Previous work of the second author and Wolf showed that given a set $A\subseteq \mathbb{F}_p^n$ of bounded $\textrm{VC}_2$-dimension, there is a high rank quadratic factor $\mathcal{B}$ of bounded complexity such that $A$ is approximately equal to a...
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance....
We introduce an idea called anti-gadgets in complexity reductions. These combinatorial gadgets have the effect of erasing the presence of some other graph fragment, as if we had managed to include a negative copy of a graph gadget. We use this idea t...
We introduce and study Certificate Game complexity, a measure of complexity based on the probability of winning a game where two players are given inputs with different function values and are asked to output some index $i$ such that $x_i\neq y_i$, i...
We present a comparative analysis of text complexity across domains using scale-free metrics. We quantify linguistic complexity via Heaps' exponent $β$ (vocabulary growth), Taylor's exponent $α$ (word-frequency fluctuation scaling), compression rat...
These are the written discussions of the paper "Bayesian measures of model complexity and fit" by D. Spiegelhalter et al. (2002), following the discussions given at the Annual Meeting of the Royal Statistical Society in Newcastle-upon-Tyne on Septemb...
The complexity of mathematical models describing respiratory mechanics has grown in recent years to integrate with cardiovascular models and incorporate nonlinear dynamics. However, additional model complexity has rarely been studied in the context o...
The letter by Mark Perakh entitled "DEFINING COMPLEXITY: A Commentary to a paper by Charles H. Bennett" is here archived with the permission of the author. This letter was downloaded from the site "On Talk Reason, http://www.talkreason.org/articles...
Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scientific and parallel computing. It changes matrix sparsity patterns to...
We study the complexity of learning mixtures of separated Gaussians with common unknown bounded covariance matrix. Specifically, we focus on learning Gaussian mixture models (GMMs) on $\mathbb{R}^d$ of the form $P= \sum_{i=1}^k w_i \mathcal{N}(\bolds...
We study the complexity of Non-Gaussian Component Analysis (NGCA) in the Statistical Query (SQ) model. Prior work developed a general methodology to prove SQ lower bounds for this task that have been applicable to a wide range of contexts. In particu...
We consider conjunctive queries with arithmetic comparisons (CQAC) and investigate the computational complexity of the problem: Given two CQAC queries, $Q$ and $Q'$, is $Q'$ contained in $Q$? We know that, for CQAC queries, the problem of testing con...
Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation. However, all these works only provide regret or sample complexity guarantees. It is still an open question if one can achieve stronger pe...
Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more interpretable, sever...
We provide new insights on eluder dimension, a complexity measure that has been extensively used to bound the regret of algorithms for online bandits and reinforcement learning with function approximation. First, we study the relationship between the...
"green dragon book" and its cover depicts a knight and a dragon in battle; the dragon is green, and labeled "Complexity of Compiler Design", while the knight
Jan 20, 2026 · Adjective intricate (comparative more intricate, superlative most intricate) Having a great deal of fine detail or complexity. Synonyms: fancy, convoluted The architecture of this clock is very …
Jan 20, 2026 · Adjective intricate (comparative more intricate, superlative most intricate) Having a great deal of fine detail or complexity. Synonyms: fancy, convoluted The architecture of this clock is very …
Modern model-free reinforcement learning methods have recently demonstrated impressive results on a number of problems. However, complex domains like dexterous manipulation remain a challenge due to the high sample complexity. To address this, curren...
Jan 23, 2026 · Trade was a major topic of discussion at the Annual Meeting 2026 in Davos. Expert participants examined everything from how geopolitical complexity is accelerating trade deals to the …