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Road to Intelligence

Research library

Papers

A curated set, not a bibliography. Each paper is listed with the problem it solved and what it changed, and every title, author list and link was checked against arXiv. Read the essentials first, in chronological order — they tell the story on their own.

Essential23

A landmark you should eventually read yourself.

Essential

Computing Machinery and Intelligence

A. M. Turing · 1950 · Mind

Replaced the unanswerable question 'Can machines think?' with a testable one — the imitation game — and anticipated learning machines decades early.

Problem
'Thinking' has no agreed definition, so the question of machine intelligence seemed impossible to discuss scientifically.
What was new
An operational test based on conversation, a systematic rebuttal of objections to machine intelligence, and a proposal to build 'child machines' that learn rather than being fully programmed.

How to read it: Very readable, even witty. Section 7, 'Learning Machines', is remarkably prescient — read it after Chapter 1.

~45 min readdoi:10.1093/mind/LIX.236.433✓ verified 2026-09-26
Essential

The perceptron: A probabilistic model for information storage and organization in the brain.

F. Rosenblatt · 1958 · Psychological Review

Introduced the perceptron — a neuron model that learns its weights from examples. Every neural network descends from it.

Problem
McCulloch–Pitts neurons could compute, but their connections had to be designed by hand.
What was new
A learning rule that adjusts connection strengths from experience, so the system improves at recognizing patterns.
~1 h readdoi:10.1037/h0042519✓ verified 2026-09-26
Essential

Learning representations by back-propagating errors

David E. Rumelhart, Geoffrey E. Hinton, Ronald J. Williams · 1986 · Nature

Showed that backpropagation lets multi-layer networks learn useful internal representations — the algorithm that still trains every neural network.

Problem
Single-layer perceptrons can't learn many functions, and no practical method was widely known for training the hidden layers of deeper networks.
What was new
Propagate error gradients backward through the network with the chain rule, and demonstrate that hidden units learn meaningful features.

How to read it: Only four pages in Nature. Read it after the chain-rule concept page.

~25 min readdoi:10.1038/323533a0✓ verified 2026-09-26
Essential

Long Short-Term Memory

Sepp Hochreiter, Jürgen Schmidhuber · 1997 · Neural Computation

LSTM added gated memory cells so recurrent networks could keep information over long sequences; it dominated sequence modelling until Transformers.

Problem
Plain recurrent networks lose gradient signal over long time lags.
What was new
A memory cell with a self-connection of weight 1 (a 'constant error carousel') protected by learned multiplicative gates.
~1 h readdoi:10.1162/neco.1997.9.8.1735✓ verified 2026-09-26
Essential

Gradient-based learning applied to document recognition

Yann LeCun, Léon Bottou et al. · 1998 · Proceedings of the IEEE

The LeNet paper: convolutional networks trained end-to-end with gradient descent for handwriting recognition, deployed commercially for reading cheques.

Problem
Handwriting recognition relied on hand-designed feature extractors plus a trainable classifier.
What was new
Learn the features too: convolutional networks trained end to end, plus whole systems trained with gradients.

How to read it: Long (46 pages). Sections I–II explain why learned features beat hand-designed ones — the heart of Chapter 4.

~1 h 30 min readdoi:10.1109/5.726791✓ verified 2026-09-26
Essential

ImageNet Classification with Deep Convolutional Neural Networks

Alex Krizhevsky, Ilya Sutskever, Geoffrey E. Hinton · 2012 · NeurIPS 2012

AlexNet won ImageNet 2012 by a wide margin and triggered the deep-learning era: big data plus GPUs plus deep networks.

Problem
Image recognition relied on hand-engineered features and had plateaued on large, varied datasets.
What was new
A deep convolutional network trained on GPUs with ReLUs and dropout on 1.2 million images, cutting top-5 error dramatically.
~40 min read✓ verified 2026-09-26
Essential

A few useful things to know about machine learning

Pedro Domingos · 2012 · Communications of the ACM

A short, practical essay on the lessons ML practitioners learn the hard way: generalization is what counts, data beats cleverness, and intuition fails in high dimensions.

