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Convolutional networks are one of the most widely employed architectures in computer vision and machine learning. In order to leverage their ability to learn complex functions, large amounts of data are required for training. Training a…

This paper explores practical aspects of using a high-level functional language for GPU-based arithmetic on ``midsize'' integers. By this we mean integers of up to about a quarter million bits, which is sufficient for most practical…

Convolutional neural networks (CNNs) have a large number of variables and hence suffer from a complexity problem for their implementation. Different methods and techniques have developed to alleviate the problem of CNN's complexity, such as…

Recently we presented TTC, a domain-specific compiler for tensor transpositions. Despite the fact that the performance of the generated code is nearly optimal, due to its offline nature, TTC cannot be utilized in all the application codes…

GPU-based fast Fourier transform (FFT) is extremely important for scientific computing and signal processing. However, we find the inefficiency of existing FFT libraries and the absence of fault tolerance against soft error. To address…

We examine the performance profile of Convolutional Neural Network training on the current generation of NVIDIA Graphics Processing Units. We introduce two new Fast Fourier Transform convolution implementations: one based on NVIDIA's cuFFT…

With the slowing of Moore's Law, heterogeneous computing platforms such as Field Programmable Gate Arrays (FPGAs) have gained increasing interest for accelerating HPC workloads. In this work we present, to the best of our knowledge, the…

The 3D Discrete Fourier Transform (DFT) is a technique used to solve problems in disparate fields. Nowadays, the commonly adopted implementation of the 3D-DFT is derived from the Fast Fourier Transform (FFT) algorithm. However, evidence…

This paper evaluates the efficacy of recent commercial processing-in-memory (PIM) solutions to accelerate fast Fourier transform (FFT), an important primitive across several domains. Specifically, we observe that efficient implementations…

Parallel algorithms relying on synchronous parallelization libraries often experience adverse performance due to global synchronization barriers. Asynchronous many-task runtimes offer task futurization capabilities that minimize or remove…

Adapting pretrained large language models (LLMs) to various downstream tasks in tens or hundreds of human languages is computationally expensive. Parameter-efficient fine-tuning (PEFT) significantly reduces the adaptation cost, by tuning…

We consider the problem of transposing tensors of arbitrary dimension and describe TTC, an open source domain-specific parallel compiler. TTC generates optimized parallel C++/CUDA C code that achieves a significant fraction of the system's…

We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…

Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides the representational plasticity required for high-entropy knowledge injection, Low-Rank Adaptation (LoRA) can…

In this paper we demonstrate the methodology for parallelizing the computation of large one-dimensional discrete fast Fourier transforms (DFFTs) on multi-core Intel Xeon processors. DFFTs based on the recursive Cooley-Tukey method have to…

Mechanistic interpretability seeks to understand how Large Language Models (LLMs) represent and process information. Recent approaches based on dictionary learning and transcoders enable representing model computation in terms of sparse,…

Polynomial multiplication is a key algorithm underlying computer algebra systems (CAS) and its efficient implementation is crucial for the performance of CAS. In this paper we design and implement algorithms for polynomial multiplication…

Parameter-Efficient Fine-tuning (PEFT) facilitates the fine-tuning of Large Language Models (LLMs) under limited resources. However, the fine-tuning performance with PEFT on complex, knowledge-intensive tasks is limited due to the…

Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in error correction coding. Hence, reducing the computational complexities of DFTs is of great significance, especially for long DFTs as increasingly longer…

Large Language Models (LLMs) have showcased remarkable impacts across a wide spectrum of natural language processing tasks. Fine-tuning these pretrained models on downstream datasets provides further significant performance gains; however,…