Related papers: Uniform Memory and Serialization for Lambda Calcul…
This paper introduces a new machine architecture for evaluating lambda expressions using the normal-order reduction, which guarantees that every lambda expression will be evaluated if the expression has its normal form and the system has…
Memory-augmented neural networks consisting of a neural controller and an external memory have shown potentials in long-term sequential learning. Current RAM-like memory models maintain memory accessing every timesteps, thus they do not…
We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of…
This paper proposes new mathematical models of the untyped Lambda-mu calculus. One is called the stream model, which is an extension of the lambda model, in which each term is interpreted as a function from streams to individual data. The…
We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location.…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs…
Memory emerges as the core module in the large language model (LLM)-based agents for long-horizon complex tasks (e.g., multi-turn dialogue, game playing, scientific discovery), where memory can enable knowledge accumulation, iterative…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
Race logic, an arrival-time-coded logic family, has demonstrated energy and performance improvements for applications ranging from dynamic programming to machine learning. However, the ad hoc mappings of algorithms into hardware result in…
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…
In this paper we address the question of how to render sequence-level networks better at handling structured input. We propose a machine reading simulator which processes text incrementally from left to right and performs shallow reasoning…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the…
We present a study on the integration of Large Language Models (LLMs) in tabular data classification, emphasizing an efficient framework. Building upon existing work done in TabLLM (arXiv:2210.10723), we introduce three novel serialization…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…