Inspired by the success of generative image models, recent work on learned image compression increasingly focuses on better probabilistic models of the natural image distribution, leading to excellent image quality. This, however, comes at the expense of a computational complexity that is several orders of magnitude higher than today’s commercial codecs, and thus prohibitive for most practical applications. With this paper, we demonstrate that by focusing on modeling visual perception rather than the data distribution, we can achieve a very good trade-off between visual quality and bit rate similar to “generative” compression models such as HiFiC, while requiring less than 1% of the multiply–accumulate operations (MACs) for decompression. We do this by optimizing C3, an overfitted image codec, for Wasserstein Distortion (WD), and evaluating the image reconstructions with a human rater study, showing that WD clearly outperforms LPIPS as an optimization objective. The study also reveals that WD outperforms other perceptual metrics such as LPIPS, DISTS, and MS-SSIM as a predictor of human ratings, remarkably achieving over 94% Pearson correlation with Elo scores.

Most neural compression models are trained on large datasets of images or videos in order to generalize to unseen data. Such generalization typically requires large and expressive architectures with a high decoding complexity. Here we introduce C3, a neural compression method with strong rate-distortion (RD) performance that instead overfits a small model to each image or video separately. The resulting decoding complexity of C3 can be an order of magnitude lower than neural baselines with similar RD performance. C3 builds on Cool-chic [43] and makes several simple and effective improvements for images. We further develop new methodology to apply C3 to videos. On the CLIC2020 image benchmark, we match the RD performance of VTM, the reference implementation of the H.266 codec, with less than 3k MACs/pixel for decoding. On the UVG video benchmark, we match the RD performance of the Video Compression Transformer [60], a well-established neural video codec, with less than 5k MACs/pixel for decoding.

We introduce Markov Neural Processes (MNPs), a new class of Stochastic Processes (SPs) which are constructed by stacking sequences of neural parameterised Markov transition operators in function space. We prove that these Markov transition operators can preserve the exchangeability and consistency of SPs. Therefore, the proposed iterative construction adds substantial flexibility and expressivity to the original framework of Neural Processes (NPs) without compromising consistency or adding restrictions. Our experiments demonstrate clear advantages of MNPs over baseline models on a variety of tasks.

Generative models are typically trained on grid-like data such as images. As a result, the size of these models usually scales directly with the underlying grid resolution. In this paper, we abandon discretized grids and instead parameterize individual data points by continuous functions. We then build generative models by learning distributions over such functions. By treating data points as functions, we can abstract away from the specific type of data we train on and construct models that are agnostic to discretization. To train our model, we use an adversarial approach with a discriminator that acts on continuous signals. Through experiments on a wide variety of data modalities including images, 3D shapes and climate data, we demonstrate that our model can learn rich distributions of functions independently of data type and resolution.

It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an image. A powerful continuous alternative is then to represent these measurements using an implicit neural representation, a neural function trained to output the appropriate measurement value for any input spatial location. In this paper, we take this idea to its next level: what would it take to perform deep learning on these functions instead, treating them as data? In this context we refer to the data as functa, and propose a framework for deep learning on functa. This view presents a number of challenges around efficient conversion from data to functa, compact representation of functa, and effectively solving downstream tasks on functa. We outline a recipe to overcome these challenges and apply it to a wide range of data modalities including images, 3D shapes, neural radiance fields (NeRF) and data on manifolds. We demonstrate that this approach has various compelling properties across data modalities, in particular on the canonical tasks of generative modeling, data imputation, novel view synthesis and classification.

Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly focused on group equivariant convolutions, building on the result that group equivariant linear maps are necessarily convolutions. In this work, we extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups. We demonstrate the generality of our approach by showing experimental results that are competitive to baseline methods on a wide range of tasks: shape counting on point clouds, molecular property regression and modelling particle trajectories under Hamiltonian dynamics.

We propose a framework for learning neural scene representations directly from images, without 3D supervision. Our key insight is that 3D structure can be imposed by ensuring that the learned representation transforms like a real 3D scene. Specifically, we introduce a loss which enforces equivariance of the scene representation with respect to 3D transformations. Our formulation allows us to infer and render scenes in real time while achieving comparable results to models requiring minutes for inference. In addition, we introduce two challenging new datasets for scene representation and neural rendering, including scenes with complex lighting and backgrounds. Through experiments, we show that our model achieves compelling results on these datasets as well as on standard ShapeNet benchmarks.

Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have shown that regularizing the dynamics of the ODE can partially alleviate this. In this paper we propose a new regularization technique: randomly sampling the end time of the ODE during training. The proposed regularization is simple to implement, has negligible overhead and is effective across a wide variety of tasks. Further, the technique is orthogonal to several other methods proposed to regularize the dynamics of ODEs and as such can be used in conjunction with them. We show through experiments on normalizing flows, time series models and image recognition that the proposed regularization can significantly decrease training time and even improve performance over baseline models.

Semantic inpainting is the task of inferring missing pixels in an image given surrounding pixels and high level image semantics. Most semantic inpainting algorithms are deterministic: given an image with missing regions, a single inpainted image is generated. However, there are often several plausible inpaintings for a given missing region. In this paper, we propose a method to perform probabilistic semantic inpainting by building a model, based on PixelCNNs, that learns a distribution of images conditioned on a subset of visible pixels. Experiments on the MNIST and CelebA datasets show that our method produces diverse and realistic inpaintings.

We show that Neural Ordinary Differential Equations (ODEs) learn representations that preserve the topology of the input space and prove that this implies the existence of functions Neural ODEs cannot represent. To address these limitations, we introduce Augmented Neural ODEs which, in addition to being more expressive models, are empirically more stable, generalize better and have a lower computational cost than Neural ODEs.

We present a framework for learning disentangled and interpretable jointly continuous and discrete representations in an unsupervised manner. By augmenting the continuous latent distribution of variational autoencoders with a relaxed discrete distribution and controlling the amount of information encoded in each latent unit, we show how continuous and categorical factors of variation can be discovered automatically from data. Experiments show that the framework disentangles continuous and discrete generative factors on various datasets and outperforms current disentangling methods when a discrete generative factor is prominent.