# How Complexity Contributes to Learning Opacity in Machine Learning

arXiv: https://arxiv.org/abs/2606.24953 · HTML: https://mlsanity.com/paper/2606.24953/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 75 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [On The Power of Curriculum Learning in Training Deep Networks](https://mlsanity.com/paper/1904.03626/) (2019)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Understanding Optimization in Deep Learning with Central Flows](https://mlsanity.com/paper/2410.24206/) (2024)
- [Post-Hoc Explanations Fail to Achieve their Purpose in Adversarial Contexts](https://mlsanity.com/paper/2201.10295/) (2022)
- [Position: Why We Must Rethink Empirical Research in Machine Learning](https://mlsanity.com/paper/2405.02200/) (2024)
- [The no-free-lunch theorems of supervised learning](https://mlsanity.com/paper/2202.04513/) (2022)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Rethinking Explainable Machine Learning as Applied Statistics](https://mlsanity.com/paper/2402.02870/) (2024)
- [A Falsificationist Account of Artificial Neural Networks](https://mlsanity.com/paper/2205.01421/) (2022)

## Abstract (arXiv)

Machine learning (ML) algorithms are known to be opaque. We do not know the reasons for their predictions. The learning process leading to the prediction function is also opaque. We do not fully understand the time evolution of the weight values of neural nets (NN) and related dynamical phenomena. While prediction opacity is widely studied, learning opacity remains largely underexplored. This article studies learning opacity trough the lens of complex dynamical systems. We argue that NN learning is essentially a complex system and that learning opacity is due to dynamical complexity and the epistemological challenges that arise from it. We identify three key properties of training complexity -- sensitivity to weight initialization, feedback in gradient based optimization, and sensitivity to the training data -- and show how each contributes to learning opacity. As these properties are fundamental to the learning process damping or eliminating them would fundamentally alter how ML systems learn. Some sources of opacity in ML may hence be irreducible.