Deep Learning: Our Miraculous Year 1990-1991

Jürgen Schmidhuber (2019, updated 2020, 2021, 2022)
Pronounce: You_again Shmidhoobuh
Preprint arxiv:2005.05744
AI Blog
Inaugural tweet: 4 Oct 2019

Deep Learning: Our Miraculous Year 1990-1991

Our impact on the world's most valuable public companies: Apple (#1), Alphabet (#2), Microsoft (#3),Facebook (#4), Amazon (#5) ... The Deep Learning Artificial Neural Networks (NNs) of our team have revolutionized Machine Learning and Artificial Intelligence, and are now heavily used in academia and industry.[DL4] In 2020/2021, we celebrated the 30th anniversaries of many of the ideas that set in motion this revolution; amazingly, they were published within fewer than 12 months during the "Annus Mirabilis" that ran from 1990-1991 at our lab in TU Munich. Back then, few people were interested, but a quarter century later, NNs based on our "Miraculous Year" were on over 3 billion devices, and used many billions of times per day, consuming a significant fraction of the world's compute.[DL4]

The following summary of what happened in 1990-91 both contains some high-level context which is accessible by a general audience, but also references to original sources for NN experts. I also mention selected later work which further developed the ideas of 1990-91 (at TU Munich, the Swiss AI Lab IDSIA, and other places), as well as related work by others.

Table of contents

Sec. 0: Background on Deep Learning in Artificial Neural Nets (NNs)
Sec. 1: First Very Deep Learner, Based on Unsupervised/Self-Supervised Pre-Training (1991)
Sec. 2: Compressing / Distilling one Neural Net into Another (1991)
Sec. 3: The Fundamental Deep Learning Problem (Vanishing / Exploding Gradients, 1991)
Sec. 4: Long Short-Term Memory: Supervised Very Deep Learning (basic insights since 1991)
Sec. 5: Artificial Curiosity Through Adversarial Generative NNs (1990)
Sec. 6: Artificial Curiosity Through NNs that Maximize Learning Progress (1991)
Sec. 7: Adversarial Networks Create Disentangled Data Representations (1991)
Sec. 8: NNs Learn to Program NNs (1991): Transformer with Linearized Self-Attention
Sec. 9: Learning Sequential Attention with NNs (1990)
Sec. 10: Gradient Descent Finds Subgoals for Hierarchical Reinforcement Learning (1990)
Sec. 11: Planning and Reinforcement Learning with Recurrent Neural World Models (1990)
Sec. 12: Goal-Defining Commands as Extra NN Inputs (1990)
Sec. 13: High-Dimensional Reward Signals as NN Inputs / General Value Functions (1990)
Sec. 14: Deterministic Policy Gradients (1990)
Sec. 15: Networks Adjust Networks / Synthetic Gradients (1990)
Sec. 16: O(n3) Gradient Computation for Online Recurrent NNs (1991)
Sec. 17: The Neural Heat Exchanger (1990): Deep Learning Through Local Computations
Sec. 18: My PhD Thesis (1991)
Sec. 19: From Unsupervised Pre-Training to Pure Supervised Learning (1991-95 and 2006-11)
Sec. 20: The Amazing FKI Tech Report Series on Artificial Intelligence in the 1990s
Sec. 21: Concluding Remarks

Background on Deep Learning in Neural Nets (NNs)

Deep Learning in Neural Networks: An Overview

The human brain has on the order of 100 billion neurons, each connected to 10,000 other neurons on average. Some are input neurons that feed the rest with data (sound, vision, tactile, pain, hunger). Others are output neurons that control muscles. Most neurons are hidden in between, where thinking takes place. Your brain apparently learns by changing the strengths or weights of the connections, which determine how strongly neurons influence each other, and which seem to encode all your lifelong experience. Similar for our artifical neural networks (NNs), which learn better than previous methods to recognize speech or handwriting or video, minimize pain, maximize pleasure, drive cars, etc.[DL1-4]

who invented backpropagation?

Most current commercial applications focus on supervised learning to make NNs imitate human teachers.[DL1-4] In the course of many trials, Seppo Linnainmaa's gradient-computing algorithm of 1970,[BP1][DLH] today often called backpropagation or the reverse mode of automatic differentiation, is used to incrementally weaken certain NN connections and strengthen others, such that the NN behaves more and more like the teacher.[BPA-C][BP2][HIN][T20][T22]

Today's most powerful NNs tend to be very deep, that is, they have many layers of neurons or many subsequent computational stages. In the 1980s, however, gradient-based training did not work well for deep NNs, only for shallow ones.[DL1-2]

This Deep Learning Problem was most obvious for recurrent NNs (RNNs). RNN architectures have been studied since the 1920s.[L20][I24-I25][K41][MC43][W45][K56][AMH1-2][PDA2] Like the human brain, but unlike the more limited feedforward NNs (FNNs), RNNs have feedback connections. This makes RNNs powerful, general purpose, parallel-sequential computers that can process input sequences of arbitrary length (think of speech data or videos). RNNs can in principle implement any program that can run on your laptop or any other computer in existence. If we want to build an Artificial General Intelligence (AGI), then its underlying computational substrate must be something more like an RNN than an FNN as FNNs are fundamentally insufficient; RNNs are to FNNs as general computers are to pocket calculators.

