Related papers: A Compilation of Succinctness Results for Arithmet…

Approximate circuits trading the power consumption for the quality of results play a key role in the development of energy-aware systems. Designing complex approximate circuits is, however, a very difficult and computationally demanding…

We study several classes of general non-linear positive maps between C*-algebras, which are not necessary completely positive maps. We characterize the class of the compositions of *-multiplicative maps and positive linear mapsas the class…

Error-tolerant applications, such as multimedia processing, machine learning, signal processing, and scientific computing, can produce satisfactory outputs even when approximate computations are performed. Approximate computing (AxC) is…

In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast…

Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…

We study a notion of positivity of Gaussian directed acyclic graphical models corresponding to a non-negativity constraint on the coefficients of the associated structural equation model. We prove that this constraint is equivalent to the…

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…

We show that sharp thresholds for Boolean functions directly imply average-case circuit lower bounds. More formally we show that any Boolean function exhibiting a sharp enough threshold at \emph{arbitrary} critical density cannot be…

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for…

Strongly simulating a quantum circuit, that is, computing an output amplitude, amounts to summing the circuit's Feynman paths, a weighted count over assignments to the Boolean ``path'' variables. The circuit's gates induce correlations…

Zhang et al. (ICML 2021, PLMR 139, pp. 12447-1245) introduced probabilistic generating circuits (PGCs) as a probabilistic model to unify probabilistic circuits (PCs) and determinantal point processes (DPPs). At a first glance, PGCs store a…

This paper presents conservative probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach…

Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…

In this paper we systematically explore questions of succinctness in modal logics employed in spatial reasoning. We show that the closure operator, despite being less expressive, is exponentially more succinct than the limit-point operator,…

Analog-mixed-signal (AMS) circuits are highly non-linear and operate on continuous real-world signals, making them far more difficult to model with data-driven AI than digital blocks. To close the gap between structured design data (device…

Stochastic computing (SC) is an emerging computing technique which offers higher computational density, and lower power over binary-encoded (BE) computation. Unlike BE computation, SC encodes values as probabilistic bitstreams which makes…

Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever…

Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series…

Let $G$ be a finite, simple, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(\mathrm{diag}(\mathbf{d})-A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We…