[HTML][HTML] Verification of deep convolutional neural networks using imagestars
… We compare our approach with the zonotope and polytope methods in two aspects including
verification time and conservativeness of the results. To do that, we train 3 CNNs in small, …
verification time and conservativeness of the results. To do that, we train 3 CNNs in small, …
Using Intersection of Unions to Minimize Multi-directional Linearization Error in Reachability Analysis
A Adimoolam, I Saha - 25th ACM International Conference on Hybrid …, 2022 - dl.acm.org
… as a union zonotope because it represents a union of zonotopes without intersection. Given
two IoU zonotopes Z and Z′, we represent the IoU zonotope resulting from their intersection …
two IoU zonotopes Z and Z′, we represent the IoU zonotope resulting from their intersection …
A Polynomial Case of Nonconvex Quadratic Optimization
We consider the following case of quadratic optimization: given Q∈ Rn× n with rank r and
given p∈ Rn and x≤ x∈ Rp (where inequalities between vectors are understood …
given p∈ Rn and x≤ x∈ Rp (where inequalities between vectors are understood …
[HTML][HTML] Fault detection for uncertain LPV systems using probabilistic set-membership parity relation
This paper considers fault detection of uncertain linear parameter varying systems that have
polynomial dependence on parametric uncertainties. A conventional set-membership (SM) …
polynomial dependence on parametric uncertainties. A conventional set-membership (SM) …
The Image Containment Problem and Some Classes of Polynomial Instances
R Pesenti, F Rinaldi - SIAM Journal on Optimization, 2007 - SIAM
… a minimum total length zonotope containing k assigned … zonotopes in R2 centered in the
origin are considered and a method to approximate a given zonotope by means of zonotopes …
origin are considered and a method to approximate a given zonotope by means of zonotopes …
[PDF][PDF] Réarrangements convexes des marches aléatoires
Y Davydov, AM Vershik - Annales de l'IHP Probabilités et statistiques, 1998 - numdam.org
… Nous étudions donc ici le comportement asymptotique des courbes des zonotopes Zn/bn …
On va considérer d’abord les zonotopes Zn engendrés par une suite de variables aléatoires …
On va considérer d’abord les zonotopes Zn engendrés par une suite de variables aléatoires …
Fault Detection and Isolation for Linear discrete-time Delayed Systems based on L∞ Observer and Zonotopic Analysis
This paper considers actuator fault detection and isolation (FDI) problem for a class of linear
discrete-time systems with constant time-delay. Based on delay-free representation, a novel …
discrete-time systems with constant time-delay. Based on delay-free representation, a novel …
A provable defense for deep residual networks
… the analysis with the Hybrid Zonotope domain. For all abstract layers, we describe their
effect on a given hybrid zonotope h with m correlated error coefficients, producing a new hybrid …
effect on a given hybrid zonotope h with m correlated error coefficients, producing a new hybrid …
Model predictive real-time monitoring of linear systems
X Chen, S Sankaranarayanan - 2017 IEEE Real-Time Systems …, 2017 - ieeexplore.ieee.org
… T x ≤ bu}, we may only need to evaluate the range of the transformed zonotope a T Z, the
range has no intersection with [bl,bu] if and only if the zonotope has no intersection with the …
range has no intersection with [bl,bu] if and only if the zonotope has no intersection with the …
Set propagation techniques for reachability analysis
… An alternative to zonotope bundles are constrained zonotopes, which are computationally
more demanding, but operations on them are exact for Minkowski sum and convex hull [18]. …
more demanding, but operations on them are exact for Minkowski sum and convex hull [18]. …