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We introduce a class of $2d$ sigma models which are parameterized by a function of one variable. In addition to the physical field $g$, these models include an auxiliary field $v_\alpha$ which mediates interactions in a prescribed way. We…

Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains…

The first part of this article is devoted to characterizing the cocycles $\alpha$ of a finite group $G$ that give rise to faithful projective representations of $G$. We prove that a $p$-group $G$ admits a faithful irreducible projective…

Social science theories often postulate causal relationships among a set of variables or events. Although directed acyclic graphs (DAGs) are increasingly used to represent these theories, their full potential has not yet been realized in…

Graphical causal models led to the development of complete non-parametric identification theory in arbitrary structured systems, and general approaches to efficient inference. Nevertheless, graphical approaches to causal inference have not…

Causal generative modeling is essential for developing reliable and transparent AI systems capable of counterfactual reasoning. While existing approaches focus on integrating causal constraints during the training of generative models, they…

Let ${\mathbf U}^-_q$ be the negative part of the quantum enveloping algebra associated to a simply laced Kac-Moody Lie algebra ${\mathfrak g}$, and $\underline{\mathbf U}^-_q$ the algebra corresponding to the fixed point subalgebra of…

Graph foundation models (GFMs) have recently emerged as a promising paradigm for achieving broad generalization across various graph data. However, existing GFMs are often trained on datasets that may not fully reflect real-world graphs,…

Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…

Non-ideal measurement computed tomography (NICT) employs suboptimal imaging protocols to expand CT applications. However, the resulting trade-offs degrade image quality, limiting clinical acceptability. Although deep learning methods have…

In Scene Graph Generation (SGG), structured representations are extracted from visual inputs as object nodes and connecting predicates, enabling image-based reasoning for diverse downstream tasks. While fully supervised SGG has improved…

At the pinnacle of computational imaging is the co-optimization of camera and algorithm. This, however, is not the only form of computational imaging. In problems such as imaging through adverse weather, the bigger challenge is how to…

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research…

The quest for accurate prediction of drug molecule properties poses a fundamental challenge in the realm of Artificial Intelligence Drug Discovery (AIDD). An effective representation of drug molecules emerges as a pivotal component in this…

The recent works on causal discovery have followed a similar trend of learning partial ancestral graphs (PAGs) since observational data constrain the true causal directed acyclic graph (DAG) only up to a Markov equivalence class. This…

The Segment Anything Model (SAM) made an eye-catching debut recently and inspired many researchers to explore its potential and limitation in terms of zero-shot generalization capability. As the first promptable foundation model for…

We present a graphical criterion for covariate adjustment that is sound and complete for four different classes of causal graphical models: directed acyclic graphs (DAGs), maximum ancestral graphs (MAGs), completed partially directed…

Generative Adversarial Networks (GANs) have emerged as a prominent research focus for image editing tasks, leveraging the powerful image generation capabilities of the GAN framework to produce remarkable results.However, prevailing…

We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those…

Invertible map equivalences are approximations of graph isomorphism that refine the well-known Weisfeiler-Leman method. They are parametrised by a number k and a set Q of primes. The intuition is that two graphs G and H which are equivalent…