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A Mathematical Theory of Communication

C. E. Shannon's 1948 paper set out a mathematical framework for communication, defining information in bits, channel capacity, and entropy, and treating messages statistically while setting aside semantic meaning.

Some Studies in Machine Learning Using the Game of Checkers

A. L. Samuel's 1959 paper reporting experiments in which a checkers program, given only the rules of the game and an imperfect set of parameters, learned in 8 to 10 hours of playing time to beat the person who wrote it.

Perceptrons: An Introduction to Computational Geometry

A 1969 book by Marvin Minsky and Seymour Papert that proved mathematical limits on what single-layer perceptrons can compute — notably that they cannot compute parity or connectedness — and has long been credited with steering research away from neural networks.

Neural networks and physical systems with emergent collective computational abilities

A 1982 paper by John J. Hopfield arguing that useful computation can emerge as a collective property of many simple, equivalent units, and describing a model whose collective behaviour gives content-addressable memory, generalisation and error correction.

Neural networks and physical systems with emergent collective computational abilities

A 1982 paper by John J. Hopfield showing that large networks of simple neuron-like units can collectively store and recall memories. It became known as the Hopfield network, and the work was recognised by the 2024 Nobel Prize in Physics.

Learning representations by back-propagating errors

In a 1986 Nature paper, Rumelhart, Hinton and Williams showed that backpropagation lets hidden units in a multilayer network learn useful internal features of a task. The method is standard in most neural networks today.

Learning to predict by the methods of temporal differences

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.

Elephants Don't Play Chess

Rodney Brooks's 1990 paper argued for building artificial intelligence from the ground up, with ongoing physical interaction with the environment as the main constraint on design, rather than through the abstract manipulation of symbols that had dominated the field for roughly thirty years.

A Training Algorithm for Optimal Margin Classifiers

Published in 1992, this paper by Boser, Guyon and Vapnik presents a training algorithm that maximizes the margin between training patterns and the decision boundary, with experiments on optical character recognition.[^1]

The Anatomy of a Large-Scale Hypertextual Web Search Engine

A 1998 conference paper by Sergey Brin and Lawrence Page describing PageRank, an algorithm that ranks web pages by the number and quality of links pointing to them, and the search engine built on that algorithm.

Latent Dirichlet Allocation

A generative probabilistic model that represents each document as a finite mixture over topics, fitted with variational approximate inference and EM, and evaluated on document modelling, text classification and collaborative filtering.

Understanding the difficulty of training deep feedforward neural networks

A 2010 paper by Xavier Glorot and Yoshua Bengio on why deep feedforward networks are hard to train: sigmoid saturation under random initialization and layer Jacobians whose singular values sit far from 1, plus a new initialization scheme that converges substantially faster.

Real-Time Human Pose Recognition in Parts from a Single Depth Image

A CVPR 2011 Best Paper that recovers 3D body joint positions from a single depth image without temporal information, by classifying pixels into body parts, and runs at 200 frames per second on consumer hardware.

Deep Sparse Rectifier Neural Networks

A 2011 paper by Glorot, Bordes and Bengio reporting that deep networks built from rectifying neurons match or beat tanh networks and reach their best performance without unsupervised pre-training on large labelled supervised tasks.

Adam: A Method for Stochastic Optimization

Adam is a stochastic optimisation algorithm from a 2014 paper by Diederik P. Kingma and Jimmy Ba that sets per-parameter step sizes from running estimates of the gradient's first and second moments, needing little memory and little hyper-parameter tuning.

Deep learning

A 2015 Nature review by Yann LeCun, Yoshua Bengio and Geoffrey Hinton explaining deep learning: models of multiple processing layers that learn layered representations of data, and the results this produced in speech, vision and other fields.

Mastering the game of Go without human knowledge

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.

Highly accurate protein structure prediction with AlphaFold

The Nature paper described AlphaFold's methods, system design, and evaluation for protein-structure prediction.

Accurate structure prediction of biomolecular interactions with AlphaFold 3

AlphaFold 3, published in Nature in May 2024, extends structure prediction to biomolecular interactions, reporting greater accuracy than docking tools for protein–ligand binding and than AlphaFold-Multimer v.2.3 for antibody–antigen complexes.

ELIZA - A Computer Program for the Study of Natural Language Communication Between Man and Machine

A January 1966 paper by Joseph Weizenbaum presenting ELIZA, a program on MIT's MAC time-sharing system that used keyword-triggered decomposition and reassembly rules to enable certain natural-language conversations between people and computers.

A Learning Algorithm for Boltzmann Machines

A 1985 Cognitive Science paper by Ackley, Hinton and Sejnowski that presents a general learning rule for connectionist networks and reports simple examples of efficient internal representations.

Practical issues in temporal difference learning (TD-Gammon)

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.

