Bias and Generalization in Deep Generative Models: An Empirical Study
In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework to systematically investigate bias and generalization in deep generative models of images. Inspired by experimental methods from cognitive psychology, we probe each learning algorithm with carefully designed training datasets to characterize when and how existing models generate novel attributes and their combinations. We identify similarities to human psychology and verify that these patterns are consistent across commonly used models and architectures.
* Summary:  This paper provides an empirical study of the generalization properties of deep implicit generative models. Previous works have mostly focused on the mathematical generalization properties of such networks [Arora et al., ICML17], while previous empirical studies lacked the rigorous methodology of this paper.  This paper introduces a methodology inspired by neuroscience to probe such models, by using toy datasets with specified high-level features. For instance, for a dataset of images made of small dots, the number of dots and the colors of the dots in each image are such features, which can be easily assessed. The paper investigates the differences between the distribution of such features in the dataset and their distribution in the generated dataset, across different models (VAE/GAN), architectures (fully connected / convolutional) and datasets.  The patterns identified by the authors are the following: - Single features are generalized in a sort of convolutional way: the distribution "impulse response" of the algorithm to an input dirac distribution (parametrized by a real value, e.g. radius of circles in an image or proportion of red) behaves akin to a linear filter. When there are multiple diracs, the convolution effects still holds, with an enhancement effects for intermediate values when the diracs are close. This behaviour is close to previous neuroscientific findings. - Features are independent: modifying many other features does not change the distribution reponse of the algorithms when studying a single feature. - When multiple combinations of features are part of the dataset, the distribution responses keep the combinations in the original distribution (high recall), but generalize to new combinations when the number of combinations grows (precision decreasing).   * Opinion:  This is a paper of very good quality. Writing is very clear. I think that the value of this paper does not solely lie in its empirical findings - some of which are surprising and may spark debate - but also in the experimental methodology it proposes to assess the properties of generative models. This methodology would be a very significant contribution to help understand generalization for deep neural networks, provided it is reproducible in a proper fashion.  * Questions :  - Do the authors plan to release the experimental code along with the toy dataset (l.146)? At least, knowing the training scheme of all networks would be very helpful.  - A weak point of the paper is the lack of discussion of the sizes of the datasets with respect to the sizes of the models. How many layers are used, how many channels/dimensions per layer? It is not sure that these values are adequate measures of the capacity of networks, but reporting them would help anyway.  - The findings in sec 5 concerning the generalization growing with the number of combinations in the original distribution is very interesting. Is using absolute values (l. 229-257) for such combinations really relevant? Did the authors observe the same thresholds for varying architectures' sizes?  - In Figures 9B and 9D, there are significant variations in the core set of generated combinations: for instance, in D, green.red/cone.sphere has 7, while red.red/cylinder.cone has 38. Yet the input distribution seems to be evenly distributed among all combinations. What could explain such a discrepancy? Is it due to a small sample size due to the fact that the shapes were evaluated by human judgement (and there were only 3 judges, cf l.118)? In this case, are the values in the last column really significant? Is it consistent across all architectures and algorithms, or are there differences?  - I find very surprising that all results are consistent with both fully-connected networks and convolutional ones and VAE/GAN. There may be hidden biases in the methodology or the datasets in this case. What about other generative algorithms, such as PixelCNN?