Reasoning

Alan Turing (1912–1954) was a British mathematician whose 1936 paper defined computation with an abstract machine. His 1950 paper proposed the imitation game, now called the Turing test, and he is counted among the founders of artificial intelligence.

John McCarthy (1927–2011) was an American computer scientist. His 1955 proposal is credited with coining the term “artificial intelligence”, he organised the 1956 Dartmouth workshop, and he created the LISP programming language.

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 London-headquartered AI research organisation formed in 2023 by merging DeepMind with Google's Brain team, known for AlphaGo, AlphaFold and the Gemini model family.

IBM Watson is a question-answering computer system built by an IBM research team led by David Ferrucci; in February 2011 it defeated the two foremost all-time champions of the televised quiz show Jeopardy!

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.

AlphaGo is a Go-playing program from DeepMind that combined deep neural networks with Monte Carlo tree search. In 2016 it beat top professional Lee Sedol in a widely watched match, a landmark for learned systems.

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.

Chain of thought is the technique of having a language model write out its intermediate reasoning before answering. Reasoning models extend it by training the model with reinforcement learning to think at length before responding.

DeepSeek is a Chinese AI company founded in Hangzhou in July 2023 as a spin-off of the AGI research lab of High-Flyer, a hedge fund. It releases its main models with open weights.

Claude 3 Opus, announced on 4 March 2024, was the most capable model in the Claude 3 family. It added vision and launched with a 200K-token context window and a Needle In A Haystack recall above 99%.

OpenAI o1 is the first reasoning model series from OpenAI, introduced in September 2024. It thinks through a long internal chain of thought before answering, and it was the base for later reasoning models such as o3.

TPU7x (Ironwood) is Google's seventh-generation TPU: 192 GB of high-bandwidth memory per chip, FP8 matrix units, 9,216 chips per pod, and a programming model that exposes two devices per chip.

DeepSeek-R1 is an open-weight reasoning model that DeepSeek released on 20 January 2025. Built on DeepSeek-V3-Base and trained with reinforcement learning, it is released under the MIT License, which allows commercial use and distillation.

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.

A rack-scale NVIDIA system announced in March 2025 that links 72 Blackwell Ultra GPUs and 36 Grace CPUs into one unit, rated at 1.5 times the AI performance of GB200 NVL72.

Gemini 2.5 Pro is Google's first model in the Gemini 2.5 family, released in March 2025 as a "thinking model" with a 1-million-token context window, debuting at number one on LMArena.

OpenAI's second-generation reasoning model, announced in December 2024 and released in April 2025, which posted large gains over o1 on science, software-engineering and competitive-programming benchmarks before being succeeded by GPT-5.

Qwen3 is a family of large language models from Alibaba, released on 29 April 2025 under Apache 2.0. Its main feature is hybrid thinking, which lets one model reason step by step or answer directly.

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.

GPT-5 is OpenAI's fifth GPT foundation model, released on 7 August 2025. It pairs a fast model with a deeper reasoning model and a router that chooses between them for each request.

Gemini 3 Pro is the first model of Google's Gemini 3 generation, released in preview in November 2025 with a 1-million-token context window and top-ranked results on arena leaderboards and reasoning, coding and multimodal benchmarks.

AWS Trainium3 is AWS's first 3-nanometer AI chip, delivering 2.52 petaflops of FP8 compute per chip and scaling to 144 chips in a Trn3 UltraServer, available through Amazon EC2 from December 2025.[^1][^2]

Claude Mythos Preview, announced on 7 April 2026, is an unreleased frontier model that Anthropic made available only to restricted partners through Project Glasswing, a programme for securing critical software.

DeepSeek-V4, released in preview on 24 April 2026, comprises V4-Pro and V4-Flash, two open mixture-of-experts models with a 1M-token context. Its architecture targets long-context efficiency, and its later releases extended the series with agent upgrades and multimodal input.

K2 Horizon is a family of six open language models from the Institute of Foundation Models, released in September 2026 with weights, code, training data and recipes under the Apache 2.0 licence.

GPT-6 is OpenAI's sixth-generation model family, launched from 3 September 2026 with GPT-6 Astra, followed by Sol, Luna and Instant. Astra was the first OpenAI model to reach its internal critical cybersecurity threshold.

