Related papers: Universality of causal graph dynamics
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. They are studied both from the…
Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical…
Causality and game theory are two influential fields that contribute significantly to decision-making in various domains. Causality defines and models causal relationships in complex policy problems, while game theory provides insights into…
Analog computation is an alternative to digital computation, that has recently re-gained prominence, since it includes neural networks and neuromorphic computing. Further important examples are cellular automata and differential analyzers.…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
Modeling causal relationships in graph representation learning remains a fundamental challenge. Existing approaches often draw on theories and methods from causal inference to identify causal subgraphs or mitigate confounders. However, due…
Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…
Causal reasoning has been an indispensable capability for humans and other intelligent animals to interact with the physical world. In this work, we propose to endow an artificial agent with the capability of causal reasoning for completing…
Healthcare artificial intelligence systems often degrade in performance when deployed across institutions, with documented performance drops and perpetuation of discriminatory patterns embedded in data. This brittleness comes, in part, from…
Understanding causal relations between temporal variables is a central challenge in time series analysis, particularly when the full causal structure is unknown. Even when the full causal structure cannot be fully specified, experts often…
In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or…
Causal reasoning is a cornerstone of how humans interpret the world. To model and reason about causality, causal graphs offer a concise yet effective solution. Given the impressive advancements in language models, a crucial question arises:…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
We study Granger causality in the context of wide-sense stationary time series, where our focus is on the topological aspects of the underlying causality graph. We establish sufficient conditions (in particular, we develop the notion of a…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…
We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of…
Imagery is frequently used to model, represent and communicate knowledge. In particular, graphs are one of the most powerful tools, being able to represent relations between objects. Causal relations are frequently represented by directed…
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality…
Networks with a high degree of symmetry are useful models for parallel processor networks. In earlier papers, we defined several global communication tasks (universal exchange, universal broadcast, universal summation) that can be critical…