Related papers: Recursion and proof theoretical characterizations …

We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…

We continue the study of the circuit class GC^0, which augments AC^0 with unbounded-fan-in gates that compute arbitrary functions inside a sufficiently small Hamming ball but must be constant outside it. While GC^0 can compute functions…

A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…

We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices…

We study the accuracy of reconstruction of a family of functions $f_\epsilon(x)$, $x\in\mathbb R^2$, $\epsilon\to0$, from their discrete Radon transform data sampled with step size $O(\epsilon)$. For each $\epsilon>0$ sufficiently small,…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Quantum machine learning offers promising advantages for classification tasks, but noise, decoherence, and connectivity constraints in current devices continue to limit the efficient execution of feature map-based circuits. Gate Assessment…

Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify…

We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…

When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional…

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…

In this note, we revisit the problem of flow approximation properties of neural ordinary differential equations (NODEs). The approximation properties have been considered as a flow controllability problem in recent literature. The neural…

The paper discusses the gate complexity of reversible circuits with the small number of additional inputs consisting of NOT, CNOT and 2-CNOT gates. We study Shannon's gate complexity function $L(n, q)$ for a reversible circuit implementing…

This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…

A major problem in exploiting microscopic systems for developing a new technology based on the principles of Quantum Information is the influence of noise which tends to work against the quantum features of such systems. It becomes then…

In the final paper of the Graph Minors series N. Robertson and P. Seymour proved that graphs are well-quasi-ordered under the immersion ordering. A direct implication of this theorem is that each class of graphs that is closed under taking…

We present a constructive method to create quantum circuits that implement oracles $|x\rangle|y\rangle|0\rangle^k \mapsto |x\rangle|y \oplus f(x)\rangle|0\rangle^k$ for $n$-variable Boolean functions $f$ with low $T$-count. In our method…

In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$-qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using…

Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of…

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link…