Mihaela Rosca

Benoit Dherin, Michael Munn, Mihaela Rosca et al.

In many contexts, simpler models are preferable to more complex models and the control of this model complexity is the goal for many methods in machine learning such as regularization, hyperparameter tuning and architecture design. In deep learning, it has been difficult to understand the underlying mechanisms of complexity control, since many traditional measures are not naturally suitable for deep neural networks. Here we develop the notion of geometric complexity, which is a measure of the variability of the model function, computed using a discrete Dirichlet energy. Using a combination of theoretical arguments and empirical results, we show that many common training heuristics such as parameter norm regularization, spectral norm regularization, flatness regularization, implicit gradient regularization, noise regularization and the choice of parameter initialization all act to control geometric complexity, providing a unifying framework in which to characterize the behavior of deep learning models.

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.

Mihaela Rosca, Marc Peter Deisenroth

Recent years have seen many insights on deep learning optimisation being brought forward by finding implicit regularisation effects of commonly used gradient-based optimisers. Understanding implicit regularisation can not only shed light on optimisation dynamics, but it can also be used to improve performance and stability across problem domains, from supervised learning to two-player games such as Generative Adversarial Networks. An avenue for finding such implicit regularisation effects has been quantifying the discretisation errors of discrete optimisers via continuous-time flows constructed by backward error analysis (BEA). The current usage of BEA is not without limitations, since not all the vector fields of continuous-time flows obtained using BEA can be written as a gradient, hindering the construction of modified losses revealing implicit regularisers. In this work, we provide a novel approach to use BEA, and show how our approach can be used to construct continuous-time flows with vector fields that can be written as gradients. We then use this to find previously unknown implicit regularisation effects, such as those induced by multiple stochastic gradient descent steps while accounting for the exact data batches used in the updates, and in generally differentiable two-player games.

Rares Iordan, Marc Peter Deisenroth, Mihaela Rosca

Recent progress has been made in understanding optimisation dynamics in neural networks trained with full-batch gradient descent with momentum with the uncovering of the edge of stability phenomenon in supervised learning. The edge of stability phenomenon occurs as the leading eigenvalue of the Hessian reaches the divergence threshold of the underlying optimisation algorithm for a quadratic loss, after which it starts oscillating around the threshold, and the loss starts to exhibit local instability but decreases over long time frames. In this work, we explore the edge of stability phenomenon in reinforcement learning (RL), specifically off-policy Q-learning algorithms across a variety of data regimes, from offline to online RL. Our experiments reveal that, despite significant differences to supervised learning, such as non-stationarity of the data distribution and the use of bootstrapping, the edge of stability phenomenon can be present in off-policy deep RL. Unlike supervised learning, however, we observe strong differences depending on the underlying loss, with DQN -- using a Huber loss -- showing a strong edge of stability effect that we do not observe with C51 -- using a cross entropy loss. Our results suggest that, while neural network structure can lead to optimisation dynamics that transfer between problem domains, certain aspects of deep RL optimisation can differentiate it from domains such as supervised learning.

Mihaela Rosca, Yan Wu, Chongli Qin et al.

The recipe behind the success of deep learning has been the combination of neural networks and gradient-based optimization. Understanding the behavior of gradient descent however, and particularly its instability, has lagged behind its empirical success. To add to the theoretical tools available to study gradient descent we propose the principal flow (PF), a continuous time flow that approximates gradient descent dynamics. To our knowledge, the PF is the only continuous flow that captures the divergent and oscillatory behaviors of gradient descent, including escaping local minima and saddle points. Through its dependence on the eigendecomposition of the Hessian the PF sheds light on the recently observed edge of stability phenomena in deep learning. Using our new understanding of instability we propose a learning rate adaptation method which enables us to control the trade-off between training stability and test set evaluation performance.

Gemini Team, Petko Georgiev, Ving Ian Lei et al. · deepmind, mila

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

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.

Mihaela Rosca, Thomas Breuel

Transliteration is a key component of machine translation systems and software internationalization. This paper demonstrates that neural sequence-to-sequence models obtain state of the art or close to state of the art results on existing datasets. In an effort to make machine transliteration accessible, we open source a new Arabic to English transliteration dataset and our trained models.

Benoit Dherin, Mihaela Rosca

We characterize regions of a loss surface as corridors when the continuous curves of steepest descent -- the solutions of the gradient flow -- become straight lines. We show that corridors provide insights into gradient-based optimization, since corridors are exactly the regions where gradient descent and the gradient flow follow the same trajectory, while the loss decreases linearly. As a result, inside corridors there are no implicit regularization effects or training instabilities that have been shown to occur due to the drift between gradient descent and the gradient flow. Using the loss linear decrease on corridors, we devise a learning rate adaptation scheme for gradient descent; we call this scheme Corridor Learning Rate (CLR). The CLR formulation coincides with a special case of Polyak step-size, discovered in the context of convex optimization. The Polyak step-size has been shown recently to have also good convergence properties for neural networks; we further confirm this here with results on CIFAR-10 and ImageNet.

Mihaela Rosca, Yan Wu, Benoit Dherin et al.

Gradient-based methods for two-player games produce rich dynamics that can solve challenging problems, yet can be difficult to stabilize and understand. Part of this complexity originates from the discrete update steps given by simultaneous or alternating gradient descent, which causes each player to drift away from the continuous gradient flow -- a phenomenon we call discretization drift. Using backward error analysis, we derive modified continuous dynamical systems that closely follow the discrete dynamics. These modified dynamics provide an insight into the notorious challenges associated with zero-sum games, including Generative Adversarial Networks. In particular, we identify distinct components of the discretization drift that can alter performance and in some cases destabilize the game. Finally, quantifying discretization drift allows us to identify regularizers that explicitly cancel harmful forms of drift or strengthen beneficial forms of drift, and thus improve performance of GAN training.

Florin Gogianu, Tudor Berariu, Mihaela Rosca et al.

Most of the recent deep reinforcement learning advances take an RL-centric perspective and focus on refinements of the training objective. We diverge from this view and show we can recover the performance of these developments not by changing the objective, but by regularising the value-function estimator. Constraining the Lipschitz constant of a single layer using spectral normalisation is sufficient to elevate the performance of a Categorical-DQN agent to that of a more elaborated \rainbow{} agent on the challenging Atari domain. We conduct ablation studies to disentangle the various effects normalisation has on the learning dynamics and show that is sufficient to modulate the parameter updates to recover most of the performance of spectral normalisation. These findings hint towards the need to also focus on the neural component and its learning dynamics to tackle the peculiarities of Deep Reinforcement Learning.

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, 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.

Yan Wu, Mihaela Rosca, Timothy Lillicrap

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is flexible and data efficient, but its application has been restricted by the strong assumption of sparsity and costly reconstruction process. A recent approach that combines CS with neural network generators has removed the constraint of sparsity, but reconstruction remains slow. Here we propose a novel framework that significantly improves both the performance and speed of signal recovery by jointly training a generator and the optimisation process for reconstruction via meta-learning. We explore training the measurements with different objectives, and derive a family of models based on minimising measurement errors. We show that Generative Adversarial Nets (GANs) can be viewed as a special case in this family of models. Borrowing insights from the CS perspective, we develop a novel way of improving GANs using gradient information from the discriminator.

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.

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.