Related papers: Covering Point Patterns
Tensor completion is a core machine learning algorithm used in recommender systems and other domains with missing data. While the matrix case is well-understood, theoretical results for tensor problems are limited, particularly when the…
Physical selectors (lasers choosing a mode, Ising machines settling on a ground state, condensates occupying a spin state) produce high-dimensional signatures at the moment of decision: full field amplitudes, multimode interference…
Current state-of-the-art machine translation systems are based on encoder-decoder architectures, that first encode the input sequence, and then generate an output sequence based on the input encoding. Both are interfaced with an attention…
Vision Transformers have achieved great success in computer visions, delivering exceptional performance across various tasks. However, their inherent reliance on sequential input enforces the manual partitioning of images into patch…
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…
Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…
This work presents an innovative method for point set self-embedding, that encodes the structural information of a dense point set into its sparser version in a visual but imperceptible form. The self-embedded point set can function as the…
In the decades-old Pattern Matching with Edits problem, given a length-$n$ string $T$ (the text), a length-$m$ string $P$ (the pattern), and a positive integer $k$ (the threshold), the task is to list the $k$-error occurrences of $P$ in…
The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the…
Minimizers are sampling schemes with numerous applications in computational biology. Assuming a fixed alphabet of size $\sigma$, a minimizer is defined by two integers $k,w\ge2$ and a linear order $\rho$ on strings of length $k$ (also…
We give a precise estimate for the number of lattice points in certain bounded subsets of $\mathbb{R}^{n}$ that involve `hyperbolic spikes' and occur naturally in multiplicative Diophantine approximation. We use Wilkie's o-minimal structure…
Completely blind sensing is the problem of recovering bandlimited signals from measurements, without any spectral information beside an upper bound on the measure of the whole support set in the frequency domain. Determining the number of…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains $N$ noisy outputs of the codeword. We study the problem of…
All current popular hand-crafted key-point detectors such as Harris corner, MSER, SIFT, SURF... rely on some specific pre-designed structures for the detection of corners, blobs, or junctions in an image. In this paper, a novel sparse…
A companion paper develops a framework in which probability measures are represented by distribution-kernel pairs (T,phi) with T a tempered distribution and phi a Schwartz kernel, so that weak moments of all orders exist unconditionally.…
Missing data is pervasive in econometric applications, and rarely is it plausible that the data are missing (completely) at random. This paper proposes a methodology for studying the robustness of results drawn from incomplete datasets.…
A constant-rate encoder--decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block decodable. Essentially, the 2-D constraint is…
We present a new approach to 3D object representation where a neural network encodes the geometry of an object directly into the weights and biases of a second 'mapping' network. This mapping network can be used to reconstruct an object by…
This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…