Problem
The folk knowledge that separates successful ML projects from failed ones was rarely written down.
What was new
Twelve compact lessons — overfitting, the curse of dimensionality, feature engineering, more data vs smarter algorithms, and more.

How to read it: The best single reading for Chapter 3. Read it after the chapter; much of it will click.

~30 min readdoi:10.1145/2347736.2347755✓ verified 2026-09-26
Essential

Efficient Estimation of Word Representations in Vector Space

Tomas Mikolov, Kai Chen et al. · 2013 · ICLR 2013 (workshop)

Showed that simple, fast models trained on billions of words produce word vectors whose geometry captures meaning — the idea behind every embedding you use today.

Problem
Neural language models learned good word representations but were too slow to train on very large corpora.
What was new
Two stripped-down architectures (CBOW and skip-gram) that drop the expensive hidden layer, making it practical to learn embeddings from huge datasets.

How to read it: Read sections 1, 3 and 4. The famous 'king − man + woman ≈ queen' analogy test is in section 4.

~40 min readarXiv:1301.3781✓ verified 2026-09-26
Essential

Sequence to Sequence Learning with Neural Networks

Ilya Sutskever, Oriol Vinyals, Quoc V. Le · 2014 · NeurIPS 2014

Established the encoder–decoder pattern: read an input sequence into a vector, then generate an output sequence from it. Its central weakness motivated attention.

Problem
Standard neural networks need fixed-size inputs and outputs, but translation maps sequences to sequences of different lengths.
What was new
A deep LSTM encoder compresses the source sentence into one vector; a second LSTM decodes the translation from it, trained end to end.

How to read it: Notice the trick of reversing the source sentence — a hint that long-range dependencies were the real problem.

~45 min readarXiv:1409.3215✓ verified 2026-09-26
Essential

Neural Machine Translation by Jointly Learning to Align and Translate

Dzmitry Bahdanau, Kyunghyun Cho, Yoshua Bengio · 2014 · ICLR 2015

Introduced attention in neural networks for language: instead of squeezing a sentence into one vector, the decoder looks back at every input word and decides which ones matter right now.

Problem
Encoder–decoder models squeezed the whole source sentence into a single fixed-length vector, and translation quality fell sharply on long sentences.
What was new
A learned alignment: at each output step the model scores every encoder state, normalizes the scores with softmax, and uses the weighted average as context.

How to read it: Figure 3's alignment heat-maps are the best picture of 'attention' ever drawn — look at them first.

~1 h readarXiv:1409.0473✓ verified 2026-09-26
Essential

Adam: A Method for Stochastic Optimization

Diederik P. Kingma, Jimmy Ba · 2014 · ICLR 2015

The default optimizer (with its AdamW variant) for training neural networks, including essentially all Transformers.

Problem
Plain stochastic gradient descent needs careful per-problem tuning and handles noisy, badly-scaled gradients poorly.
What was new
Adapt each parameter's step size using running averages of the gradient and its square.
~40 min readarXiv:1412.6980✓ verified 2026-09-26
Essential

Deep Residual Learning for Image Recognition

Kaiming He, Xiangyu Zhang et al. · 2015 · CVPR 2016

Residual (skip) connections made very deep networks trainable. Every Transformer block relies on the same trick.

Problem
Adding more layers to deep networks made training error worse, not better — deeper models were harder to optimize.
What was new
Let each block learn a correction added to its input (x + F(x)), giving gradients a direct path through the network.
~45 min readarXiv:1512.03385✓ verified 2026-09-26
Essential

Neural Machine Translation of Rare Words with Subword Units

Rico Sennrich, Barry Haddow, Alexandra Birch · 2015 · ACL 2016

Brought byte-pair encoding (BPE) to neural NLP — the ancestor of the tokenizers in GPT-style models.

