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We propose a Multiscale Invertible Generative Network (MsIGN) and associated training algorithm that leverages multiscale structure to solve high-dimensional Bayesian inference. To address the curse of dimensionality, MsIGN exploits the low-dimensional nature of the posterior, and generates samples from coarse to fine scale (low to high dimension) by iteratively upsampling and refining samples. MsIGN is trained in a multi-stage manner to minimize the Jeffreys divergence, which avoids mode dropping in high-dimensional cases. On two high-dimensional Bayesian inverse problems, we show superior performance of MsIGN over previous approaches in posterior approximation and multiple mode capture. On the natural image synthesis task, MsIGN achieves superior performance in bits-per-dimension over baseline models and yields great interpret-ability of its neurons in intermediate layers.
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Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that subdivision and (affine) coupling can be repeated recursively within the resulting subsets, leading to an efficiently invertible block with dense, triangular Jacobian. By formulating our recursive coupling scheme via a hierarchical architecture, HINT allows sampling from a joint distribution p(y,x) and the corresponding posterior p(x|y) using a single invertible network. We evaluate our method on some standard data sets and benchmark its full power for density estimation and Bayesian inference on a novel data set of 2D shapes in Fourier parameterization, which enables consistent visualization of samples for different dimensionalities.
This work presents an unsupervised deep learning scheme that exploiting high-dimensional assisted score-based generative model for color image restoration tasks. Considering that the sample number and internal dimension in score-based generative model have key influence on estimating the gradients of data distribution, two different high-dimensional ways are proposed: The channel-copy transformation increases the sample number and the pixel-scale transformation decreases feasible space dimension. Subsequently, a set of high-dimensional tensors represented by these transformations are used to train the network through denoising score matching. Then, sampling is performed by annealing Langevin dynamics and alternative data-consistency update. Furthermore, to alleviate the difficulty of learning high-dimensional representation, a progressive strategy is proposed to leverage the performance. The proposed unsupervised learning and iterative restoration algo-rithm, which involves a pre-trained generative network to obtain prior, has transparent and clear interpretation compared to other data-driven approaches. Experimental results on demosaicking and inpainting conveyed the remarkable performance and diversity of our proposed method.
Flow-based generative models have shown excellent ability to explicitly learn the probability density function of data via a sequence of invertible transformations. Yet, modeling long-range dependencies over normalizing flows remains understudied. To fill the gap, in this paper, we introduce two types of invertible attention mechanisms for generative flow models. To be precise, we propose map-based and scaled dot-product attention for unconditional and conditional generative flow models. The key idea is to exploit split-based attention mechanisms to learn the attention weights and input representations on every two splits of flow feature maps. Our method provides invertible attention modules with tractable Jacobian determinants, enabling seamless integration of it at any positions of the flow-based models. The proposed attention mechanism can model the global data dependencies, leading to more comprehensive flow models. Evaluation on multiple generation tasks demonstrates that the introduced attention flow idea results in efficient flow models and compares favorably against the state-of-the-art unconditional and conditional generative flow methods.
Generative adversarial networks (GANs) are highly effective unsupervised learning frameworks that can generate very sharp data, even for data such as images with complex, highly multimodal distributions. However GANs are known to be very hard to train, suffering from problems such as mode collapse and disturbing visual artifacts. Batch normalization (BN) techniques have been introduced to address the training. Though BN accelerates the training in the beginning, our experiments show that the use of BN can be unstable and negatively impact the quality of the trained model. The evaluation of BN and numerous other recent schemes for improving GAN training is hindered by the lack of an effective objective quality measure for GAN models. To address these issues, we first introduce a weight normalization (WN) approach for GAN training that significantly improves the stability, efficiency and the quality of the generated samples. To allow a methodical evaluation, we introduce squared Euclidean reconstruction error on a test set as a new objective measure, to assess training performance in terms of speed, stability, and quality of generated samples. Our experiments with a standard DCGAN architecture on commonly used datasets (CelebA, LSUN bedroom, and CIFAR-10) indicate that training using WN is generally superior to BN for GANs, achieving 10% lower mean squared loss for reconstruction and significantly better qualitative results than BN. We further demonstrate the stability of WN on a 21-layer ResNet trained with the CelebA data set. The code for this paper is available at https://github.com/stormraiser/gan-weightnorm-resnet
The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts of data. However, shapes represented as silhouette images are challenging to model due to complicated likelihood functions leading to intractable posteriors. In this paper we present a generative model of shapes which provides a low dimensional latent encoding which importantly resides on a smooth manifold with respect to the silhouette images. The proposed model propagates uncertainty in a principled manner allowing it to learn from small amounts of data and providing predictions with associated uncertainty. We provide experiments that show how our proposed model provides favorable quantitative results compared with the state-of-the-art while simultaneously providing a representation that resides on a low-dimensional interpretable manifold.
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