Shakir Mohamed

Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson et al. · deepmind

Global medium-range weather forecasting is critical to decision-making across many social and economic domains. Traditional numerical weather prediction uses increased compute resources to improve forecast accuracy, but cannot directly use historical weather data to improve the underlying model. We introduce a machine learning-based method called "GraphCast", which can be trained directly from reanalysis data. It predicts hundreds of weather variables, over 10 days at 0.25 degree resolution globally, in under one minute. We show that GraphCast significantly outperforms the most accurate operational deterministic systems on 90% of 1380 verification targets, and its forecasts support better severe event prediction, including tropical cyclones, atmospheric rivers, and extreme temperatures. GraphCast is a key advance in accurate and efficient weather forecasting, and helps realize the promise of machine learning for modeling complex dynamical systems.

Suman Ravuri, Mélanie Rey, Shakir Mohamed et al.

Understanding how well a deep generative model captures a distribution of high-dimensional data remains an important open challenge. It is especially difficult for certain model classes, such as Generative Adversarial Networks and Diffusion Models, whose models do not admit exact likelihoods. In this work, we demonstrate that generalized empirical likelihood (GEL) methods offer a family of diagnostic tools that can identify many deficiencies of deep generative models (DGMs). We show, with appropriate specification of moment conditions, that the proposed method can identify which modes have been dropped, the degree to which DGMs are mode imbalanced, and whether DGMs sufficiently capture intra-class diversity. We show how to combine techniques from Maximum Mean Discrepancy and Generalized Empirical Likelihood to create not only distribution tests that retain per-sample interpretability, but also metrics that include label information. We find that such tests predict the degree of mode dropping and mode imbalance up to 60% better than metrics such as improved precision/recall. We provide an implementation at https://github.com/deepmind/understanding_deep_generative_models_with_generalized_empirical_likelihood/.

Jackie Kay, Atoosa Kasirzadeh, Shakir Mohamed

This paper investigates how generative AI can potentially undermine the integrity of collective knowledge and the processes we rely on to acquire, assess, and trust information, posing a significant threat to our knowledge ecosystem and democratic discourse. Grounded in social and political philosophy, we introduce the concept of \emph{generative algorithmic epistemic injustice}. We identify four key dimensions of this phenomenon: amplified and manipulative testimonial injustice, along with hermeneutical ignorance and access injustice. We illustrate each dimension with real-world examples that reveal how generative AI can produce or amplify misinformation, perpetuate representational harm, and create epistemic inequities, particularly in multilingual contexts. By highlighting these injustices, we aim to inform the development of epistemically just generative AI systems, proposing strategies for resistance, system design principles, and two approaches that leverage generative AI to foster a more equitable information ecosystem, thereby safeguarding democratic values and the integrity of knowledge production.

Piotr Mirowski, David Warde-Farley, Mihaela Rosca et al.

Atmospheric states derived from reanalysis comprise a substantial portion of weather and climate simulation outputs. Many stakeholders -- such as researchers, policy makers, and insurers -- use this data to better understand the earth system and guide policy decisions. Atmospheric states have also received increased interest as machine learning approaches to weather prediction have shown promising results. A key issue for all audiences is that dense time series of these high-dimensional states comprise an enormous amount of data, precluding all but the most well resourced groups from accessing and using historical data and future projections. To address this problem, we propose a method for compressing atmospheric states using methods from the neural network literature, adapting spherical data to processing by conventional neural architectures through the use of the area-preserving HEALPix projection. We investigate two model classes for building neural compressors: the hyperprior model from the neural image compression literature and recent vector-quantised models. We show that both families of models satisfy the desiderata of small average error, a small number of high-error reconstructed pixels, faithful reproduction of extreme events such as hurricanes and heatwaves, preservation of the spectral power distribution across spatial scales. We demonstrate compression ratios in excess of 1000x, with compression and decompression at a rate of approximately one second per global atmospheric state.

LearnLM Team, Eedi, Albert Wang et al.

