Taco S. Cohen

Ties van Rozendaal, Johann Brehmer, Yunfan Zhang et al.

We introduce a video compression algorithm based on instance-adaptive learning. On each video sequence to be transmitted, we finetune a pretrained compression model. The optimal parameters are transmitted to the receiver along with the latent code. By entropy-coding the parameter updates under a suitable mixture model prior, we ensure that the network parameters can be encoded efficiently. This instance-adaptive compression algorithm is agnostic about the choice of base model and has the potential to improve any neural video codec. On UVG, HEVC, and Xiph datasets, our codec improves the performance of a scale-space flow model by between 21% and 27% BD-rate savings, and that of a state-of-the-art B-frame model by 17 to 20% BD-rate savings. We also demonstrate that instance-adaptive finetuning improves the robustness to domain shift. Finally, our approach reduces the capacity requirements of compression models. We show that it enables a competitive performance even after reducing the network size by 70%.

Amirhossein Habibian, Davide Abati, Taco S. Cohen et al.

We propose Skip-Convolutions to leverage the large amount of redundancies in video streams and save computations. Each video is represented as a series of changes across frames and network activations, denoted as residuals. We reformulate standard convolution to be efficiently computed on residual frames: each layer is coupled with a binary gate deciding whether a residual is important to the model prediction,~\eg foreground regions, or it can be safely skipped, e.g. background regions. These gates can either be implemented as an efficient network trained jointly with convolution kernels, or can simply skip the residuals based on their magnitude. Gating functions can also incorporate block-wise sparsity structures, as required for efficient implementation on hardware platforms. By replacing all convolutions with Skip-Convolutions in two state-of-the-art architectures, namely EfficientDet and HRNet, we reduce their computational cost consistently by a factor of 3~4x for two different tasks, without any accuracy drop. Extensive comparisons with existing model compression, as well as image and video efficiency methods demonstrate that Skip-Convolutions set a new state-of-the-art by effectively exploiting the temporal redundancies in videos.

Ankitesh K. Singh, Hilmi E. Egilmez, Reza Pourreza et al.

Most of the existing deep learning based end-to-end video coding (DLEC) architectures are designed specifically for RGB color format, yet the video coding standards, including H.264/AVC, H.265/HEVC and H.266/VVC developed over past few decades, have been designed primarily for YUV 4:2:0 format, where the chrominance (U and V) components are subsampled to achieve superior compression performances considering the human visual system. While a broad number of papers on DLEC compare these two distinct coding schemes in RGB domain, it is ideal to have a common evaluation framework in YUV 4:2:0 domain for a more fair comparison. This paper introduces a new DLEC architecture for video coding to effectively support YUV 4:2:0 and compares its performance against the HEVC standard under a common evaluation framework. The experimental results on YUV 4:2:0 video sequences show that the proposed architecture can outperform HEVC in intra-frame coding, however inter-frame coding is not as efficient on contrary to the RGB coding results reported in recent papers.

Hilmi E. Egilmez, Ankitesh K. Singh, Muhammed Coban et al.

Most of the existing deep learning based end-to-end image/video coding (DLEC) architectures are designed for non-subsampled RGB color format. However, in order to achieve a superior coding performance, many state-of-the-art block-based compression standards such as High Efficiency Video Coding (HEVC/H.265) and Versatile Video Coding (VVC/H.266) are designed primarily for YUV 4:2:0 format, where U and V components are subsampled by considering the human visual system. This paper investigates various DLEC designs to support YUV 4:2:0 format by comparing their performance against the main profiles of HEVC and VVC standards under a common evaluation framework. Moreover, a new transform network architecture is proposed to improve the efficiency of coding YUV 4:2:0 data. The experimental results on YUV 4:2:0 datasets show that the proposed architecture significantly outperforms naive extensions of existing architectures designed for RGB format and achieves about 10% average BD-rate improvement over the intra-frame coding in HEVC.