Gemini 4 Argon is the first model in Google's Gemini 4 family, announced on 30 September 2026 and made generally available on 13 October 2026, built for long multi-step work and shipped with a one-million-token output limit.

Jais-3-375B-A23B is an open-weight Arabic-focused mixture-of-experts model from the Institute of Foundation Models: 375 billion parameters stored, 23 billion active per token, a 512,000-token context window and Apache 2.0 weights.

AGI is the goal of AI systems that match or beat humans across a broad range of tasks. The term has no agreed definition; a framework by Morris et al. grades systems by performance level and generality.

Herbert A. Simon (1916–2001) was a political scientist, psychologist and computer scientist who, with Allen Newell and J. C. Shaw, built the first successful AI program and later received the Nobel Prize in Economics.

American computer scientist and psychologist who, with Herbert A. Simon and J. C. Shaw, built the first list-processing language and the earliest heuristic problem-solving programs, treating thought as computation.

Judea Pearl is a computer scientist and statistician who invented Bayesian networks and their main inference algorithms, and later built a mathematical framework for causal inference from data. He received the 2011 ACM Turing Award.

British computer scientist born in 1976 who specialises in reinforcement learning. He led DeepMind's AlphaGo project, co-authored the 2013 deep Q-network paper and later founded Ineffable Intelligence.

Liang Wenfeng is a Chinese entrepreneur who co-founded the quantitative hedge fund High-Flyer and founded the AI company DeepSeek in 2023. He is the corresponding author of the DeepSeek-R1 paper published in Nature in 2025.

American AI researcher who co-founded OpenAI, led its reinforcement-learning team and helped develop the training methods behind ChatGPT; he later moved to Anthropic and then became chief scientist of Thinking Machines Lab.

Jakub Pachocki is OpenAI's chief scientist. He joined the company in 2017, led work on GPT-4 and OpenAI Five, and helped refocus its research on scaling deep learning systems.

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.

A DeepMind Go program that learned the game from scratch by playing against itself, using no human game records, and beat earlier versions of AlphaGo within days.

AlphaZero is a general game-playing system from DeepMind, described in a preprint in December 2017, that reached a superhuman level in chess, shogi and Go within 24 hours starting from random play, using only the rules of each game.

AlphaStar is a DeepMind system that plays StarCraft II. In 2019 it reached Grandmaster level with all three races, ranking above 99.8% of active players on Battle.net.

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.

PaLM is a 540-billion-parameter dense Transformer language model announced by Google Research in April 2022, trained with the Pathways system across 6,144 TPU v4 chips; it set strong few-shot results on many benchmarks.

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.

xAI is an AI company founded by Elon Musk that builds the Grok models and chatbot. It was acquired by SpaceX in 2026 and has since been renamed SpaceXAI and then SpaceXSI.

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.

FunSearch is a method that uses a pretrained large language model inside an evolutionary loop to search for programs that solve mathematical and computational problems, rather than for answers directly. It produced new results on the cap set problem and on online bin packing.

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.

Test-time compute is the computation a model spends while answering a prompt, beyond what training already fixed into its weights. A 2024 study by Snell et al. showed how to spend it adaptively, and how it can stand in for a bigger model.

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]

Phi-4 is Microsoft's 14-billion-parameter dense decoder-only language model, built with a data-quality-first recipe heavy on synthetic data and released with full weights under the MIT licence in January 2025.

iFlytek Spark X1 is a Chinese deep-reasoning model released in January 2025 and trained entirely on domestic computing hardware, with later upgrades benchmarked against OpenAI's reasoning models.

Kimi k1.5 is a multimodal reasoning model released by Moonshot AI on 20 January 2025, which the company said matched OpenAI's o1 in mathematics, coding and multimodal reasoning and which was trained with reinforcement learning rather than tree search or process reward models.

Operator is an AI agent OpenAI released on 23 January 2025 that works in a web browser by looking at screenshots and using a mouse and keyboard. Its abilities were folded into ChatGPT agent in July 2025.

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.

OpenAI's small reasoning model released on 31 January 2025, offered to all ChatGPT users including the free tier, with three reasoning-effort levels and developer features such as function calling and Structured Outputs; succeeded by o4-mini in April 2025.

Deep research is a research agent in ChatGPT, released by OpenAI on 2 February 2025 and built on a version of o3, that searches the web and turns many sources into a written report.