One-to-one tutoring is widely considered the gold standard for personalized education, yet it remains prohibitively expensive to scale. To evaluate whether generative AI might help expand access to this resource, we conducted an exploratory randomized controlled trial (RCT) with $N = 165$ students across five UK secondary schools. We integrated LearnLM -- a generative AI model fine-tuned for pedagogy -- into chat-based tutoring sessions on the Eedi mathematics platform. In the RCT, expert tutors directly supervised LearnLM, with the remit to revise each message it drafted until they would be satisfied sending it themselves. LearnLM proved to be a reliable source of pedagogical instruction, with supervising tutors approving 76.4% of its drafted messages making zero or minimal edits (i.e., changing only one or two characters). This translated into effective tutoring support: students guided by LearnLM performed at least as well as students chatting with human tutors on each learning outcome we measured. In fact, students who received support from LearnLM were 5.5 percentage points more likely to solve novel problems on subsequent topics (with a success rate of 66.2%) than those who received tutoring from human tutors alone (rate of 60.7%). In interviews, tutors highlighted LearnLM's strength at drafting Socratic questions that encouraged deeper reflection from students, with multiple tutors even reporting that they learned new pedagogical practices from the model. Overall, our results suggest that pedagogically fine-tuned AI tutoring systems may play a promising role in delivering effective, individualized learning support at scale.

Gheorghe Comanici, Eric Bieber, Mike Schaekermann et al. · amazon-science, baidu

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

Ilan Price, Alvaro Sanchez-Gonzalez, Ferran Alet et al.

Weather forecasts are fundamentally uncertain, so predicting the range of probable weather scenarios is crucial for important decisions, from warning the public about hazardous weather, to planning renewable energy use. Here, we introduce GenCast, a probabilistic weather model with greater skill and speed than the top operational medium-range weather forecast in the world, the European Centre for Medium-Range Forecasts (ECMWF)'s ensemble forecast, ENS. Unlike traditional approaches, which are based on numerical weather prediction (NWP), GenCast is a machine learning weather prediction (MLWP) method, trained on decades of reanalysis data. GenCast generates an ensemble of stochastic 15-day global forecasts, at 12-hour steps and 0.25 degree latitude-longitude resolution, for over 80 surface and atmospheric variables, in 8 minutes. It has greater skill than ENS on 97.4% of 1320 targets we evaluated, and better predicts extreme weather, tropical cyclones, and wind power production. This work helps open the next chapter in operational weather forecasting, where critical weather-dependent decisions are made with greater accuracy and efficiency.

Irina Jurenka, Markus Kunesch, Kevin R. McKee et al.

A major challenge facing the world is the provision of equitable and universal access to quality education. Recent advances in generative AI (gen AI) have created excitement about the potential of new technologies to offer a personal tutor for every learner and a teaching assistant for every teacher. The full extent of this dream, however, has not yet materialised. We argue that this is primarily due to the difficulties with verbalising pedagogical intuitions into gen AI prompts and the lack of good evaluation practices, reinforced by the challenges in defining excellent pedagogy. Here we present our work collaborating with learners and educators to translate high level principles from learning science into a pragmatic set of seven diverse educational benchmarks, spanning quantitative, qualitative, automatic and human evaluations; and to develop a new set of fine-tuning datasets to improve the pedagogical capabilities of Gemini, introducing LearnLM-Tutor. Our evaluations show that LearnLM-Tutor is consistently preferred over a prompt tuned Gemini by educators and learners on a number of pedagogical dimensions. We hope that this work can serve as a first step towards developing a comprehensive educational evaluation framework, and that this can enable rapid progress within the AI and EdTech communities towards maximising the positive impact of gen AI in education.

LearnLM Team, Abhinit Modi, Aditya Srikanth Veerubhotla et al. · amazon-science, cmu

Today's generative AI systems are tuned to present information by default, rather than engage users in service of learning as a human tutor would. To address the wide range of potential education use cases for these systems, we reframe the challenge of injecting pedagogical behavior as one of \textit{pedagogical instruction following}, where training and evaluation examples include system-level instructions describing the specific pedagogy attributes present or desired in subsequent model turns. This framing avoids committing our models to any particular definition of pedagogy, and instead allows teachers or developers to specify desired model behavior. It also clears a path to improving Gemini models for learning -- by enabling the addition of our pedagogical data to post-training mixtures -- alongside their rapidly expanding set of capabilities. Both represent important changes from our initial tech report. We show how training with pedagogical instruction following produces a LearnLM model (available on Google AI Studio) that experts substantially prefer across a diverse set of learning scenarios, with average preference strengths of +31\% over GPT-4o, +11\% over Claude 3.5 Sonnet, and +13\% over the Gemini 1.5 Pro model on which LearnLM was based.