Ties van Rozendaal, Iris A. M. Huijben, Taco S. Cohen

Neural data compression has been shown to outperform classical methods in terms of $RD$ performance, with results still improving rapidly. At a high level, neural compression is based on an autoencoder that tries to reconstruct the input instance from a (quantized) latent representation, coupled with a prior that is used to losslessly compress these latents. Due to limitations on model capacity and imperfect optimization and generalization, such models will suboptimally compress test data in general. However, one of the great strengths of learned compression is that if the test-time data distribution is known and relatively low-entropy (e.g. a camera watching a static scene, a dash cam in an autonomous car, etc.), the model can easily be finetuned or adapted to this distribution, leading to improved $RD$ performance. In this paper we take this concept to the extreme, adapting the full model to a single video, and sending model updates (quantized and compressed using a parameter-space prior) along with the latent representation. Unlike previous work, we finetune not only the encoder/latents but the entire model, and - during finetuning - take into account both the effect of model quantization and the additional costs incurred by sending the model updates. We evaluate an image compression model on I-frames (sampled at 2 fps) from videos of the Xiph dataset, and demonstrate that full-model adaptation improves $RD$ performance by ~1 dB, with respect to encoder-only finetuning.

Ties van Rozendaal, Guillaume Sautière, Taco S. Cohen

When training end-to-end learned models for lossy compression, one has to balance the rate and distortion losses. This is typically done by manually setting a tradeoff parameter $β$, an approach called $β$-VAE. Using this approach it is difficult to target a specific rate or distortion value, because the result can be very sensitive to $β$, and the appropriate value for $β$ depends on the model and problem setup. As a result, model comparison requires extensive per-model $β$-tuning, and producing a whole rate-distortion curve (by varying $β$) for each model to be compared. We argue that the constrained optimization method of Rezende and Viola, 2018 is a lot more appropriate for training lossy compression models because it allows us to obtain the best possible rate subject to a distortion constraint. This enables pointwise model comparisons, by training two models with the same distortion target and comparing their rate. We show that the method does manage to satisfy the constraint on a realistic image compression task, outperforms a constrained optimization method based on a hinge-loss, and is more practical to use for model selection than a $β$-VAE.

Mirgahney Mohamed, Gabriele Cesa, Taco S. Cohen et al.

Thanks to their improved data efficiency, equivariant neural networks have gained increased interest in the deep learning community. They have been successfully applied in the medical domain where symmetries in the data can be effectively exploited to build more accurate and robust models. To be able to reach a much larger body of patients, mobile, on-device implementations of deep learning solutions have been developed for medical applications. However, equivariant models are commonly implemented using large and computationally expensive architectures, not suitable to run on mobile devices. In this work, we design and test an equivariant version of MobileNetV2 and further optimize it with model quantization to enable more efficient inference. We achieve close-to state of the art performance on the Patch Camelyon (PCam) medical dataset while being more computationally efficient.

Emiel Hoogeboom, Taco S. Cohen, Jakub M. Tomczak

Media is generally stored digitally and is therefore discrete. Many successful deep distribution models in deep learning learn a density, i.e., the distribution of a continuous random variable. Naïve optimization on discrete data leads to arbitrarily high likelihoods, and instead, it has become standard practice to add noise to datapoints. In this paper, we present a general framework for dequantization that captures existing methods as a special case. We derive two new dequantization objectives: importance-weighted (iw) dequantization and Rényi dequantization. In addition, we introduce autoregressive dequantization (ARD) for more flexible dequantization distributions. Empirically we find that iw and Rényi dequantization considerably improve performance for uniform dequantization distributions. ARD achieves a negative log-likelihood of 3.06 bits per dimension on CIFAR10, which to the best of our knowledge is state-of-the-art among distribution models that do not require autoregressive inverses for sampling.

Amirhossein Habibian, Ties van Rozendaal, Jakub M. Tomczak et al.

In this paper we present a a deep generative model for lossy video compression. We employ a model that consists of a 3D autoencoder with a discrete latent space and an autoregressive prior used for entropy coding. Both autoencoder and prior are trained jointly to minimize a rate-distortion loss, which is closely related to the ELBO used in variational autoencoders. Despite its simplicity, we find that our method outperforms the state-of-the-art learned video compression networks based on motion compensation or interpolation. We systematically evaluate various design choices, such as the use of frame-based or spatio-temporal autoencoders, and the type of autoregressive prior. In addition, we present three extensions of the basic method that demonstrate the benefits over classical approaches to compression. First, we introduce semantic compression, where the model is trained to allocate more bits to objects of interest. Second, we study adaptive compression, where the model is adapted to a domain with limited variability, e.g., videos taken from an autonomous car, to achieve superior compression on that domain. Finally, we introduce multimodal compression, where we demonstrate the effectiveness of our model in joint compression of multiple modalities captured by non-standard imaging sensors, such as quad cameras. We believe that this opens up novel video compression applications, which have not been feasible with classical codecs.

