Ferenc Huszár

Royson Lee, Rui Li, Stylianos I. Venieris et al.

Recent image degradation estimation methods have enabled single-image super-resolution (SR) approaches to better upsample real-world images. Among these methods, explicit kernel estimation approaches have demonstrated unprecedented performance at handling unknown degradations. Nonetheless, a number of limitations constrain their efficacy when used by downstream SR models. Specifically, this family of methods yields i) excessive inference time due to long per-image adaptation times and ii) inferior image fidelity due to kernel mismatch. In this work, we introduce a learning-to-learn approach that meta-learns from the information contained in a distribution of images, thereby enabling significantly faster adaptation to new images with substantially improved performance in both kernel estimation and image fidelity. Specifically, we meta-train a kernel-generating GAN, named MetaKernelGAN, on a range of tasks, such that when a new image is presented, the generator starts from an informed kernel estimate and the discriminator starts with a strong capability to distinguish between patch distributions. Compared with state-of-the-art methods, our experiments show that MetaKernelGAN better estimates the magnitude and covariance of the kernel, leading to state-of-the-art blind SR results within a similar computational regime when combined with a non-blind SR model. Through supervised learning of an unsupervised learner, our method maintains the generalizability of the unsupervised learner, improves the optimization stability of kernel estimation, and hence image adaptation, and leads to a faster inference with a speedup between 14.24 to 102.1x over existing methods.

Royson Lee, Minyoung Kim, Da Li et al.

Federated learning (FL) research has made progress in developing algorithms for distributed learning of global models, as well as algorithms for local personalization of those common models to the specifics of each client's local data distribution. However, different FL problems may require different personalization strategies, and it may not even be possible to define an effective one-size-fits-all personalization strategy for all clients: depending on how similar each client's optimal predictor is to that of the global model, different personalization strategies may be preferred. In this paper, we consider the federated meta-learning problem of learning personalization strategies. Specifically, we consider meta-nets that induce the batch-norm and learning rate parameters for each client given local data statistics. By learning these meta-nets through FL, we allow the whole FL network to collaborate in learning a customized personalization strategy for each client. Empirical results show that this framework improves on a range of standard hand-crafted personalization baselines in both label and feature shift situations.

Anna Mészáros, Szilvia Ujváry, Wieland Brendel et al.

LLMs show remarkable emergent abilities, such as inferring concepts from presumably out-of-distribution prompts, known as in-context learning. Though this success is often attributed to the Transformer architecture, our systematic understanding is limited. In complex real-world data sets, even defining what is out-of-distribution is not obvious. To better understand the OOD behaviour of autoregressive LLMs, we focus on formal languages, which are defined by the intersection of rules. We define a new scenario of OOD compositional generalization, termed rule extrapolation. Rule extrapolation describes OOD scenarios, where the prompt violates at least one rule. We evaluate rule extrapolation in formal languages with varying complexity in linear and recurrent architectures, the Transformer, and state space models to understand the architectures' influence on rule extrapolation. We also lay the first stones of a normative theory of rule extrapolation, inspired by the Solomonoff prior in algorithmic information theory.

Szilvia Ujváry, Zsigmond Telek, Anna Kerekes et al.

Sharpness-aware minimization (SAM) aims to improve the generalisation of gradient-based learning by seeking out flat minima. In this work, we establish connections between SAM and Mean-Field Variational Inference (MFVI) of neural network parameters. We show that both these methods have interpretations as optimizing notions of flatness, and when using the reparametrisation trick, they both boil down to calculating the gradient at a perturbed version of the current mean parameter. This thinking motivates our study of algorithms that combine or interpolate between SAM and MFVI. We evaluate the proposed variational algorithms on several benchmark datasets, and compare their performance to variants of SAM. Taking a broader perspective, our work suggests that SAM-like updates can be used as a drop-in replacement for the reparametrisation trick.

Siyuan Guo, Viktor Tóth, Bernhard Schölkopf et al.