LearnLM Team, Abhinit Modi, Aditya Srikanth Veerubhotla et al. · amazon-science, cmu

Artificial intelligence (AI) is poised to transform education, but the research community lacks a robust, general benchmark to evaluate AI models for learning. To assess state-of-the-art support for educational use cases, we ran an "arena for learning" where educators and pedagogy experts conduct blind, head-to-head, multi-turn comparisons of leading AI models. In particular, $N = 189$ educators drew from their experience to role-play realistic learning use cases, interacting with two models sequentially, after which $N = 206$ experts judged which model better supported the user's learning goals. The arena evaluated a slate of state-of-the-art models: Gemini 2.5 Pro, Claude 3.7 Sonnet, GPT-4o, and OpenAI o3. Excluding ties, experts preferred Gemini 2.5 Pro in 73.2% of these match-ups -- ranking it first overall in the arena. Gemini 2.5 Pro also demonstrated markedly higher performance across key principles of good pedagogy. Altogether, these results position Gemini 2.5 Pro as a leading model for learning.

Lindiwe Brigitte Malobola, Negar Rostamzadeh, Shakir Mohamed

Fashion is one of the ways in which we show ourselves to the world. It is a reflection of our personal decisions and one of the ways in which people distinguish and represent themselves. In this paper, we focus on the fashion design process and expand computer vision for fashion beyond its current focus on western fashion. We discuss the history of Southern African se-Shweshwe fabric fashion, the collection of a se-Shweshwe dataset, and the application of sketch-to-design image generation for affordable fashion-design. The application to fashion raises both technical questions of training with small amounts of data, and also important questions for computer vision beyond fairness, in particular ethical considerations on creating and employing fashion datasets, and how computer vision supports cultural representation and might avoid algorithmic cultural appropriation.

Suman Ravuri, Karel Lenc, Matthew Willson et al.

Precipitation nowcasting, the high-resolution forecasting of precipitation up to two hours ahead, supports the real-world socio-economic needs of many sectors reliant on weather-dependent decision-making. State-of-the-art operational nowcasting methods typically advect precipitation fields with radar-based wind estimates, and struggle to capture important non-linear events such as convective initiations. Recently introduced deep learning methods use radar to directly predict future rain rates, free of physical constraints. While they accurately predict low-intensity rainfall, their operational utility is limited because their lack of constraints produces blurry nowcasts at longer lead times, yielding poor performance on more rare medium-to-heavy rain events. To address these challenges, we present a Deep Generative Model for the probabilistic nowcasting of precipitation from radar. Our model produces realistic and spatio-temporally consistent predictions over regions up to 1536 km x 1280 km and with lead times from 5-90 min ahead. In a systematic evaluation by more than fifty expert forecasters from the Met Office, our generative model ranked first for its accuracy and usefulness in 88% of cases against two competitive methods, demonstrating its decision-making value and ability to provide physical insight to real-world experts. When verified quantitatively, these nowcasts are skillful without resorting to blurring. We show that generative nowcasting can provide probabilistic predictions that improve forecast value and support operational utility, and at resolutions and lead times where alternative methods struggle.

Nenad Tomasev, Kevin R. McKee, Jackie Kay et al.

Advances in algorithmic fairness have largely omitted sexual orientation and gender identity. We explore queer concerns in privacy, censorship, language, online safety, health, and employment to study the positive and negative effects of artificial intelligence on queer communities. These issues underscore the need for new directions in fairness research that take into account a multiplicity of considerations, from privacy preservation, context sensitivity and process fairness, to an awareness of sociotechnical impact and the increasingly important role of inclusive and participatory research processes. Most current approaches for algorithmic fairness assume that the target characteristics for fairness--frequently, race and legal gender--can be observed or recorded. Sexual orientation and gender identity are prototypical instances of unobserved characteristics, which are frequently missing, unknown or fundamentally unmeasurable. This paper highlights the importance of developing new approaches for algorithmic fairness that break away from the prevailing assumption of observed characteristics.

