Error analysis of generative adversarial network

The generative adversarial network (GAN) is an important model developed for high-dimensional distribution learning in recent years. However, there is a pressing need for a comprehensive method to understand its error convergence rate. In this research, we focus on studying the error convergence rate of the GAN model that is based on a class of functions encompassing the discriminator and generator neural networks. These functions are VC type with bounded envelope function under our assumptions, enabling the application of the Talagrand inequality. By employing the Talagrand inequality and Borel-Cantelli lemma, we establish a tight convergence rate for the error of GAN. This method can also be applied on existing error estimations of GAN and yields improved convergence rates. In particular, the error defined with the neural network distance is a special case error in our definition.

Visual Question Generation in Bengali

The task of Visual Question Generation (VQG) is to generate human-like questions relevant to the given image. As VQG is an emerging research field, existing works tend to focus only on resource-rich language such as English due to the availability of datasets. In this paper, we propose the first Bengali Visual Question Generation task and develop a novel transformer-based encoder-decoder architecture that generates questions in Bengali when given an image. We propose multiple variants of models - (i) image-only: baseline model of generating questions from images without additional information, (ii) image-category and image-answer-category: guided VQG where we condition the model to generate questions based on the answer and the category of expected question. These models are trained and evaluated on the translated VQAv2.0 dataset. Our quantitative and qualitative results establish the first state of the art models for VQG task in Bengali and demonstrate that our models are capable of generating grammatically correct and relevant questions. Our quantitative results show that our image-cat model achieves a BLUE-1 score of 33.12 and BLEU-3 score of 7.56 which is the highest of the other two variants. We also perform a human evaluation to assess the quality of the generation tasks. Human evaluation suggests that image-cat model is capable of generating goal-driven and attribute-specific questions and also stays relevant to the corresponding image.

The objective function equality property of infoGAN for two-layer network

Information Maximizing Generative Adversarial Network (infoGAN) can be understood as a minimax problem involving two networks: discriminators and generators with mutual information functions. The infoGAN incorporates various components, including latent variables, mutual information, and objective function. This research demonstrates that the two objective functions in infoGAN become equivalent as the discriminator and generator sample size approaches infinity. This equivalence is established by considering the disparity between the empirical and population versions of the objective function. The bound on this difference is determined by the Rademacher complexity of the discriminator and generator function class. Furthermore, the utilization of a two-layer network for both the discriminator and generator, featuring Lipschitz and non-decreasing activation functions, validates this equality