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 InstaAug, a method for automatically learning input-specific augmentations from data. Previous methods for learning augmentations have typically assumed independence between the original input and the transformation applied to that input. This can be highly restrictive, as the invariances we hope our augmentation will capture are themselves often highly input dependent. InstaAug instead introduces a learnable invariance module that maps from inputs to tailored transformation parameters, allowing local invariances to be captured. This can be simultaneously trained alongside the downstream model in a fully end-to-end manner, or separately learned for a pre-trained model. We empirically demonstrate that InstaAug learns meaningful input-dependent augmentations for a wide range of transformation classes, which in turn provides better performance on both supervised and self-supervised tasks.

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.

Lipschitz constants of neural networks have been explored in various contexts in deep learning, such as provable adversarial robustness, estimating Wasserstein distance, stabilising training of GANs, and formulating invertible neural networks. Such works have focused on bounding the Lipschitz constant of fully connected or convolutional networks, composed of linear maps and pointwise non-linearities. In this paper, we investigate the Lipschitz constant of self-attention, a non-linear neural network module widely used in sequence modelling. We prove that the standard dot-product self-attention is not Lipschitz for unbounded input domain, and propose an alternative L2 self-attention that is Lipschitz. We derive an upper bound on the Lipschitz constant of L2 self-attention and provide empirical evidence for its asymptotic tightness. To demonstrate the practical relevance of our theoretical work, we formulate invertible self-attention and use it in a Transformer-based architecture for a character-level language modelling task.

Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions, to reduce the spatial dimensions of feature maps and to allow the receptive fields to grow exponentially with depth. However, it is known that such subsampling operations are not translation equivariant, unlike convolutions that are translation equivariant. Here, we first introduce translation equivariant subsampling/upsampling layers that can be used to construct exact translation equivariant CNNs. We then generalise these layers beyond translations to general groups, thus proposing group equivariant subsampling/upsampling. We use these layers to construct group equivariant autoencoders (GAEs) that allow us to learn low-dimensional equivariant representations. We empirically verify on images that the representations are indeed equivariant to input translations and rotations, and thus generalise well to unseen positions and orientations. We further use GAEs in models that learn object-centric representations on multi-object datasets, and show improved data efficiency and decomposition compared to non-equivariant baselines.

We develop a functional encoder-decoder approach to supervised meta-learning, where labeled data is encoded into an infinite-dimensional functional representation rather than a finite-dimensional one. Furthermore, rather than directly producing the representation, we learn a neural update rule resembling functional gradient descent which iteratively improves the representation. The final representation is used to condition the decoder to make predictions on unlabeled data. Our approach is the first to demonstrates the success of encoder-decoder style meta-learning methods like conditional neural processes on large-scale few-shot classification benchmarks such as miniImageNet and tieredImageNet, where it achieves state-of-the-art performance.

Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician employs a kernel search algorithm using Gaussian Processes (GP) to provide interpretable statistical models for regression problems. However this does not scale due to its O(N^3) running time for the model selection. We propose Scalable Kernel Composition (SKC), a scalable kernel search algorithm that extends the Automatic Statistician to bigger data sets. In doing so, we derive a cheap upper bound on the GP marginal likelihood that is used in SKC with the variational lower bound to sandwich the marginal likelihood. We show that the upper bound is significantly tighter than the lower bound and useful for model selection.

We define and address the problem of unsupervised learning of disentangled representations on data generated from independent factors of variation. We propose FactorVAE, a method that disentangles by encouraging the distribution of representations to be factorial and hence independent across the dimensions. We show that it improves upon beta-VAE by providing a better trade-off between disentanglement and reconstruction quality and being more robust to the number of training iterations. Moreover, we highlight the problems of a commonly used disentanglement metric and introduce a new metric that does not suffer from them.

We present Sequential Attend, Infer, Repeat (SQAIR), an interpretable deep generative model for image sequences. It can reliably discover and track objects through the sequence; it can also conditionally generate future frames, thereby simulating expected motion of objects. This is achieved by explicitly encoding object numbers, locations and appearances in the latent variables of the model. SQAIR retains all strengths of its predecessor, Attend, Infer, Repeat (AIR, Eslami et. al. 2016), including unsupervised learning, made possible by inductive biases present in the model structure. We use a moving multi-\textsc{mnist} dataset to show limitations of AIR in detecting overlapping or partially occluded objects, and show how \textsc{sqair} overcomes them by leveraging temporal consistency of objects. Finally, we also apply SQAIR to real-world pedestrian CCTV data, where it learns to reliably detect, track and generate walking pedestrians with no supervision.