Samuel Smith

Antonio Orvieto, Samuel L Smith, Albert Gu et al. · deepmind

Recurrent Neural Networks (RNNs) offer fast inference on long sequences but are hard to optimize and slow to train. Deep state-space models (SSMs) have recently been shown to perform remarkably well on long sequence modeling tasks, and have the added benefits of fast parallelizable training and RNN-like fast inference. However, while SSMs are superficially similar to RNNs, there are important differences that make it unclear where their performance boost over RNNs comes from. In this paper, we show that careful design of deep RNNs using standard signal propagation arguments can recover the impressive performance of deep SSMs on long-range reasoning tasks, while also matching their training speed. To achieve this, we analyze and ablate a series of changes to standard RNNs including linearizing and diagonalizing the recurrence, using better parameterizations and initializations, and ensuring proper normalization of the forward pass. Our results provide new insights on the origins of the impressive performance of deep SSMs, while also introducing an RNN block called the Linear Recurrent Unit that matches both their performance on the Long Range Arena benchmark and their computational efficiency.

Leonard Berrada, Soham De, Judy Hanwen Shen et al. · deepmind, stanford

Privacy-preserving machine learning aims to train models on private data without leaking sensitive information. Differential privacy (DP) is considered the gold standard framework for privacy-preserving training, as it provides formal privacy guarantees. However, compared to their non-private counterparts, models trained with DP often have significantly reduced accuracy. Private classifiers are also believed to exhibit larger performance disparities across subpopulations, raising fairness concerns. The poor performance of classifiers trained with DP has prevented the widespread adoption of privacy preserving machine learning in industry. Here we show that pre-trained foundation models fine-tuned with DP can achieve similar accuracy to non-private classifiers, even in the presence of significant distribution shifts between pre-training data and downstream tasks. We achieve private accuracies within a few percent of the non-private state of the art across four datasets, including two medical imaging benchmarks. Furthermore, our private medical classifiers do not exhibit larger performance disparities across demographic groups than non-private models. This milestone to make DP training a practical and reliable technology has the potential to widely enable machine learning practitioners to train safely on sensitive datasets while protecting individuals' privacy.

Soham De, Leonard Berrada, Jamie Hayes et al. · deepmind

Differential Privacy (DP) provides a formal privacy guarantee preventing adversaries with access to a machine learning model from extracting information about individual training points. Differentially Private Stochastic Gradient Descent (DP-SGD), the most popular DP training method for deep learning, realizes this protection by injecting noise during training. However previous works have found that DP-SGD often leads to a significant degradation in performance on standard image classification benchmarks. Furthermore, some authors have postulated that DP-SGD inherently performs poorly on large models, since the norm of the noise required to preserve privacy is proportional to the model dimension. In contrast, we demonstrate that DP-SGD on over-parameterized models can perform significantly better than previously thought. Combining careful hyper-parameter tuning with simple techniques to ensure signal propagation and improve the convergence rate, we obtain a new SOTA without extra data on CIFAR-10 of 81.4% under (8, 10^{-5})-DP using a 40-layer Wide-ResNet, improving over the previous SOTA of 71.7%. When fine-tuning a pre-trained NFNet-F3, we achieve a remarkable 83.8% top-1 accuracy on ImageNet under (0.5, 8*10^{-7})-DP. Additionally, we also achieve 86.7% top-1 accuracy under (8, 8 \cdot 10^{-7})-DP, which is just 4.3% below the current non-private SOTA for this task. We believe our results are a significant step towards closing the accuracy gap between private and non-private image classification.

Antonio Orvieto, Soham De, Caglar Gulcehre et al. · deepmind

Deep neural networks based on linear RNNs interleaved with position-wise MLPs are gaining traction as competitive approaches for sequence modeling. Examples of such architectures include state-space models (SSMs) like S4, LRU, and Mamba: recently proposed models that achieve promising performance on text, genetics, and other data that require long-range reasoning. Despite experimental evidence highlighting these architectures' effectiveness and computational efficiency, their expressive power remains relatively unexplored, especially in connection to specific choices crucial in practice - e.g., carefully designed initialization distribution and potential use of complex numbers. In this paper, we show that combining MLPs with both real or complex linear diagonal recurrences leads to arbitrarily precise approximation of regular causal sequence-to-sequence maps. At the heart of our proof, we rely on a separation of concerns: the linear RNN provides a lossless encoding of the input sequence, and the MLP performs non-linear processing on this encoding. While we show that real diagonal linear recurrences are enough to achieve universality in this architecture, we prove that employing complex eigenvalues near unit disk - i.e., empirically the most successful strategy in S4 - greatly helps the RNN in storing information. We connect this finding with the vanishing gradient issue and provide experiments supporting our claims.

