Related papers: Information-Theoretic Limits of Safety Verificatio…
This paper presents a novel approach for augmenting proof-based verification with performance-style analysis of the kind employed in state-of-the-art model checking tools for probabilistic systems. Quantitative safety properties usually…
We prove a fundamental impossibility theorem: neural networks cannot simultaneously learn well-calibrated confidence estimates with meaningful diversity when trained using binary correct/incorrect supervision. Through rigorous mathematical…
In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$…
Control barrier functions for port-Hamiltonian systems inherit model uncertainty when the Hamiltonian is learned from data. We show how to propagate this uncertainty into a safety filter with independently tunable credibility budgets. To…
For a class of systems of semi-linear elliptic equations, including \[ -\Delta u_i=f_i(x,u_i) - \beta u_i\sum_{j\neq i}a_{ij}u_j^p,\qquad i=1,\dots,k, \] for $p=2$ (variational-type interaction) or $p = 1$ (symmetric-type interaction), we…
Random reversible and quantum circuits form random walks on the alternating group $\mathrm{Alt}(2^n)$ and unitary group $\mathrm{SU}(2^n)$, respectively. Known bounds on the spectral gap for the $t$-th moment of these random walks have…
In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for…
We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…
Many control problems in environments that can be modeled as Markov decision processes (MDPs) concern infinite-time horizon specifications. The classical aim in this context is to compute a control policy that maximizes the probability of…
We investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we prove that sensitivity relations plus the…
We study the repeated optimal stopping problem, in which the same optimal stopping instance with an unknown distribution is solved repeatedly over $T$ rounds. We aim to simultaneously achieve strong per-round performance guarantees relative…
We present the framework of delta-complete analysis for bounded reachability problems of general hybrid systems. We perform bounded reachability checking through solving delta-decision problems over the reals. The techniques take into…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
We consider a dynamic programming problem with arbitrary state space and bounded rewards. Is it possible to define in an unique way a limit value for the problem, where the "patience" of the decision-maker tends to infinity ? We consider,…
Infinite networks are complex interconnected systems comprising a countably infinite number of subsystems, for which no fixed upper bound on the number of participating subsystems is specified a priori since it may vary over time as agents…
We introduce a simple single-system game inspired by the Clauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitary gates and projective measurements, we prove that any strategy in our game can be mapped to a strategy in…
Prior work of Beverland et al. has shown that any exact Clifford+$T$ implementation of the $n$-qubit Toffoli gate must use at least $n$ $T$ gates. Here we show how to get away with exponentially fewer $T$ gates, at the cost of incurring a…
Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts…
We report on intermediate results of -- to the best of our knowledge -- the first study of completeness thresholds for (partially) bounded memory safety proofs. Specifically, we consider heap-manipulating programs that iterate over arrays…
The information metric provides a unique notion of distance along any continuous family of physical theories, placing two theories further apart the more distinguishable they are. As such, the information metric is typically singular at…