Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Alexander, Samuel Allen"'
Autor:
Alexander, Samuel Allen, Dawson, Bryan
In the hyperreals constructed using a free ultrafilter on R, where [f] is the hyperreal represented by f:R->R, it is tempting to define a derivative operator by [f]'=[f'], but unfortunately this is not generally well-defined. We show that if the ultr
Externí odkaz:
http://arxiv.org/abs/2411.14689
Publikováno v:
EPTCS 379, 2023, pp. 4-15
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions
Externí odkaz:
http://arxiv.org/abs/2307.05053
Inspired by recent progress in multi-agent Reinforcement Learning (RL), in this work we examine the collective intelligent behaviour of theoretical universal agents by introducing a weighted mixture operation. Given a weighted set of agents, their we
Externí odkaz:
http://arxiv.org/abs/2302.06083
Autor:
Alexander, Samuel Allen
One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule which iterat
Externí odkaz:
http://arxiv.org/abs/2211.04578
Autor:
Alexander, Samuel Allen
We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.
Comment: 1 page
Comment: 1 page
Externí odkaz:
http://arxiv.org/abs/2206.02031
We consider an extended notion of reinforcement learning in which the environment can simulate the agent and base its outputs on the agent's hypothetical behavior. Since good performance usually requires paying attention to whatever things the enviro
Externí odkaz:
http://arxiv.org/abs/2110.06890
Can an agent's intelligence level be negative? We extend the Legg-Hutter agent-environment framework to include punishments and argue for an affirmative answer to that question. We show that if the background encodings and Universal Turing Machine (U
Externí odkaz:
http://arxiv.org/abs/2110.02450
Autor:
Alexander, Samuel Allen
We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for
Externí odkaz:
http://arxiv.org/abs/2008.11535
Autor:
Alexander, Samuel Allen
Can an AGI create a more intelligent AGI? Under idealized assumptions, for a certain theoretical type of intelligence, our answer is: "Not without outside help". This is a paper on the mathematical structure of AGI populations when parent AGIs create
Externí odkaz:
http://arxiv.org/abs/2005.08801
Autor:
Alexander, Samuel Allen
Publikováno v:
Journal of Artificial General Intelligence 11(1): 70--85 (2020)
After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an
Externí odkaz:
http://arxiv.org/abs/2002.10221