Sahra Ghalebikesabi, Leonard Berrada, Sven Gowal et al. · deepmind

The ability to generate privacy-preserving synthetic versions of sensitive image datasets could unlock numerous ML applications currently constrained by data availability. Due to their astonishing image generation quality, diffusion models are a prime candidate for generating high-quality synthetic data. However, recent studies have found that, by default, the outputs of some diffusion models do not preserve training data privacy. By privately fine-tuning ImageNet pre-trained diffusion models with more than 80M parameters, we obtain SOTA results on CIFAR-10 and Camelyon17 in terms of both FID and the accuracy of downstream classifiers trained on synthetic data. We decrease the SOTA FID on CIFAR-10 from 26.2 to 9.8, and increase the accuracy from 51.0% to 88.0%. On synthetic data from Camelyon17, we achieve a downstream accuracy of 91.1% which is close to the SOTA of 96.5% when training on the real data. We leverage the ability of generative models to create infinite amounts of data to maximise the downstream prediction performance, and further show how to use synthetic data for hyperparameter tuning. Our results demonstrate that diffusion models fine-tuned with differential privacy can produce useful and provably private synthetic data, even in applications with significant distribution shift between the pre-training and fine-tuning distributions.

Bobby He, James Martens, Guodong Zhang et al. · utoronto

Skip connections and normalisation layers form two standard architectural components that are ubiquitous for the training of Deep Neural Networks (DNNs), but whose precise roles are poorly understood. Recent approaches such as Deep Kernel Shaping have made progress towards reducing our reliance on them, using insights from wide NN kernel theory to improve signal propagation in vanilla DNNs (which we define as networks without skips or normalisation). However, these approaches are incompatible with the self-attention layers present in transformers, whose kernels are intrinsically more complicated to analyse and control. And so the question remains: is it possible to train deep vanilla transformers? We answer this question in the affirmative by designing several approaches that use combinations of parameter initialisations, bias matrices and location-dependent rescaling to achieve faithful signal propagation in vanilla transformers. Our methods address various intricacies specific to signal propagation in transformers, including the interaction with positional encoding and causal masking. In experiments on WikiText-103 and C4, our approaches enable deep transformers without normalisation to train at speeds matching their standard counterparts, and deep vanilla transformers to reach the same performance as standard ones after about 5 times more iterations.

Samuel L. Smith, Andrew Brock, Leonard Berrada et al. · deepmind

Many researchers believe that ConvNets perform well on small or moderately sized datasets, but are not competitive with Vision Transformers when given access to datasets on the web-scale. We challenge this belief by evaluating a performant ConvNet architecture pre-trained on JFT-4B, a large labelled dataset of images often used for training foundation models. We consider pre-training compute budgets between 0.4k and 110k TPU-v4 core compute hours, and train a series of networks of increasing depth and width from the NFNet model family. We observe a log-log scaling law between held out loss and compute budget. After fine-tuning on ImageNet, NFNets match the reported performance of Vision Transformers with comparable compute budgets. Our strongest fine-tuned model achieves a Top-1 accuracy of 90.4%.

Gemma Team, Thomas Mesnard, Cassidy Hardin et al. · deepmind

This work introduces Gemma, a family of lightweight, state-of-the art open models built from the research and technology used to create Gemini models. Gemma models demonstrate strong performance across academic benchmarks for language understanding, reasoning, and safety. We release two sizes of models (2 billion and 7 billion parameters), and provide both pretrained and fine-tuned checkpoints. Gemma outperforms similarly sized open models on 11 out of 18 text-based tasks, and we present comprehensive evaluations of safety and responsibility aspects of the models, alongside a detailed description of model development. We believe the responsible release of LLMs is critical for improving the safety of frontier models, and for enabling the next wave of LLM innovations.

Andrew Brock, Soham De, Samuel L. Smith et al.

