# Two-Phase Dynamics of Interactions Explains the Starting Point of a DNN Learning Over-Fitted Features

arXiv: https://arxiv.org/abs/2405.10262 · HTML: https://mlsanity.com/paper/2405.10262/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 16 May 2024.

## Builds on (most cited first, 20 of 20)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [Real Time Image Saliency for Black Box Classifiers](https://mlsanity.com/paper/1705.07857/) (2017)
- [A Unified Approach to Interpreting and Boosting Adversarial Transferability](https://mlsanity.com/paper/2010.04055/) (2020)
- [Defining and Quantifying the Emergence of Sparse Concepts in DNNs](https://mlsanity.com/paper/2111.06206/) (2021)
- [Does a Neural Network Really Encode Symbolic Concepts?](https://mlsanity.com/paper/2302.13080/) (2023)
- [Explaining Generalization Power of a DNN Using Interactive Concepts](https://mlsanity.com/paper/2302.13091/) (2023)
- [A Unified Game-Theoretic Interpretation of Adversarial Robustness](https://mlsanity.com/paper/2111.03536/) (2021)
- [Defining and Extracting generalizable interaction primitives from DNNs](https://mlsanity.com/paper/2401.16318/) (2024)
- [Interpreting Attributions and Interactions of Adversarial Attacks](https://mlsanity.com/paper/2108.06895/) (2021)
- [Technical Note: Defining and Quantifying AND-OR Interactions for Faithful and Concise Explanation of DNNs](https://mlsanity.com/paper/2304.13312/) (2023)
- [Explaining How a Neural Network Play the Go Game and Let People Learn](https://mlsanity.com/paper/2310.09838/) (2023)

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

- [Explainable and Interpretable Multimodal Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2412.02104/) (2024)
- [Towards the Dynamics of a DNN Learning Symbolic Interactions](https://mlsanity.com/paper/2407.19198/) (2024)
- [Revisiting Generalization Power of a DNN in Terms of Symbolic Interactions](https://mlsanity.com/paper/2502.10162/) (2025)
- [Technical Report: Quantifying and Analyzing the Generalization Power of a DNN](https://mlsanity.com/paper/2505.06993/) (2025)
- [Disentangling Regional Primitives for Image Generation](https://mlsanity.com/paper/2410.04421/) (2024)

## Abstract (arXiv)

This paper investigates the dynamics of a deep neural network (DNN) learning interactions. Previous studies have discovered and mathematically proven that given each input sample, a well-trained DNN usually only encodes a small number of interactions (non-linear relationships) between input variables in the sample. A series of theorems have been derived to prove that we can consider the DNN's inference equivalent to using these interactions as primitive patterns for inference. In this paper, we discover the DNN learns interactions in two phases. The first phase mainly penalizes interactions of medium and high orders, and the second phase mainly learns interactions of gradually increasing orders. We can consider the two-phase phenomenon as the starting point of a DNN learning over-fitted features. Such a phenomenon has been widely shared by DNNs with various architectures trained for different tasks. Therefore, the discovery of the two-phase dynamics provides a detailed mechanism for how a DNN gradually learns different inference patterns (interactions). In particular, we have also verified the claim that high-order interactions have weaker generalization power than low-order interactions. Thus, the discovered two-phase dynamics also explains how the generalization power of a DNN changes during the training process.