Constraint-based causal discovery methods leverage conditional independence tests to infer causal relationships in a wide variety of applications. Just as the majority of machine learning methods, existing work focuses on studying $\textit{independent and identically distributed}$ data. However, it is known that even with infinite i.i.d.$\ $ data, constraint-based methods can only identify causal structures up to broad Markov equivalence classes, posing a fundamental limitation for causal discovery. In this work, we observe that exchangeable data contains richer conditional independence structure than i.i.d.$\ $ data, and show how the richer structure can be leveraged for causal discovery. We first present causal de Finetti theorems, which state that exchangeable distributions with certain non-trivial conditional independences can always be represented as $\textit{independent causal mechanism (ICM)}$ generative processes. We then present our main identifiability theorem, which shows that given data from an ICM generative process, its unique causal structure can be identified through performing conditional independence tests. We finally develop a causal discovery algorithm and demonstrate its applicability to inferring causal relationships from multi-environment data. Our code and models are publicly available at: https://github.com/syguo96/Causal-de-Finetti

Patrik Reizinger, Szilvia Ujváry, Anna Mészáros et al.

The last decade has seen blossoming research in deep learning theory attempting to answer, "Why does deep learning generalize?" A powerful shift in perspective precipitated this progress: the study of overparametrized models in the interpolation regime. In this paper, we argue that another perspective shift is due, since some of the desirable qualities of LLMs are not a consequence of good statistical generalization and require a separate theoretical explanation. Our core argument relies on the observation that AR probabilistic models are inherently non-identifiable: models zero or near-zero KL divergence apart -- thus, equivalent test loss -- can exhibit markedly different behaviors. We support our position with mathematical examples and empirical observations, illustrating why non-identifiability has practical relevance through three case studies: (1) the non-identifiability of zero-shot rule extrapolation; (2) the approximate non-identifiability of in-context learning; and (3) the non-identifiability of fine-tunability. We review promising research directions focusing on LLM-relevant generalization measures, transferability, and inductive biases.

Royson Lee, Javier Fernandez-Marques, Shell Xu Hu et al.

Federated learning (FL) has enabled distributed learning of a model across multiple clients in a privacy-preserving manner. One of the main challenges of FL is to accommodate clients with varying hardware capacities; clients have differing compute and memory requirements. To tackle this challenge, recent state-of-the-art approaches leverage the use of early exits. Nonetheless, these approaches fall short of mitigating the challenges of joint learning multiple exit classifiers, often relying on hand-picked heuristic solutions for knowledge distillation among classifiers and/or utilizing additional layers for weaker classifiers. In this work, instead of utilizing multiple classifiers, we propose a recurrent early exit approach named ReeFL that fuses features from different sub-models into a single shared classifier. Specifically, we use a transformer-based early-exit module shared among sub-models to i) better exploit multi-layer feature representations for task-specific prediction and ii) modulate the feature representation of the backbone model for subsequent predictions. We additionally present a per-client self-distillation approach where the best sub-model is automatically selected as the teacher of the other sub-models at each client. Our experiments on standard image and speech classification benchmarks across various emerging federated fine-tuning baselines demonstrate ReeFL's effectiveness over previous works.

Siyuan Guo, Aniket Didolkar, Nan Rosemary Ke et al. · mila

We are beginning to see progress in language model assisted scientific discovery. Motivated by the use of LLMs as a general scientific assistant, this paper assesses the domain knowledge of LLMs through its understanding of different mathematical skills required to solve problems. In particular, we look at not just what the pre-trained model already knows, but how it learned to learn from information during in-context learning or instruction-tuning through exploiting the complex knowledge structure within mathematics. Motivated by the Neural Tangent Kernel (NTK), we propose \textit{NTKEval} to assess changes in LLM's probability distribution via training on different kinds of math data. Our systematic analysis finds evidence of domain understanding during in-context learning. By contrast, certain instruction-tuning leads to similar performance changes irrespective of training on different data, suggesting a lack of domain understanding across different skills.

Patrik Reizinger, Siyuan Guo, Ferenc Huszár et al.

