Related papers: Demuth's path to randomness
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
In 1989 H. Tverberg proposed a quite general conjecture in Discrete geometry, which could be considered as the common basis for many results in Combinatorial geometry and at the same time as a discrete analogue of the common transversal…
Neural networks are ubiquitous in many tasks, but trusting their predictions is an open issue. Uncertainty quantification is required for many applications, and disentangled aleatoric and epistemic uncertainties are best. In this paper, we…
The realization that selfish interests need to be accounted for in the design of algorithms has produced many contributions in computer science under the umbrella of algorithmic mechanism design. Novel algorithmic properties and paradigms…
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…
To achieve the greatest possible speed, practitioners regularly implement randomized algorithms for low-rank approximation and least-squares regression with structured dimension reduction maps. Despite significant research effort, basic…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
Let $P_r(n)$ be the set of partitions of n with non negative rth differences. Let $\lambda$ be a partition chosen uniformly at random among the set $P_r(n)$. Let $d(\lambda)$ be a positive rth difference chosen uniformly at random in…
Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…
Ever since the original algorithm by Nesterov (1983), the true nature of the acceleration phenomenon has remained elusive, with various interpretations of why the method is actually faster. The diagnosis of the algorithm through the lens of…
We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our main contributions are presentation results for the monads,…
This review motivates and synthesizes research efforts in neuroscience-inspired artificial intelligence and biomimetic computing in terms of mortal computation. Specifically, we characterize the notion of mortality by recasting ideas in…
One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies…
The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal…
This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent…
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career…
Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that…
Currently, there is a gap between the tools used by probability theorists and those used in formal reasoning about probabilistic programs. On the one hand, a probability theorist decomposes probabilistic state along the simple and natural…
We determine, up to the equivalence of first-order interdefinability, all structures which are first-order definable in the random partial order. It turns out that these structures fall into precisely five equivalence classes. We achieve…