Mihaela Rosca, Theophane Weber, Arthur Gretton et al.

How sensitive should machine learning models be to input changes? We tackle the question of model smoothness and show that it is a useful inductive bias which aids generalization, adversarial robustness, generative modeling and reinforcement learning. We explore current methods of imposing smoothness constraints and observe they lack the flexibility to adapt to new tasks, they don't account for data modalities, they interact with losses, architectures and optimization in ways not yet fully understood. We conclude that new advances in the field are hinging on finding ways to incorporate data, tasks and learning into our definitions of smoothness.

Shakir Mohamed, Marie-Therese Png, William Isaac

This paper explores the important role of critical science, and in particular of post-colonial and decolonial theories, in understanding and shaping the ongoing advances in artificial intelligence. Artificial Intelligence (AI) is viewed as amongst the technological advances that will reshape modern societies and their relations. Whilst the design and deployment of systems that continually adapt holds the promise of far-reaching positive change, they simultaneously pose significant risks, especially to already vulnerable peoples. Values and power are central to this discussion. Decolonial theories use historical hindsight to explain patterns of power that shape our intellectual, political, economic, and social world. By embedding a decolonial critical approach within its technical practice, AI communities can develop foresight and tactics that can better align research and technology development with established ethical principles, centring vulnerable peoples who continue to bear the brunt of negative impacts of innovation and scientific progress. We highlight problematic applications that are instances of coloniality, and using a decolonial lens, submit three tactics that can form a decolonial field of artificial intelligence: creating a critical technical practice of AI, seeking reverse tutelage and reverse pedagogies, and the renewal of affective and political communities. The years ahead will usher in a wave of new scientific breakthroughs and technologies driven by AI research, making it incumbent upon AI communities to strengthen the social contract through ethical foresight and the multiplicity of intellectual perspectives available to us; ultimately supporting future technologies that enable greater well-being, with the goal of beneficence and justice for all.

Rachel Prudden, Samantha Adams, Dmitry Kangin et al.

A 'nowcast' is a type of weather forecast which makes predictions in the very short term, typically less than two hours - a period in which traditional numerical weather prediction can be limited. This type of weather prediction has important applications for commercial aviation; public and outdoor events; and the construction industry, power utilities, and ground transportation services that conduct much of their work outdoors. Importantly, one of the key needs for nowcasting systems is in the provision of accurate warnings of adverse weather events, such as heavy rain and flooding, for the protection of life and property in such situations. Typical nowcasting approaches are based on simple extrapolation models applied to observations, primarily rainfall radar. In this paper we review existing techniques to radar-based nowcasting from environmental sciences, as well as the statistical approaches that are applicable from the field of machine learning. Nowcasting continues to be an important component of operational systems and we believe new advances are possible with new partnerships between the environmental science and machine learning communities.

Jessica Hamrick, Shakir Mohamed

Machine learning is currently involved in some of the most vigorous debates it has ever seen. Such debates often seem to go around in circles, reaching no conclusion or resolution. This is perhaps unsurprising given that researchers in machine learning come to these discussions with very different frames of reference, making it challenging for them to align perspectives and find common ground. As a remedy for this dilemma, we advocate for the adoption of a common conceptual framework which can be used to understand, analyze, and discuss research. We present one such framework which is popular in cognitive science and neuroscience and which we believe has great utility in machine learning as well: Marr's levels of analysis. Through a series of case studies, we demonstrate how the levels facilitate an understanding and dissection of several methods from machine learning. By adopting the levels of analysis in one's own work, we argue that researchers can be better equipped to engage in the debates necessary to drive forward progress in our field.

George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende et al.

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent work on normalizing flows, ranging from improving their expressive power to expanding their application. We believe the field has now matured and is in need of a unified perspective. In this review, we attempt to provide such a perspective by describing flows through the lens of probabilistic modeling and inference. We place special emphasis on the fundamental principles of flow design, and discuss foundational topics such as expressive power and computational trade-offs. We also broaden the conceptual framing of flows by relating them to more general probability transformations. Lastly, we summarize the use of flows for tasks such as generative modeling, approximate inference, and supervised learning.

