Related papers: Computing with Polynomial Ordinary Differential Eq…
Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
Dynamic simulators are computational models governed by differential equations that evolve over time. They are essential for scientific and engineering applications but remain challenging to emulate because of the unpredictable behavior of…
We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Robustness analysis is very important in biology and neuroscience, to unravel behavioural patterns of systems that are conserved despite large parametric uncertainties. To make studies of probabilistic robustness more efficient and scalable…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…
So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start…
We study the complexity of problems solvable in deterministic polynomial time with access to an NP or Quantum Merlin-Arthur (QMA)-oracle, such as $P^{NP}$ and $P^{QMA}$, respectively. The former allows one to classify problems more finely…
Classical circuit complexity characterizes parallel computation in purely combinatorial terms, ignoring the physical constraints that govern real hardware. The standard classes $\mathbf{NC}$, $\mathbf{AC}$, and $\mathbf{TC}$ treat unlimited…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
Since the first idea of using GPU to general purpose computing, things have evolved over the years and now there are several approaches to GPU programming. GPU computing practically began with the introduction of CUDA (Compute Unified…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
We study the computational relationship between replicability (Impagliazzo et al. [STOC `22], Ghazi et al. [NeurIPS `21]) and other stability notions. Specifically, we focus on replicable PAC learning and its connections to differential…