Problem
Word-level vocabularies can't represent rare or unseen words; character-level models make sequences very long.
What was new
Start from characters and repeatedly merge the most frequent adjacent pair, yielding a vocabulary of subword units.
~35 min readarXiv:1508.07909✓ verified 2026-09-26
Essential

Mastering the game of Go with deep neural networks and tree search

David Silver, Aja Huang et al. · 2016 · Nature

AlphaGo combined learned intuition (neural networks) with classical search — and beat top professionals at a game long thought decades away.

Problem
Go's search space is far too large for the brute-force search that worked in chess.
What was new
Policy and value networks, trained from human games and self-play reinforcement learning, guiding Monte Carlo tree search.

How to read it: A perfect bridge between this chapter's two halves: symbolic search, guided by learned networks.

~1 h readdoi:10.1038/nature16961✓ verified 2026-09-26
Essential

Attention Is All You Need

Ashish Vaswani, Noam Shazeer et al. · 2017 · NeurIPS 2017

Introduced the Transformer — the architecture behind BERT, GPT and nearly every modern large language model, and later adapted to vision, audio and more.

Problem
Recurrent models process tokens one after another, which limits parallel training and forces distant words to interact through many sequential steps.
What was new
Dropped recurrence entirely: stacks of multi-head self-attention and feed-forward layers, with positional encodings, residual connections and layer normalization.

How to read it: Section 3 is the architecture — read it with Figure 1 open. Sections 3.2.1–3.2.2 contain the attention equation. You can skim the training details on a first pass.

~1 h 15 min readarXiv:1706.03762✓ verified 2026-09-26
Essential

Deep reinforcement learning from human preferences

Paul Christiano, Jan Leike et al. · 2017 · NeurIPS 2017

Showed that agents can be trained from human comparisons between behaviours rather than a hand-written reward — the foundation of RLHF.

Problem
For many tasks, writing a reward function that captures what we want is hard or impossible.
What was new
Learn a reward model from pairwise human preferences, then optimize a policy against it with reinforcement learning.
~45 min readarXiv:1706.03741✓ verified 2026-09-26
Essential

BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

Jacob Devlin, Ming-Wei Chang et al. · 2018 · NAACL 2019

Made 'pretrain once, fine-tune everywhere' the default in NLP, using an encoder-only Transformer that reads context in both directions.

Problem
Language models read left-to-right, so their representations of a word couldn't use the words that came after it.
What was new
Masked language modeling: hide random tokens and train an encoder to fill them in from both sides.
~50 min readarXiv:1810.04805✓ verified 2026-09-26
Essential

Language Models are Few-Shot Learners

Tom B. Brown, Benjamin Mann et al. · 2020 · NeurIPS 2020

GPT-3 (175B parameters) showed that a large enough language model can perform new tasks from a few examples in its prompt, without any gradient updates.

Problem
Each new NLP task needed its own labelled dataset and fine-tuning run.
What was new
Scale a decoder-only Transformer by ~100× and evaluate zero-, one- and few-shot 'in-context learning' across many tasks.

How to read it: 75 pages. Sections 1–2 and Figure 1.2 carry the core idea; Section 6 on broader impacts is worth reading too.

~1 h 30 min readarXiv:2005.14165✓ verified 2026-09-26
Essential

Scaling Laws for Neural Language Models

Jared Kaplan, Sam McCandlish et al. · 2020

Found that language-model loss falls as a smooth power law in parameters, data and compute — making model scale something you could plan.

Problem
There was no quantitative way to predict how much better a larger model would be.
What was new
Empirical power-law fits of loss against model size, dataset size and compute, over many orders of magnitude.
~1 h readarXiv:2001.08361✓ verified 2026-09-26
Essential

Learning Transferable Visual Models From Natural Language Supervision

Alec Radford, Jong Wook Kim et al. · 2021 · ICML 2021

CLIP learned a shared space for images and text from web captions — the backbone of much multimodal AI and text-to-image generation.

