Zobrazeno 1 - 10
of 69
pro vyhledávání: '"Vákár, Matthijs"'
We study the categorical structure of the Grothendieck construction of an indexed category $\mathcal{L}:\mathcal{C}^{op}\to\mathbf{CAT}$ and characterise fibred limits, colimits, and monoidal structures. Next, we give sufficient conditions for the mo
Externí odkaz:
http://arxiv.org/abs/2405.07724
We consider the canonical pseudodistributive law between various free limit completion pseudomonads and the free coproduct completion pseudomonad. When the class of limits includes pullbacks, we show that this consideration leads to notions of extens
Externí odkaz:
http://arxiv.org/abs/2405.02185
We delve into the concept of categories with products that distribute over coproducts, which we call doubly-infinitary distributive categories. We show various instances of doubly-infinitary distributive categories aiming for a comparative analysis w
Externí odkaz:
http://arxiv.org/abs/2403.10447
Autor:
Smeding, Tom, Vákár, Matthijs
We show how the basic Combinatory Homomorphic Automatic Differentiation (CHAD) algorithm can be optimised, using well-known methods, to yield a simple, composable, and generally applicable reverse-mode automatic differentiation (AD) technique that ha
Externí odkaz:
http://arxiv.org/abs/2307.05738
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a very stra
Externí odkaz:
http://arxiv.org/abs/2210.08530
We give a simple, direct and reusable logical relations technique for languages with term and type recursion and partially defined differentiable functions. We demonstrate it by working out the case of Automatic Differentiation (AD) correctness: name
Externí odkaz:
http://arxiv.org/abs/2210.07724
Autor:
Smeding, Tom, Vákár, Matthijs
Where dual-numbers forward-mode automatic differentiation (AD) pairs each scalar value with its tangent value, dual-numbers reverse-mode AD attempts to achieve reverse AD using a similarly simple idea: by pairing each scalar value with a backpropagat
Externí odkaz:
http://arxiv.org/abs/2207.03418
Autor:
Smeding, Tom, Vákár, Matthijs
Where dual-numbers forward-mode automatic differentiation (AD) pairs each scalar value with its tangent derivative, dual-numbers /reverse-mode/ AD attempts to achieve reverse AD using a similarly simple idea: by pairing each scalar value with a backp
Externí odkaz:
http://arxiv.org/abs/2205.11368
Autor:
Vákár, Matthijs
This review paper surveys work by Isham, Butterfield, Doering, Landsman, Spitters, Heunen et al. about topos-theoretic analyses of quantum theory. It aims to provide a synthesized account of their various approaches.
Externí odkaz:
http://arxiv.org/abs/2110.06793
Autor:
Vákár, Matthijs
This set of lecture notes first gives an introduction to the geometry of principal bundles. Next, it demonstrates how they can be used to formalize the concept of gauge theories, arising in physics. A basic familiarity is assumed with the differentia
Externí odkaz:
http://arxiv.org/abs/2110.06334