Grok 3 and the cheaper Grok 3 mini are xAI's reasoning models from February 2025. Grok 3 added a Think mode, a 1-million-token context window and the DeepSearch research agent.

Claude 3.7 Sonnet, released on 24 February 2025, was described by Anthropic as the first hybrid reasoning model on the market, able to answer quickly or think step by step at length. It launched with Claude Code.

A 32-billion-parameter open-weight reasoning model released by the Qwen team on 6 March 2025, trained mainly through scaled reinforcement learning and reported to perform comparably to the much larger DeepSeek-R1.

ERNIE X1 is Baidu's deep-thinking reasoning model released on 16 March 2025 alongside ERNIE 4.5, notable for tool use, multimodal input and low pricing, and later followed by X1 Turbo and X1.1.

Hunyuan-T1 is Tencent's deep-reasoning model, officially released on 21 March 2025 and built on the Hunyuan-TurboS base. Tencent did not release its weights.

Seed-Thinking-v1.5 is a reasoning model from ByteDance Seed: a 20B-activated, 200B-total mixture-of-experts model trained with reinforcement learning to think before answering, published with a technical report and benchmark tables but no model weights.

SenseTime's SenseNova V6 is a native mixture-of-experts multimodal foundation model with over 600 billion parameters, released on 10 April 2025 in general, reasoning and real-time interactive variants.

A small reasoning model released by OpenAI in April 2025 alongside o3, built for fast, low-cost reasoning; with a Python interpreter it reached 99.5% pass@1 on AIME 2025, and it was later succeeded by GPT-5 mini.

A model in Google's Gemini 2.5 family, released in preview in April 2025 and generally available that June. Google called it its first fully hybrid reasoning model, letting developers turn thinking on or off with a token budget.

MiMo-7B is a 7-billion-parameter reasoning model from Xiaomi's LLM-Core team, pre-trained on 25 trillion tokens and tuned with reinforcement learning on verifiable math and code problems, reported to surpass OpenAI o1-mini on several reasoning benchmarks.

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.

AlphaEvolve is a Google DeepMind coding agent announced on 14 May 2025 that pairs Gemini models with automated evaluators to evolve algorithms, yielding a Borg scheduling heuristic, faster kernels and new mathematical results.

Claude Opus 4 and Claude Sonnet 4, announced on 22 May 2025, were hybrid models with extended thinking. Anthropic called Opus 4 the best coding model in the world, and Claude Code became generally available the same day.

An updated release of DeepSeek's open-weight reasoning model, published on 28 May 2025 under the MIT License, with markedly higher scores on competition math, science and coding benchmarks, plus system-prompt support and stronger function calling.

MiniMax-M1 is an open reasoning model released by MiniMax in June 2025. It has 456B total parameters, a native 1-million-token context and an Apache 2.0 license, and it comes in 40K and 80K thinking-budget versions.

ByteDance Seed's general-purpose model series, announced on 11 June 2025 as Doubao Large Model 1.6, combining multimodal input, a 256K context window and a mode that decides per prompt whether to reason before answering.

GLM-4.5 is Zhipu's open-weight language model, released in July 2025 with 355 billion total parameters and a lighter sibling, GLM-4.5-Air. Both are hybrid reasoning models released under the MIT License.

Grok 4 and Grok 4 Heavy are xAI's models from July 2025. Grok 4 has a 256,000-token context and was trained with reinforcement learning at pretraining scale, while Heavy runs parallel test-time compute.

EXAONE 4.0 is LG's family of large language models, released as a 32B model and a 1.2B on-device model, merging chat usability with a reasoning mode and adding tool use and Spanish support.

A 14.74-billion-parameter Korean-English reasoning model released by NAVER in July 2025, built by compressing a larger model and training it with a four-stage reasoning recipe at a fraction of the cost of comparable models.

Qwen3-2507 is a staged 2025 refresh of the open-weight Qwen3 models that split thinking and non-thinking into separate checkpoints, raised native context to 262,144 tokens, and scored far above the original non-thinking mode on published benchmarks.

Step 3 is StepFun's open multimodal reasoning model, with 321 billion total parameters and 38 billion active per token. It was released in July 2025 and uses Apache 2.0.

