# Explaining Generalization Power of a DNN Using Interactive Concepts

arXiv: https://arxiv.org/abs/2302.13091 · HTML: https://mlsanity.com/paper/2302.13091/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 25 Feb 2023.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [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)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [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)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Sharper bounds for uniformly stable algorithms](https://mlsanity.com/paper/1910.07833/) (2019)
- [Sharpened Generalization Bounds based on Conditional Mutual Information and an Application to Noisy, Iterative Algorithms](https://mlsanity.com/paper/2004.12983/) (2020)
- [Stiffness: A New Perspective on Generalization in Neural Networks](https://mlsanity.com/paper/1901.09491/) (2019)
- [Toward Better Generalization Bounds with Locally Elastic Stability](https://mlsanity.com/paper/2010.13988/) (2020)
- [Defining and Quantifying the Emergence of Sparse Concepts in DNNs](https://mlsanity.com/paper/2111.06206/) (2021)
- [Towards a Unified Information-Theoretic Framework for Generalization](https://mlsanity.com/paper/2111.05275/) (2021)
- [From Noisy Prediction to True Label: Noisy Prediction Calibration via Generative Model](https://mlsanity.com/paper/2205.00690/) (2022)
- [A Game-Theoretic Taxonomy of Visual Concepts in DNNs](https://mlsanity.com/paper/2106.10938/) (2021)
- [A Hypothesis for the Aesthetic Appreciation in Neural Networks](https://mlsanity.com/paper/2108.02646/) (2021)

## Built on by (most cited first, 25 of 25)

- [Explainable and Interpretable Multimodal Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2412.02104/) (2024)
- [Defining and Extracting generalizable interaction primitives from DNNs](https://mlsanity.com/paper/2401.16318/) (2024)
- [Towards the Dynamics of a DNN Learning Symbolic Interactions](https://mlsanity.com/paper/2407.19198/) (2024)
- [Technical Note: Defining and Quantifying AND-OR Interactions for Faithful and Concise Explanation of DNNs](https://mlsanity.com/paper/2304.13312/) (2023)
- [Can the Inference Logic of Large Language Models be Disentangled into Symbolic Concepts?](https://mlsanity.com/paper/2304.01083/) (2023)
- [INTER: Mitigating Hallucination in Large Vision-Language Models by Interaction Guidance Sampling](https://mlsanity.com/paper/2507.05056/) (2025)
- [Where We Have Arrived in Proving the Emergence of Sparse Symbolic Concepts in AI Models](https://mlsanity.com/paper/2305.01939/) (2023)
- [Towards Symbolic XAI -- Explanation Through Human Understandable Logical Relationships Between Features](https://mlsanity.com/paper/2408.17198/) (2024)
- [Two-Phase Dynamics of Interactions Explains the Starting Point of a DNN Learning Over-Fitted Features](https://mlsanity.com/paper/2405.10262/) (2024)
- [Layerwise Change of Knowledge in Neural Networks](https://mlsanity.com/paper/2409.08712/) (2024)
- [Quantifying In-Context Reasoning Effects and Memorization Effects in LLMs](https://mlsanity.com/paper/2405.11880/) (2024)
- [NeurFlow: Interpreting Neural Networks through Neuron Groups and Functional Interactions](https://mlsanity.com/paper/2502.16105/) (2025)
- [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)
- [InfoCons: Identifying Interpretable Critical Concepts in Point Clouds via Information Theory](https://mlsanity.com/paper/2505.19820/) (2025)
- [Why pre-training is beneficial for downstream classification tasks?](https://mlsanity.com/paper/2410.08455/) (2024)
- [Evaluating the Correctness of Inference Patterns Used by LLMs for Judgment](https://mlsanity.com/paper/2410.09083/) (2024)
- [Cross-LLM Consistency in Inference: Evidence from Shared Interactions](https://mlsanity.com/paper/2606.08129/) (2026)
- [Dissecting RGB-D Learning for Improved Multi-modal Fusion](https://mlsanity.com/paper/2308.10019/) (2023)
- [Disentangling Regional Primitives for Image Generation](https://mlsanity.com/paper/2410.04421/) (2024)
- [Conscious Gaze: Adaptive Attention Mechanisms for Hallucination Mitigation in Vision-Language Models](https://mlsanity.com/paper/2512.05546/) (2025)
- [Hierarchical Sparse Circuit Extraction from Billion-Parameter Language Models through Scalable Attribution Graph Decomposition](https://mlsanity.com/paper/2601.12879/) (2026)
- [Reconciling Contradictory Views on the Effectiveness of SFT in LLMs: An Interaction Perspective](https://mlsanity.com/paper/2605.17967/) (2026)
- [A Unified Approach to Interpreting Knowledge Distillation for Large Language Models via Interactions](https://mlsanity.com/paper/2607.08776/) (2026)
- [Evaluating and Explaining Prompt Sensitivity of LLMs Using Interactions](https://mlsanity.com/paper/2608.18539/) (2026)

## Abstract (arXiv)

This paper explains the generalization power of a deep neural network (DNN) from the perspective of interactions. Although there is no universally accepted definition of the concepts encoded by a DNN, the sparsity of interactions in a DNN has been proved, i.e., the output score of a DNN can be well explained by a small number of interactions between input variables. In this way, to some extent, we can consider such interactions as interactive concepts encoded by the DNN. Therefore, in this paper, we derive an analytic explanation of inconsistency of concepts of different complexities. This may shed new lights on using the generalization power of concepts to explain the generalization power of the entire DNN. Besides, we discover that the DNN with stronger generalization power usually learns simple concepts more quickly and encodes fewer complex concepts. We also discover the detouring dynamics of learning complex concepts, which explains both the high learning difficulty and the low generalization power of complex concepts. The code will be released when the paper is accepted.