Miranda C. N. Cheng, Vassilis Anagiannis, Maurice Weiler et al.

In this proceeding we give an overview of the idea of covariance (or equivariance) featured in the recent development of convolutional neural networks (CNNs). We study the similarities and differences between the use of covariance in theoretical physics and in the CNN context. Additionally, we demonstrate that the simple assumption of covariance, together with the required properties of locality, linearity and weight sharing, is sufficient to uniquely determine the form of the convolution.

Taco S. Cohen, Maurice Weiler, Berkay Kicanaoglu et al.

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical imaging problems that exhibit symmetries. Here we show how this principle can be extended beyond global symmetries to local gauge transformations. This enables the development of a very general class of convolutional neural networks on manifolds that depend only on the intrinsic geometry, and which includes many popular methods from equivariant and geometric deep learning. We implement gauge equivariant CNNs for signals defined on the surface of the icosahedron, which provides a reasonable approximation of the sphere. By choosing to work with this very regular manifold, we are able to implement the gauge equivariant convolution using a single conv2d call, making it a highly scalable and practical alternative to Spherical CNNs. Using this method, we demonstrate substantial improvements over previous methods on the task of segmenting omnidirectional images and global climate patterns.

Luca Falorsi, Pim de Haan, Tim R. Davidson et al.

The manifold hypothesis states that many kinds of high-dimensional data are concentrated near a low-dimensional manifold. If the topology of this data manifold is non-trivial, a continuous encoder network cannot embed it in a one-to-one manner without creating holes of low density in the latent space. This is at odds with the Gaussian prior assumption typically made in Variational Auto-Encoders (VAEs), because the density of a Gaussian concentrates near a blob-like manifold. In this paper we investigate the use of manifold-valued latent variables. Specifically, we focus on the important case of continuously differentiable symmetry groups (Lie groups), such as the group of 3D rotations $\operatorname{SO}(3)$. We show how a VAE with $\operatorname{SO}(3)$-valued latent variables can be constructed, by extending the reparameterization trick to compact connected Lie groups. Our experiments show that choosing manifold-valued latent variables that match the topology of the latent data manifold, is crucial to preserve the topological structure and learn a well-behaved latent space.

Jasper Linmans, Jim Winkens, Bastiaan S. Veeling et al.

We propose a semantic segmentation model that exploits rotation and reflection symmetries. We demonstrate significant gains in sample efficiency due to increased weight sharing, as well as improvements in robustness to symmetry transformations. The group equivariant CNN framework is extended for segmentation by introducing a new equivariant (G->Z2)-convolution that transforms feature maps on a group to planar feature maps. Also, equivariant transposed convolution is formulated for up-sampling in an encoder-decoder network. To demonstrate improvements in sample efficiency we evaluate on multiple data regimes of a rotation-equivariant segmentation task: cancer metastases detection in histopathology images. We further show the effectiveness of exploiting more symmetries by varying the size of the group.

Marysia Winkels, Taco S. Cohen

Convolutional Neural Networks (CNNs) require a large amount of annotated data to learn from, which is often difficult to obtain in the medical domain. In this paper we show that the sample complexity of CNNs can be significantly improved by using 3D roto-translation group convolutions (G-Convs) instead of the more conventional translational convolutions. These 3D G-CNNs were applied to the problem of false positive reduction for pulmonary nodule detection, and proved to be substantially more effective in terms of performance, sensitivity to malignant nodules, and speed of convergence compared to a strong and comparable baseline architecture with regular convolutions, data augmentation and a similar number of parameters. For every dataset size tested, the G-CNN achieved a FROC score close to the CNN trained on ten times more data.

Taco S. Cohen, Mario Geiger, Maurice Weiler

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where symmetries are present. In geometrical terms, regular G-CNNs represent data in terms of scalar fields ("feature channels"), whereas the steerable G-CNN can also use vector or tensor fields ("capsules") to represent data. In algebraic terms, the feature spaces in regular G-CNNs transform according to a regular representation of the group G, whereas the feature spaces in Steerable G-CNNs transform according to the more general induced representations of G. In order to make the network equivariant, each layer in a G-CNN is required to intertwine between the induced representations associated with its input and output space. In this paper we present a general mathematical framework for G-CNNs on homogeneous spaces like Euclidean space or the sphere. We show, using elementary methods, that the layers of an equivariant network are convolutional if and only if the input and output feature spaces transform according to an induced representation. This result, which follows from G.W. Mackey's abstract theory on induced representations, establishes G-CNNs as a universal class of equivariant network architectures, and generalizes the important recent work of Kondor & Trivedi on the intertwiners between regular representations.

