Related papers: Rigorous Roundoff Error Analysis of Probabilistic …

Gappa uses interval arithmetic to certify bounds on mathematical expressions that involve rounded as well as exact operators. Gappa generates a theorem with its proof for each bound treated. The proof can be checked with a higher order…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the…

We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…

Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…

Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

Probabilistic programs often trade accuracy for efficiency, and thus may, with a small probability, return an incorrect result. It is important to obtain precise bounds for the probability of these errors, but existing verification…

This paper studies performative risk minimization, a formulation of stochastic optimization under decision-dependent distributions. We consider the general case where the performative risk can be non-convex, for which we develop efficient…

Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap…

There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given…

Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…

Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the \emph{message complexity} of distributed computing problems and its relationship (if any) with round complexity is still quite…

Polyak-Ruppert averaging is a widely used technique to achieve the optimal asymptotic variance of stochastic approximation (SA) algorithms, yet its high-probability performance guarantees remain underexplored in general settings. In this…

For probabilistic programs, it is usually not possible to automatically derive exact information about their properties, such as the distribution of states at a given program point. Instead, one can attempt to derive approximations, such as…

Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders.…

The upcoming IEEE-P3109 standard for low-precision floating-point arithmetic can become the foundation of future machine learning hardware and software. Unlike IEEE-754, P3109 introduces a parametric framework defined by bitwidth,…

Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…

Recently, stochastic rounding (SR) has been implemented in specialized hardware but most current computing nodes do not yet support this rounding mode. Several works empirically illustrate the benefit of stochastic rounding in various…

Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…