# Traceable Spectral Inference via Influence Functions: Efficient Data Attribution and Error Proxies for the Ariel Mission

arXiv: https://arxiv.org/abs/2608.23458 · HTML: https://mlsanity.com/paper/2608.23458/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [A Swiss Army Infinitesimal Jackknife](https://mlsanity.com/paper/1806.00550/) (2018)
- [Diffusion Attribution Score: Evaluating Training Data Influence in Diffusion Models](https://mlsanity.com/paper/2410.18639/) (2024)
- [An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval](https://mlsanity.com/paper/1905.10659/) (2019)
- [Lessons Learned from the 1st ARIEL Machine Learning Challenge: Correcting Transiting Exoplanet Light Curves for Stellar Spots](https://mlsanity.com/paper/2010.15996/) (2020)
- [Operational range bounding of spectroscopy models with anomaly detection](https://mlsanity.com/paper/2408.02581/) (2024)
- [Extreme Learning Machines for Exoplanet Simulations: A Faster, Lightweight Alternative to Deep Learning](https://mlsanity.com/paper/2506.19679/) (2025)

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

- [Operational Range Bounding in Spectroscopy: A Safety Cage Framework for Machine Learning Models](https://mlsanity.com/paper/2609.13514/) (2026)

## Abstract (arXiv)

Interpretability is critical for machine learning models deployed in scientific space missions such as ESA's Ariel, where ground truth is unavailable during operations and physical plausibility must be assessed. While most explainable AI methods focus on feature attribution, this work investigates training data attribution through influence functions and introduces three key contributions for operational spectroscopy pipelines. First, influence is reformulated in terms of prediction rather than loss, enabling label-free deployment. Second, by leveraging the closed-form ridge solution of an Extreme Learning Machine, infinitesimal prediction influence is efficiently computed. Third, an influence-based conservative error proxy is derived by propagating training residuals through the influence sensitivities. Evaluated against simulated spectra, the proposed proxy correlates strongly with scale and shape-based spectral errors. Furthermore, influence functions enable the identification of the most influential samples and the approximation of the most harmful ones. Together, these results suggest that this approach can serve as an operational framework for scientific machine learning.