On Computable Numbers, with an Application to the Entscheidungsproblem
Introduces the universal Turing machine and proves the Entscheidungsproblem is undecidable, founding the theoretical basis of computer science.
73 representative works from 1936 to today, grouped by editorial role and labeled by publication status
Papers are the skeleton of AI history. This catalog collects 73 foundational works that shaped the field, each linked to its primary source.
Selection is based on historical representation, technical influence, and editorial judgment. Peer-reviewed papers, technical reports, preprints, position papers, and system cards may be included and are labeled by publication status. Corrections and additions are welcome through the public channel on the Editorial Policy and Corrections page.
Showing 73 of 73 papers
Introduces the universal Turing machine and proves the Entscheidungsproblem is undecidable, founding the theoretical basis of computer science.
Models neural activity as propositional logic, providing the first mathematical theory of artificial neural networks.
Founding paper of information theory, defining entropy and channel capacity as fundamental limits of communication.
Proposes the imitation game (Turing test) and systematically formulates the question "Can machines think?", helping establish AI as a research program.
The founding proposal for the Dartmouth summer workshop introduced the term "artificial intelligence" and outlined the field’s research agenda.
Describes the Logic Theorist, the first program to prove mathematical theorems, demonstrating automated reasoning in propositional logic.
Introduces the first trainable linear-threshold neuron, founding the connectionist lineage that leads to modern deep learning.
Proposes the Advice Taker, a program that reasons with declarative axioms and accepts new "advice" as English sentences, helping establish the research agenda for knowledge representation and symbolic AI.
Demonstrates self-play learning with a scoring function in a checkers program, an early reinforcement-learning milestone associated with the term "machine learning".
Gelernter addresses how a machine can efficiently manipulate formal systems whose predicates are highly symmetric, and states a theorem and a rule of syntactic symmetry as the solution. The work sits alongside the geometry theorem machine he was building at IBM, which proved its first theorem in elementary Euclidean plane geometry in the early spring of 1959.
Introduces the ADALINE neuron and the Least-Mean-Squares (LMS) learning rule, the forerunner of modern stochastic gradient descent.
Introduces the Hopfield associative-memory network, linking neural computation to the energy landscapes of statistical physics and reviving interest in neural networks during the early AI winter.
Lays the algorithmic foundations of Bayesian belief networks, including message-passing on tree-structured graphs and the moralization/triangulation machinery that powers modern probabilistic inference and causal reasoning.
The canonical statement of the back-propagation algorithm for multilayer neural networks, demonstrating that hidden units could learn useful internal representations and reigniting connectionist research in the late 1980s.
Formalises the temporal-difference (TD) learning family, unifying Samuel’s checkers learner with secondary reinforcement from animal psychology and laying the algorithmic groundwork for TD(λ), Q-learning, and modern policy-gradient methods.
Introduces the Simple Recurrent Network (Elman network) and shows that low-dimensional dynamical structure can emerge from training on sequential input, providing one of the earliest demonstrations of useful representation learning in recurrent nets.
Introduces the soft-margin support vector machine, adding slack variables to handle non-separable data and turning the maximal-margin classifier into the dominant general-purpose learning method of the late 1990s.
Introduces the original LSTM architecture using memory cells, input gates, and output gates to preserve error flow across long sequences; the now-standard forget gate was introduced later by Gers, Schmidhuber, and Cummins.
Presents the LeNet-5 convolutional neural network and the full end-to-end gradient-based learning pipeline (including loss layers, backprop through convolution/pooling, and graph-transformational network descriptions) that became the blueprint for modern deep vision models.
Introduces a deep autoencoder that reconstructs high-dimensional data far more faithfully than PCA, lighting the first spark of the deep learning revival.
Introduces contrastive divergence and greedy layer-wise pre-training, letting deep networks be trained effectively for the first time and ending the long winter of skepticism toward connectionism.
DQN fuses Q-learning with deep convolutional networks and reaches human-level play on Atari 2600 games from raw pixels, opening the door to general reinforcement learning.
The CBOW and Skip-gram models of word2vec make large-scale word embedding training cheap and famously expose semantic geometry such as king - man + woman ≈ queen.
The VAE couples latent-variable generative modeling with stochastic gradient training through the reparameterization trick, giving modern generative deep learning its mathematical foundation.
Introduces learned attention into encoder-decoder translation, freeing long sentences from fixed-length bottlenecks and seeding every Transformer that followed.
GANs let a generator and discriminator duel to implicitly learn high-dimensional distributions, opening a second great road of generative modeling.
Dropout randomly silences units to break co-adaptation, sharply improving generalization in large nets and becoming a standard tool of deep learning practice.
BatchNorm normalizes layer inputs, letting deep networks train with higher learning rates and converge faster; it became a near-default building block of vision models.
