Related papers: Improved stochastic rounding
Large-scale numerical computations make increasing use of low-precision (LP) floating point formats and mixed precision arithmetic, which can be enhanced by the technique of stochastic rounding (SR), that is, rounding an intermediate…
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…
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…
Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with high probability, unlike for standard…
Conventional stochastic rounding (CSR) is widely employed in the training of neural networks (NNs), showing promising training results even in low-precision computations. We introduce an improved stochastic rounding method, that is simple…
Stochastic rounding (SR) offers an alternative to the deterministic IEEE-754 floating-point rounding modes. In some applications such as PDEs, ODEs and neural networks, SR empirically improves the numerical behavior and convergence to…
Stochastic Rounding is a probabilistic rounding mode that is surprisingly effective in large-scale computations and low-precision arithmetic. Its random nature promotes error cancellation rather than error accumulation, resulting in slower…
Stochastic rounding (SR) is a probabilistic rounding mode that mitigates errors in large-scale numerical computations, especially when prone to stagnation effects. Beyond numerical analysis, SR has shown significant benefits in practical…
LLM training is resource-intensive. Quantized training improves computational and memory efficiency but introduces quantization noise, which can hinder convergence and degrade model accuracy. Stochastic Rounding (SR) has emerged as a…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
Stochastic computing has a long history as an alternative method of performing arithmetic on a computer. While it can be considered an unbiased estimator of real numbers, it has a variance and MSE on the order of $\Omega(\frac{1}{N})$. On…
When implementing the gradient descent method in low precision, the employment of stochastic rounding schemes helps to prevent stagnation of convergence caused by the vanishing gradient effect. Unbiased stochastic rounding yields zero bias…
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
The stochastic simulation algorithm (SSA) is widely used to perform exact forward simulation of discrete stochastic processes in biology. However, the computational cost, driven by sequential event-by-event sampling across large ensembles,…
The main objective of this work is to investigate non-linear errors and pairwise summation using stochastic rounding (SR) in variance computation algorithms. We estimate the forward error of computations under SR through two methods: the…
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…
The quality of numerical computations can be measured through their forward error, for which finding good error bounds is challenging in general. For several algorithms and using stochastic rounding (SR), probabilistic analysis has been…
When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study the influence of rounding errors on the convergence of the…
Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput and reduce energy consumption. As a growing number of…