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A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
Owing to their low-complexity iterations, Frank-Wolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity…
The mean field (MF) theory of multilayer neural networks centers around a particular infinite-width scaling, where the learning dynamics is closely tracked by the MF limit. A random fluctuation around this infinite-width limit is expected…
Floating-point data is widely used across various domains. Depending on the required precision, each floating-point value can occupy several bytes. Lossless storage of this information is crucial due to its critical accuracy, as seen in…
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of…
Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits.…
Large Language Models (LLMs) are powerful but incur high memory and computation costs. Quantization is an effective solution, with INT weights and FP activations being widely adopted to preserve accuracy. Prior works further reduce FP…
We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)] for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments suggest that our bounds are fairly robust to changing block…
In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…
Quantized Neural Networks (QNNs) use low bit-width fixed-point numbers for representing weight parameters and activations, and are often used in real-world applications due to their saving of computation resources and reproducibility of…
A mixed precision Fast Fourier transform (FFT) implementation is presented. The procedure uses per-block microscaling (MX), a global power-of-two prescale, and prequantized low bit twiddles. We evaluate forward and round-trip FFT fidelity…
Intra prediction is an essential component in the image coding. This paper gives an intra prediction framework completely based on neural network modes (NM). Each NM can be regarded as a regression from the neighboring reference blocks to…
The progress in neuromorphic computing is fueled by the development of novel nonvolatile memories capable of storing analog information and implementing neural computation efficiently. However, like most other analog circuits, these devices…
The construction of topological error correction codes requires the ability to fabricate a lattice of physical qubits embedded on a manifold with a non-trivial topology such that the quantum information is encoded in the global degrees of…
With the advancement of blockchain technology, chained Byzantine Fault Tolerant (BFT) protocols have been increasingly adopted in practical systems, making their performance a crucial aspect of the study. In this paper, we introduce a…
The increasing demand for energy-efficient solutions has led to the emergence of an approximate computing paradigm that enables power-efficient implementations in various application areas such as image and data processing. The median…
In this paper we comprehensively investigate block-wise product (BWP) BCH codes, wherein raw data is arranged in the form of block-wise matrix and each row and column BCH codes intersect on one data block. We first devise efficient BCH…
Understanding the three-dimensional motion of bubbles is essential for interpreting transport and mixing in multiphase flows, especially when bubbles deform under shear or move rapidly through the flow field. In many laboratory setups, only…
Edge devices are being deployed at increasing volumes to sense and act on information from the physical world. The discrete Fourier transform (DFT) is often necessary to make this sensed data suitable for further processing -- such as by…
The finite field multiplier is mainly used in many of today's state of the art digital systems and its hardware implementation for bit parallel operation may require millions of logic gates. Natural causes or soft errors in digital design…