Shakir Mohamed, Mihaela Rosca, Michael Figurnov et al.

This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; the problem of sensitivity analysis. In machine learning research, this gradient problem lies at the core of many learning problems, in supervised, unsupervised and reinforcement learning. We will generally seek to rewrite such gradients in a form that allows for Monte Carlo estimation, allowing them to be easily and efficiently used and analysed. We explore three strategies--the pathwise, score function, and measure-valued gradient estimators--exploring their historical development, derivation, and underlying assumptions. We describe their use in other fields, show how they are related and can be combined, and expand on their possible generalisations. Wherever Monte Carlo gradient estimators have been derived and deployed in the past, important advances have followed. A deeper and more widely-held understanding of this problem will lead to further advances, and it is these advances that we wish to support.

Cyprien de Masson d'Autume, Mihaela Rosca, Jack Rae et al.

Generative Adversarial Networks (GANs) enjoy great success at image generation, but have proven difficult to train in the domain of natural language. Challenges with gradient estimation, optimization instability, and mode collapse have lead practitioners to resort to maximum likelihood pre-training, followed by small amounts of adversarial fine-tuning. The benefits of GAN fine-tuning for language generation are unclear, as the resulting models produce comparable or worse samples than traditional language models. We show it is in fact possible to train a language GAN from scratch -- without maximum likelihood pre-training. We combine existing techniques such as large batch sizes, dense rewards and discriminator regularization to stabilize and improve language GANs. The resulting model, ScratchGAN, performs comparably to maximum likelihood training on EMNLP2017 News and WikiText-103 corpora according to quality and diversity metrics.

Suman Ravuri, Shakir Mohamed, Mihaela Rosca et al.

We propose a method of moments (MoM) algorithm for training large-scale implicit generative models. Moment estimation in this setting encounters two problems: it is often difficult to define the millions of moments needed to learn the model parameters, and it is hard to determine which properties are useful when specifying moments. To address the first issue, we introduce a moment network, and define the moments as the network's hidden units and the gradient of the network's output with the respect to its parameters. To tackle the second problem, we use asymptotic theory to highlight desiderata for moments -- namely they should minimize the asymptotic variance of estimated model parameters -- and introduce an objective to learn better moments. The sequence of objectives created by this Method of Learned Moments (MoLM) can train high-quality neural image samplers. On CIFAR-10, we demonstrate that MoLM-trained generators achieve significantly higher Inception Scores and lower Frechet Inception Distances than those trained with gradient penalty-regularized and spectrally-normalized adversarial objectives. These generators also achieve nearly perfect Multi-Scale Structural Similarity Scores on CelebA, and can create high-quality samples of 128x128 images.

Michael Figurnov, Shakir Mohamed, Andriy Mnih

By providing a simple and efficient way of computing low-variance gradients of continuous random variables, the reparameterization trick has become the technique of choice for training a variety of latent variable models. However, it is not applicable to a number of important continuous distributions. We introduce an alternative approach to computing reparameterization gradients based on implicit differentiation and demonstrate its broader applicability by applying it to Gamma, Beta, Dirichlet, and von Mises distributions, which cannot be used with the classic reparameterization trick. Our experiments show that the proposed approach is faster and more accurate than the existing gradient estimators for these distributions.

Greg Wayne, Chia-Chun Hung, David Amos et al.

Animals execute goal-directed behaviours despite the limited range and scope of their sensors. To cope, they explore environments and store memories maintaining estimates of important information that is not presently available. Recently, progress has been made with artificial intelligence (AI) agents that learn to perform tasks from sensory input, even at a human level, by merging reinforcement learning (RL) algorithms with deep neural networks, and the excitement surrounding these results has led to the pursuit of related ideas as explanations of non-human animal learning. However, we demonstrate that contemporary RL algorithms struggle to solve simple tasks when enough information is concealed from the sensors of the agent, a property called "partial observability". An obvious requirement for handling partially observed tasks is access to extensive memory, but we show memory is not enough; it is critical that the right information be stored in the right format. We develop a model, the Memory, RL, and Inference Network (MERLIN), in which memory formation is guided by a process of predictive modeling. MERLIN facilitates the solution of tasks in 3D virtual reality environments for which partial observability is severe and memories must be maintained over long durations. Our model demonstrates a single learning agent architecture that can solve canonical behavioural tasks in psychology and neurobiology without strong simplifying assumptions about the dimensionality of sensory input or the duration of experiences.