Identifying latent representations or causal structures is important for good generalization and downstream task performance. However, both fields have been developed rather independently. We observe that several methods in both representation and causal structure learning rely on the same data-generating process (DGP), namely, exchangeable but not i.i.d. (independent and identically distributed) data. We provide a unified framework, termed Identifiable Exchangeable Mechanisms (IEM), for representation and structure learning under the lens of exchangeability. IEM provides new insights that let us relax the necessary conditions for causal structure identification in exchangeable non--i.i.d. data. We also demonstrate the existence of a duality condition in identifiable representation learning, leading to new identifiability results. We hope this work will pave the way for further research in causal representation learning.

Tomo Lazovich, Luca Belli, Aaron Gonzales et al.

The harmful impacts of algorithmic decision systems have recently come into focus, with many examples of systems such as machine learning (ML) models amplifying existing societal biases. Most metrics attempting to quantify disparities resulting from ML algorithms focus on differences between groups, dividing users based on demographic identities and comparing model performance or overall outcomes between these groups. However, in industry settings, such information is often not available, and inferring these characteristics carries its own risks and biases. Moreover, typical metrics that focus on a single classifier's output ignore the complex network of systems that produce outcomes in real-world settings. In this paper, we evaluate a set of metrics originating from economics, distributional inequality metrics, and their ability to measure disparities in content exposure in a production recommendation system, the Twitter algorithmic timeline. We define desirable criteria for metrics to be used in an operational setting, specifically by ML practitioners. We characterize different types of engagement with content on Twitter using these metrics, and use these results to evaluate the metrics with respect to the desired criteria. We show that we can use these metrics to identify content suggestion algorithms that contribute more strongly to skewed outcomes between users. Overall, we conclude that these metrics can be useful tools for understanding disparate outcomes in online social networks.

Anna Kerekes, Anna Mészáros, Ferenc Huszár

In gradient descent, changing how we parametrize the model can lead to drastically different optimization trajectories, giving rise to a surprising range of meaningful inductive biases: identifying sparse classifiers or reconstructing low-rank matrices without explicit regularization. This implicit regularization has been hypothesised to be a contributing factor to good generalization in deep learning. However, natural gradient descent is approximately invariant to reparameterization, it always follows the same trajectory and finds the same optimum. The question naturally arises: What happens if we eliminate the role of parameterization, which solution will be found, what new properties occur? We characterize the behaviour of natural gradient flow in deep linear networks for separable classification under logistic loss and deep matrix factorization. Some of our findings extend to nonlinear neural networks with sufficient but finite over-parametrization. We demonstrate that there exist learning problems where natural gradient descent fails to generalize, while gradient descent with the right architecture performs well.

Ted Moskovitz, Michael Arbel, Ferenc Huszar et al.

A novel optimization approach is proposed for application to policy gradient methods and evolution strategies for reinforcement learning (RL). The procedure uses a computationally efficient Wasserstein natural gradient (WNG) descent that takes advantage of the geometry induced by a Wasserstein penalty to speed optimization. This method follows the recent theme in RL of including a divergence penalty in the objective to establish a trust region. Experiments on challenging tasks demonstrate improvements in both computational cost and performance over advanced baselines.

Dalin Guo, Sofia Ira Ktena, Ferenc Huszar et al.

Recommender systems trained in a continuous learning fashion are plagued by the feedback loop problem, also known as algorithmic bias. This causes a newly trained model to act greedily and favor items that have already been engaged by users. This behavior is particularly harmful in personalised ads recommendations, as it can also cause new campaigns to remain unexplored. Exploration aims to address this limitation by providing new information about the environment, which encompasses user preference, and can lead to higher long-term reward. In this work, we formulate a display advertising recommender as a contextual bandit and implement exploration techniques that require sampling from the posterior distribution of click-through-rates in a computationally tractable manner. Traditional large-scale deep learning models do not provide uncertainty estimates by default. We approximate these uncertainty measurements of the predictions by employing a bootstrapped model with multiple heads and dropout units. We benchmark a number of different models in an offline simulation environment using a publicly available dataset of user-ads engagements. We test our proposed deep Bayesian bandits algorithm in the offline simulation and online AB setting with large-scale production traffic, where we demonstrate a positive gain of our exploration model.