The PageRank Citation Ranking: Bringing Order to the Web

Brin and Page's PageRank technical report treats hyperlinks as citations to rank web pages and was used to build Google's search engine; it is one of the heavily cited papers on their early work.

Phone recognition with the mean-covariance restricted Boltzmann Machine

A 2010 NIPS paper by Dahl, Ranzato, Mohamed and Hinton applies Deep Belief Nets and a mean-covariance RBM to acoustic modeling, reaching 20.5% phone error on speaker-independent TIMIT phone recognition.

Natural Language Processing (Almost) from Scratch

A 2011 Journal of Machine Learning Research paper by Collobert, Weston, Bottou, Karlen, Kavukcuoglu and Kuksa, presenting one neural network architecture and learning algorithm for part-of-speech tagging, chunking, named entity recognition and semantic role labeling, trained on mostly unlabeled data with little task-specific engineering.

Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups

A 2012 article in IEEE Signal Processing Magazine in which four research groups argued that deep neural networks, replacing Gaussian mixture models, gave better acoustic models for speech recognition.

Distributed Representations of Words and Phrases and their Compositionality

A 2013 paper by Mikolov, Sutskever, Chen, Corrado and Dean presents continuous Skip-gram as an efficient method for learning distributed word and phrase representations, with extensions that improve vector quality and training speed.

Dropout: A Simple Way to Prevent Neural Networks from Overfitting

A 2014 paper by Srivastava, Hinton, Krizhevsky, Sutskever and Salakhutdinov introducing dropout, a training trick that randomly removes units so large neural networks overfit less.

Deep Speech: Scaling up end-to-end speech recognition

A 2014 paper presenting an end-to-end deep-learning speech recognition system that removes hand-engineered noise modules and the phoneme dictionary, relying instead on recurrent networks trained across multiple GPUs and synthesized data.

Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

A 2015 paper by Sergey Ioffe and Christian Szegedy that proposed normalising each layer's inputs per training mini-batch, which allowed higher learning rates, looser initialisation and much faster training of deep networks.

Identity Mappings in Deep Residual Networks

A 2016 analysis of residual networks arguing that with identity skip connections and the activation placed after addition, signals travel directly between blocks; a new residual unit built on this eases training, and a 1001-layer network reaches 4.62% error on CIFAR-10.

mixup: Beyond Empirical Risk Minimization

mixup is a training principle from a 2017 paper by Zhang, Cisse, Dauphin and Lopez-Paz that trains networks on convex combinations of pairs of examples and their labels, improving generalisation on image, speech and tabular benchmarks.

A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play

A 2017 arXiv paper, later published in Science, reporting that a single self-play reinforcement learning algorithm, AlphaZero, mastered chess, shogi and Go and beat strong specialised programs in each.

Neural Ordinary Differential Equations

A 2018 paper by Chen, Rubanova, Bettencourt and Duvenaud that replaces a fixed sequence of hidden layers with a neural network describing the derivative of the hidden state, so outputs are computed by an ODE solver — yielding continuous-depth models with constant memory cost.[^1]

Mastering Atari, Go, chess and shogi by planning with a learned model

MuZero is a DeepMind reinforcement-learning algorithm that learns a model of its environment and plans inside that model, mastering Atari, Go, chess and shogi without being given the rules of those games.

Magnetic control of tokamak plasmas through deep reinforcement learning

A 2022 Nature paper by Degrave, Felici and colleagues showing that a deep reinforcement learning controller can learn on its own to command all of a tokamak's magnetic control coils, producing and holding a range of plasma shapes.

Learning skillful medium-range global weather forecasting

GraphCast is a graph neural network trained on four decades of reanalysis data that produces 10-day global weather forecasts at 0.25 degree resolution in under a minute, outperforming the leading operational deterministic systems on most verification targets.

GPQA: A Graduate-Level Google-Proof Q&A Benchmark

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%.

Scaling deep learning for materials discovery

A 2023 Nature paper from researchers at Google DeepMind presenting a scaled-up deep-learning approach to predicting stable crystal structures, screening 2.2 million candidates and reporting a large jump in stability-prediction accuracy.

FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI

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]

Maxout Networks

A 2013 paper by Goodfellow, Warde-Farley, Mirza, Courville and Bengio introduces maxout units, whose output is the maximum of a set of inputs, designed to work with dropout, and reports state-of-the-art results on four benchmarks.

Speech Recognition with Deep Recurrent Neural Networks

A 2013 paper by Graves, Mohamed and Hinton that examines deep recurrent neural networks for speech recognition, arguing for end-to-end sequence training with methods such as connectionist temporal classification.

Group Normalization

Group Normalization is a 2018 paper by Yuxin Wu and Kaiming He that proposes normalizing channels in groups, independent of batch size, to address batch normalization's weakness when batches are small.

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