Related papers: Computing in matrix groups without memory
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
This paper introduces a special type of systems, defines their properties, and then demonstrates that a reduction machine for pure untyped extensional lambda calculus can be implemented as a system of the introduced type. Specifically, we…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the…
Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization,…
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
Sorting is a fundamental operation across numerous computational domains. Traditionally, this process involves transferring data from main memory to a processing unit for sorting, followed by writing the sorted data back to memory. This…
RRAM-based in-Memory Computing is an exciting road for implementing highly energy efficient neural networks. This vision is however challenged by RRAM variability, as the efficient implementation of in-memory computing does not allow error…
Scientific computing requires handling large linear models, which are often composed of structured matrices. With increasing model size, dense representations quickly become infeasible to compute or store. Matrix-free implementations are…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…
A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the very same error rate as the optimal (programmable) discrimination machine for any size of…
The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
The greatest demand for today's computing is machine learning. This paper analyzes three machine learning algorithms: transformers, spatial convolution, and FFT. The analysis is novel in three aspects. First, it measures the cost of memory…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
Memory-centric computing aims to enable computation capability in and near all places where data is generated and stored. As such, it can greatly reduce the large negative performance and energy impact of data access and data movement, by…
Matrix multiplication is the dominant computation during Machine Learning (ML) inference. To efficiently perform such multiplication operations, Compute-in-memory (CiM) paradigms have emerged as a highly energy efficient solution. However,…