# Explaining Neural Matrix Factorization with Gradient Rollback

arXiv: https://arxiv.org/abs/2010.05516 · HTML: https://mlsanity.com/paper/2010.05516/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [Adversarial Attacks on Knowledge Graph Embeddings via Instance Attribution Methods](https://mlsanity.com/paper/2111.03120/) (2021)
- [Poisoning Knowledge Graph Embeddings via Relation Inference Patterns](https://mlsanity.com/paper/2111.06345/) (2021)
- [Explaining Link Predictions in Knowledge Graph Embedding Models with Influential Examples](https://mlsanity.com/paper/2212.02651/) (2022)
- [KGEx: Explaining Knowledge Graph Embeddings via Subgraph Sampling and Knowledge Distillation](https://mlsanity.com/paper/2310.01065/) (2023)
- [TWIG: Towards pre-hoc Hyperparameter Optimisation and Cross-Graph Generalisation via Simulated KGE Models](https://mlsanity.com/paper/2402.06097/) (2024)

## Abstract (arXiv)

Explaining the predictions of neural black-box models is an important problem, especially when such models are used in applications where user trust is crucial. Estimating the influence of training examples on a learned neural model's behavior allows us to identify training examples most responsible for a given prediction and, therefore, to faithfully explain the output of a black-box model. The most generally applicable existing method is based on influence functions, which scale poorly for larger sample sizes and models. We propose gradient rollback, a general approach for influence estimation, applicable to neural models where each parameter update step during gradient descent touches a smaller number of parameters, even if the overall number of parameters is large. Neural matrix factorization models trained with gradient descent are part of this model class. These models are popular and have found a wide range of applications in industry. Especially knowledge graph embedding methods, which belong to this class, are used extensively. We show that gradient rollback is highly efficient at both training and test time. Moreover, we show theoretically that the difference between gradient rollback's influence approximation and the true influence on a model's behavior is smaller than known bounds on the stability of stochastic gradient descent. This establishes that gradient rollback is robustly estimating example influence. We also conduct experiments which show that gradient rollback provides faithful explanations for knowledge base completion and recommender datasets.