# Free energy of Bayesian Convolutional Neural Network with Skip Connection

arXiv: https://arxiv.org/abs/2307.01417 · HTML: https://mlsanity.com/paper/2307.01417/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 4 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Deep Learning is Singular, and That's Good](https://mlsanity.com/paper/2010.11560/) (2020)
- [Learning Deep ResNet Blocks Sequentially using Boosting Theory](https://mlsanity.com/paper/1706.04964/) (2017)
- [The Exact Asymptotic Form of Bayesian Generalization Error in Latent Dirichlet Allocation](https://mlsanity.com/paper/2008.01304/) (2020)
- [Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases](https://mlsanity.com/paper/2303.15739/) (2023)

## Built on by (most cited first, 4 of 4)

- [Review and Prospect of Algebraic Research in Equivalent Framework between Statistical Mechanics and Machine Learning Theory](https://mlsanity.com/paper/2406.10234/) (2024)
- [Upper Bound of Bayesian Generalization Error in Partial Concept Bottleneck Model (CBM): Partial CBM outperforms naive CBM](https://mlsanity.com/paper/2403.09206/) (2024)
- [Statistical inference for quantum singular models](https://mlsanity.com/paper/2411.16396/) (2024)
- [ZClassifier: Temperature Tuning and Manifold Approximation via KL Divergence on Logit Space](https://mlsanity.com/paper/2507.10638/) (2025)

## Abstract (arXiv)

Since the success of Residual Network(ResNet), many of architectures of Convolutional Neural Networks(CNNs) have adopted skip connection. While the generalization performance of CNN with skip connection has been explained within the framework of Ensemble Learning, the dependency on the number of parameters have not been revealed. In this paper, we show that Bayesian free energy of Convolutional Neural Network both with and without skip connection in Bayesian learning. The upper bound of free energy of Bayesian CNN with skip connection does not depend on the oveparametrization and, the generalization error of Bayesian CNN has similar property.