Graphical Quadratic Algebra
<|reference_start|>Graphical Quadratic Algebra: We introduce Graphical Quadratic Algebra (GQA), a string diagrammatic calculus extending the language of Graphical Affine Algebra with a new generator characterised by invariance under rotation matrices. We show that GQA is a sound and complete axiomatisation for three different models: quadratic relations, which are a compositional formalism for least-squares problems, Gaussian stochastic processes, and Gaussian stochastic processes extended with non-determinisms. The equational theory of GQA sheds light on the connections between these perspectives, giving an algebraic interpretation to the interplay of stochastic behaviour, relational behaviour, non-determinism, and conditioning. As applications, we discuss various case studies, including linear regression, probabilistic programming, and electrical circuits with realistic (noisy) components.<|reference_end|>
@article{stein2024graphical,
    title={Graphical Quadratic Algebra},
    author={Dario Stein, Fabio Zanasi, Robin Piedeleu, Richard Samuelson},
    journal={arXiv preprint arXiv:2403.02284},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.02284},
    primaryClass={cs.LO math.CT math.OC}
}