Results 21 to 30 of about 55,495 (230)
Kolmogorov Complexity and Solovay Functions [PDF]
, 2009 Solovay proved that there exists a computable upper bound f of the prefix-free Kolmogorov complexity function K such that f (x) = K(x) for infinitely many x. In this paper, we consider the class of computable functions f such that K(x)
Bienvenu, Laurent, Downey, Rod
core +6 more sources
Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems [PDF]
, 2003 Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic ...
Falcioni, M. +3 more
core +3 more sources
Universality laws for randomized dimension reduction, with applications [PDF]
arXiv.org, 2015 Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This
Samet Oymak, J. Tropp
semanticscholar +1 more source
Optimal Rates for Zero-Order Convex Optimization: The Power of Two Function Evaluations [PDF]
IEEE Transactions on Information Theory, 2013 We consider derivative-free algorithms for stochastic and nonstochastic convex optimization problems that use only function values rather than gradients.
John C. Duchi +3 more
semanticscholar +1 more source
Around Kolmogorov complexity: basic notions and results
, 2015 Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic.
A Nies, M Li, RG Downey
core +2 more sources
Algorithmic Randomness and Capacity of Closed Sets
, 2011 We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed sets K which have
A. McLinden and R.D. Mauldin +11 more
core +1 more source
Finding subsets of positive measure [PDF]
, 2014 An important theorem of geometric measure theory (first proved by Besicovitch and Davies for Euclidean space) says that every analytic set of non-zero $s$-dimensional Hausdorff measure $\mathcal H^s$ contains a closed subset of non-zero (and indeed ...
Kjos-Hanssen, Bjørn, Reimann, Jan
core +1 more source
Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning [PDF]
Annual Meeting of the Association for Computational Linguistics, 2020 Although pretrained language models can be fine-tuned to produce state-of-the-art results for a very wide range of language understanding tasks, the dynamics of this process are not well understood, especially in the low data regime.
Armen Aghajanyan +2 more
semanticscholar +1 more source
The dimension of ergodic random sequences [PDF]
, 2011 Let \mu be a computable ergodic shift-invariant measure over the Cantor space. Providing a constructive proof of Shannon-McMillan-Breiman theorem, V'yugin proved that if a sequence x is Martin-L\"of random w.r.t.
Hoyrup, Mathieu
core +5 more sources
Reducing Revenue to Welfare Maximization: Approximation Algorithms and other Generalizations [PDF]
, 2013 It was recently shown in [http://arxiv.org/abs/1207.5518] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multi-dimensional Bayesian auction problems with arbitrary (possibly combinatorial) feasibility ...
Cai, Yang +2 more
core +5 more sources