Problem
Vision models needed large hand-labelled datasets and only recognized fixed label sets.
What was new
Contrastive training on hundreds of millions of image–caption pairs, enabling zero-shot classification from text descriptions.
~1 h readarXiv:2103.00020✓ verified 2026-09-26
Essential

Training Compute-Optimal Large Language Models

Jordan Hoffmann, Sebastian Borgeaud et al. · 2022 · NeurIPS 2022

Showed that many large models were undertrained: for a fixed compute budget, parameters and training tokens should grow roughly in proportion.

Problem
Earlier scaling recommendations favoured very large models trained on comparatively little data.
What was new
Trained 400+ models to fit compute-optimal trade-offs; the 70B 'Chinchilla' model outperformed much larger models trained on fewer tokens.
~1 h readarXiv:2203.15556✓ verified 2026-09-26
Essential

Chain-of-Thought Prompting Elicits Reasoning in Large Language Models

Jason Wei, Xuezhi Wang et al. · 2022 · NeurIPS 2022

Showed that prompting large models to write out intermediate steps markedly improves multi-step reasoning — the seed of today's reasoning models.

Problem
Large models often failed at arithmetic and multi-step reasoning when asked for the answer directly.
What was new
Few-shot examples that include step-by-step reasoning, which large enough models imitate.
~40 min readarXiv:2201.11903✓ verified 2026-09-26
Essential

Training language models to follow instructions with human feedback

Long Ouyang, Jeff Wu et al. · 2022 · NeurIPS 2022

InstructGPT: the supervised fine-tuning + reward model + RL recipe that turned GPT-3 into an instruction-following assistant, and the template for ChatGPT.

Problem
Pretrained language models continue text; they don't reliably follow instructions or behave helpfully.
What was new
Fine-tune on human demonstrations, train a reward model on human rankings, then optimize the model against it with PPO.

How to read it: Figure 2 is the three-step RLHF pipeline you'll meet in Chapter 10.

~1 h readarXiv:2203.02155✓ verified 2026-09-26

Important25

Worth reading once you're comfortable with the essentials.

Important

A logical calculus of the ideas immanent in nervous activity

Warren S. McCulloch, Walter Pitts · 1943 · The Bulletin of Mathematical Biophysics

The first mathematical model of a neuron as a logic unit — the seed of both neural networks and the idea that thought could be computation.

Problem
How could networks of simple nerve cells carry out logical reasoning?
What was new
Idealized binary neurons with thresholds, shown to be able to compute logical functions when connected into networks.

How to read it: Historically important but hard to read today. The idea — neurons as threshold logic gates — is what matters.

~1 h readdoi:10.1007/BF02478259✓ verified 2026-09-26
Important

A Mathematical Theory of Communication

C. E. Shannon · 1948 · Bell System Technical Journal

Founded information theory: it defined entropy as a measure of uncertainty and showed how much any message can be compressed. Cross-entropy loss and perplexity come straight from here.

Problem
There was no precise way to measure information, or to say how efficiently it could be encoded and transmitted over a noisy channel.
What was new
Entropy H = −Σ p log p as the average information of a source, plus limits on compression and reliable communication. It even includes early statistical models of English text built from n-gram frequencies.

How to read it: Don't read it cover to cover. Part I (sections 1–7) contains entropy and the famous 'series of approximations to English' — a 1948 language model.

~2 h readdoi:10.1002/j.1538-7305.1948.tb01338.x✓ verified 2026-09-26
Important

A Proposal for the Dartmouth Summer Research Project on Artificial Intelligence, August 31, 1955

John McCarthy, Marvin L. Minsky et al. · 1955 · Reprinted in AI Magazine 27(4), 2006

The document that named the field 'artificial intelligence' and set out its founding ambition.

Problem
Scattered work on thinking machines had no shared name, agenda or community.
What was new
A two-month study proposed on the conjecture that every aspect of learning or intelligence can in principle be described precisely enough for a machine to simulate it.

How to read it: Short. Notice how many of its topics — language, neuron nets, abstraction, self-improvement — are still open problems.

