Related papers: Uniform Memory and Serialization for Lambda Calcul…
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in this domain are typically large, with rows and columns…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Classifying the training data correctly without over-fitting is one of the goals in machine learning. In this paper, we propose a generalization-memorization mechanism, including a generalization-memorization decision and a memory modeling…
We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches…
We show that transformer-based large language models are computationally universal when augmented with an external memory. Any deterministic language model that conditions on strings of bounded length is equivalent to a finite automaton,…
We present the type system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
Computations, where the number of results is much smaller than the input data and are produced through some sort of accumulation, are called Reductions. Reductions appear in many scientific applications. Usually, reductions admit an…
Machine learning promises methods that generalize well from finite labeled data. However, the brittleness of existing neural net approaches is revealed by notable failures, such as the existence of adversarial examples that are…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term…
Memory consistency models have been developed to specify what values may be returned by a read given that, in a distributed system, memory operations may only be partially ordered. Before this work, consistency models were defined…
The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that…
Transformer models gain popularity because of their superior inference accuracy and inference throughput. However, the transformer is computation-intensive, causing a long inference time. The existing works on transformer inference…
Neural Turing Machines (NTM) contain memory component that simulates "working memory" in the brain to store and retrieve information to ease simple algorithms learning. So far, only linearly organized memory is proposed, and during…
In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of…
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…
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…
Reservoir computing is a versatile paradigm in computational neuroscience and machine learning, that exploits the non-linear dynamics of a dynamical system - the reservoir - to efficiently process time-dependent information. Since its…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
Attention mechanism is a significant part of Transformer models. It helps extract features from embedded vectors by adding global information and its expressivity has been proved to be powerful. Nevertheless, the quadratic complexity…
This paper shows that the recent approach to quantitative typing systems for programming languages can be extended to pattern matching features. Indeed, we define two resource aware type systems, named U and E, for a lambda-calculus…