Related papers: Properties of Carry Value Transformation
The Self-Optimal-Transport (SOT) feature transform is designed to upgrade the set of features of a data instance to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order…
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.
The recently proposed Visual image Transformers (ViT) with pure attention have achieved promising performance on image recognition tasks, such as image classification. However, the routine of the current ViT model is to maintain a…
This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density…
We study valued fields equipped with an automorphism. We prove that all of them have an extension admitting an equivariant cross-section of the valuation. In residual characteristic zero, and in the presence of such a cross-section, we show…
This paper considers contrastive training for cross-modal 0-shot transfer wherein a pre-trained model in one modality is used for representation learning in another domain using pairwise data. The learnt models in the latter domain can then…
The XTR (conteXtual Token Retrieval) algorithm is a modification to ColBERT retrieval that avoids the costly step of fully gathering and reranking the candidates' embeddings by imputing their missing similarity scores from the initial token…
Standard Transformers impose near-exponential decay on the influence of distant tokens, conflicting with the power-law structure of long-range dependencies in natural language. We introduce the \emph{Variable-Order Retention Transformer}…
We provided proof here that coefficient of variation (CV) is a direct measure of risk using an equation that has been derived here for the first time. We also presented a method to generate a stock CV based on return that strongly…
Deep learning often faces the challenge of efficiently processing dynamic inputs, such as sensor data or user inputs. For example, an AI writing assistant is required to update its suggestions in real time as a document is edited.…
In this paper, we study the different possibilities to add two vectors of digits of a given length $m$. Our results show that there are at least $2^{m-1}$ different additions of such vectors, while there exist only two types of addition…
State-of-the-art neural machine translation methods employ massive amounts of parameters. Drastically reducing computational costs of such methods without affecting performance has been up to this point unsuccessful. To this end, we propose…
This paper leverages the statistics of extreme values to predict the worst-case convergence times of machine learning algorithms. Timing is a critical non-functional property of ML systems, and providing the worst-case converge times is…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
The Refined Instrumental Variable method for discrete-time systems (RIV) and its variant for continuous-time systems (RIVC) are popular methods for the identification of linear systems in open-loop. The continuous-time equivalent of the…
Considering a linearly ordered set, we introduce its symmetric version, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring. We show that imposing symmetry…
This work concerns a comparison of SVM kernel methods in text categorization tasks. In particular I define a kernel function that estimates the similarity between two objects computing by their compressed lengths. In fact, compression…
In pursuit of detecting unstinted objects that extend beyond predefined categories, prior arts of open-vocabulary object detection (OVD) typically resort to pretrained vision-language models (VLMs) for base-to-novel category generalization.…
The asynchronous computability theorem (ACT) uses concepts from combinatorial topology to characterize which tasks have wait-free solutions in read-write memory. A task can be expressed as a relation between two chromatic simplicial…
In this paper, we introduce and prove QR Sort, a novel non-comparative integer sorting algorithm. This algorithm uses principles derived from the Quotient-Remainder Theorem and Counting Sort subroutines to sort input sequences stably. QR…