~20 min read✓ verified 2026-09-26
Important

Some Studies in Machine Learning Using the Game of Checkers

A. L. Samuel · 1959 · IBM Journal of Research and Development

One of the first programs that improved by learning from play — an early demonstration that learning can beat hand-tuning.

Problem
Writing a strong game evaluation by hand required expertise the programmer might not have.
What was new
Search combined with an evaluation function whose weights were adjusted automatically from experience, including self-play.
~1 h readdoi:10.1147/rd.33.0210✓ verified 2026-09-26
Important

A Formal Basis for the Heuristic Determination of Minimum Cost Paths

Peter Hart, Nils Nilsson, Bertram Raphael · 1968 · IEEE Transactions on Systems Science and Cybernetics

Introduced A*, the heuristic search algorithm still used in route planning, games and robotics.

Problem
Blind search explores far too many states; how can knowledge about the goal guide it without losing optimality?
What was new
Rank states by cost-so-far plus an estimate of cost-to-go; with an estimate that never overestimates, the first path found is optimal.
~40 min readdoi:10.1109/TSSC.1968.300136✓ verified 2026-09-26
Important

Computer science as empirical inquiry

Allen Newell, Herbert A. Simon · 1976 · Communications of the ACM

The classic statement of the symbolic-AI worldview: the physical symbol system hypothesis and heuristic search as the heart of intelligence.

Problem
What, if anything, do all intelligent systems have in common?
What was new
The claim that a physical symbol system has the necessary and sufficient means for general intelligent action.

How to read it: Their 1975 Turing Award lecture. Read it as the best case for the approach this chapter shows running into limits.

~40 min readdoi:10.1145/360018.360022✓ verified 2026-09-26
Important

Multilayer feedforward networks are universal approximators

Kurt Hornik, Maxwell Stinchcombe, Halbert White · 1989 · Neural Networks

Proved that a network with a single hidden layer can approximate essentially any continuous function, given enough units — the 'universal approximation' result.

Problem
Were multi-layer networks fundamentally limited, as single-layer perceptrons had been shown to be?
What was new
A proof that standard feedforward networks with one hidden layer are universal approximators.

How to read it: A theoretical result: it says a good network exists, not that training will find it or how big it must be.

~40 min readdoi:10.1016/0893-6080(89)90020-8✓ verified 2026-09-26
Important

Learning long-term dependencies with gradient descent is difficult

Yoshua Bengio, Patrice Simard, Paolo Frasconi · 1994 · IEEE Transactions on Neural Networks

Showed why gradients vanish or explode when trained across many steps — the core obstacle for deep and recurrent networks.

Problem
Recurrent networks failed to learn dependencies spanning long time gaps.
What was new
Analysis showing a trade-off between storing information robustly and propagating useful gradients, so gradients shrink exponentially with distance.
~50 min readdoi:10.1109/72.279181✓ verified 2026-09-26
Important

Support-vector networks

Corinna Cortes, Vladimir Vapnik · 1995 · Machine Learning

Introduced the soft-margin support vector machine, the dominant classifier of the late 1990s and 2000s.

Problem
How do you pick, among all boundaries that separate the data, the one most likely to generalize — and handle data that isn't perfectly separable?
What was new
Maximize the margin to the nearest points, allow some violations with a penalty, and use kernels to separate data in high-dimensional feature spaces.
~1 h readdoi:10.1007/BF00994018✓ verified 2026-09-26
Important

Random Forests

Leo Breiman · 2001 · Machine Learning

Random forests — many decision trees trained on random subsets of data and features, then averaged — remain one of the strongest methods for tabular data.

Problem
Single decision trees overfit easily and are unstable: small data changes produce very different trees.
What was new
Average many decorrelated trees, each grown on a bootstrap sample with a random subset of features at each split.
~50 min readdoi:10.1023/A:1010933404324✓ verified 2026-09-26
Important

A Neural Probabilistic Language Model

Yoshua Bengio, Réjean Ducharme et al. · 2003 · Journal of Machine Learning Research

Learned word representations and next-word probabilities jointly, so similar words could help the model generalize to word sequences it had never counted.