Batch normalization is a key component of most image classification models, but it has many undesirable properties stemming from its dependence on the batch size and interactions between examples. Although recent work has succeeded in training deep ResNets without normalization layers, these models do not match the test accuracies of the best batch-normalized networks, and are often unstable for large learning rates or strong data augmentations. In this work, we develop an adaptive gradient clipping technique which overcomes these instabilities, and design a significantly improved class of Normalizer-Free ResNets. Our smaller models match the test accuracy of an EfficientNet-B7 on ImageNet while being up to 8.7x faster to train, and our largest models attain a new state-of-the-art top-1 accuracy of 86.5%. In addition, Normalizer-Free models attain significantly better performance than their batch-normalized counterparts when finetuning on ImageNet after large-scale pre-training on a dataset of 300 million labeled images, with our best models obtaining an accuracy of 89.2%. Our code is available at https://github.com/deepmind/ deepmind-research/tree/master/nfnets

Zheng Chen, Zongwei Wu, Eduard Zamfir et al.

This paper reviews the NTIRE 2024 challenge on image super-resolution ($\times$4), highlighting the solutions proposed and the outcomes obtained. The challenge involves generating corresponding high-resolution (HR) images, magnified by a factor of four, from low-resolution (LR) inputs using prior information. The LR images originate from bicubic downsampling degradation. The aim of the challenge is to obtain designs/solutions with the most advanced SR performance, with no constraints on computational resources (e.g., model size and FLOPs) or training data. The track of this challenge assesses performance with the PSNR metric on the DIV2K testing dataset. The competition attracted 199 registrants, with 20 teams submitting valid entries. This collective endeavour not only pushes the boundaries of performance in single-image SR but also offers a comprehensive overview of current trends in this field.

Aleksandar Botev, Soham De, Samuel L Smith et al. · deepmind

We introduce RecurrentGemma, a family of open language models which uses Google's novel Griffin architecture. Griffin combines linear recurrences with local attention to achieve excellent performance on language. It has a fixed-sized state, which reduces memory use and enables efficient inference on long sequences. We provide two sizes of models, containing 2B and 9B parameters, and provide pre-trained and instruction tuned variants for both. Our models achieve comparable performance to similarly-sized Gemma baselines despite being trained on fewer tokens.

Tudor Berariu, Wojciech Czarnecki, Soham De et al.

One aim shared by multiple settings, such as continual learning or transfer learning, is to leverage previously acquired knowledge to converge faster on the current task. Usually this is done through fine-tuning, where an implicit assumption is that the network maintains its plasticity, meaning that the performance it can reach on any given task is not affected negatively by previously seen tasks. It has been observed recently that a pretrained model on data from the same distribution as the one it is fine-tuned on might not reach the same generalisation as a freshly initialised one. We build and extend this observation, providing a hypothesis for the mechanics behind it. We discuss the implication of losing plasticity for continual learning which heavily relies on optimising pretrained models.

Stanislav Fort, Andrew Brock, Razvan Pascanu et al.

In computer vision, it is standard practice to draw a single sample from the data augmentation procedure for each unique image in the mini-batch. However recent work has suggested drawing multiple samples can achieve higher test accuracies. In this work, we provide a detailed empirical evaluation of how the number of augmentation samples per unique image influences model performance on held out data when training deep ResNets. We demonstrate drawing multiple samples per image consistently enhances the test accuracy achieved for both small and large batch training. Crucially, this benefit arises even if different numbers of augmentations per image perform the same number of parameter updates and gradient evaluations (requiring the same total compute). Although prior work has found variance in the gradient estimate arising from subsampling the dataset has an implicit regularization benefit, our experiments suggest variance which arises from the data augmentation process harms generalization. We apply these insights to the highly performant NFNet-F5, achieving 86.8$\%$ top-1 w/o extra data on ImageNet.

Samuel L. Smith, Benoit Dherin, David G. T. Barrett et al.

For infinitesimal learning rates, stochastic gradient descent (SGD) follows the path of gradient flow on the full batch loss function. However moderately large learning rates can achieve higher test accuracies, and this generalization benefit is not explained by convergence bounds, since the learning rate which maximizes test accuracy is often larger than the learning rate which minimizes training loss. To interpret this phenomenon we prove that for SGD with random shuffling, the mean SGD iterate also stays close to the path of gradient flow if the learning rate is small and finite, but on a modified loss. This modified loss is composed of the original loss function and an implicit regularizer, which penalizes the norms of the minibatch gradients. Under mild assumptions, when the batch size is small the scale of the implicit regularization term is proportional to the ratio of the learning rate to the batch size. We verify empirically that explicitly including the implicit regularizer in the loss can enhance the test accuracy when the learning rate is small.

