Reasoning Papers

Alan Turing's 1936 paper defined computable numbers through an abstract machine, now called the Turing machine, and showed that no general method can decide whether any given mathematical statement is provable.

In 1950 Alan Turing replaced the question "Can machines think?" with the imitation game, now called the Turing test, and answered the main objections to machine intelligence one by one.

John McCarthy's 1959 paper proposing the advice taker, a program that would solve problems by manipulating sentences in formal languages and act when it deduced an imperative — an early statement of logical AI.

Marvin Minsky's 1961 survey in Proceedings of the IRE organized heuristic programming into five problem areas — search, pattern recognition, learning, planning and induction — and argued that machines would need to build models of their environments.

Richard Sutton's 1988 paper introduced temporal-difference learning, a family of incremental prediction methods that assign credit from changes between successive predictions and are shown to be more economical and accurate than conventional supervised approaches on most prediction problems.

A 2015 Nature paper by Mnih, Kavukcuoglu, Silver and colleagues showed that one deep Q-network agent, given only screen pixels and the game score, learned to play 49 Atari 2600 games at a level comparable to a professional human tester.

A 2016 paper by Barret Zoph and Quoc V. Le that uses a recurrent network trained with reinforcement learning to design neural network architectures automatically, matching human-designed models on CIFAR-10 and beating LSTM on Penn Treebank.

AlphaGo Zero learned Go only by playing against itself, starting from random play, and beat the earlier champion-defeating AlphaGo 100 games to 0 after three days of training. The Nature paper appeared in October 2017.

A 2019 paper by Francois Chollet that defines intelligence as skill-acquisition efficiency and introduces the Abstraction and Reasoning Corpus (ARC), a benchmark of grid tasks that assumes no specialised knowledge or language.

A benchmark released in 2020 that tests language models across 57 subjects, from elementary mathematics to law, and showed that even the largest models of the time were far from expert-level.

A 2021 paper showing that finetuning a language model on many tasks described by instructions — instruction tuning — makes it much better at unseen tasks without examples, surpassing a larger model on most benchmarks tested.

The DeepSeek-R1 report described how a reasoning model was trained largely with reinforcement learning, rewarding correct answers, and reached performance comparable to OpenAI's o1 on math, code and reasoning benchmarks. Its weights were released openly.

The Qwen3 Technical Report presents Alibaba's Qwen3 family of dense and mixture-of-experts language models, which unify thinking and non-thinking modes, add a controllable thinking budget, and are released under the Apache 2.0 licence.

A 2025 paper introducing ARC-AGI-2, a benchmark of input-output puzzle tasks built to measure abstract reasoning in frontier AI systems, with human testing as a baseline and a task set designed to give a more granular signal of progress.

The Gemini 2.5 technical report, submitted to arXiv on 7 July 2025, documents Google's Gemini 2.5 Pro and 2.5 Flash models: their reasoning, long-context video handling, and cost-versus-capability positioning.

Gerald Tesauro's 1992 paper tested whether temporal difference learning could master a complex real-world task, using self-play backgammon as the case study.

A 2013 paper by Mnih, Kavukcuoglu, Silver and colleagues showed a convolutional neural network trained with a Q-learning variant learning to play seven Atari 2600 games directly from raw pixels, beating prior methods on six and human experts on three.

A 2014 paper by Graves, Wayne and Danihelka that couples a neural network to an external memory it reads and writes through attention, making the whole machine differentiable and trainable by gradient descent.

The 2016 Nature paper describing AlphaGo, which combined deep neural networks with tree search. In October 2015 its distributed version beat the European Go champion Fan Hui 5-0, the first time a program defeated a professional player in full-sized Go without handicap.

MATH is a dataset of 12,500 challenging competition mathematics problems, each with a full step-by-step solution. Released in 2021, it was built to measure and train mathematical reasoning in models.

GSM8K is an OpenAI benchmark of 8.5K grade school math word problems, released with a paper showing that even the largest Transformer models scored poorly, and that training verifiers to select among many candidate solutions improved results.

A 2022 paper by Jason Wei and colleagues at Google Research showing that prompting a large language model with examples that include intermediate reasoning steps, rather than answers alone, substantially improves its performance on arithmetic, commonsense and symbolic reasoning tasks.

BIG-bench is a large community-built benchmark of 204 tasks designed to test language models on problems believed to lie beyond their current abilities, described in a paper posted in June 2022.

A 2022 paper arguing that some abilities of large language models appear only once models are large enough, and cannot be predicted by extrapolating from smaller models — so further scaling may keep widening what these models can do.

A March 2023 paper by Microsoft researchers testing an early GPT-4, arguing it shows strikingly general, near-human performance across many domains and could be seen as an early but incomplete step toward AGI.

GPQA is a benchmark of 448 expert-written multiple-choice questions in biology, physics and chemistry, built so that skilled non-experts cannot look the answers up, and hard enough that the strongest GPT-4 baseline scored 39% while domain experts reached 65%.

GAIA is a benchmark of real-world questions that are easy for humans but hard for AI assistants, testing reasoning, multimodality, web browsing, and tool use. It compares AI progress against average human performance.

MMLU-Pro is a 2024 benchmark that makes the widely used MMLU knowledge test harder: its questions are reasoning-focused and each has ten answer options instead of four.

FrontierMath is a benchmark of hundreds of original, unpublished mathematics problems written and vetted by expert mathematicians, introduced by Epoch AI to test advanced mathematical reasoning in AI. At release, state-of-the-art models solved under 2% of the problems.[^1][^2]

Humanity's Last Exam (HLE) is a 2,500-question, multi-modal benchmark spanning dozens of academic subjects, built by experts worldwide so that frontier language models can still be measured after saturating older tests.

A paper showing that a 32B model fine-tuned on 1,000 carefully chosen questions and run with a simple "budget forcing" trick can beat o1-preview on competition maths by up to 27%, with model, data and code released.

A 2025 paper proposing Absolute Zero, a reinforcement-learning paradigm in which one model writes its own code-reasoning tasks and then solves them, with a code executor as the only judge, reaching state of the art on coding and maths without external training data.

HellaSwag is a 2019 benchmark in which a machine must pick the most plausible continuation of a short event description. Its wrong answers are generated and filtered to fool models rather than people.