This paper presents a family of neural network compression methods of simulated atmospheric states, with the aim of reducing the currently immense storage requirements of such data from cloud scale (petabytes) to desktop scale (terabytes). This need for compression has come about over past 50 years, characterized by a steady push to increase the resolution of atmospheric simulations, increasing the size and storage demands of the resulting datasets (e.g., Neumann et al. (2019), Schneider et al. (2023), Stevens et al. (2024)), while atmospheric simulation has come to play an increasingly critical role in scientific, industrial and policy-level pursuits. Higher spatial resolutions unlock the ability of simulators to deliver more accurate predictions and resolve ever more atmospheric phenomena. For example, while current models often operate at 25 - 50 km resolution, resolving storms requires 1 km resolution (Stevens et al., 2020), while resolving the motion of (and radiative effects due to) low clouds require 100 m resolution (Satoh et al., 2019; Schneider et al., 2017). Machine learning models for weather prediction also face opportunities and challenges with higher resolution: while additional granularity may afford better modeling opportunities, even the present size of atmospheric states poses a significant bottleneck for loading training data and serving model outputs (Chantry et al., 2021). To put the data storage problem in perspective, storing 40 years of reanalysis data from the ECMWF Reanalysis v5 dataset (ERA5, Hersbach et al. (2020)) at full spatial and temporal resolution (i.e.

Most neural compression models are trained on large datasets of images or videos in order to generalize to unseen data. Such generalization typically requires large and expressive architectures with a high decoding complexity. Here we introduce C3, a neural compression method with strong rate-distortion (RD) performance that instead overfits a small model to each image or video separately. The resulting decoding complexity of C3 can be an order of magnitude lower than neural baselines with similar RD performance. C3 builds on COOL-CHIC (Ladune et al.) and makes several simple and effective improvements for images. We further develop new methodology to apply C3 to videos. On the CLIC2020 image benchmark, we match the RD performance of VTM, the reference implementation of the H.266 codec, with less than 3k MACs/pixel for decoding. On the UVG video benchmark, we match the RD performance of the Video Compression Transformer (Mentzer et al.), a well-established neural video codec, with less than 5k MACs/pixel for decoding.

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erd\H{o}s, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

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

Re-initializing a neural network during training has been observed to improve generalization in recent works. Yet it is neither widely adopted in deep learning practice nor is it often used in state-of-the-art training protocols. This raises the question of when re-initialization works, and whether it should be used together with regularization techniques such as data augmentation, weight decay and learning rate schedules. In this work, we conduct an extensive empirical comparison of standard training with a selection of re-initialization methods to answer this question, training over 15,000 models on a variety of image classification benchmarks. We first establish that such methods are consistently beneficial for generalization in the absence of any other regularization. However, when deployed alongside other carefully tuned regularization techniques, re-initialization methods offer little to no added benefit for generalization, although optimal generalization performance becomes less sensitive to the choice of learning rate and weight decay hyperparameters. To investigate the impact of re-initialization methods on noisy data, we also consider learning under label noise. Surprisingly, in this case, re-initialization significantly improves upon standard training, even in the presence of other carefully tuned regularization techniques.

Neural fields, also known as implicit neural representations, have emerged as a powerful means to represent complex signals of various modalities. Based on this Dupont et al. (2022) introduce a framework that views neural fields as data, termed *functa*, and proposes to do deep learning directly on this dataset of neural fields. In this work, we show that the proposed framework faces limitations when scaling up to even moderately complex datasets such as CIFAR-10. We then propose *spatial functa*, which overcome these limitations by using spatially arranged latent representations of neural fields, thereby allowing us to scale up the approach to ImageNet-1k at 256x256 resolution. We demonstrate competitive performance to Vision Transformers (Steiner et al., 2022) on classification and Latent Diffusion (Rombach et al., 2022) on image generation respectively.

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

Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly focused on group equivariant convolutions, building on the result that group equivariant linear maps are necessarily convolutions. In this work, we extend the scope of the literature to non-linear neural network modules, namely self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups. We demonstrate the generality of our approach by showing experimental results that are competitive to baseline methods on a wide range of tasks: shape counting on point clouds, molecular property regression and modelling particle trajectories under Hamiltonian dynamics.

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

Meta-learning methods leverage past experience to learn data-driven inductive biases from related problems, increasing learning efficiency on new tasks. This ability renders them particularly suitable for sequential decision making with limited experience. Within this problem family, we argue for the use of such approaches in the study of model-based approaches to Bayesian Optimisation, contextual bandits and Reinforcement Learning. We approach the problem by learning distributions over functions using Neural Processes (NPs), a recently introduced probabilistic meta-learning method. This allows the treatment of model uncertainty to tackle the exploration/exploitation dilemma. We show that NPs are suitable for sequential decision making on a diverse set of domains, including adversarial task search, recommender systems and model-based reinforcement learning.