Related papers: Upper and Lower Bounds on the Space Complexity of …
Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through…
In the era of big data, methods for improving memory and computational efficiency have become crucial for successful deployment of technologies. Hashing is one of the most effective approaches to deal with computational limitations that…
In this work we propose algorithms to explicitly construct a conservative estimate of the configuration spaces of rigid objects in 2D and 3D. Our approach is able to detect compact path components and narrow passages in configuration space…
We introduce new techniques for proving lower bounds on the running time of randomized algorithms for asynchronous agreement against powerful adversaries. In particular, we define a \emph{strongly adaptive adversary} that is computationally…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…
Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are…
Large-capacity Content Addressable Memory (CAM) is a key element in a wide variety of applications. The inevitable complexities of scaling MOS transistors introduce a major challenge in the realization of such systems. Convergence of…
Still under debate is the question of whether machine learning is capable of going beyond black-box modeling for complex physical systems. We investigate the generalizing and interpretability properties of learning algorithms. To this end,…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
In this thesis we discuss architectural designs and training methods for a neural network to have the ability of dissecting an image into objects of interest without supervision. The main challenge in 2D unsupervised object segmentation is…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the…
Non-maximum suppression is an integral part of the object detection pipeline. First, it sorts all detection boxes on the basis of their scores. The detection box M with the maximum score is selected and all other detection boxes with a…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
Whether in fundamental physics, cybersecurity or finance, the detection of anomalies with machine learning techniques is a highly relevant and active field of research, as it potentially accelerates the discovery of novel physics or…
When the inverse of an algorithm is well-defined -- that is, when its output can be deterministically transformed into the input producing it -- we say that the algorithm is invertible. While one can describe an invertible algorithm using a…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
Consider a system of N identical hard spherical particles moving in a d-dimensional box and undergoing elastic, possibly multi-particle, collisions. We develop a new algorithm that recovers the pre-collision state from the post-collision…