Andrew Brock, Soham De, Samuel L. Smith

Batch Normalization is a key component in almost all state-of-the-art image classifiers, but it also introduces practical challenges: it breaks the independence between training examples within a batch, can incur compute and memory overhead, and often results in unexpected bugs. Building on recent theoretical analyses of deep ResNets at initialization, we propose a simple set of analysis tools to characterize signal propagation on the forward pass, and leverage these tools to design highly performant ResNets without activation normalization layers. Crucial to our success is an adapted version of the recently proposed Weight Standardization. Our analysis tools show how this technique preserves the signal in networks with ReLU or Swish activation functions by ensuring that the per-channel activation means do not grow with depth. Across a range of FLOP budgets, our networks attain performance competitive with the state-of-the-art EfficientNets on ImageNet.

Pierre H. Richemond, Jean-Bastien Grill, Florent Altché et al.

Bootstrap Your Own Latent (BYOL) is a self-supervised learning approach for image representation. From an augmented view of an image, BYOL trains an online network to predict a target network representation of a different augmented view of the same image. Unlike contrastive methods, BYOL does not explicitly use a repulsion term built from negative pairs in its training objective. Yet, it avoids collapse to a trivial, constant representation. Thus, it has recently been hypothesized that batch normalization (BN) is critical to prevent collapse in BYOL. Indeed, BN flows gradients across batch elements, and could leak information about negative views in the batch, which could act as an implicit negative (contrastive) term. However, we experimentally show that replacing BN with a batch-independent normalization scheme (namely, a combination of group normalization and weight standardization) achieves performance comparable to vanilla BYOL ($73.9\%$ vs. $74.3\%$ top-1 accuracy under the linear evaluation protocol on ImageNet with ResNet-$50$). Our finding disproves the hypothesis that the use of batch statistics is a crucial ingredient for BYOL to learn useful representations.

Samuel L. Smith, Erich Elsen, Soham De

It has long been argued that minibatch stochastic gradient descent can generalize better than large batch gradient descent in deep neural networks. However recent papers have questioned this claim, arguing that this effect is simply a consequence of suboptimal hyperparameter tuning or insufficient compute budgets when the batch size is large. In this paper, we perform carefully designed experiments and rigorous hyperparameter sweeps on a range of popular models, which verify that small or moderately large batch sizes can substantially outperform very large batches on the test set. This occurs even when both models are trained for the same number of iterations and large batches achieve smaller training losses. Our results confirm that the noise in stochastic gradients can enhance generalization. We study how the optimal learning rate schedule changes as the epoch budget grows, and we provide a theoretical account of our observations based on the stochastic differential equation perspective of SGD dynamics.

Soham De, Samuel L. Smith

Batch normalization dramatically increases the largest trainable depth of residual networks, and this benefit has been crucial to the empirical success of deep residual networks on a wide range of benchmarks. We show that this key benefit arises because, at initialization, batch normalization downscales the residual branch relative to the skip connection, by a normalizing factor on the order of the square root of the network depth. This ensures that, early in training, the function computed by normalized residual blocks in deep networks is close to the identity function (on average). We use this insight to develop a simple initialization scheme that can train deep residual networks without normalization. We also provide a detailed empirical study of residual networks, which clarifies that, although batch normalized networks can be trained with larger learning rates, this effect is only beneficial in specific compute regimes, and has minimal benefits when the batch size is small.

Daniel S. Park, Jascha Sohl-Dickstein, Quoc V. Le et al.

We investigate how the final parameters found by stochastic gradient descent are influenced by over-parameterization. We generate families of models by increasing the number of channels in a base network, and then perform a large hyper-parameter search to study how the test error depends on learning rate, batch size, and network width. We find that the optimal SGD hyper-parameters are determined by a "normalized noise scale," which is a function of the batch size, learning rate, and initialization conditions. In the absence of batch normalization, the optimal normalized noise scale is directly proportional to width. Wider networks, with their higher optimal noise scale, also achieve higher test accuracy. These observations hold for MLPs, ConvNets, and ResNets, and for two different parameterization schemes ("Standard" and "NTK"). We observe a similar trend with batch normalization for ResNets. Surprisingly, since the largest stable learning rate is bounded, the largest batch size consistent with the optimal normalized noise scale decreases as the width increases.

Samuel L. Smith, Daniel Duckworth, Semon Rezchikov et al.

