Related papers: The Complex Langevin method: When can it be truste…
We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method…
The complex Langevin method is a general method to treat systems with complex action, such as QCD at nonzero density. The formal justification relies on the absence of certain boundary terms, both at infinity and at the unavoidable poles of…
Research in logic encryption over the last decade has resulted in various techniques to prevent different security threats such as Trojan insertion, intellectual property leakage, and reverse engineering. However, there is little agreement…
Stochastic differential equations, especially the one called Langevin equation, play an important role in many fields of modern science. In this paper, we use the bicolour rooted tree method, which is based on the stochastic Taylor…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
This paper presents a method for alleviating sign problems in lattice path integrals, including those associated with finite fermion density in relativistic systems. The method makes use of information gained from some systematic expansion…
Our lives become increasingly dependent on safety- and security-critical systems, so formal techniques are advocated for engineering such systems. One of such techniques is validation obligations that enable formalizing requirements early…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…
Nowadays we are witnessing a transformation of the business processes towards a more computation driven approach. The ever increasing usage of Machine Learning techniques is the clearest example of such trend. This sort of revolution is…
Deductive verification is an effective method to ensure that a given system exposes the intended behavior. In spite of its proven usefulness and feasibility in selected projects, deductive verification is still not a mainstream technique.…
After a short review of one of proposals to avoid complex stochastic processes in Complex Langevin studies, the recent progress in the former is reported. In particular, the new developments allow now to construct positive and normalizable…
Despite the vast body of research literature proposing algorithms with formal guarantees, the amount of verifiable code in today's systems remains minimal. This discrepancy stems from the inherent difficulty of verifying code, particularly…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
Trustworthy machine learning is of primary importance to the practical deployment of deep learning models. While state-of-the-art models achieve astonishingly good performance in terms of accuracy, recent literature reveals that their…
The numerical sign problem has long been a major obstacle to first-principles calculations in various important fields of physics. We report that the recently proposed algorithm, tempered Lefschetz thimble method (TLTM), and its worldvolume…
Despite the versatility of generalized linear mixed models in handling complex experimental designs, they often suffer from misspecification and convergence problems. This makes inference on the values of coefficients problematic. To…
We discuss conditions under which expectation values computed from a complex Langevin process $Z$ will converge to integral averages over a given complex valued weight function. The difficulties in proving a general result are pointed out.…