If we accept this, and the generalisation of this example, then the remainder of our thought experiment becomes admissable — and, we hope, useful as an illustration of analysis using our model. 5.1. Straightfo
et al. Generalisation in humans and deep neural networks. NeurIPS Proc. (2018). Zhou, Z. & Firestone, C. Humans can decipher adversarial images. Nat. Commun. 10, 1334 (2019). PubMed PubMed Central Google Scholar Rajalingham, R. et al. Large-scale, high-resolution comparison of the ...
(This is an extended blog post version of my talk “Ultraproducts as a Bridge Between Discrete and Continuous Analysis” that I gave at the Simons institute for the theory of computing at the workshop “Neo-Classical methods in discrete analysis“. Some of the material here is drawn from pr...
It is in fact likely that almost all of the theory below extends to base spaces which are -finite rather than finite (for instance, by damping the measure to become finite, without introducing any further null events), although we will not pursue this further generalisation here. The ...
2. Entanglement is the key difference between quantum information processing and computing and its classical counterpart. 3. Quantum information theorists have reconstructed QM as a probability theory based on information-theoretic principles. In these reconstructions, they build the entirety of finite-di...
A credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution. The generalisation to multivariate problems is the credible region. Credible intervals ...
is so much research and development to be done. The development of content delivery networks sought to deal with extreme bandwidth pressures, first as video streaming was growing in demand as well as the number of content providers. That was in the past. With the emergence of cloud computing,...
In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the ...
generalisation and creative thinking. We have vastly better common sense than machines, we’re agile, nimble and energy efficient too. And don’t forget that it’s humans that have rights and vote – and we can revolt too. Humans are also a deeply social species and physical connection is ...
Being a generalisation of the Thue-Siegel-Roth theorem, it is unsurprising that the known proofs of the subspace theorem are also ineffective with regards to the constant . (However, the number of exceptional subspaces may be bounded effectively; cf. the situation with the Skolem-Mahler-Lech th...