Recent work has argued that stochastic gradient descent can approximate the Bayesian uncertainty in model parameters near local minima. In this work we develop a similar correspondence for minibatch natural gradient descent (NGD). We prove that for sufficiently small learning rates, if the model predictions on the training set approach the true conditional distribution of labels given inputs, the stationary distribution of minibatch NGD approaches a Bayesian posterior near local minima. The temperature $T = εN / (2B)$ is controlled by the learning rate $ε$, training set size $N$ and batch size $B$. However minibatch NGD is not parameterisation invariant and it does not sample a valid posterior away from local minima. We therefore propose a novel optimiser, "stochastic NGD", which introduces the additional correction terms required to preserve both properties.

Vitalii Zhelezniak, Dan Busbridge, April Shen et al.

Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal representation space, in which semantically close symbols are mapped to representations that are close under a similarity measure induced by the model's objective function. In addition, we present a straightforward procedure that, without any retraining or architectural modifications, allows deep recurrent models to perform equally well (and sometimes better) when compared to shallow models. To validate our analysis, we conduct a set of consistent empirical evaluations and introduce several new sentence embedding models in the process. Even though this work is presented within the context of natural language processing, the insights are readily applicable to other domains that rely on distributed representations for transfer tasks.

Samuel L. Smith, Pieter-Jan Kindermans, Chris Ying et al.

It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate $ε$ and scaling the batch size $B \propto ε$. Finally, one can increase the momentum coefficient $m$ and scale $B \propto 1/(1-m)$, although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train ResNet-50 on ImageNet to $76.1\%$ validation accuracy in under 30 minutes.

Samuel L. Smith, Quoc V. Le

We consider two questions at the heart of machine learning; how can we predict if a minimum will generalize to the test set, and why does stochastic gradient descent find minima that generalize well? Our work responds to Zhang et al. (2016), who showed deep neural networks can easily memorize randomly labeled training data, despite generalizing well on real labels of the same inputs. We show that the same phenomenon occurs in small linear models. These observations are explained by the Bayesian evidence, which penalizes sharp minima but is invariant to model parameterization. We also demonstrate that, when one holds the learning rate fixed, there is an optimum batch size which maximizes the test set accuracy. We propose that the noise introduced by small mini-batches drives the parameters towards minima whose evidence is large. Interpreting stochastic gradient descent as a stochastic differential equation, we identify the "noise scale" $g = ε(\frac{N}{B} - 1) \approx εN/B$, where $ε$ is the learning rate, $N$ the training set size and $B$ the batch size. Consequently the optimum batch size is proportional to both the learning rate and the size of the training set, $B_{opt} \propto εN$. We verify these predictions empirically.

Samuel L. Smith, David H. P. Turban, Steven Hamblin et al.

Usually bilingual word vectors are trained "online". Mikolov et al. showed they can also be found "offline", whereby two pre-trained embeddings are aligned with a linear transformation, using dictionaries compiled from expert knowledge. In this work, we prove that the linear transformation between two spaces should be orthogonal. This transformation can be obtained using the singular value decomposition. We introduce a novel "inverted softmax" for identifying translation pairs, with which we improve the precision @1 of Mikolov's original mapping from 34% to 43%, when translating a test set composed of both common and rare English words into Italian. Orthogonal transformations are more robust to noise, enabling us to learn the transformation without expert bilingual signal by constructing a "pseudo-dictionary" from the identical character strings which appear in both languages, achieving 40% precision on the same test set. Finally, we extend our method to retrieve the true translations of English sentences from a corpus of 200k Italian sentences with a precision @1 of 68%.

Samuel L Smith

Algorithms which sort lists of real numbers into ascending order have been studied for decades. They are typically based on a series of pairwise comparisons and run entirely on chip. However people routinely sort lists which depend on subjective or complex judgements that cannot be automated. Examples include marketing research; where surveys are used to learn about customer preferences for products, the recruiting process; where interviewers attempt to rank potential employees, and sporting tournaments; where we infer team rankings from a series of one on one matches. We develop a novel sorting algorithm, where each pairwise comparison reflects a subjective human judgement about which element is bigger or better. We introduce a finite and large error rate to each judgement, and we take the cost of each comparison to significantly exceed the cost of other computational steps. The algorithm must request the most informative sequence of comparisons from the user; in order to identify the correct sorted list with minimum human input. Our Discrete Adiabatic Monte Carlo approach exploits the gradual acquisition of information by tracking a set of plausible hypotheses which are updated after each additional comparison.