Caojin Zhang, Yicun Liu, Yuanpu Xie et al.

Deep Neural Networks (DNNs) with sparse input features have been widely used in recommender systems in industry. These models have large memory requirements and need a huge amount of training data. The large model size usually entails a cost, in the range of millions of dollars, for storage and communication with the inference services. In this paper, we propose a hybrid hashing method to combine frequency hashing and double hashing techniques for model size reduction, without compromising performance. We evaluate the proposed models on two product surfaces. In both cases, experiment results demonstrated that we can reduce the model size by around 90 % while keeping the performance on par with the original baselines.

Sofia Ira Ktena, Alykhan Tejani, Lucas Theis et al.

One of the challenges in display advertising is that the distribution of features and click through rate (CTR) can exhibit large shifts over time due to seasonality, changes to ad campaigns and other factors. The predominant strategy to keep up with these shifts is to train predictive models continuously, on fresh data, in order to prevent them from becoming stale. However, in many ad systems positive labels are only observed after a possibly long and random delay. These delayed labels pose a challenge to data freshness in continuous training: fresh data may not have complete label information at the time they are ingested by the training algorithm. Naive strategies which consider any data point a negative example until a positive label becomes available tend to underestimate CTR, resulting in inferior user experience and suboptimal performance for advertisers. The focus of this paper is to identify the best combination of loss functions and models that enable large-scale learning from a continuous stream of data in the presence of delayed labels. In this work, we compare 5 different loss functions, 3 of them applied to this problem for the first time. We benchmark their performance in offline settings on both public and proprietary datasets in conjunction with shallow and deep model architectures. We also discuss the engineering cost associated with implementing each loss function in a production environment. Finally, we carried out online experiments with the top performing methods, in order to validate their performance in a continuous training scheme. While training on 668 million in-house data points offline, our proposed methods outperform previous state-of-the-art by 3% relative cross entropy (RCE). During online experiments, we observed 55% gain in revenue per thousand requests (RPMq) against naive log loss.

Iryna Korshunova, Jonas Degrave, Ferenc Huszár et al.

We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations. Our model is provably exchangeable, meaning that the joint distribution over observations is invariant under permutation: this property lies at the heart of Bayesian inference. The model does not require variational approximations to train, and new samples can be generated conditional on previous samples, with cost linear in the size of the conditioning set. The advantages of our architecture are demonstrated on learning tasks that require generalisation from short observed sequences while modelling sequence variability, such as conditional image generation, few-shot learning, and anomaly detection.

Lucas Theis, Iryna Korshunova, Alykhan Tejani et al.

Predicting human fixations from images has recently seen large improvements by leveraging deep representations which were pretrained for object recognition. However, as we show in this paper, these networks are highly overparameterized for the task of fixation prediction. We first present a simple yet principled greedy pruning method which we call Fisher pruning. Through a combination of knowledge distillation and Fisher pruning, we obtain much more runtime-efficient architectures for saliency prediction, achieving a 10x speedup for the same AUC performance as a state of the art network on the CAT2000 dataset. Speeding up single-image gaze prediction is important for many real-world applications, but it is also a crucial step in the development of video saliency models, where the amount of data to be processed is substantially larger.

Ferenc Huszár

Elastic weight consolidation (EWC, Kirkpatrick et al, 2017) is a novel algorithm designed to safeguard against catastrophic forgetting in neural networks. EWC can be seen as an approximation to Laplace propagation (Eskin et al, 2004), and this view is consistent with the motivation given by Kirkpatrick et al (2017). In this note, I present an extended derivation that covers the case when there are more than two tasks. I show that the quadratic penalties in EWC are inconsistent with this derivation and might lead to double-counting data from earlier tasks.

Lucas Theis, Wenzhe Shi, Andrew Cunningham et al.