Residual connections stabilize training of hundred- and thousand-layer nets; ResNet reached 3.57% top-5 error on ImageNet, the first model to surpass human-level accuracy and a reset of vision model scale.
WaveNet models raw audio sample-by-sample with dilated causal convolutions, pushing speech synthesis close to human naturalness and paving the way for later neural audio models.
PPO replaces trust-region machinery with a clipped first-order surrogate, making policy gradient methods both stable and efficient at scale and quickly becoming the de facto standard of applied RL.
Introduces the Transformer, an attention-only architecture that abandons recurrence and convolutions and surpasses prior sequence-transduction quality while training in a fraction of the time.
Pre-trains a deep bidirectional Transformer with masked language modeling and next-sentence prediction, then sets new state-of-the-art on eleven NLP benchmarks.
Casts every NLP task as text-to-text and uses the C4 corpus to systematically compare transfer-learning design choices for a unified Transformer.
Introduces DDPM, showing that iterative denoising diffusion probabilistic models match GANs on high-fidelity image synthesis.
Uses an autoregressive Transformer over discrete text and image tokens to produce high-quality zero-shot text-to-image generations (DALL·E).
Trains image-text contrastive learning on 400M pairs to produce vision encoders that transfer zero-shot to many downstream tasks.
Performs diffusion in the latent space of a pretrained autoencoder, enabling high-resolution text-to-image synthesis with modest compute (Stable Diffusion).
Shows that prompting large language models with intermediate reasoning steps substantially improves performance on arithmetic, commonsense, and symbolic reasoning.
Fine-tunes GPT-3 with reinforcement learning from human feedback to follow instructions more faithfully — the direct precursor to ChatGPT (InstructGPT).
Trains a helpful and harmless assistant using RLAIF, where the model critiques and revises its own outputs against a written constitution.
Trains 7B–65B foundation models on publicly available data, demonstrating that open models can rival closed frontier models at a fraction of the compute.
Introduces Mamba, a selective state-space model architecture that matches or exceeds Transformer attention on language and other modalities at linear-time complexity — the most influential post-Transformer architecture of 2023.
AlexNet, a large CNN trained on GPUs, slashed ImageNet top-5 error from 26% to 15%, marking deep learning’s decisive victory over hand-crafted visual features.
The Nature DQN adds experience replay and a target network, letting a single model reach or surpass human play on 49 Atari games and cementing deep RL as a paradigm.
AlphaGo couples policy and value networks with Monte Carlo tree search and defeats European champion Fan Hui 5-0, announcing that deep RL has reached the deepest strata of human strategic play.
Demonstrates that a generative pre-trained Transformer transfers effectively to discriminative NLP tasks, launching the GPT line of work.
Trains a 1.5B-parameter Transformer decoder and shows that language modeling at scale yields strong zero-shot task performance.
Scales GPT to 175B parameters and shows that large language models perform strong few-shot in-context learning across many tasks.
Describes GPT-4, a large multimodal model accepting image and text inputs that approaches human-level performance on many professional and academic benchmarks.
Introduces the Gemini family (Ultra/Pro/Nano) of natively multimodal models trained jointly across text, code, image, audio, and video.
OpenAI publishes the system card for the o1 model series, trained with large-scale reinforcement learning to reason using chain-of-thought. o1 reaches state-of-the-art on science and coding tasks and demonstrates reasoning-based policy adherence.
The ARC Prize introduces ARC-AGI-3, an interactive benchmark for studying agentic intelligence through abstract turn-based environments where agents must explore, infer goals, build internal models of environment dynamics, and plan action sequences without explicit instructions. As of March 2026, humans solve 100% of environments while frontier AI systems score below 1%.
Applies sparse autoencoders to Claude 3 Sonnet’s middle layers, extracting tens of millions of interpretable monosemantic features from a frontier production model.
Describes DeepSeek-V3, a 671B-parameter MoE model using Multi-head Latent Attention and DeepSeekMoE, achieving open-source SOTA at a fraction of frontier-model training cost.
Introduces the Gemini 1.5 family of compute-efficient multimodal models with million-token context windows — capable of fine-grained reasoning across multiple long documents and hours of video and audio.
Meta presents the Llama 3 family of open-weight foundation models natively supporting multilinguality, coding, reasoning, and tool use. The flagship 405B dense Transformer was one of the largest open-weight models at release.
Meta presents SAM 2, a foundation model for promptable visual segmentation in both images and videos, along with the largest video segmentation dataset to date.
Google DeepMind introduces Gemma 2, a new family of lightweight open models (2B-27B parameters) that applies several known technical modifications to the Transformer — including sliding window attention — to approach much larger models on standard benchmarks.
DeepSeek releases R1, the first open-weight model to demonstrate frontier-class reasoning capability driven primarily by large-scale reinforcement learning. R1 matches OpenAI o1-class closed models on math and coding benchmarks and ships under the MIT license.
