24 accepted papers
Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this,…
In reinforcement learning, specifying reward functions that capture the intended task can be very challenging. Reward learning aims to address this issue by *learning* the reward function. However, a learned reward model may have a low error on the data distribution, and yet subsequently produce a p…
We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable $\mathrm{E}(n)$-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically…
We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of ${\operatorname{E}}(p, q)$-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces $\mathbb{R}^{p,q}$. They specialize, for instance, to ${\operatorname{E}}(3)$-equivariance on $\mathbb{R}…
We propose a general framework for constructing powerful, sequential hypothesis tests for a large class of nonparametric testing problems. The null hypothesis for these problems is defined in an abstract form using the action of two known operators on the data distribution. This abstraction allows f…
Early-exit neural networks (EENNs) facilitate adaptive inference by producing predictions at multiple stages of the forward pass. In safety-critical applications, these predictions are only meaningful when complemented with reliable uncertainty estimates. Yet, due to their sequential structure, an…
Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inf…
Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent…
We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the *Clifford group*: a subgroup inside the Clifford algebra tailored to achieve several favorable properties. Primarily, the grou…
Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this structure to develop a computationally efficient approach to state…
Incorporating equivariance to symmetry groups as a constraint during neural network training can improve performance and generalization for tasks exhibiting those symmetries, but such symmetries are often not perfectly nor explicitly present. This motivates algorithmically optimizing the architectur…
Independent component analysis (ICA) is a blind source separation method for linear disentanglement of independent latent sources from observed data. We investigate the special setting of noisy linear ICA, referred to as ShIndICA, where the observations are split among different views, each receivi…
Optimizing multiple competing objectives is a common problem across science and industry. The inherent inextricable trade-off between those objectives leads one to the task of exploring their Pareto front. A meaningful quantity for the purpose of the latter is the hypervolume indicator, which is use…
Likelihood-to-evidence ratio estimation is usually cast as either a binary (NRE-A) or a multiclass (NRE-B) classification task. In contrast to the binary classification framework, the current formulation of the multiclass version has an intrinsic and unknown bias term, making otherwise informative d…
We perform approximate inference in state-space models with nonlinear state transitions. Without parameterizing a generative model, we apply Bayesian update formulas using a local linearity approximation parameterized by neural networks. It comes accompanied by a maximum likelihood objective that re…
Safely deploying machine learning models to the real world is often a challenging process. For example, models trained with data obtained from a specific geographic location tend to fail when queried with data obtained elsewhere, agents trained in a simulation can struggle to adapt when deployed in…
Generative flows and diffusion models have been predominantly trained on ordinal data, for example natural images. This paper introduces two extensions of flows and diffusion for categorical data such as language or image segmentation: Argmax Flows and Multinomial Diffusion. Argmax Flows are defined…
Machine learning models trained with purely observational data and the principle of empirical risk minimization (Vapnik 1992) can fail to generalize to unseen domains. In this paper, we focus on the case where the problem arises through spurious correlation between the observed domains and the actua…
Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function class with easy evaluation of the Jacobian determinant, or an ef…
Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural simulation-based inference algorithm which simultaneously of…
The information bottleneck principle provides an information-theoretic method for representation learning, by training an encoder to retain all information which is relevant for predicting the label while minimizing the amount of other, excess information in the representation. The original formulat…
We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-linear structural causal models that allow for cycles, latent confounders and arbitrary probability distributions. We also gene…
Reparameterizable densities are an important way to learn probability distributions in a deep learning setting. For many distributions it is possible to create low-variance gradient estimators by utilizing a ‘reparameterization trick’. Due to the absence of a general reparameterization trick, much r…
Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the $p$-Wasserstein distance between the generator and the true data distribution is equivalent to the unconstrained min-min optimization of the $p$-Wasserstein distance…