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From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…

In this paper, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized…

Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…

This paper introduces an incremental training framework for compressing popular Deep Neural Network (DNN) based unfolded multiple-input-multiple-output (MIMO) detection algorithms like DetNet. The idea of incremental training is explored to…

Convolutional neural networks have recently achieved significant breakthroughs in various image classification tasks. However, they are computationally expensive,which can make their feasible mplementation on embedded and low-power devices…

Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…

The (asymptotic) complexity of matrix multiplication (over the complex field) is measured by a real parameter w > 0, called the exponent of matrix multiplication (over the complex field), which is defined to be the smallest real number w >…

Prompting methods recently achieve impressive success in few-shot learning. These methods modify input samples with prompt sentence pieces, and decode label tokens to map samples to corresponding labels. However, such a paradigm is very…

Clinical note classification is a common clinical NLP task. However, annotated data-sets are scarse. Prompt-based learning has recently emerged as an effective method to adapt pre-trained models for text classification using only few…

In recent work, Lemire (2021) presented a fast algorithm to convert number strings into binary floating-point numbers. The algorithm has been adopted by several important systems: e.g., it is part of the runtime libraries of GCC 12, Rust…

Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput…

There is a growing interest in the use of reduced-precision arithmetic, exacerbated by the recent interest in artificial intelligence, especially with deep learning. Most architectures already provide reduced-precision capabilities (e.g.,…

Transformers, central to the successes in modern Natural Language Processing, often falter on arithmetic tasks despite their vast capabilities --which paradoxically include remarkable coding abilities. We observe that a crucial challenge is…

In this paper, we propose an improved iterative method for solving the monotone inclusion problem in the form of $0 \in Ax + Dx + N_{C}(x)$ in real Hilbert space, where $A$ is a maximally monotone operator, $D$ and $B$ are monotone and…

The widespread adoption of machine learning algorithms necessitates hardware acceleration to ensure efficient performance. This acceleration relies on custom matrix engines that operate on full or reduced-precision floating-point…

Matrix-matrix multiplication is a key computational kernel for numerous applications in science and engineering, with ample parallelism and data locality that lends itself well to high-performance implementations. Many matrix…

Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes whose coefficients are restricted to the set $\{-1, 0, 1\}$…

Estimating ego-pose from cameras is an important problem in robotics with applications ranging from mobile robotics to augmented reality. While SOTA models are becoming increasingly accurate, they can still be unwieldy due to high…

We propose in this paper a new coding scheme called twisted-pair superposition transmission (TPST). The encoding is to "mix together" a pair of basic codes by superposition, while the decoding can be implemented as a successive cancellation…

We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…