Related papers: A Formally Verified HOL Algebra for Dynamic Reliab…
In Part 1, we describe six projective-type model structures on the category of differential graded modules over a differential graded algebra A over a commutative ring R. When R is a field, the six collapse to three and are well-known, at…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
A multigrid framework is described for multiphysics applications. The framework allows one to construct, adapt, and tailor a monolithic multigrid methodology to different linear systems coming from discretized partial differential…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
The control of Biomedical Systems in Physical Human-Robot Interaction (pHRI) plays a pivotal role in achieving the desired behavior by ensuring the intended transfer function and stability of subsystems within the overall system.…
A significant range of geometric structures whose rigidity is explored for both practical and theoretical purposes are formed by modifying generically isostatic triangulated spheres. In the block and hole structures (P, p), some edges are…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary high-order accuracy in theory. Moreover, these schemes can…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…
Formal verification techniques have been playing an important role in pre-silicon validation processes. One of the most important points considered in performing formal verification is to define good verification scopes; we should define…
We develop a rewriting theory suitable for diagrammatic algebras and lay down the foundations of a systematic study of their higher structures. In this paper, we focus on the question of finding bases. As an application, we give the first…
One important assumption underlying common classification models is the stationarity of the data. However, in real-world streaming applications, the data concept indicated by the joint distribution of feature and label is not stationary but…
In this paper, we propose a fundamentally new approach to Datalog evaluation. Given a linear Datalog program DB written using N constants and binary predicates, we first translate if-and-only-if completions of clauses in DB into a set…
The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep…
This work proposes a novel distributed framework for verifying the incremental stability of large-scale systems with unknown dynamics and known interconnection structures using graph neural networks. Our proposed approach relies on the…
Future generations of processors will exhibit an increase of faults over their lifetime, and it becomes increasingly expensive to solve the resulting reliability issues purely at the hardware level. We propose to model computations in terms…
While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the…
Deep neural network (DNN) verification is an emerging field, with diverse verification engines quickly becoming available. Demonstrating the effectiveness of these engines on real-world DNNs is an important step towards their wider…