We propose a new approach to the problem of optimizing autoencoders for lossy image compression. New media formats, changing hardware technology, as well as diverse requirements and content types create a need for compression algorithms which are more flexible than existing codecs. Autoencoders have the potential to address this need, but are difficult to optimize directly due to the inherent non-differentiabilty of the compression loss. We here show that minimal changes to the loss are sufficient to train deep autoencoders competitive with JPEG 2000 and outperforming recently proposed approaches based on RNNs. Our network is furthermore computationally efficient thanks to a sub-pixel architecture, which makes it suitable for high-resolution images. This is in contrast to previous work on autoencoders for compression using coarser approximations, shallower architectures, computationally expensive methods, or focusing on small images.

Ferenc Huszár

Generative adversarial networks (GANs) have given us a great tool to fit implicit generative models to data. Implicit distributions are ones we can sample from easily, and take derivatives of samples with respect to model parameters. These models are highly expressive and we argue they can prove just as useful for variational inference (VI) as they are for generative modelling. Several papers have proposed GAN-like algorithms for inference, however, connections to the theory of VI are not always well understood. This paper provides a unifying review of existing algorithms establishing connections between variational autoencoders, adversarially learned inference, operator VI, GAN-based image reconstruction, and more. Secondly, the paper provides a framework for building new algorithms: depending on the way the variational bound is expressed we introduce prior-contrastive and joint-contrastive methods, and show practical inference algorithms based on either density ratio estimation or denoising.

Casper Kaae Sønderby, Jose Caballero, Lucas Theis et al.

Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high-resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often with a pixel-wise mean squared error (MSE) loss. However, the outputs from such methods tend to be blurry, over-smoothed and generally appear implausible. A more desirable approach would employ Maximum a Posteriori (MAP) inference, preferring solutions that always have a high probability under the image prior, and thus appear more plausible. Direct MAP estimation for SR is non-trivial, as it requires us to build a model for the image prior from samples. Furthermore, MAP inference is often performed via optimisation-based iterative algorithms which don't compare well with the efficiency of neural-network-based alternatives. Here we introduce new methods for amortised MAP inference whereby we calculate the MAP estimate directly using a convolutional neural network. We first introduce a novel neural network architecture that performs a projection to the affine subspace of valid SR solutions ensuring that the high resolution output of the network is always consistent with the low resolution input. We show that, using this architecture, the amortised MAP inference problem reduces to minimising the cross-entropy between two distributions, similar to training generative models. We propose three methods to solve this optimisation problem: (1) Generative Adversarial Networks (GAN) (2) denoiser-guided SR which backpropagates gradient-estimates from denoising to train the network, and (3) a baseline method using a maximum-likelihood-trained image prior. Our experiments show that the GAN based approach performs best on real image data. Lastly, we establish a connection between GANs and amortised variational inference as in e.g. variational autoencoders.

Wenzhe Shi, Jose Caballero, Lucas Theis et al.

In this note, we want to focus on aspects related to two questions most people asked us at CVPR about the network we presented. Firstly, What is the relationship between our proposed layer and the deconvolution layer? And secondly, why are convolutions in low-resolution (LR) space a better choice? These are key questions we tried to answer in the paper, but we were not able to go into as much depth and clarity as we would have liked in the space allowance. To better answer these questions in this note, we first discuss the relationships between the deconvolution layer in the forms of the transposed convolution layer, the sub-pixel convolutional layer and our efficient sub-pixel convolutional layer. We will refer to our efficient sub-pixel convolutional layer as a convolutional layer in LR space to distinguish it from the common sub-pixel convolutional layer. We will then show that for a fixed computational budget and complexity, a network with convolutions exclusively in LR space has more representation power at the same speed than a network that first upsamples the input in high resolution space.

Wenzhe Shi, Jose Caballero, Ferenc Huszár et al.

