# Steering Neural Network Training through Interpretable Constraints Based on Partial Dependence

arXiv: https://arxiv.org/abs/2607.08641 · HTML: https://mlsanity.com/paper/2607.08641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## 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)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Grad-CAM++: Improved Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/1710.11063/) (2017)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models](https://mlsanity.com/paper/1612.08468/) (2016)
- [Post-hoc Interpretability for Neural NLP: A Survey](https://mlsanity.com/paper/2108.04840/) (2021)
- [Visual Interpretability for Deep Learning: a Survey](https://mlsanity.com/paper/1802.00614/) (2018)
- [Interpretations are useful: penalizing explanations to align neural networks with prior knowledge](https://mlsanity.com/paper/1909.13584/) (2019)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Incorporating Priors with Feature Attribution on Text Classification](https://mlsanity.com/paper/1906.08286/) (2019)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [Rationale-Augmented Convolutional Neural Networks for Text Classification](https://mlsanity.com/paper/1605.04469/) (2016)
- [Visual correspondence-based explanations improve AI robustness and human-AI team accuracy](https://mlsanity.com/paper/2208.00780/) (2022)
- [Going Beyond XAI: A Systematic Survey for Explanation-Guided Learning](https://mlsanity.com/paper/2212.03954/) (2022)
- [Aligning Eyes between Humans and Deep Neural Network through Interactive Attention Alignment](https://mlsanity.com/paper/2202.02838/) (2022)
- [RES: A Robust Framework for Guiding Visual Explanation](https://mlsanity.com/paper/2206.13413/) (2022)
- [Linearly Constrained Neural Networks](https://mlsanity.com/paper/2002.01600/) (2020)
- [Regional Tree Regularization for Interpretability in Black Box Models](https://mlsanity.com/paper/1908.04494/) (2019)
- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [Hybrid additive modeling with partial dependence for supervised regression and dynamical systems forecasting](https://mlsanity.com/paper/2307.02229/) (2023)

## Abstract (arXiv)

Over the last few years, there has been an increased interest in making machine learning models more interpretable. Although a great deal of effort goes into developing techniques for interpreting the interactions learned by a given model, fewer studies focus on assessing the quality of such explanations. Even fewer focus on how to adjust the model to produce explanations faithful to prior knowledge, a process known as explanation-guided learning. Furthermore, most approaches in this area focus on classification problems and usually assume prior knowledge about which input features or regions are most important. In this work, we introduce a new approach to steering neural networks based on partial dependence, such that their average response to certain features aligns with specific functional domain knowledge about the problem. We empirically demonstrate on a range of regression problems, including dynamical systems forecasting, that models whose training has been controlled using our method perform better than unconstrained models and are more data-efficient. Moreover, we highlight that interpretations obtained from the former actually align with the user-provided knowledge, whereas those obtained from the latter do not.