Related papers: Mathematical reasoning and the computer

``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words…

Code has become a standard component of modern foundation language model (LM) training, yet its role beyond programming remains unclear. We revisit the claim that code improves reasoning through controlled pretraining experiments on a…

Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical…

Mastering one or more programming languages has historically been the gateway to implementing ideas on a computer. Today, that gateway is widening with advances in large language models (LLMs) and artificial intelligence (AI)-powered coding…

The potential for Large Language Models (LLMs) to generate new information offers a potential step change for research and innovation. This is challenging to assert as it can be difficult to determine what an LLM has previously seen during…

Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the province of humans. As these tools become…

In the last year or so and going back many decades there has been extensive claims by major computational scientists, engineers, and others that AGI, artificial general intelligence, is five or ten years away, but without a scintilla of…

Rapid progress in machine learning for natural language processing has the potential to transform debates about how humans learn language. However, the learning environments and biases of current artificial learners and humans diverge in…

What might sound like the beginning of a joke has become an attractive prospect for many cognitive scientists: the use of deep neural network models (DNNs) as models of human behavior in perceptual and cognitive tasks. Although DNNs have…

Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…

This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by…

Some of the strongest evidence that human minds should be thought about in terms of symbolic systems has been the way they combine ideas, produce novelty, and learn quickly. We argue that modern neural networks -- and the artificial…

Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…

Recent artificial neural networks that process natural language achieve unprecedented performance in tasks requiring sentence-level understanding. As such, they could be interesting models of the integration of linguistic information in the…

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…

A recent normative turn in computer science has brought concerns about fairness, bias, and accountability to the core of the field. Yet recent scholarship has warned that much of this technical work treats problematic features of the status…

This paper investigates the ability of large language models (LLMs) to solve statistical tasks, as well as their capacity to assess the quality of reasoning. While state-of-the-art LLMs have demonstrated remarkable performance in a range of…

While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of…