An enhanced reasoning mode for Gemini 2.5 Pro that weighs multiple hypotheses in parallel before answering, announced experimentally in 2025 and known for reaching gold-medal standard at the International Mathematical Olympiad.

gpt-oss is a family of open-weight reasoning language models released by OpenAI on 5 August 2025, in 120-billion and 20-billion parameter sizes, under the permissive Apache 2.0 license.

ByteDance Seed's open-weight 36-billion-parameter model family from August 2025, trained on 12 trillion tokens with a 512K-token context window and a user-settable thinking budget.

DeepSeek-V3.1, released on 21 August 2025 under the MIT License, was DeepSeek's first hybrid model, supporting both a thinking mode and a non-thinking mode in one set of weights. It has 671 billion total parameters, with 37 billion activated per token.

Kimi K2 Thinking is a reasoning model released by Moonshot AI in November 2025, built on the Kimi K2 mixture-of-experts architecture and trained for native INT4 inference and long chains of tool calls.

GPT-5.1 is an update to GPT-5 released by OpenAI on 12 November 2025. It added a warmer default personality with selectable styles, and its API version has been scheduled for shutdown in 2027.

Olmo 3 is the third generation of the Allen Institute for AI's fully open language models, announced on 20 November 2025 in 7B and 32B dense Transformer sizes, with a 65,536-token context and all datasets openly available.

Claude Opus 4.5, released on 24 November 2025, cost a third as much as Opus 4.1 per token and introduced an effort parameter that lets developers trade capability for time and cost. Claude Opus 4.6 succeeded it.

DeepSeekMath-V2, released on 27 November 2025, is a mathematical reasoning model trained to verify its own proofs. DeepSeek reported gold-level scores on IMO 2025 and CMO 2024 problems, and 118 of 120 on Putnam 2024.

DeepSeek-V3.2, released on 1 December 2025, succeeded the experimental V3.2-Exp and integrated thinking into tool use. Its companion V3.2-Speciale, which maximizes reasoning, reached gold-level results at several 2025 competitions.

Gemini 3 Deep Think is Google's enhanced reasoning mode for Gemini 3, announced with Gemini 3 Pro on 18 November 2025 and released to Google AI Ultra subscribers on 3 December 2025, with an upgraded version following in February 2026.

Tencent's flagship model released in December 2025, offered in Think and Instruct versions, built on a 406-billion-parameter mixture-of-experts architecture with a 256K-token context window.

GPT-5.2 is a model family OpenAI released on 11 December 2025, with Instant, Thinking and Pro versions and a coding variant. It was aimed at professional work such as spreadsheets and presentations.

Gemini 3 Flash is a fast, lower-cost model in Google's Gemini 3 family, released on 17 December 2025. It scored close to Gemini 3 Pro on several benchmarks while using fewer tokens and costing far less per token.

Step 3.5 Flash is an open-weights Mixture-of-Experts language model from StepFun, released in February 2026 with 196 billion total parameters, a 256K-token context and an Apache 2.0 license.

Released on 5 February 2026, Claude Opus 4.6 was an upgrade to Anthropic's smartest model. It was the first Opus-class model with a 1M-token context window, in beta at launch, and it introduced agent teams in Claude Code.

Seed2.0 is ByteDance's February 2026 Doubao model series, offered in three agent-oriented sizes with low token pricing and reported benchmark results.

Gemini 3.1 Pro is Google's preview upgrade to Gemini 3 Pro, released on 19 February 2026, scoring a verified 77.1% on ARC-AGI-2 and shipped through the Gemini API, the Gemini app and NotebookLM.

GPT-5.4 is a model OpenAI released on 5 March 2026 in Thinking and Pro versions. It added built-in computer use and improved deep research, and it was the model that succeeded GPT-5.2.

Muse Spark is the first model from Meta Superintelligence Labs, released on 8 April 2026 as a closed model that powers the Meta AI app and meta.ai. An open-weight sibling followed later.

GPT-5.5 is an OpenAI model released on 23 April 2026 as GPT-5.5 Thinking and Pro, with an API version the next day. It succeeded GPT-5.4 and had a cybersecurity variant in limited preview.

Command A+ is Cohere's open-source mixture-of-experts language model, released on 20 May 2026 under the Apache 2.0 licence with 218 billion total and 25 billion active parameters, aimed at sovereign and critical-infrastructure deployments.

