Author name cluster

David Ruhe

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6 papers

2 author rows

ICLR Conference 2024 Conference Paper

Clifford Group Equivariant Simplicial Message Passing Networks

Cong Liu
David Ruhe
Floor Eijkelboom
Patrick Forré

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 more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term *shared* simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.

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ICML Conference 2024 Conference Paper

Clifford-Steerable Convolutional Neural Networks

Maksim Zhdanov 0001
David Ruhe
Maurice Weiler
Ana Lucic
Johannes Brandstetter
Patrick Forré

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 $\mathbb{R}^3$ and Poincaré-equivariance on Minkowski spacetime $\mathbb{R}^{1, 3}$. Our approach is based on an implicit parametrization of ${\operatorname{O}}(p, q)$-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.

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ICML Conference 2024 Conference Paper

Rolling Diffusion Models

David Ruhe
Jonathan Heek
Tim Salimans
Emiel Hoogeboom

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

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NeurIPS Conference 2023 Conference Paper

Clifford Group Equivariant Neural Networks

David Ruhe
Johannes Brandstetter
Patrick Forré

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 group's action forms an orthogonal automorphism that extends beyond the typical vector space to the entire Clifford algebra while respecting the multivector grading. This leads to several non-equivalent subrepresentations corresponding to the multivector decomposition. Furthermore, we prove that the action respects not just the vector space structure of the Clifford algebra but also its multiplicative structure, i. e. , the geometric product. These findings imply that every polynomial in multivectors, including their grade projections, constitutes an equivariant map with respect to the Clifford group, allowing us to parameterize equivariant neural network layers. An advantage worth mentioning is that we obtain expressive layers that can elegantly generalize to inner-product spaces of any dimension. We demonstrate, notably from a single core implementation, state-of-the-art performance on several distinct tasks, including a three-dimensional $n$-body experiment, a four-dimensional Lorentz-equivariant high-energy physics experiment, and a five-dimensional convex hull experiment.

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ICML Conference 2023 Conference Paper

Geometric Clifford Algebra Networks

David Ruhe
Jayesh K. Gupta
Steven De Keninck
Max Welling
Johannes Brandstetter

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the $\mathrm{Pin}(p, q, r)$ group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

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ICLR Conference 2022 Conference Paper

Self-Supervised Inference in State-Space Models

David Ruhe
Patrick Forré

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 requires no supervision via uncorrupt observations or ground truth latent states. The optimization backpropagates through a recursion similar to the classical Kalman filter and smoother. Additionally, using an approximate conditional independence, we can perform smoothing without having to parameterize a separate model. In scientific applications, domain knowledge can give a linear approximation of the latent transition maps, which we can easily incorporate into our model. Usage of such domain knowledge is reflected in excellent results (despite our model's simplicity) on the chaotic Lorenz system compared to fully supervised and variational inference methods. Finally, we show competitive results on an audio denoising experiment.

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