Mihaela Rosca, Balaji Lakshminarayanan, Shakir Mohamed

With the increasingly widespread deployment of generative models, there is a mounting need for a deeper understanding of their behaviors and limitations. In this paper, we expose the limitations of Variational Autoencoders (VAEs), which consistently fail to learn marginal distributions in both latent and visible spaces. We show this to be a consequence of learning by matching conditional distributions, and the limitations of explicit model and posterior distributions. It is popular to consider Generative Adversarial Networks (GANs) as a means of overcoming these limitations, leading to hybrids of VAEs and GANs. We perform a large-scale evaluation of several VAE-GAN hybrids and analyze the implications of class probability estimation for learning distributions. While promising, we conclude that at present, VAE-GAN hybrids have limited applicability: they are harder to scale, evaluate, and use for inference compared to VAEs; and they do not improve over the generation quality of GANs.

William Fedus, Mihaela Rosca, Balaji Lakshminarayanan et al.

Generative adversarial networks (GANs) are a family of generative models that do not minimize a single training criterion. Unlike other generative models, the data distribution is learned via a game between a generator (the generative model) and a discriminator (a teacher providing training signal) that each minimize their own cost. GANs are designed to reach a Nash equilibrium at which each player cannot reduce their cost without changing the other players' parameters. One useful approach for the theory of GANs is to show that a divergence between the training distribution and the model distribution obtains its minimum value at equilibrium. Several recent research directions have been motivated by the idea that this divergence is the primary guide for the learning process and that every step of learning should decrease the divergence. We show that this view is overly restrictive. During GAN training, the discriminator provides learning signal in situations where the gradients of the divergences between distributions would not be useful. We provide empirical counterexamples to the view of GAN training as divergence minimization. Specifically, we demonstrate that GANs are able to learn distributions in situations where the divergence minimization point of view predicts they would fail. We also show that gradient penalties motivated from the divergence minimization perspective are equally helpful when applied in other contexts in which the divergence minimization perspective does not predict they would be helpful. This contributes to a growing body of evidence that GAN training may be more usefully viewed as approaching Nash equilibria via trajectories that do not necessarily minimize a specific divergence at each step.

Mihaela Rosca, Balaji Lakshminarayanan, David Warde-Farley et al.

Auto-encoding generative adversarial networks (GANs) combine the standard GAN algorithm, which discriminates between real and model-generated data, with a reconstruction loss given by an auto-encoder. Such models aim to prevent mode collapse in the learned generative model by ensuring that it is grounded in all the available training data. In this paper, we develop a principle upon which auto-encoders can be combined with generative adversarial networks by exploiting the hierarchical structure of the generative model. The underlying principle shows that variational inference can be used a basic tool for learning, but with the in- tractable likelihood replaced by a synthetic likelihood, and the unknown posterior distribution replaced by an implicit distribution; both synthetic likelihoods and implicit posterior distributions can be learned using discriminators. This allows us to develop a natural fusion of variational auto-encoders and generative adversarial networks, combining the best of both these methods. We describe a unified objective for optimization, discuss the constraints needed to guide learning, connect to the wide range of existing work, and use a battery of tests to systematically and quantitatively assess the performance of our method.

Marc G. Bellemare, Ivo Danihelka, Will Dabney et al.

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying geometry between outcomes. The value of being sensitive to this geometry has been demonstrated, among others, in ordinal regression and generative modelling. In this paper we describe three natural properties of probability divergences that reflect requirements from machine learning: sum invariance, scale sensitivity, and unbiased sample gradients. The Wasserstein metric possesses the first two properties but, unlike the Kullback-Leibler divergence, does not possess the third. We provide empirical evidence suggesting that this is a serious issue in practice. Leveraging insights from probabilistic forecasting we propose an alternative to the Wasserstein metric, the Cramér distance. We show that the Cramér distance possesses all three desired properties, combining the best of the Wasserstein and Kullback-Leibler divergences. To illustrate the relevance of the Cramér distance in practice we design a new algorithm, the Cramér Generative Adversarial Network (GAN), and show that it performs significantly better than the related Wasserstein GAN.

