Author name cluster

Rianne van den Berg

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10 papers

2 author rows

ICLR Conference 2023 Conference Paper

Clifford Neural Layers for PDE Modeling

Johannes Brandstetter
Rianne van den Berg
Max Welling
Jayesh K. Gupta

Partial differential equations (PDEs) see widespread use in sciences and engineering to describe simulation of physical processes as scalar and vector fields interacting and coevolving over time. Due to the computationally expensive nature of their standard solution methods, neural PDE surrogates have become an active research topic to accelerate these simulations. However, current methods do not explicitly take into account the relationship between different fields and their internal components, which are often correlated. Viewing the time evolution of such correlated fields through the lens of multivector fields allows us to overcome these limitations. Multivector fields consist of scalar, vector, as well as higher-order components, such as bivectors and trivectors. Their algebraic properties, such as multiplication, addition and other arithmetic operations can be described by Clifford algebras. To our knowledge, this paper presents the first usage of such multivector representations together with Clifford convolutions and Clifford Fourier transforms in the context of deep learning. The resulting Clifford neural layers are universally applicable and will find direct use in the areas of fluid dynamics, weather forecasting, and the modeling of physical systems in general. We empirically evaluate the benefit of Clifford neural layers by replacing convolution and Fourier operations in common neural PDE surrogates by their Clifford counterparts on 2D Navier-Stokes and weather modeling tasks, as well as 3D Maxwell equations. For similar parameter count, Clifford neural layers consistently improve generalization capabilities of the tested neural PDE surrogates.

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ICLR Conference 2022 Conference Paper

Autoregressive Diffusion Models

Emiel Hoogeboom
Alexey A. Gritsenko
Jasmijn Bastings
Ben Poole
Rianne van den Berg
Tim Salimans

We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special cases of ARDMs under mild assumptions. ARDMs are simple to implement and easy to train. Unlike standard ARMs, they do not require causal masking of model representations, and can be trained using an efficient objective similar to modern probabilistic diffusion models that scales favourably to highly-dimensional data. At test time, ARDMs support parallel generation which can be adapted to fit any given generation budget. We find that ARDMs require significantly fewer steps than discrete diffusion models to attain the same performance. Finally, we apply ARDMs to lossless compression, and show that they are uniquely suited to this task. Contrary to existing approaches based on bits-back coding, ARDMs obtain compelling results not only on complete datasets, but also on compressing single data points. Moreover, this can be done using a modest number of network calls for (de)compression due to the model's adaptable parallel generation.

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ICLR Conference 2021 Conference Paper

IDF++: Analyzing and Improving Integer Discrete Flows for Lossless Compression

Rianne van den Berg
Alexey A. Gritsenko
Mostafa Dehghani 0001
Casper Kaae Sønderby
Tim Salimans

In this paper we analyse and improve integer discrete flows for lossless compression. Integer discrete flows are a recently proposed class of models that learn invertible transformations for integer-valued random variables. Their discrete nature makes them particularly suitable for lossless compression with entropy coding schemes. We start by investigating a recent theoretical claim that states that invertible flows for discrete random variables are less flexible than their continuous counterparts. We demonstrate with a proof that this claim does not hold for integer discrete flows due to the embedding of data with finite support into the countably infinite integer lattice. Furthermore, we zoom in on the effect of gradient bias due to the straight-through estimator in integer discrete flows, and demonstrate that its influence is highly dependent on architecture choices and less prominent than previously thought. Finally, we show how different architecture modifications improve the performance of this model class for lossless compression, and that they also enable more efficient compression: a model with half the number of flow layers performs on par with or better than the original integer discrete flow model.

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NeurIPS Conference 2021 Conference Paper

Structured Denoising Diffusion Models in Discrete State-Spaces

Jacob Austin
Daniel D. Johnson
Jonathan Ho
Daniel Tarlow
Rianne van den Berg

Denoising diffusion probabilistic models (DDPMs) [Ho et al. 2021] have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. [2021], by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

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NeurIPS Conference 2020 Conference Paper

A Spectral Energy Distance for Parallel Speech Synthesis

Alexey Gritsenko
Tim Salimans
Rianne van den Berg
Jasper Snoek
Nal Kalchbrenner

Speech synthesis is an important practical generative modeling problem that has seen great progress over the last few years, with likelihood-based autoregressive neural models now outperforming traditional concatenative systems. A downside of such autoregressive models is that they require executing tens of thousands of sequential operations per second of generated audio, making them ill-suited for deployment on specialized deep learning hardware. Here, we propose a new learning method that allows us to train highly parallel models of speech, without requiring access to an analytical likelihood function. Our approach is based on a generalized energy distance between the distributions of the generated and real audio. This spectral energy distance is a proper scoring rule with respect to the distribution over magnitude-spectrograms of the generated waveform audio and offers statistical consistency guarantees. The distance can be calculated from minibatches without bias, and does not involve adversarial learning, yielding a stable and consistent method for training implicit generative models. Empirically, we achieve state-of-the-art generation quality among implicit generative models, as judged by the recently-proposed cFDSD metric. When combining our method with adversarial techniques, we also improve upon the recently-proposed GAN-TTS model in terms of Mean Opinion Score as judged by trained human evaluators.