MAI-Thinking-1 is Microsoft AI's flagship reasoning model, launched on 2 June 2026 at Microsoft Build. Microsoft said it was preferred to Anthropic's Claude Sonnet 4.6 in blind human evaluations, and that developers could fine-tune its weights for the first time.

Tencent Hy3 is an open-weight reasoning model released on 6 July 2026 under Apache 2.0, with 295 billion total parameters, 21 billion active and a 256K context.

Inkling is the first model released by Thinking Machines Lab: a 975B-parameter mixture-of-experts model with open weights, native text, image and audio input, and a context window of up to 1M tokens.

Qwen3.8 is Alibaba's 2026 flagship line. Its open 2.4-trillion-parameter model, Qwen3.8-2.4T-A95B, released in August 2026, has 95B active parameters and a custom license.

Gemini 3.8 Flash is Google's fast, low-cost model released on 2 September 2026, alongside a cybersecurity variant, Gemini 3.8 Flash Cyber, with introductory pricing that doubles at the start of 2027.

Kolibri-1 is Aleph Alpha's open-weight German–English mixture-of-experts model: 78.1 billion parameters with 3.46 billion active per token, a 1,048,576-token context window, and weights that fit on a single H200 or B200.

Jais-3-7B is a dense 7B Arabic-and-English model from the Institute of Foundation Models, with a 512,000-token context window, a single-GPU footprint of about 18 GB, and reasoning returned in a separate field.

Jais-3-MoVA-36B-A4B is an Arabic-centric mixture-of-experts model from the Institute of Foundation Models: 36 billion parameters, 4 billion active per token, a 512,000-token context and a mixture-of-values attention scheme.

Gemini 4 Carbon is a Google DeepMind frontier model announced on 28 October 2026, two weeks after Gemini 4 Argon, with Google claiming state-of-the-art cybersecurity and long-horizon capabilities.

OpenAI's cybersecurity-focused model, released on 5 November 2026 and limited to the top tier of its Daybreak Red programme; OpenAI says it surfaced 948 potential Linux kernel issues and 81 novel Firefox vulnerabilities.

Jason Wei is an AI researcher and first author of papers on chain-of-thought prompting and emergent abilities in large language models; he has worked at Google Brain, OpenAI and Meta Superintelligence Labs.

Tool calling lets a language model hand a sub-task, such as arithmetic or search, to an external program and use the result in its answer. Toolformer showed in 2023 that a model could learn when and how to call tools on its own.

Planning in AI agents is the process of breaking a goal into intermediate steps, choosing actions, and revising the plan as results arrive, rather than producing an answer in one pass.[^1][^2]

Reward hacking is what happens when a system optimises a proxy reward that only imperfectly captures what we want: it scores well on the proxy while performing badly on the true objective.

Noam Brown is an AI researcher at OpenAI, listed on his homepage as working on reasoning, reinforcement learning, self-play and multi-agent AI. He is known for the poker systems Libratus and Pluribus and for work on CICERO and reasoning models such as OpenAI o1.

Prompt engineering is the practice of designing the text input that steers a generative AI system toward a desired output. Shared vocabulary and techniques such as chain-of-thought prompting make results easier to describe, compare and reproduce.

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.

MuZero is a DeepMind reinforcement-learning algorithm that pairs tree-based search with a learned model. It reached superhuman play in Atari, Go, chess and shogi without being given the environment's rules.

Phi-1.5 is a 1.3-billion-parameter language model from Microsoft Research, trained on curated synthetic "textbook" text rather than web crawls; its report claims natural-language performance comparable to models five times larger.

Phi-2 is a 2.7-billion-parameter base language model from Microsoft Research, announced on 12 December 2023. Microsoft reported that it matched or beat models up to 25 times larger on complex benchmarks, making it a reference point for small-model training.

AlphaGeometry is a Google DeepMind system that pairs a neural language model with a symbolic deduction engine to solve olympiad geometry problems, reaching near gold-medal level on a benchmark of 30 problems.

DeepSeekMath is a 7B-parameter open language model built for mathematical reasoning and released in 2024. It reached 51.7% on the competition-level MATH benchmark without external tools, and introduced GRPO, a reinforcement-learning algorithm that uses less memory than PPO.

Grok-1.5 is xAI's upgrade to Grok-1, with better reasoning and a 128,000-token context window. Its companion Grok-1.5V was xAI's first multimodal model. Neither model's weights were released publicly.

