Related papers: Mathematical reasoning and the computer

To reduce the need for human annotations, large language models (LLMs) have been proposed as judges of the quality of other candidate models. The performance of LLM judges is typically evaluated by measuring the correlation with human…

Quantum computers can in principle solve certain problems exponentially more quickly than their classical counterparts. We have not yet reached the advent of useful quantum computation, but when we do, it will affect nearly all scientific…

We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…

This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…

Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…

Generative AI techniques have opened the path for new generations of machines in diverse domains. These machines have various capabilities for example, they can produce images, generate answers or stories, and write codes based on the…

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open…

Recent advancements in Large Language Models (LLMs) have demonstrated remarkable capabilities in various domains. However, effective decision-making relies heavily on strong reasoning abilities. Reasoning is the foundation for…

Machines are being increasingly used in decision-making processes, resulting in the realization that decisions need explanations. Unfortunately, an increasing number of these deployed models are of a 'black-box' nature where the reasoning…

Large language models (LLMs) with billions of parameters exhibit in-context learning abilities, enabling few-shot learning on tasks that the model was not specifically trained for. Traditional models achieve breakthrough performance on…

Neural networks are among the most accurate supervised learning methods in use today. However, their opacity makes them difficult to trust in critical applications, especially when conditions in training may differ from those in practice.…

Recent advancements in Large Language Models (LLMs) have showcased striking results on existing logical reasoning benchmarks, with some models even surpassing human performance. However, the true depth of their competencies and robustness…

What is reasoning? This question has driven centuries of philosophical inquiry, from Aristotle's syllogisms to modern computational complexity theory. In the age of large language models achieving superhuman performance on benchmarks like…

This article aims to demonstrate how the approach to computing is being disrupted by deep learning (artificial neural networks), not only in terms of techniques but also in our interactions with machines. It also addresses the philosophical…

Recent advances have greatly increased the capabilities of large language models (LLMs), but our understanding of the models and their safety has not progressed as fast. In this paper we aim to understand LLMs deeper by studying their…

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…

The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics…

In large language models (LLMs), code and reasoning reinforce each other: code offers an abstract, modular, and logic-driven structure that supports reasoning, while reasoning translates high-level goals into smaller, executable steps that…

Learning representations of algorithms is an emerging area of machine learning, seeking to bridge concepts from neural networks with classical algorithms. Several important works have investigated whether neural networks can effectively…

Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…