Related papers: Projective characterization of higher-order quantu…
In this paper we propose a conceptual framework for higher-order artificial neural networks. The idea of higher-order networks arises naturally when a model is required to learn some group of transformations, every element of which is…
Large language models have steadily increased in size to achieve improved performance; however, this growth has also led to greater inference time and computational demands. Consequently, there is rising interest in model size reduction…
A central task in quantum information processing is to characterize quantum processes. In the realm of optical quantum information processing, this amounts to characterizing the transformations of the mode creation and annihilation…
We extend the notion of a Thomas projective connection (a projective equivalence class of linear connections) for supermanifolds. As a by-product, we arrive at a generalisation of the multidimensional Schwarzian derivative for the super…
Qualitative relationships illustrate how changing one property (e.g., moving velocity) affects another (e.g., kinetic energy) and constitutes a considerable portion of textual knowledge. Current approaches use either semantic parsers to…
Several recent papers have proposed increasing the expressive power of graph neural networks by exploiting subgraphs or other topological structures. In parallel, researchers have investigated higher order permutation equivariant networks.…
In this paper, we study quantitative properties of quantum programs. Properties of interest include (positive) almost-sure termination, expected runtime or expected cost, that is, for example, the expected number of applications of a given…
The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional…
We extend the framework of variational autoencoders to represent transformations explicitly in the latent space. In the family of hierarchical graphical models that emerges, the latent space is populated by higher order objects that are…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
An extension of Transformers is proposed that enables explicit relational reasoning through a novel module called the Abstractor. At the core of the Abstractor is a variant of attention called relational cross-attention. The approach is…
While Transformers have rapidly gained popularity in various computer vision applications, post-hoc explanations of their internal mechanisms remain largely unexplored. Vision Transformers extract visual information by representing image…
A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…
The effect of inclusion of higher-order interactions in the {\it XY} model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape…
In this paper, we study the influence of non-abelian superselection rules on the transfer of quantum information with the help of qubits on the base of an algebraic model and formulate quantum protocols. We pay the main attention to the…