Related papers: Laplace-HDC: Understanding the geometry of binary …
In this paper, we study the holographic quantum error correcting code properties in different boundary fractal-like structures. We construct and explore different examples of the uberholographic bulk reconstruction corresponding to these…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…
Nowadays, hyperspectral image classification widely copes with spatial information to improve accuracy. One of the most popular way to integrate such information is to extract hierarchical features from a multiscale segmentation. In the…
The measure between heterogeneous data is still an open problem. Many research works have been developed to learn a common subspace where the similarity between different modalities can be calculated directly. However, most of existing…
Lattice and special nonlattice multilevel constellations constructed from binary codes, such as Constructions A, C, and D, have relevant applications in Mathematics (sphere packing) and in Communication (multi-stage decoding and efficient…
Hyperdimensional computing (HDC) enables efficient data encoding and processing in high-dimensional space, benefiting machine learning and data analysis. However, underutilization of these spaces can lead to overfitting and reduced model…
We propose a dynamic graph representation method, showcasing its rich representational capacity and establishing some of its theoretical properties. Our representation falls under the bind-and-sum approach in hyperdimensional computing…
Recent works on learned image compression perform encoding and decoding processes in a full-resolution manner, resulting in two problems when deployed for practical applications. First, parallel acceleration of the autoregressive entropy…
In this work, we begin to investigate the possibility of training a deep neural network on the task of binary code understanding. Specifically, the network would take, as input, features derived directly from binaries and output English…
Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…
Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
The latest video coding standard, Versatile Video Coding (VVC), achieves almost twice coding efficiency compared to its predecessor, the High Efficiency Video Coding (HEVC). However, achieving this efficiency (for intra coding) requires 31x…
Hyperspectral image classification (HIC) is an active research topic in remote sensing. Hyperspectral images typically generate large data cubes posing big challenges in data acquisition, storage, transmission and processing. To overcome…
Conventional video compression (VC) methods are based on motion compensated transform coding, and the steps of motion estimation, mode and quantization parameter selection, and entropy coding are optimized individually due to the…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…