Related papers: Certified Mapper: Repeated testing for acyclicity …
Reinforcement learning (RL) methods have demonstrated their efficiency in simulation environments. However, many applications for which RL offers great potential, such as autonomous driving, are also safety critical and require a certified…
Datasets typically contain inaccuracies due to human error and societal biases, and these inaccuracies can affect the outcomes of models trained on such datasets. We present a technique for certifying whether linear regression models are…
Modeling network traffic is gaining importance in order to counter modern threats of ever increasing sophistication. It is though surprisingly difficult and costly to construct reliable classifiers on top of telemetry data due to the…
We present a simulation-based approach for generating barrier certificate functions for safety verification of cyber-physical systems (CPS) that contain neural network-based controllers. A linear programming solver is utilized to find a…
A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…
Simulation is essential to validate autonomous driving systems. However, a simple simulation, even for an extremely high number of simulated miles or hours, is not sufficient. We need well-founded criteria showing that simulation does…
This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…
We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model…
We present a characterisation of blenders based on mapping properties of certain sets of curves that can be rigorously verified by computer-assisted methods. We develop an algorithm to construct these sets of curves that requires only a…
As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in…
In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a…
ML models are typically trained using large datasets of high quality. However, training datasets often contain inconsistent or incomplete data. To tackle this issue, one solution is to develop algorithms that can check whether a prediction…
Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state…
In recent years, free energy perturbation (FEP) calculations have garnered increasing attention as tools to support drug discovery. The lead optimization mapper (Lomap) was proposed as an algorithm to calculate the relative free energy…
In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these checking algorithms must either be mechanically verified or their results must be verifiable by independent checkers. We analyze…
Mappings of a finite set into itself with restriction on the cycle lengths are considered (the so-called A-mappings). Asymptotics is given for the number of these mappings with a power-law reduction of the remainder.
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Recent works leveraging Graph Neural Networks to approach graph matching tasks have shown promising results. Recent progress in learning discrete distributions poses new opportunities for learning graph matching models. In this work, we…
Can one estimate the number of remaining faults in a software system? A credible estimation technique would be immensely useful to project managers as well as customers. It would also be of theoretical interest, as a general law of software…
As large language models (LLMs) advance toward expert-level performance in engineering domains, reliable reasoning under user-specified constraints becomes critical. In circuit analysis, for example, a numerically correct solution is…