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UAI Conference 2019 Conference Paper

Differentiable Probabilistic Models of Scientific Imaging with the Fourier Slice Theorem

Karen Ullrich
Rianne van den Berg
Marcus A. Brubaker
David J. Fleet
Max Welling

Scientific imaging techniques such as optical and electron microscopy and computed tomography (CT) scanning are used to study the 3D structure of an object through 2D observations. These observations are related to the original 3D object through orthogonal integral projections. For common 3D reconstruction algorithms, computational efficiency requires the modeling of the 3D structures to take place in Fourier space by applying the Fourier slice theorem. At present, it is unclear how to differentiate through the projection operator, and hence current learning algorithms can not rely on gradient based methods to optimize 3D structure models. In this paper we show how back-propagation through the projection operator in Fourier space can be achieved. We demonstrate the validity of the approach with experiments on 3D reconstruction of proteins. We further extend our approach to learning probabilistic models of 3D objects. This allows us to predict regions of low sampling rates or estimate noise. A higher sample efficiency can be reached by utilizing the learned uncertainties of the 3D structure as an unsupervised estimate of the model fit. Finally, we demonstrate how the reconstruction algorithm can be extended with an amortized inference scheme on unknown attributes such as object pose. Through empirical studies we show that joint inference of the 3D structure and the object pose becomes more difficult when the ground truth object contains more symmetries. Due to the presence of for instance (approximate) rotational symmetries, the pose estimation can easily get stuck in local optima, inhibiting a fine-grained high-quality estimate of the 3D structure.

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ICML Conference 2019 Conference Paper

Emerging Convolutions for Generative Normalizing Flows

Emiel Hoogeboom
Rianne van den Berg
Max Welling

Generative flows are attractive because they admit exact likelihood optimization and efficient image synthesis. Recently, Kingma & Dhariwal (2018) demonstrated with Glow that generative flows are capable of generating high quality images. We generalize the 1 {\texttimes} 1 convolutions proposed in Glow to invertible d {\texttimes} d convolutions, which are more flexible since they operate on both channel and spatial axes. We propose two methods to produce invertible convolutions, that have receptive fields identical to standard convolutions: Emerging convolutions are obtained by chaining specific autoregressive convolutions, and periodic convolutions are decoupled in the frequency domain. Our experiments show that the flexibility of d {\texttimes} d convolutions significantly improves the performance of generative flow models on galaxy images, CIFAR10 and ImageNet.

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NeurIPS Conference 2019 Conference Paper

Integer Discrete Flows and Lossless Compression

Emiel Hoogeboom
Jorn Peters
Rianne van den Berg
Max Welling

Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, conventional flows assume continuous data, which may lead to reconstruction errors when quantized for compression. For that reason, we introduce a flow-based generative model for ordinal discrete data called Integer Discrete Flow (IDF): a bijective integer map that can learn rich transformations on high-dimensional data. As building blocks for IDFs, we introduce a flexible transformation layer called integer discrete coupling. Our experiments show that IDFs are competitive with other flow-based generative models. Furthermore, we demonstrate that IDF based compression achieves state-of-the-art lossless compression rates on CIFAR10, ImageNet32, and ImageNet64. To the best of our knowledge, this is the first lossless compression method that uses invertible neural networks.

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UAI Conference 2019 Conference Paper

Sinkhorn AutoEncoders

Giorgio Patrini
Rianne van den Berg
Patrick Forré
Marcello Carioni
Samarth Bhargav 0001
Max Welling
Tim Genewein
Frank Nielsen

Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the $p$-Wasserstein distance between the generator and the true data distribution is equivalent to the unconstrained min-min optimization of the $p$-Wasserstein distance between the encoder aggregated posterior and the prior in latent space, plus a reconstruction error. We also identify the role of its trade-off hyperparameter as the capacity of the generator: its Lipschitz constant. Moreover, we prove that optimizing the encoder over any class of universal approximators, such as deterministic neural networks, is enough to come arbitrarily close to the optimum. We therefore advertise this framework, which holds for any metric space and prior, as a sweet-spot of current generative autoencoding objectives. We then introduce the Sinkhorn autoencoder (SAE), which approximates and minimizes the $p$-Wasserstein distance in latent space via backprogation through the Sinkhorn algorithm. SAE directly works on samples, i. e. it models the aggregated posterior as an implicit distribution, with no need for a reparameterization trick for gradients estimations. SAE is thus able to work with different metric spaces and priors with minimal adaptations. We demonstrate the flexibility of SAE on latent spaces with different geometries and priors and compare with other methods on benchmark data sets.

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UAI Conference 2018 Conference Paper

Sylvester Normalizing Flows for Variational Inference

Rianne van den Berg
Leonard Hasenclever
Jakub M. Tomczak
Max Welling

Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single-unit bottleneck from planar flows, making a single transformation much more flexible. We compare the performance of Sylvester normalizing flows against planar flows and inverse autoregressive flows and demonstrate that they compare favorably on several datasets.

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