Recently, several models based on deep neural networks have achieved great success in terms of both reconstruction accuracy and computational performance for single image super-resolution. In these methods, the low resolution (LR) input image is upscaled to the high resolution (HR) space using a single filter, commonly bicubic interpolation, before reconstruction. This means that the super-resolution (SR) operation is performed in HR space. We demonstrate that this is sub-optimal and adds computational complexity. In this paper, we present the first convolutional neural network (CNN) capable of real-time SR of 1080p videos on a single K2 GPU. To achieve this, we propose a novel CNN architecture where the feature maps are extracted in the LR space. In addition, we introduce an efficient sub-pixel convolution layer which learns an array of upscaling filters to upscale the final LR feature maps into the HR output. By doing so, we effectively replace the handcrafted bicubic filter in the SR pipeline with more complex upscaling filters specifically trained for each feature map, whilst also reducing the computational complexity of the overall SR operation. We evaluate the proposed approach using images and videos from publicly available datasets and show that it performs significantly better (+0.15dB on Images and +0.39dB on Videos) and is an order of magnitude faster than previous CNN-based methods.

Christian Ledig, Lucas Theis, Ferenc Huszar et al.

Despite the breakthroughs in accuracy and speed of single image super-resolution using faster and deeper convolutional neural networks, one central problem remains largely unsolved: how do we recover the finer texture details when we super-resolve at large upscaling factors? The behavior of optimization-based super-resolution methods is principally driven by the choice of the objective function. Recent work has largely focused on minimizing the mean squared reconstruction error. The resulting estimates have high peak signal-to-noise ratios, but they are often lacking high-frequency details and are perceptually unsatisfying in the sense that they fail to match the fidelity expected at the higher resolution. In this paper, we present SRGAN, a generative adversarial network (GAN) for image super-resolution (SR). To our knowledge, it is the first framework capable of inferring photo-realistic natural images for 4x upscaling factors. To achieve this, we propose a perceptual loss function which consists of an adversarial loss and a content loss. The adversarial loss pushes our solution to the natural image manifold using a discriminator network that is trained to differentiate between the super-resolved images and original photo-realistic images. In addition, we use a content loss motivated by perceptual similarity instead of similarity in pixel space. Our deep residual network is able to recover photo-realistic textures from heavily downsampled images on public benchmarks. An extensive mean-opinion-score (MOS) test shows hugely significant gains in perceptual quality using SRGAN. The MOS scores obtained with SRGAN are closer to those of the original high-resolution images than to those obtained with any state-of-the-art method.

Ferenc Huszár

Modern applications and progress in deep learning research have created renewed interest for generative models of text and of images. However, even today it is unclear what objective functions one should use to train and evaluate these models. In this paper we present two contributions. Firstly, we present a critique of scheduled sampling, a state-of-the-art training method that contributed to the winning entry to the MSCOCO image captioning benchmark in 2015. Here we show that despite this impressive empirical performance, the objective function underlying scheduled sampling is improper and leads to an inconsistent learning algorithm. Secondly, we revisit the problems that scheduled sampling was meant to address, and present an alternative interpretation. We argue that maximum likelihood is an inappropriate training objective when the end-goal is to generate natural-looking samples. We go on to derive an ideal objective function to use in this situation instead. We introduce a generalisation of adversarial training, and show how such method can interpolate between maximum likelihood training and our ideal training objective. To our knowledge this is the first theoretical analysis that explains why adversarial training tends to produce samples with higher perceived quality.

Ferenc Huszar, David Duvenaud

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior variance in Bayesian quadrature. We then show that sequential Bayesian quadrature can be viewed as a weighted version of kernel herding which achieves performance superior to any other weighted herding method. We demonstrate empirically a rate of convergence faster than O(1/N). Our results also imply an upper bound on the empirical error of the Bayesian quadrature estimate.

Ferenc Huszár, David Duvenaud

Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised when selecting samples in kernel herding is equivalent to the posterior variance in Bayesian quadrature. We then show that sequential Bayesian quadrature can be viewed as a weighted version of kernel herding which achieves performance superior to any other weighted herding method. We demonstrate empirically a rate of convergence faster than O(1/N). Our results also imply an upper bound on the empirical error of the Bayesian quadrature estimate.