Large-scale physical systems defined on irregular grids pose significant scalability challenges for deep learning methods, especially in the presence of long-range interactions and multi-scale coupling. Traditional approaches that compute all pairwise interactions, such as attention, become computationally prohibitive as they scale quadratically with the number of nodes. We present Erwin, a hierarchical transformer inspired by methods from computational many-body physics, which combines the efficiency of tree-based algorithms with the expressivity of attention mechanisms. Erwin employs ball tree partitioning to organize computation, which enables linear-time attention by processing nodes in parallel within local neighborhoods of fixed size. Through progressive coarsening and refinement of the ball tree structure, complemented by a novel cross-ball interaction mechanism, it captures both fine-grained local details and global features. We demonstrate Erwin's effectiveness across multiple domains, including cosmology, molecular dynamics, and particle fluid dynamics, where it consistently outperforms baseline methods both in accuracy and computational efficiency.

Autoregressive and recurrent networks have achieved remarkable progress across various fields, from weather forecasting to molecular generation and Large Language Models. Despite their strong predictive capabilities, these models lack a rigorous framework for addressing uncertainty, which is key in scientific applications such as PDE solving, molecular generation and Machine Learning Force Fields. To address this shortcoming we present BARNN: a variational Bayesian Autoregressive and Recurrent Neural Network. BARNNs aim to provide a principled way to turn any autoregressive or recurrent model into its Bayesian version. BARNN is based on the variational dropout method, allowing to apply it to large recurrent neural networks as well. We also introduce a temporal version of the "Variational Mixtures of Posteriors" prior (tVAMP-prior) to make Bayesian inference efficient and well-calibrated. Extensive experiments on PDE modelling and molecular generation demonstrate that BARNN not only achieves comparable or superior accuracy compared to existing methods, but also excels in uncertainty quantification and modelling long-range dependencies.

We build a new neural network architecture that has iterative modules that update N-dimensional oscillatory neurons via a generalization of the well-known non-linear dynamical model called the Kuramoto model (Kuramoto, 1984). The Kuramoto model describes the synchronization of oscillators; each Kuramoto update applies forces to connected oscillators, encouraging them to become aligned or anti-aligned. This process is similar to binding in neuroscience and can be understood as distributed and continuous clustering. Thus, networks with this mechanism tend to compress their representations via synchronization. We incorporate the Kuramoto model into an artificial neural network, by applying the differential equation that describes the Kuramoto model to each individual neuron. The resulting artificial Kuramoto oscillatory neurons (AKOrN) can be combined with layer architectures such as fully connected layers, convolutions, and attention mechanisms. We explore the capabilities of AKOrN and find that its neuronal mechanism drastically changes the behavior of the network. AKOrN strongly binds object features with competitive performance to slot-based models in object discovery, enhances the reasoning capability of self-attention, and increases robustness against random, adversarial, and natural perturbations with surprisingly good calibration.

There is a vast literature on representation learning based on principles such as coding efficiency, statistical independence, causality, controllability, or symmetry. In this paper we propose to learn representations from sequence data by factorizing the transformations of the latent variables into sparse components. Input data are first encoded as distributions of latent activations and subsequently transformed using a probability flow model, before being decoded to predict a future input state. The flow model is decomposed into a number of rotational (divergence-free) vector fields and a number of potential flow (curl-free) fields. Our sparsity prior encourages only a small number of these fields to be active at any instant and infers the speed with which the probability flows along these fields. Training this model is completely unsupervised using a standard variational objective and results in a new form of disentangled representations where the input is not only represented by a combination of independent factors, but also by a combination of independent transformation primitives given by the learned flow fields. When viewing the transformations as symmetries one may interpret this as learning approximately equivariant representations. Empirically we demonstrate that this model achieves state of the art in terms of both data likelihood and unsupervised approximate equivariance errors on datasets composed of sequence transformations.

Diffusion generative models transform noise into data by inverting a process that progressively adds noise to data samples. Inspired by concepts from the renormalization group in physics, which analyzes systems across different scales, we revisit diffusion models by exploring three key design aspects: 1) the choice of representation in which the diffusion process operates (e.g. pixel-, PCA-, Fourier-, or wavelet-basis), 2) the prior distribution that data is transformed into during diffusion (e.g. Gaussian with covariance $\Sigma$), and 3) the scheduling of noise levels applied separately to different parts of the data, captured by a component-wise noise schedule. Incorporating the flexibility in these choices, we develop a unified framework for diffusion generative models with greatly enhanced design freedom. In particular, we introduce soft-conditioning models that smoothly interpolate between standard diffusion models and autoregressive models (in any basis), conceptually bridging these two approaches. Our framework opens up a wide design space which may lead to more efficient training and data generation, and paves the way to novel architectures integrating different generative approaches and generation tasks.

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

Deep learning foundation models are revolutionizing many facets of science by leveraging vast amounts of data to learn general-purpose representations that can be adapted to tackle diverse downstream tasks. Foundation models hold the promise to also transform our ability to model our planet and its subsystems by exploiting the vast expanse of Earth system data. Here we introduce Aurora, a large-scale foundation model of the atmosphere trained on over a million hours of diverse weather and climate data. Aurora leverages the strengths of the foundation modelling approach to produce operational forecasts for a wide variety of atmospheric prediction problems, including those with limited training data, heterogeneous variables, and extreme events. In under a minute, Aurora produces 5-day global air pollution predictions and 10-day high-resolution weather forecasts that outperform state-of-the-art classical simulation tools and the best specialized deep learning models. Taken together, these results indicate that foundation models can transform environmental forecasting.

The COVID19 pandemic had enormous economic and societal consequences. Contact tracing is an effective way to reduce infection rates by detecting potential virus carriers early. However, this was not generally adopted in the recent pandemic, and privacy concerns are cited as the most important reason. We substantially improve the privacy guarantees of the current state of the art in decentralized contact tracing. Whereas previous work was based on statistical inference only, we augment the inference with a learned neural network and ensure that this neural augmentation satisfies differential privacy. In a simulator for COVID19 even at ε = 1 per message, this can significantly improve the detection of potentially infected individuals and, as a result of targeted testing, reduce infection rates. The COVID19 pandemic had enormous consequences (Kim et al., 2022; Kaye et al., 2021; Boden et al., 2021; Vindegaard & Benros, 2020). Contact-tracing algorithms could make early predictions of virus carriers, signaling individuals to get tested and thereby reducing the spread of the virus (Baker et al., 2021).

In human cognition, the binding problem describes the open question of how the brain flexibly integrates diverse information into cohesive object representations. Analogously, in machine learning, there is a pursuit for models capable of strong generalization and reasoning by learning object-centric representations in an unsupervised manner. Drawing from neuroscientific theories, Rotating Features learn such representations by introducing vector-valued features that encapsulate object characteristics in their magnitudes and object affiliation in their orientations. The "$\chi$-binding" mechanism, embedded in every layer of the architecture, has been shown to be crucial, but remains poorly understood. In this paper, we propose an alternative "cosine binding" mechanism, which explicitly computes the alignment between features and adjusts weights accordingly, and we show that it achieves equivalent performance. This allows us to draw direct connections to self-attention and biological neural processes, and to shed light on the fundamental dynamics for object-centric representations to emerge in Rotating Features.

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.