Problem
An n-gram table sees most possible word sequences zero times, and counting alone cannot share evidence between similar words.
What was new
A neural probability model that looks up a distributed vector for each context word and learns those vectors with the prediction task.

How to read it: Read the abstract and Figure 1 first: the embedding lookup and the probability model are learned together.

~45 min read✓ verified 2026-09-26
Important

Understanding the difficulty of training deep feedforward neural networks

Xavier Glorot, Yoshua Bengio · 2010 · AISTATS 2010

Explained why deep networks with sigmoid units and naive initialization trained poorly, and introduced 'Xavier' initialization.

Problem
Deep networks trained with standard gradient descent from random initialization got stuck or trained very slowly.
What was new
An analysis of how activations and gradients change across layers, and an initialization that keeps their variance roughly constant.
~40 min read✓ verified 2026-09-26
Important

Leakage in data mining

Shachar Kaufman, Saharon Rosset et al. · 2012 · ACM Transactions on Knowledge Discovery from Data

Named and systematized data leakage — information in training data that won't exist at prediction time — one of the most common ways ML results turn out to be fake.

Problem
Models that looked excellent in evaluation failed in deployment because their training data contained hints about the answer.
What was new
A formal definition of leakage, a catalogue of real examples, and methods to detect and avoid it.
~45 min readdoi:10.1145/2382577.2382579✓ verified 2026-09-26
Important

Distributed Representations of Words and Phrases and their Compositionality

Tomas Mikolov, Ilya Sutskever et al. · 2013 · NeurIPS 2013

Introduced negative sampling as a faster way to train skip-gram word vectors and explicitly discussed the limits of word-only representations.

Problem
Full-vocabulary prediction was expensive, especially for large corpora and vocabularies.
What was new
Train a word-context pair against a few sampled non-pairs, alongside subsampling of frequent words and phrase discovery.
~40 min readarXiv:1310.4546✓ verified 2026-09-26
Important

GloVe: Global Vectors for Word Representation

Jeffrey Pennington, Richard Socher, Christopher Manning · 2014 · EMNLP 2014

Showed another path to word vectors: fit them to global word co-occurrence statistics rather than only local prediction examples.

Problem
Local context prediction does not explicitly use the full corpus-wide co-occurrence table.
What was new
Fit vector dot products to log co-occurrence counts so vector relationships reflect probability ratios.
~45 min readdoi:10.3115/v1/D14-1162✓ verified 2026-09-26
Important

Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation

Kyunghyun Cho, Bart van Merrienboer et al. · 2014 · EMNLP 2014

Proposed a jointly trained RNN encoder and decoder for mapping one sequence to another, with the gated recurrent unit in the architecture.

Problem
Translation must map an input phrase to an output phrase of a different length.
What was new
Encode a variable-length source into one vector, then decode a variable-length target; use gates to control recurrent memory.
~50 min readarXiv:1406.1078✓ verified 2026-09-26
Important

Dropout: A Simple Way to Prevent Neural Networks from Overfitting

Nitish Srivastava, Geoffrey Hinton et al. · 2014 · Journal of Machine Learning Research

Dropout — randomly switching off units during training — became a standard, simple regularizer for neural networks.

Problem
Large neural networks overfit, and averaging many separately trained networks is expensive.
What was new
Randomly drop units during training, effectively training an ensemble of thinned networks that share weights; use the full network at test time.
~50 min read✓ verified 2026-09-26
Important

Human-level control through deep reinforcement learning

Volodymyr Mnih, Koray Kavukcuoglu et al. · 2015 · Nature

A single deep network learned to play dozens of Atari games from raw pixels and score alone — deep learning meets reinforcement learning.

Problem
Reinforcement learning had struggled to learn directly from high-dimensional sensory input.
What was new
Deep Q-networks trained with experience replay and a periodically updated target network.
~45 min readdoi:10.1038/nature14236✓ verified 2026-09-26
Important

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

Sergey Ioffe, Christian Szegedy · 2015 · ICML 2015

Batch normalization made deep networks train faster and more reliably with higher learning rates; it became standard in convolutional networks.