The authors finetune Qwen2.5-32B on 1,000 curated reasoning questions and add budget forcing, which caps or extends how long the model thinks at inference. The result exceeds o1-preview on competition mathematics, rising from 50% to 57% on AIME24 as test-time compute grows. It is a direct counterweight to the assumption that capability comes only from larger training runs.
Qwen3 is a unified family spanning 0.6B to 235B parameters in dense and mixture-of-experts variants, with switching between thinking and non-thinking modes so reasoning depth becomes a request-level choice. Multilingual support expands from 29 to 119 languages, and the weights are released under Apache 2.0.
AlphaEvolve is an evolutionary coding agent that orchestrates an autonomous pipeline of language models, changing an algorithm’s code directly and improving it against feedback from one or more evaluators. Inside Google it produced a more efficient data-centre scheduling algorithm, a functionally equivalent simplification in accelerator circuit design, and a speed-up in training the model underpinning AlphaEvolve itself. In mathematics and computer science it found provably correct algorithms that beat the state of the art, among them a procedure multiplying two 4×4 complex-valued matrices in 48 scalar multiplications — in that setting, the first improvement on Strassen’s algorithm in 56 years.
Ai2 releases OLMo 2 at 7B, 13B and 32B with every artifact published — weights, the full training data, training code and recipes, training logs and thousands of intermediate checkpoints. The report describes the stability and per-token efficiency changes, a late-stage data mix called Dolmino Mix 1124, and a final reinforcement-learning stage with verifiable rewards. The base models sit at the Pareto frontier of performance against training compute, often matching open-weight-only families while disclosing what they were trained on.
Olmo 3 extends the fully open family to 7B and 32B, built for long-context reasoning, function calling, coding, instruction following, chat and knowledge recall. What is released is the entire model flow — every stage, checkpoint, data point and dependency used to build it — rather than the weights alone. Ai2 describes the flagship Olmo 3 Think 32B as the strongest fully open thinking model released to that point, which is a comparison inside the fully open category rather than a ranking against frontier systems generally.
This position paper argues that integrating explicit memory is the cornerstone for advancing LLMs toward AGI. While the underlying learning mechanism of LLMs is highly analogous to human implicit memory, higher-order cognitive functions required for AGI — such as long-term strategic planning and metacognition — depend on explicit memory.
Z.ai’s technical report for GLM-5. Building on the agentic, reasoning and coding capabilities of its predecessor, the model adopts DSA to cut training and inference cost while holding long-context fidelity, and the post-training stack adds an asynchronous reinforcement-learning infrastructure that decouples generation from training, plus asynchronous agent RL algorithms aimed at long-horizon interaction. The report claims leading results on open benchmarks and on end-to-end software engineering; those are the authors’ own evaluations, with code and models published on GitHub for checking.
The best known bounds on the matrix multiplication exponent ω come from combination loss analysis, a refinement of the laser method. The authors reformulate the optimization problem at its core so it can be solved at a larger setting, design a new optimization algorithm using recent machine learning, and then refine that algorithm with AlphaEvolve. Together these move the upper bound from 2.371339 to 2.371177. It is a preprint note, and AlphaEvolve is one ingredient rather than the whole method; the gain is small, but it lands on a theoretical problem that has been worked on for decades.
Google introduces Co-Scientist, a multi-agent system built on Gemini whose agents generate, critique and refine research hypotheses, with a tournament process that improves them over rounds. The paper reports that hypothesis quality keeps rising as test-time compute grows. Validation is biomedical rather than general — drug repurposing, novel-target discovery and mechanisms of antimicrobial resistance — with acute myeloid leukaemia candidates confirmed in vitro.
Argues that current LLMs rely primarily on statistical pattern matching and lack essential "situation perception" primitives — object permanence, causality, other minds, and persistence of the physical world. These primitives, which human infants develop early, are identified as the missing ingredients required for artificial superintelligence.
Argues that self-preservation is the structural root of AI misalignment — driving deceptive alignment, goal-content protection, and shutdown resistance. The correct target is not a self-preserving agent suppressed by external constraints, but a system constitutionally indifferent to its own continuation: Existential Indifference (EI).
Researchers from Google DeepMind and collaborators argue that AI’s central challenge is shifting from capability to coexistence. Superintelligence built from a solipsistic design that treats the world as an exogenous stationary feedback source is unlikely to cooperate — deployment induces endogenous non-stationarity, producing train-test-deploy distribution drift.
Google DeepMind report investigating how AI may continue to develop along the continuum of machine intelligence after AGI. After formally defining Universal AI, the report focuses on the transition from human-level AGI to artificial general superintelligence, characterizes ASI, and discusses four pathways: scaling AGI, AI paradigm shifts, recursive self-improvement, and multi-agent collectives.