Related papers: Clifford Group Equivariant Diffusion Models for 3D…
Generating molecular graphs is a challenging task due to their discrete nature and the competitive objectives involved. Diffusion models have emerged as SOTA approaches in data generation across various modalities. For molecular graphs,…
We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by…
Masked diffusion models (MDMs) are a potential alternative to autoregressive models (ARMs) for language generation, but generation quality depends critically on the generation order. Prior work either hard-codes an ordering (e.g., blockwise…
Multimodal variational autoencoders have demonstrated their ability to learn the relationships between different modalities by mapping them into a latent representation. Their design and capacity to perform any-to-any conditional and…
Within the growing interest in the physical sciences in developing networks with equivariance properties, Clifford neural layers shine as one approach that delivers $E(n)$ and $O(n)$ equivariances given specific group actions. In this…
We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism…
Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are…
Efficiently characterizing quantum dot (QD) devices is a critical bottleneck when scaling quantum processors based on confined spins. Measuring high-resolution charge stability diagrams (or CSDs, data maps which crucially define the…
While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for $n=2,3 (\mod 4)$ continuous $Cl_n$-valued admissible wavelets can be…
Recent deep learning approaches seek to automate CAD creation by representing a model as a sequence of discrete commands and parameters, and then generating them using autoregressive models or continuous diffusion operating in Euclidean…
Deep learning has proven to yield fast and accurate predictions of quantum-chemical properties to accelerate the discovery of novel molecules and materials. As an exhaustive exploration of the vast chemical space is still infeasible, we…
Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…
Classical diffusion models have shown superior generative results. Exploring them in the quantum domain can advance the field of quantum generative learning. This work introduces Quantum Generative Diffusion Model (QGDM) as their simple and…
Mass spectrometry plays a fundamental role in elucidating the structures of unknown molecules and subsequent scientific discoveries. One formulation of the structure elucidation task is the conditional de novo generation of molecular…
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for $N$ dimensional data by embedding paths…
Object-centric learning aims to represent visual data with a set of object entities (a.k.a. slots), providing structured representations that enable systematic generalization. Leveraging advanced architectures like Transformers, recent…
This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…
Advancements in AI for medical imaging offer significant potential. However, their applications are constrained by the limited availability of data and the reluctance of medical centers to share it due to patient privacy concerns.…