Problem
Training deep networks was slow and sensitive to initialization and learning rate.
What was new
Normalize each layer's activations using the mean and variance of the current mini-batch, with learned scale and shift.

How to read it: The paper's explanation ('internal covariate shift') has been questioned since; the technique's usefulness has not.

~40 min readarXiv:1502.03167✓ verified 2026-09-26
Important

Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification

Kaiming He, Xiangyu Zhang et al. · 2015 · ICCV 2015

Introduced the initialization ('He' or 'Kaiming' initialization) suited to ReLU networks, plus the PReLU activation.

Problem
Initializations designed for sigmoid-like units made very deep ReLU networks fail to train.
What was new
Scale initial weights by √(2 / fan-in) to keep activation variance stable through ReLU layers.
~40 min readarXiv:1502.01852✓ verified 2026-09-26
Important

Layer Normalization

Jimmy Lei Ba, Jamie Ryan Kiros, Geoffrey E. Hinton · 2016

The normalization used inside Transformers; it keeps activations at a stable scale regardless of batch size.

Problem
Batch normalization depends on batch statistics, which is awkward for recurrent networks and small or variable batches.
What was new
Normalize across the features of each individual example instead of across the batch.
~30 min readarXiv:1607.06450✓ verified 2026-09-26
Important

An overview of gradient descent optimization algorithms

Sebastian Ruder · 2016

The standard readable survey of SGD, momentum, RMSprop, Adam and friends — one paper that explains the whole optimizer family tree.

Problem
Optimizers were used as black boxes; their motivations and differences were scattered across many papers.
What was new
A single, intuitive comparison of gradient-descent variants, their update rules and when each helps.

How to read it: Very approachable. Read it after trying the Gradient Descent Playground.

~40 min readarXiv:1609.04747✓ verified 2026-09-26
Important

Decoupled Weight Decay Regularization

Ilya Loshchilov, Frank Hutter · 2017 · ICLR 2019

Introduced AdamW, the variant of Adam used to train most modern Transformers and LLMs.

Problem
With Adam, the usual L2 regularization doesn't behave like true weight decay, hurting generalization.
What was new
Apply weight decay directly to the weights, separately ('decoupled') from Adam's adaptive gradient step.
~40 min readarXiv:1711.05101✓ verified 2026-09-26
Important

Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer

Colin Raffel, Noam Shazeer et al. · 2019 · JMLR 2020

Framed every NLP task as text in, text out, using an encoder–decoder Transformer — and ran a huge, careful set of ablations that is still a model of empirical method.

Problem
Transfer-learning results were hard to compare because every paper changed many things at once.
What was new
One text-to-text format for all tasks, plus a systematic study of objectives, architectures and data.

How to read it: Long (67 pages). Read the introduction and Section 3.2's architecture comparison; treat the rest as a reference.

~2 h readarXiv:1910.10683✓ verified 2026-09-26
Important

DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

DeepSeek-AI et al. · 2025

An openly released reasoning model, with a detailed account of training long chains of reasoning mainly through reinforcement learning on verifiable problems.

Problem
How reasoning models were trained was largely undisclosed.
What was new
Large-scale RL with rule-based rewards on math and code, plus distillation of the resulting reasoning into smaller open models.
~1 h readarXiv:2501.12948✓ verified 2026-09-26

Optional9

For going deeper on a specific thread.

Optional

On lines and planes of closest fit to systems of points in space

Karl Pearson · 1901 · Philosophical Magazine

The origin of principal component analysis: find the directions along which data varies most.

Problem
How can many correlated measurements be summarized by a few underlying directions?
What was new
Fit the line or plane that minimizes perpendicular distances to the points — what we now call the first principal components.
~30 min readdoi:10.1080/14786440109462720✓ verified 2026-09-26
Optional

A Stochastic Approximation Method

Herbert Robbins, Sutton Monro · 1951 · The Annals of Mathematical Statistics

The mathematical ancestor of stochastic gradient descent: it showed that noisy, step-by-step updates can still converge to the right answer.

