Related papers: Reductions in local certification
We study the problem of computing weighted sum-of-squares (WSOS) certificates for positive polynomials over a compact semialgebraic set. Building on the theory of interior-point methods for convex optimization, we introduce the concept of…
We revisit facial reduction from the point of view of projective geometry. This leads us to a homogenization strategy in conic programming that eliminates the phenomenon of weak infeasibility. For semidefinite programs (and others), this…
We consider three classification systems for distributed decision tasks: With unbounded computation and certificates, defined by Balliu, D'Angelo, Fraigniaud, and Olivetti [JCSS'18], and with (two flavors of) polynomially bounded local…
In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and…
While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are…
Finite-State Dynamics (FSD) is one of the simplest and constrained distributed systems. An FSD is defined by an $n$-node network, with each node maintaining an internal state selected from a finite set. At each time-step, these nodes…
Neural network verification mainly focuses on local robustness properties, which can be checked by bounding the image (set of outputs) of a given input set. However, often it is important to know whether a given property holds globally for…
We introduce lower-bound certificates for classical planning tasks, which can be used to prove the unsolvability of a task or the optimality of a plan in a way that can be verified by an independent third party. We describe a general…
In this paper, we initiate a systematic study of graph resilience. The (local) resilience of a graph G with respect to a property P measures how much one has to change G (locally) in order to destroy P. Estimating the resilience leads to…
Currently the most popular method of providing robustness certificates is randomized smoothing where an input is smoothed via some probability distribution. We propose a novel approach to randomized smoothing over multiplicative parameters.…
Randomized smoothing is the dominant standard for provable defenses against adversarial examples. Nevertheless, this method has recently been proven to suffer from important information theoretic limitations. In this paper, we argue that…
In this work, we provide an upper bound for global certification of graph homomorphism, a generalization of graph coloring. In certification, the nodes of a network should decide if the network satisfies a given property, thanks to small…
Extensive efforts have been made to understand and improve the fairness of machine learning models based on observational metrics, especially in high-stakes domains such as medical insurance, education, and hiring decisions. However, there…
In response to subtle adversarial examples flipping classifications of neural network models, recent research has promoted certified robustness as a solution. There, invariance of predictions to all norm-bounded attacks is achieved through…
We present a new combinatorial characterization for local optimality of a codeword in an irregular Tanner code. The main novelty in this characterization is that it is based on a linear combination of subtrees in the computation trees.…
In safety-critical applications that rely on the solution of an optimization problem, the certification of the optimization algorithm is of vital importance. Certification and suboptimality results are available for a wide range of…
In many statistical applications, the dimension is too large to handle for standard high-dimensional machine learning procedures. This is particularly true for graphical models, where the interpretation of a large graph is difficult and…
Certified defenses promise provable robustness guarantees. We study the malicious exploitation of probabilistic certification frameworks to better understand the limits of guarantee provisions. Now, the objective is to not only mislead a…
A low-degree test is a collection of simple, local rules for checking the proximity of an arbitrary function to a low-degree polynomial. Each rule depends on the function's values at a small number of places. If a function satisfies many…
We study the question of local testability of low (constant) degree functions from a product domain $S_1 \times \dots \times {S}_n$ to a field $\mathbb{F}$, where ${S_i} \subseteq \mathbb{F}$ can be arbitrary constant sized sets. We show…