Emiel Hoogeboom, Jorn W. T. Peters, Taco S. Cohen et al.

The effectiveness of Convolutional Neural Networks stems in large part from their ability to exploit the translation invariance that is inherent in many learning problems. Recently, it was shown that CNNs can exploit other invariances, such as rotation invariance, by using group convolutions instead of planar convolutions. However, for reasons of performance and ease of implementation, it has been necessary to limit the group convolution to transformations that can be applied to the filters without interpolation. Thus, for images with square pixels, only integer translations, rotations by multiples of 90 degrees, and reflections are admissible. Whereas the square tiling provides a 4-fold rotational symmetry, a hexagonal tiling of the plane has a 6-fold rotational symmetry. In this paper we show how one can efficiently implement planar convolution and group convolution over hexagonal lattices, by re-using existing highly optimized convolution routines. We find that, due to the reduced anisotropy of hexagonal filters, planar HexaConv provides better accuracy than planar convolution with square filters, given a fixed parameter budget. Furthermore, we find that the increased degree of symmetry of the hexagonal grid increases the effectiveness of group convolutions, by allowing for more parameter sharing. We show that our method significantly outperforms conventional CNNs on the AID aerial scene classification dataset, even outperforming ImageNet pre-trained models.

Taco S. Cohen, Mario Geiger, Jonas Koehler et al.

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective. In this paper we introduce the building blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression.

Taco S. Cohen, Max Welling

It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and flexible class of equivariant convolutional networks. We show that steerable CNNs achieve state of the art results on the CIFAR image classification benchmark. The mathematical theory of steerable representations reveals a type system in which any steerable representation is a composition of elementary feature types, each one associated with a particular kind of symmetry. We show how the parameter cost of a steerable filter bank depends on the types of the input and output features, and show how to use this knowledge to construct CNNs that utilize parameters effectively.

Luisa M. Zintgraf, Taco S. Cohen, Max Welling

We present a method for visualising the response of a deep neural network to a specific input. For image data for instance our method will highlight areas that provide evidence in favor of, and against choosing a certain class. The method overcomes several shortcomings of previous methods and provides great additional insight into the decision making process of convolutional networks, which is important both to improve models and to accelerate the adoption of such methods in e.g. medicine. In experiments on ImageNet data, we illustrate how the method works and can be applied in different ways to understand deep neural nets.

Taco S. Cohen, Max Welling

We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution layers. G-convolutions increase the expressive capacity of the network without increasing the number of parameters. Group convolution layers are easy to use and can be implemented with negligible computational overhead for discrete groups generated by translations, reflections and rotations. G-CNNs achieve state of the art results on CIFAR10 and rotated MNIST.

Taco S. Cohen, Max Welling

In a range of fields including the geosciences, molecular biology, robotics and computer vision, one encounters problems that involve random variables on manifolds. Currently, there is a lack of flexible probabilistic models on manifolds that are fast and easy to train. We define an extremely flexible class of exponential family distributions on manifolds such as the torus, sphere, and rotation groups, and show that for these distributions the gradient of the log-likelihood can be computed efficiently using a non-commutative generalization of the Fast Fourier Transform (FFT). We discuss applications to Bayesian camera motion estimation (where harmonic exponential families serve as conjugate priors), and modelling of the spatial distribution of earthquakes on the surface of the earth. Our experimental results show that harmonic densities yield a significantly higher likelihood than the best competing method, while being orders of magnitude faster to train.

Taco S. Cohen, Max Welling

When a three-dimensional object moves relative to an observer, a change occurs on the observer's image plane and in the visual representation computed by a learned model. Starting with the idea that a good visual representation is one that transforms linearly under scene motions, we show, using the theory of group representations, that any such representation is equivalent to a combination of the elementary irreducible representations. We derive a striking relationship between irreducibility and the statistical dependency structure of the representation, by showing that under restricted conditions, irreducible representations are decorrelated. Under partial observability, as induced by the perspective projection of a scene onto the image plane, the motion group does not have a linear action on the space of images, so that it becomes necessary to perform inference over a latent representation that does transform linearly. This idea is demonstrated in a model of rotating NORB objects that employs a latent representation of the non-commutative 3D rotation group SO(3).