相关论文: Funnels: Exact maximum likelihood with dimensional…
We introduce the DNNLikelihood, a novel framework to easily encode, through Deep Neural Networks (DNN), the full experimental information contained in complicated likelihood functions (LFs). We show how to efficiently parametrise the LF,…
The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose…
A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based…
Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings,…
Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations…
Normalising Flows are non-parametric statistical models characterised by their dual capabilities of density estimation and generation. This duality requires an inherently invertible architecture. However, the requirement of invertibility…
Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…
Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…
Despite their advantages, normalizing flows generally suffer from several shortcomings including their tendency to generate unrealistic data (e.g., images) and their failing to detect out-of-distribution data. One reason for these…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…
Normalizing Flows (NFs) are widely used in deep generative models for their exact likelihood estimation and efficient sampling. However, they require substantial memory since the latent space matches the input dimension. Multi-scale…
We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free (SFdf) approximation based on a discrete $L^2$ projection. Within…
Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations…
Improving information flow in deep networks helps to ease the training difficulties and utilize parameters more efficiently. Here we propose a new convolutional neural network architecture with alternately updated clique (CliqueNet). In…
Motivated by applications in conditional sampling, given a probability measure $\mu$ and a diffeomorphism $\phi$, we consider the problem of simultaneously approximating $\phi$ and the pushforward $\phi_{\#}\mu$ by means of the flow of a…
Recent progress in deep convolutional neural networks (CNNs) have enabled a simple paradigm of architecture design: larger models typically achieve better accuracy. Due to this, in modern CNN architectures, it becomes more important to…