Related papers: Supersimulators
The number of quantifiers needed to express first-order (FO) properties is captured by two-player combinatorial games called multi-structural games. We analyze these games on binary strings with an ordering relation, using a technique we…
We prove bounds for the approximation and estimation of certain binary classification functions using ReLU neural networks. Our estimation bounds provide a priori performance guarantees for empirical risk minimization using networks of a…
The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high…
Learned representations in deep reinforcement learning (DRL) have to extract task-relevant information from complex observations, balancing between robustness to distraction and informativeness to the policy. Such stable and rich…
Deterministic models are approximations of reality that are easy to interpret and often easier to build than stochastic alternatives. Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic…
This work initiates the systematic study of explicit distributions that are indistinguishable from a single exponential-size combinatorial object. In this we extend the work of Goldreich, Goldwasser and Nussboim (SICOMP 2010) that focused…
Many parallel and distributed computing research results are obtained in simulation, using simulators that mimic real-world executions on some target system. Each such simulator is configured by picking values for parameters that define the…
We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for…
We study the learnability of linear separators in $\Re^d$ in the presence of bounded (a.k.a Massart) noise. This is a realistic generalization of the random classification noise model, where the adversary can flip each example $x$ with…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves the convexity of the random multifunction. We provide several…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…
The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples…
A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…