# Generative Modeling of Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1412.6296 · HTML: https://mlsanity.com/paper/1412.6296/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2014.

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

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- [Energy Correction Model in the Feature Space for Out-of-Distribution Detection](https://mlsanity.com/paper/2403.10403/) (2024)
- [Joint-stochastic-approximation Random Fields with Application to Semi-supervised Learning](https://mlsanity.com/paper/2505.20330/) (2025)

## Abstract (arXiv)

The convolutional neural networks (CNNs) have proven to be a powerful tool for discriminative learning. Recently researchers have also started to show interest in the generative aspects of CNNs in order to gain a deeper understanding of what they have learned and how to further improve them. This paper investigates generative modeling of CNNs. The main contributions include: (1) We construct a generative model for the CNN in the form of exponential tilting of a reference distribution. (2) We propose a generative gradient for pre-training CNNs by a non-parametric importance sampling scheme, which is fundamentally different from the commonly used discriminative gradient, and yet has the same computational architecture and cost as the latter. (3) We propose a generative visualization method for the CNNs by sampling from an explicit parametric image distribution. The proposed visualization method can directly draw synthetic samples for any given node in a trained CNN by the Hamiltonian Monte Carlo (HMC) algorithm, without resorting to any extra hold-out images. Experiments on the challenging ImageNet benchmark show that the proposed generative gradient pre-training consistently helps improve the performances of CNNs, and the proposed generative visualization method generates meaningful and varied samples of synthetic images from a large-scale deep CNN.