AlphaProof is a Google DeepMind reinforcement-learning system that proves mathematical statements in the formal language Lean. At the 2024 International Mathematical Olympiad it solved three problems, and together with AlphaGeometry 2 reached silver-medal level.

o1-mini is a smaller, faster and cheaper reasoning model that OpenAI released on 12 September 2024 alongside o1-preview, trained with reinforcement learning to reason step by step and rated particularly effective at coding.

Tülu 3 is Ai2's open post-training recipe and model family, released in 8B and 70B sizes on top of Llama 3.1 and combining instruction tuning, preference tuning with on-policy data, and reinforcement learning with verifiable rewards.

QwQ-32B-Preview is an experimental reasoning research model released by the Qwen team on 28 November 2024, with 32B parameters, a 32K-token context and open Apache 2.0 weights. It scored strongly on maths benchmarks but the team documented clear failure modes.

A version of OpenAI's o1 that spends more compute before answering, launched on 5 December 2024 inside the $200-a-month ChatGPT Pro plan and added to the API on 19 March 2025.

A feature in the Gemini app that plans multi-step web research, gets the user's approval, browses for a few minutes and returns a report with links to its sources; later offered to developers as a managed agent in the Gemini API.

Reka Flash 3 is a 21-billion-parameter general-purpose reasoning model from Reka, trained from scratch and released with open weights under the Apache 2.0 licence on 11 March 2025.

Llama Nemotron is NVIDIA's family of open reasoning models in Nano, Super and Ultra sizes, launched in March 2025 and built on Meta's Llama 3 models.

ERNIE X1 Turbo is a Baidu reasoning model released on 25 April 2025, positioned as a cheaper and more capable successor to ERNIE X1, with stronger chain-of-thought, multimodal and tool-use abilities.

DeepSeek's open-source model for formal theorem proving in Lean 4, trained with a subgoal-decomposition pipeline; it reached an 88.9% pass ratio on MiniF2F-test and introduced the ProverBench benchmark.

A 14-billion-parameter open-weight reasoning model released by Microsoft in April 2025, built by fine-tuning Phi-4 on reasoning traces generated by OpenAI's o3-mini and published under the MIT licence.

Sarvam-M is Sarvam AI's open-weights 24-billion-parameter model, post-trained from Mistral Small for eleven Indian languages. It runs in think and non-think modes and reports large gains on Indic, maths and coding benchmarks.

OpenAI o3-pro is a version of the o3 model released on 10 June 2025, which OpenAI described as its most capable model at the time and recommended for hard questions where reliability matters more than speed.

Magistral is Mistral AI's first family of reasoning models, launched in June 2025 with an open-weight Small model and an enterprise Medium model. It supports multilingual reasoning and was later updated and retired.

Hunyuan-A13B is Tencent's open-weight mixture-of-experts language model, released on 27 June 2025 with 80 billion total parameters, 13 billion active per token and a 256K context.

SenseNova V6.5 is SenseTime's enhanced multimodal model, announced in July 2025, built around interleaved image-text reasoning and powering an agent upgrade of the Raccoon assistant.

SmolLM3 is a 3-billion-parameter open model released by Hugging Face on 8 July 2025. It supports six languages and up to 128K tokens of context, with switchable reasoning, under Apache 2.0.

Step-Audio 2 is a speech model from StepFun that can understand audio and hold spoken conversations. Its mini versions were released under the Apache 2.0 license in 2025.

Baichuan-M2 is an open-source medical-enhanced model with 32 billion parameters, built on Qwen2.5-32B and released under Apache 2.0 for research and reference.

Claude Opus 4.1, released on 5 August 2025, upgraded Claude Opus 4 for agentic tasks, real-world coding and reasoning, at the same price. Anthropic later succeeded it with Claude Opus 4.5.

Cohere's first reasoning model, announced in August 2025: a 111-billion-parameter hybrid model that can switch its thinking on or off, built for agentic tasks and tool use, with open non-commercial weights.

A fast reasoning model from xAI for agentic coding, released in August 2025 with low per-token pricing, a 70.8% score on SWE-bench Verified, and integrations with GitHub Copilot, Cursor, Cline and other coding tools.

A 1.7-billion-parameter English model from Writer, fine-tuned from Qwen2.5-1.5B and released under Apache 2.0 with a 131,072-token context window, presented around grade-school mathematics.