Problem
How do you find the root of a function when you can only observe noisy measurements of it?
What was new
An iterative procedure with decreasing step sizes that provably converges despite the noise.

How to read it: A pure mathematics paper. Knowing it exists — and that SGD's convergence story starts here — is enough for now.

~45 min readdoi:10.1214/aoms/1177729586✓ verified 2026-09-26
Optional

On Information and Sufficiency

S. Kullback, R. A. Leibler · 1951 · The Annals of Mathematical Statistics

Introduced the divergence now called KL divergence — used in distillation, RLHF's penalty term, variational methods and more.

Problem
How do you measure how different one probability distribution is from another, in information-theoretic terms?
What was new
A directed measure of the information lost when one distribution is used to approximate another.
~45 min readdoi:10.1214/aoms/1177729694✓ verified 2026-09-26
Optional

ELIZA—a computer program for the study of natural language communication between man and machine

Joseph Weizenbaum · 1966 · Communications of the ACM

A pattern-matching chatbot that people readily attributed understanding to — an early lesson in how easily fluent text is mistaken for intelligence.

Problem
Could a simple program sustain something that felt like conversation?
What was new
Keyword-triggered transformation rules (the famous 'DOCTOR' script) producing plausible replies with no model of meaning.
~25 min readdoi:10.1145/365153.365168✓ verified 2026-09-26
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Least squares quantization in PCM

S. Lloyd · 1982 · IEEE Transactions on Information Theory

The paper behind 'Lloyd's algorithm', the standard iterative procedure for k-means clustering (circulated at Bell Labs in 1957, published 1982).

Problem
How should a continuous signal be quantized into a few levels with the least squared error?
What was new
Alternate between assigning points to their nearest centre and moving each centre to the mean of its points.
~40 min readdoi:10.1109/TIT.1982.1056489✓ verified 2026-09-26
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Approximation by superpositions of a sigmoidal function

G. Cybenko · 1989 · Mathematics of Control, Signals, and Systems

An independent universal-approximation proof for networks with sigmoid hidden units.

Problem
Can sums of sigmoid functions approximate arbitrary continuous functions?
What was new
Yes — finite superpositions of sigmoids are dense in the space of continuous functions on a bounded domain.
~30 min readdoi:10.1007/BF02551274✓ verified 2026-09-26
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Regression Shrinkage and Selection Via the Lasso

Robert Tibshirani · 1996 · Journal of the Royal Statistical Society, Series B

Introduced the lasso (L1 regularization), which shrinks weights and sets many exactly to zero — regularization and feature selection at once.

Problem
Least-squares regression overfits with many features and produces hard-to-interpret models.
What was new
Penalize the sum of absolute weight values; the geometry of this penalty drives many weights to exactly zero.
~50 min readdoi:10.1111/j.2517-6161.1996.tb02080.x✓ verified 2026-09-26
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Gaussian Error Linear Units (GELUs)

Dan Hendrycks, Kevin Gimpel · 2016

The GELU activation, a smooth relative of ReLU used in BERT, GPT-2 and many later Transformers.

Problem
ReLU's hard cut-off at zero isn't smooth and ignores the size of negative inputs.
What was new
Weight each input by the probability a standard Gaussian falls below it: x·Φ(x).
~30 min readarXiv:1606.08415✓ verified 2026-09-26
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On Layer Normalization in the Transformer Architecture

Ruibin Xiong, Yunchang Yang et al. · 2020 · ICML 2020

Explains why modern Transformers put layer normalization before each sublayer ('pre-LN') rather than after it.

Problem
The original post-LN Transformer needed a careful learning-rate warm-up to train stably.
What was new
Analysis showing pre-LN keeps gradients well-behaved at initialization, allowing training without warm-up.
~1 h readarXiv:2002.04745✓ verified 2026-09-26