Related papers: Rectangular, Range, and Restricted AONTs: Three Ge…
Nonlinear topology is an emerging field that combines the intrinsic reconfigurability of nonlinear systems with the robustness of topological protection, offering fertile ground for unconventional phenomena and novel applications. Recently,…
This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being…
Although foundation models (FMs) claim to be powerful, their generalization ability significantly decreases when faced with distribution shifts, weak supervision, or malicious attacks in the open world. On the other hand, most domain…
An experiment or theory is classically explainable if it can be reproduced by some noncontextual ontological model. In this work, we adapt the notion of ontological models and generalized noncontextuality so it applies to the framework of…
Existing works on Binary Neural Network (BNN) mainly focus on model's weights and activations while discarding considerations on the input raw data. This article introduces Generic Learned Thermometer (GLT), an encoding technique to improve…
This paper provides norm-based generalization bounds for the Transformer architecture that do not depend on the input sequence length. We employ a covering number based approach to prove our bounds. We use three novel covering number bounds…
Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization…
Methods such as Layer Normalization (LN) and Batch Normalization (BN) have proven to be effective in improving the training of Recurrent Neural Networks (RNNs). However, existing methods normalize using only the instantaneous information at…
Addition theorems have been indispensable tools for the reduction of quantum transition amplitudes. They are normally utilized at the start of the process to move the angular dependence within plane waves and Coulomb potentials, and the…
Despite their central role in the success of foundational models and large-scale language modeling, the theoretical foundations governing the operation of Transformers remain only partially understood. Contemporary research has largely…
Asymmetric Numeral Systems (ANS) is a class of entropy encoders that had an immense impact on the data compression, substituting arithmetic and Huffman coding. It was studied by different authors but the precise asymptotics of its…
Ring signatures are a powerful primitive that allows a member to sign on behalf of a group, without revealing their identity. Recently, ring signatures have received additional attention as an ingredient for post-quantum deniable…
Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…
Optical coherence tomography (OCT) can perform non-invasive high-resolution three-dimensional (3D) imaging and has been widely used in biomedical fields, while it is inevitably affected by coherence speckle noise which degrades OCT imaging…
We show the universality of depth-2 group convolutional neural networks (GCNNs) in a unified and constructive manner based on the ridgelet theory. Despite widespread use in applications, the approximation property of (G)CNNs has not been…
Convolutional Neural Networks (CNNs) rely on fixed-size kernels scanning local patches, which limits their ability to capture global context or long-range dependencies without very deep architectures. Vision Transformers (ViTs), in turn,…
Normalization layers are ubiquitous in modern neural networks and have long been considered essential. This work demonstrates that Transformers without normalization can achieve the same or better performance using a remarkably simple…
Alternative set theory (AST) may be suitable for the ones who try to capture objects or phenomenons with some kind of indefiniteness of a border. While AST provides various notions for advanced mathematical studies, correspondence of them…
Human cognition can leverage fundamental conceptual knowledge, like geometric and kinematic ones, to appropriately perceive, comprehend and interact with novel objects. Motivated by this finding, we aim to endow machine intelligence with an…
An operational definition of contextuality is introduced which generalizes the standard notion in three ways: (1) it applies to arbitrary operational theories rather than just quantum theory, (2) it applies to arbitrary experimental…