Related papers: On Approximate 8-bit Floating-Point Operations Usi…
Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum…
As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data…
If the non-zero finite floating-point numbers are interpreted as point intervals, then the effect of rounding can be interpreted as computing one of the bounds of the result according to interval arithmetic. We give an interval…
Quantized low-precision neural networks are very popular because they require less computational resources for inference and can provide high performance, which is vital for real-time and embedded recognition systems. However, their…
A new technique is proposed for fault-tolerant linear, sesquilinear and bijective (LSB) operations on $M$ integer data streams ($M\geq3$), such as: scaling, additions/subtractions, inner or outer vector products, permutations and…
It is well known that the computation of accurate trajectories of the Lorenz system is a difficult problem. Computed solutions are very sensitive to the discretization error determined by the time step size and polynomial order of the…
Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations which act on a superposition of inputs. These have to be compiled to a…
As large language models (LLMs) grow in parameter size and context length, computation precision has been reduced from 16-bit to 4-bit to improve inference efficiency. However, this reduction causes accuracy degradation due to activation…
Invertible logic can operate in one of two modes: 1) a forward mode, in which inputs are presented and a single, correct output is produced, and 2) a reverse mode, in which the output is fixed and the inputs take on values consistent with…
Transformers have significantly advanced AI and machine learning through their powerful attention mechanism. However, computing attention on long sequences can become a computational bottleneck. FlashAttention mitigates this by fusing the…
Multipliers are widely-used arithmetic operators in digital signal processing and machine learning circuits. Due to their relatively high complexity, they can have high latency and be a significant source of power consumption. One strategy…
Neural network quantization is a promising compression technique to reduce memory footprint and save energy consumption, potentially leading to real-time inference. However, there is a performance gap between quantized and full-precision…
Robustness problems due to the substitution of the exact computation on real numbers by the rounded floating point arithmetic are often an obstacle to obtain practical implementation of geometric algorithms. If the adoption of the --exact…
Accurate simulations of various physical processes on digital computers requires huge computing performance, therefore accelerating these scientific and engineering applications has a great importance. Density of programmable logic devices…
Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be…
Motivated by the increasing interest in the posit numeric format, in this paper we evaluate the accuracy and efficiency of posit arithmetic in contrast to the traditional IEEE 754 32-bit floating-point (FP32) arithmetic. We first design and…
The Compute-and-Forward protocol in quasi-static channels normally employs lattice codes based on the rational integers $\mathbb{Z}$, Gaussian integers $\mathbb{Z}\left[i\right]$ or Eisenstein integers $\mathbb{Z}\left[\omega\right]$, while…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…