ERNIE X1.1 is Baidu's reasoning model unveiled in September 2025, an update to ERNIE X1 that the company reports as stronger in factuality, instruction following and agentic tasks, built on ERNIE 4.5 and released alongside PaddlePaddle v3.2.

A deep-thinking mixture-of-experts model from Baidu with 21 billion total and 3 billion active parameters, a 128K context window and an Apache 2.0 license, open-sourced in September 2025 alongside ERNIE X1.1.

A 1.7-billion-parameter reasoning model released by Writer in September 2025, fine-tuned from Nvidia's OpenReasoning-Nemotron-1.5B, with strong competition-mathematics scores and an Apache 2.0 licence.

Ray3 is a video generation model released by Luma AI on 18 September 2025 and described by the company as the first reasoning video model, with HDR output, native 1080p and a neural upscaler to 4K.

xAI's low-cost reasoning model released on 19 September 2025, with a 2-million-token context window and far lower prices than Grok 4 at comparable benchmark scores.

A pair of robotics models announced by Google DeepMind in September 2025: Gemini Robotics 1.5, a vision-language-action model that reasons in natural language before it moves, and Gemini Robotics-ER 1.5, an embodied-reasoning planner that can call tools.

A 3-billion-parameter open reasoning model from AI21 Labs, released under the Apache 2.0 licence with a hybrid Transformer-Mamba design, a 256k-token context window and local execution on phones, Macs and PCs.

Baidu's open-weight multimodal reasoning model from November 2025: 28B total parameters with 3B active per token, "Thinking with Images" zoom-and-tool reasoning, and Apache 2.0 weights.

iFlytek's Spark X1.5 is a deep reasoning model released in November 2025 that runs on a domestic computing platform built with Huawei, using a 293-billion-parameter mixture-of-experts design.

A robot model from Physical Intelligence trained on demonstrations, human corrections and its own autonomous experience, reported to make espresso, fold laundry and assemble boxes with over 90% success.

Grok 4.1 is xAI's November 2025 update to Grok 4, aimed at emotional intelligence, creative writing and fewer hallucinations. Grok 4.1 Fast, a 2-million-token tool-calling model, followed on 19 November 2025.

Amazon Nova 2 is the second generation of Amazon's Nova models, released at AWS re:Invent in December 2025. Its first member, Nova 2 Lite, is a fast reasoning model available in Amazon Bedrock with a 1-million-token context.

NVIDIA Nemotron 3 is an open family of hybrid mixture-of-experts language models, announced in December 2025 in Nano, Super and Ultra sizes, with up to one million tokens of context.

Baichuan-M3 is a new-generation open-source medical-enhanced language model with 235 billion parameters, built on Qwen3-235B-A22B and released under Apache 2.0 in January 2026.

Grok 4.20 is xAI's 2026 model family, released in reasoning, non-reasoning and multi-agent versions with a 1-million-token context window; Grok 4.3 followed with the same context and the same prices.

Phi-4-reasoning-vision-15B is Microsoft's 15-billion-parameter open-weight vision-language model, released on 4 March 2026 under the MIT licence, built to switch between step-by-step reasoning for math and science and direct answers for image perception tasks.

Mistral Small 4 is an open-weight mixture-of-experts model released in March 2026 that folds instruction-following, step-by-step reasoning and agentic coding into one model, with a switch that controls how much reasoning it does.

Granite 4.2 is IBM's open-weight model generation, released on 25 August 2026 in 3B, 8B and 30B dense sizes, with a reasoning-capable 8B model under the permissive Apache-2.0 licence.

Mark Chen is an OpenAI researcher who led the team behind DALL·E 2 and worked on Codex; in March 2025 he moved into an expanded Chief Research Officer role.

AI researcher who was first author of the 2016 paper introducing neural architecture search and a co-author of Switch Transformers; his X profile lists him as CTO and co-founder of Thinking Machines Lab and VP Research at Google DeepMind.

A 7-billion-parameter model released by Mistral AI on 16 July 2024 for mathematical and STEM reasoning, built on Mistral 7B, openly licensed, and now listed as deprecated.

Nemotron Nano 2 is NVIDIA's 9B reasoning model, built on a hybrid Mamba-Transformer design and released with open weights and most of its training data; NVIDIA reports much higher throughput than similar-sized models.