Related papers: Computing in matrix groups without memory
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
MemComputing is a new model of computation that exploits the non-equilibrium property-we call 'memory'-of any physical system to respond to external perturbations by keeping track of how it has reacted at previous times. Its digital,…
The rapid advancement of deep neural networks has significantly improved various tasks, such as image and speech recognition. However, as the complexity of these models increases, so does the computational cost and the number of parameters,…
Critical aspects of computational imaging systems, such as experimental design and image priors, can be optimized through deep networks formed by the unrolled iterations of classical model-based reconstructions (termed physics-based…
In this paper, we investigate the complexity of computing minimal faithful permutation representations for groups without abelian normal subgroups (a.k.a. Fitting-free groups). When our groups are given as quotients of permutation groups,…
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…
Incremental learning enables artificial agents to learn from sequential data. While important progress was made by exploiting deep neural networks, incremental learning remains very challenging. This is particularly the case when no memory…
This paper introduces the Modular Neural Computer (MNC), a memory-augmented neural architecture for exact algorithmic computation on variable-length inputs. The model combines an external associative memory of scalar cells, explicit read…
Memcomputing is a novel paradigm of computation that utilizes dynamical elements with memory to both store and process information on the same physical location. Its building blocks can be fabricated in hardware with standard electronic…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
From logical reasoning to mental simulation, biological and artificial neural systems possess an incredible capacity for computation. Such neural computers offer a fundamentally novel computing paradigm by representing data continuously and…
We introduce the Fast Free Memory method (FFM), a new fast method for the numerical evaluation of convolution products. Inheriting from the Fast Multipole Method, the FFM is a descent-only and kernel-independent algorithm. We give the…
Memories are stored, retained, and recollected through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions we construct a broad class of…
We propose a method that meta-learns a knowledge on matrix factorization from various matrices, and uses the knowledge for factorizing unseen matrices. The proposed method uses a neural network that takes a matrix as input, and generates…
Computer architecture is searching for new ways to make use of increasingly available digital logic without the serial bottlenecks of CPU-based design. Recent work has demonstrated a fully CPU-less approach to executing functional programs,…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
Reservoir Computing is a type of recursive neural network commonly used for recognizing and predicting spatio-temporal events relying on a complex hierarchy of nested feedback loops to generate a memory functionality. The Reservoir…
This paper addresses spatial programming of sparse matrix computations for productive performance. The challenge is how to express an irregular computation and its optimizations in a regular way. A sparse matrix has (non-zero) values and a…