Silvia Chiappa, Sébastien Racaniere, Daan Wierstra et al.

Models that can simulate how environments change in response to actions can be used by agents to plan and act efficiently. We improve on previous environment simulators from high-dimensional pixel observations by introducing recurrent neural networks that are able to make temporally and spatially coherent predictions for hundreds of time-steps into the future. We present an in-depth analysis of the factors affecting performance, providing the most extensive attempt to advance the understanding of the properties of these models. We address the issue of computationally inefficiency with a model that does not need to generate a high-dimensional image at each time-step. We show that our approach can be used to improve exploration and is adaptable to many diverse environments, namely 10 Atari games, a 3D car racing environment, and complex 3D mazes.

Mevlana Gemici, Chia-Chun Hung, Adam Santoro et al.

We consider the general problem of modeling temporal data with long-range dependencies, wherein new observations are fully or partially predictable based on temporally-distant, past observations. A sufficiently powerful temporal model should separate predictable elements of the sequence from unpredictable elements, express uncertainty about those unpredictable elements, and rapidly identify novel elements that may help to predict the future. To create such models, we introduce Generative Temporal Models augmented with external memory systems. They are developed within the variational inference framework, which provides both a practical training methodology and methods to gain insight into the models' operation. We show, on a range of problems with sparse, long-term temporal dependencies, that these models store information from early in a sequence, and reuse this stored information efficiently. This allows them to perform substantially better than existing models based on well-known recurrent neural networks, like LSTMs.

Mevlana C. Gemici, Danilo Rezende, Shakir Mohamed

We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as used in protein folding, robot limbs, gene-expression) and in general directional statistics. In spite of the multitude of algorithms available for density estimation in the Euclidean spaces $\mathbf{R}^n$ that scale to large n (e.g. normalizing flows, kernel methods and variational approximations), most of these methods are not immediately suitable for density estimation in more general Riemannian manifolds. We revisit techniques related to homeomorphisms from differential geometry for projecting densities to sub-manifolds and use it to generalize the idea of normalizing flows to more general Riemannian manifolds. The resulting algorithm is scalable, simple to implement and suitable for use with automatic differentiation. We demonstrate concrete examples of this method on the n-sphere $\mathbf{S}^n$.

Shakir Mohamed, Balaji Lakshminarayanan

Generative adversarial networks (GANs) provide an algorithmic framework for constructing generative models with several appealing properties: they do not require a likelihood function to be specified, only a generating procedure; they provide samples that are sharp and compelling; and they allow us to harness our knowledge of building highly accurate neural network classifiers. Here, we develop our understanding of GANs with the aim of forming a rich view of this growing area of machine learning---to build connections to the diverse set of statistical thinking on this topic, of which much can be gained by a mutual exchange of ideas. We frame GANs within the wider landscape of algorithms for learning in implicit generative models--models that only specify a stochastic procedure with which to generate data--and relate these ideas to modelling problems in related fields, such as econometrics and approximate Bayesian computation. We develop likelihood-free inference methods and highlight hypothesis testing as a principle for learning in implicit generative models, using which we are able to derive the objective function used by GANs, and many other related objectives. The testing viewpoint directs our focus to the general problem of density ratio estimation. There are four approaches for density ratio estimation, one of which is a solution using classifiers to distinguish real from generated data. Other approaches such as divergence minimisation and moment matching have also been explored in the GAN literature, and we synthesise these views to form an understanding in terms of the relationships between them and the wider literature, highlighting avenues for future exploration and cross-pollination.

Danilo Jimenez Rezende, S. M. Ali Eslami, Shakir Mohamed et al.

