiv 17 Feb 2025.

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

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Not Just a Black Box: Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1605.01713/) (2016)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Explaining NonLinear Classification Decisions with Deep Taylor Decomposition](https://mlsanity.com/paper/1512.02479/) (2015)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Learnable latent embeddings for joint behavioral and neural analysis](https://mlsanity.com/paper/2204.00673/) (2022)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [Explaining Time Series Predictions with Dynamic Masks](https://mlsanity.com/paper/2106.05303/) (2021)
- [Improving Deep Learning Interpretability by Saliency Guided Training](https://mlsanity.com/paper/2111.14338/) (2021)
- [Temporal Dependencies in Feature Importance for Time Series Predictions](https://mlsanity.com/paper/2107.14317/) (2021)
- [Explaining Time Series via Contrastive and Locally Sparse Perturbations](https://mlsanity.com/paper/2401.08552/) (2024)
- [Computationally Efficient Measures of Internal Neuron Importance](https://mlsanity.com/paper/1807.09946/) (2018)
- [CoRTX: Contrastive Framework for Real-time Explanation](https://mlsanity.com/paper/2303.02794/) (2023)
- [Towards Rigorous Interpretations: a Formalisation of Feature Attribution](https://mlsanity.com/paper/2104.12437/) (2021)

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

- [Characterizing control between interacting subsystems with deep Jacobian estimation](https://mlsanity.com/paper/2507.01946/) (2025)
- [Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions](https://mlsanity.com/paper/2510.21706/) (2025)

## Abstract (arXiv)

Gradient-based attribution methods aim to explain decisions of deep learning models but so far lack identifiability guarantees. Here, we propose a method to generate attribution maps with identifiability guarantees by developing a regularized contrastive learning algorithm trained on time-series data plus a new attribution method called Inverted Neuron Gradient (collectively named xCEBRA). We show theoretically that xCEBRA has favorable properties for identifying the Jacobian matrix of the data generating process. Empirically, we demonstrate robust approximation of zero vs. non-zero entries in the ground-truth attribution map on synthetic datasets, and significant improvements across previous attribution methods based on feature ablation, Shapley values, and other gradient-based methods. Our work constitutes a first example of identifiable inference of time-series attribution maps and opens avenues to a better understanding of time-series data, such as for neural dynamics and decision-processes within neural networks.