Related papers: Determining Smallest Path Size of Multiplication T…
Pebble transducers are nested two-way transducers which can drop marks (named "pebbles") on their input word. Such machines can compute functions whose output size is polynomial in the size of their input. They can be seen as simple…
There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…
In many instances of fixed-point multiplication, a full precision result is not required. Instead it is sufficient to return a faithfully rounded result. Faithful rounding permits the machine representable number either immediately above or…
We present a pipelined multiplier with reduced activities and minimized interconnect based on online digit-serial arithmetic. The working precision has been truncated such that $p<n$ bits are used to compute $n$ bits product, resulting in…
We sometimes need to compute the most significant digits of the product of small integers with a multiplier requiring much storage: e.g., a large integer (e.g., $5^{100}$) or an irrational number ($\pi$). We only need to access the most…
This paper presents an approximate signed multiplier architecture that incorporates a sign-focused compressor, specifically designed for edge detection applications in machine learning and signal processing. The multiplier incorporates two…
Transformer-based large language models have achieved remarkable performance across various natural language processing tasks. However, they often struggle with seemingly easy tasks like arithmetic despite their vast capabilities. This…
Sequence-to-sequence models have achieved impressive results on various tasks. However, they are unsuitable for tasks that require incremental predictions to be made as more data arrives or tasks that have long input sequences and output…
Implementing a quantum circuit on specific hardware with a reduced available gate set is often associated with a substantial increase in the length of the equivalent circuit. This process is also known as transpilation and due to…
Algebraic matrix multiplication algorithms are designed by bounding the rank of matrix multiplication tensors, and then using a recursive method. However, designing algorithms in this way quickly leads to large constant factors: if one…
In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…
We study coded distributed matrix multiplication from an approximate recovery viewpoint. We consider a system of $P$ computation nodes where each node stores $1/m$ of each multiplicand via linear encoding. Our main result shows that the…
Automating string transformations has been one of the killer applications of program synthesis. Existing synthesizers that solve this problem produce programs in domain-specific languages (DSL) that are engineered to help the synthesizer,…
Convolutional Neural Networks have achieved unprecedented success in image classification, recognition, or detection applications. However, their large-scale deployment in embedded devices is still limited by the huge computational…
Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning…
Deep neural networks (DNNs) have achieved great breakthroughs in many fields such as image classification and natural language processing. However, the execution of DNNs needs to conduct massive numbers of multiply-accumulate (MAC)…
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…
This paper considers the problem of calculating the matrix multiplication of two massive matrices $\mathbf{A}$ and $\mathbf{B}$ distributedly. We provide a modulo technique that can be applied to coded distributed matrix multiplication…
Natural numbers which are nontrivial multiples of some permutation of their base-$b$ digit representations are called permutiples. Specific cases include numbers which are multiples of cyclic permutations (cyclic numbers) and reversals of…
We provide a spectrum of new theoretical insights and practical results for finding a Minimum Dilation Triangulation (MDT), a natural geometric optimization problem of considerable previous attention: Given a set $P$ of $n$ points in the…