A key goal of computer vision is to recover the underlying 3D structure from 2D observations of the world. In this paper we learn strong deep generative models of 3D structures, and recover these structures from 3D and 2D images via probabilistic inference. We demonstrate high-quality samples and report log-likelihoods on several datasets, including ShapeNet [2], and establish the first benchmarks in the literature. We also show how these models and their inference networks can be trained end-to-end from 2D images. This demonstrates for the first time the feasibility of learning to infer 3D representations of the world in a purely unsupervised manner.

Irina Higgins, Loic Matthey, Xavier Glorot et al.

Automated discovery of early visual concepts from raw image data is a major open challenge in AI research. Addressing this problem, we propose an unsupervised approach for learning disentangled representations of the underlying factors of variation. We draw inspiration from neuroscience, and show how this can be achieved in an unsupervised generative model by applying the same learning pressures as have been suggested to act in the ventral visual stream in the brain. By enforcing redundancy reduction, encouraging statistical independence, and exposure to data with transform continuities analogous to those to which human infants are exposed, we obtain a variational autoencoder (VAE) framework capable of learning disentangled factors. Our approach makes few assumptions and works well across a wide variety of datasets. Furthermore, our solution has useful emergent properties, such as zero-shot inference and an intuitive understanding of "objectness".

Danilo Jimenez Rezende, Shakir Mohamed, Ivo Danihelka et al.

Humans have an impressive ability to reason about new concepts and experiences from just a single example. In particular, humans have an ability for one-shot generalization: an ability to encounter a new concept, understand its structure, and then be able to generate compelling alternative variations of the concept. We develop machine learning systems with this important capacity by developing new deep generative models, models that combine the representational power of deep learning with the inferential power of Bayesian reasoning. We develop a class of sequential generative models that are built on the principles of feedback and attention. These two characteristics lead to generative models that are among the state-of-the art in density estimation and image generation. We demonstrate the one-shot generalization ability of our models using three tasks: unconditional sampling, generating new exemplars of a given concept, and generating new exemplars of a family of concepts. In all cases our models are able to generate compelling and diverse samples---having seen new examples just once---providing an important class of general-purpose models for one-shot machine learning.

Shakir Mohamed, Danilo Jimenez Rezende

The mutual information is a core statistical quantity that has applications in all areas of machine learning, whether this is in training of density models over multiple data modalities, in maximising the efficiency of noisy transmission channels, or when learning behaviour policies for exploration by artificial agents. Most learning algorithms that involve optimisation of the mutual information rely on the Blahut-Arimoto algorithm --- an enumerative algorithm with exponential complexity that is not suitable for modern machine learning applications. This paper provides a new approach for scalable optimisation of the mutual information by merging techniques from variational inference and deep learning. We develop our approach by focusing on the problem of intrinsically-motivated learning, where the mutual information forms the definition of a well-known internal drive known as empowerment. Using a variational lower bound on the mutual information, combined with convolutional networks for handling visual input streams, we develop a stochastic optimisation algorithm that allows for scalable information maximisation and empowerment-based reasoning directly from pixels to actions.

Danilo Jimenez Rezende, Shakir Mohamed

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

Diederik P. Kingma, Danilo J. Rezende, Shakir Mohamed et al.

The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.

Danilo Jimenez Rezende, Shakir Mohamed, Daan Wierstra

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent approximate posterior distributions, and that acts as a stochastic encoder of the data. We develop stochastic back-propagation -- rules for back-propagation through stochastic variables -- and use this to develop an algorithm that allows for joint optimisation of the parameters of both the generative and recognition model. We demonstrate on several real-world data sets that the model generates realistic samples, provides accurate imputations of missing data and is a useful tool for high-dimensional data visualisation.

Marc Peter Deisenroth, Shakir Mohamed

Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data sets requires flexible and accurate models. In this paper, we promote Gaussian process dynamical systems (GPDS) as a rich model class that is appropriate for such analysis. In particular, we present a message passing algorithm for approximate inference in GPDSs based on expectation propagation. By posing inference as a general message passing problem, we iterate forward-backward smoothing. Thus, we obtain more accurate posterior distributions over latent structures, resulting in improved predictive performance compared to state-of-the-art GPDS smoothers, which are special cases of our general message passing algorithm. Hence, we provide a unifying approach within which to contextualize message passing in GPDSs.