Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the capabilities of neural networks in the symbolic AI domain, researchers have explored the ability of deep neural networks to learn mathematical constructions, such as addition and multiplication, logic inference, such as theorem provers, and even the execution of computer programs. The latter is known to be too complex a task for neural networks. Therefore, the results were not always successful, and often required the introduction of biased elements in the learning process, in addition to restricting the scope of possible programs to be executed. In this work, we will analyze the ability of neural networks to learn how to execute programs as a whole. To do so, we propose a different approach. Instead of using an imperative programming language, with complex structures, we use the Lambda Calculus ({\lambda}-Calculus), a simple, but Turing-Complete mathematical formalism, which serves as the basis for modern functional programming languages and is at the heart of computability theory. We will introduce the use of integrated neural learning and lambda calculi formalization. Finally, we explore execution of a program in {\lambda}-Calculus is based on reductions, we will show that it is enough to learn how to perform these reductions so that we can execute any program. Keywords: Machine Learning, Lambda Calculus, Neurosymbolic AI, Neural Networks, Transformer Model, Sequence-to-Sequence Models, Computational Models

翻译：在过去的几十年中，基于深度神经网络的模型已成为机器学习的主导范式。此外，人工神经网络在符号学习中的应用近年来日益受到关注。为研究神经网络在符号人工智能领域的能力，研究者探索了深度神经网络学习数学构造（如加法与乘法）、逻辑推理（如定理证明）乃至计算机程序执行的能力。其中，程序执行被认为对神经网络而言过于复杂，因此结果并非总是成功，且通常需要在学习过程中引入偏置元素，同时限制可执行程序的范围。在本工作中，我们将分析神经网络整体学习执行程序的能力。为此，我们提出一种不同的方法：不使用具有复杂结构的命令式编程语言，而采用λ演算——一种简单但图灵完备的数学形式体系，它是现代函数式编程语言的基础，并位于可计算性理论的核心。我们将引入集成神经学习与λ演算形式化的方法。最后，鉴于λ演算中的程序执行基于归约，我们将证明只需学习如何执行这些归约，便可执行任意程序。关键词：机器学习、λ演算、神经符号人工智能、神经网络、Transformer 模型、序列到序列模型、计算模型