Related papers: From Tensor Networks to Tractable Circuits, and ba…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories.…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…
Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…
The relationship between the properties of a dynamical system and the structure of its defining equations has long been studied in many contexts. Here we study this problem for the class of conjunctive (resp. disjunctive) Boolean networks,…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative,…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them…
Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…
Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems. Their expressive and computational power is characterized by an underlying…
Network models are used to study interconnected systems across many physical, biological, and social disciplines. Such models often assume a particular network-generating mechanism, which when fit to data produces estimates of…
This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…