In particular, unlike FNNs, RNNs can in principle deal with problems of arbitrary depth.[DL1] Early RNNs of the 1980s, however, failed to learn deep problems in practice. From early in my career, I wanted to overcome this drawback, to achieve RNN-based "general purpose Deep Learning" or "general Deep Learning."

1. First Very Deep NNs, Based on Unsupervised or Self-Supervised Pre-Training (1991)

First Very Deep Learner of 1991

My first idea to overcome the Deep Learning Problem mentioned above was to facilitate supervised learning in deep RNNs by unsupervised pre-training of a hierarchical stack of RNNs (1991), to obtain a first "Very Deep Learner" called the Neural Sequence Chunker[UN0] or Neural History Compressor.[UN1] Each higher level minimizes the description length (or negative log probability) of the data representation in the level below, using the Predictive Coding trick: try to predict the next input in the incoming data stream, given the previous inputs, and update neural activations only in case of unpredictable data, thus storing only what's not yet known. In other words, the chunker learns to compress the data stream such that the Deep Learning Problem becomes less severe, and can be solved by standard backpropagation. Although computers back then were about a million times slower per dollar than today, by 1993, my method was able to solve previously unsolvable "Very Deep Learning" tasks of depth > 1000[UN2] (requiring more than 1,000 subsequent computational stages—the more such stages, the deeper the learning). In 1993, we also published a continuous version of the Neural History Compressor.[UN3]

To my knowledge, the Sequence Chunker[UN0] also was the first system made of RNNs operating on different (self-organizing) time scales.[UN] (But I also had a way of distilling all those RNNs down into a single deep RNN operating on a single time scale—see Sec. 2.) A few years later, others also started publishing on multi-time scale RNNs[HB96] (see also the Clockwork RNN[CW]).

More than a decade after this work,[UN1] a similar method for more limited feedforward NNs (FNNs) was published, facilitating supervised learning by unsupervised pre-training of stacks of FNNs called Deep Belief Networks (DBNs).[UN4] The 2006 justification was essentially the one I used in the early 1990s for my RNN stack: each higher level tries to reduce the description length (or negative log probability) of the data representation in the level below.[HIN]

First Deep Learner to win a contest on object detection in large images—First Deep Learner to win a medical imaging contest

Soon after the unsupervised pre-training-based Very Deep Learner above, the Deep Learning Problem (see Sec. 3) was also overcome through our purely supervised LSTM (Sec. 4). Much later, between 2006 and 2011, my lab also drove a very similar shift from unsupervised pre-training to pure supervised learning, two decades after our Miraculous Year, this time for the less general feedforward NNs (FNNs) rather than recurrent NNs (RNNs), with revolutionary applications to cancer detection and many other problems. See Sec. 19 for more on this.

Of course, Deep Learning in feedforward NNs started much earlier, with Ivakhnenko & Lapa, who published the first general, working learning algorithms for deep multilayer perceptrons with arbitrarily many layers back in 1965.[DEEP1] For example, Ivakhnenko's paper from 1971[DEEP2] already described a Deep Learning net with 8 layers, trained by a highly cited method still popular in the new millennium.[DL2] But unlike the deep FNNs of Ivakhnenko and his successors of the 1970s and 80s, our deep RNNs had general purpose parallel-sequential computational architectures.[UN-UN3] By the early 1990s, most NN research was still limited to rather shallow nets with fewer than 10 subsequent computational stages, while our methods already enabled over 1,000 such stages. In this sense we were the ones who made NNs really deep, especially RNNs, the deepest and most powerful nets of them all.

2. Compressing/Distilling an NN into Another NN (1991)

My First Deep Learning System of 1991 + Deep Learning Timeline 1962-2013

My above-mentioned paper on the Neural History Compressor (see Sec. 1) also introduced a way of compressing the network hierarchy (whose higher levels are typically running on much slower self-organising time scales than lower levels) into a single deep RNN[UN1] which thus learned to solve very deep problems despite the obstacles mentioned in Sec. 0. This is described in Section 4 of the paper on the "conscious" chunker and a "subconscious" automatiser,[UN1] which introduced a general principle for transferring the knowledge of one NN to another. Suppose a teacher NN has learned to predict (conditional expectations of) data, given other data. Its knowledge can be compressed into a student NN, by training the student NN to imitate the behavior of the teacher NN (while also re-training the student NN on previously learned skills such that it does not forget them).

I called this "collapsing" or "compressing" the behavior of one net into another. Today, this is widely used, and also called "distilling"[DIST2][HIN][T22] or "cloning" the behavior of a teacher net into a student net.

3. The Fundamental Deep Learning Problem: Vanishing / Exploding Gradients (1991)

Sepp Hochreiter's Analysis of the Fundamental Deep Learning Problem (1991)

The background section Sec. 0 pointed out that Deep Learning is hard. But why is it hard? A main reason is what I like to call the Fundamental Deep Learning Problem identified and analyzed in 1991 by my first student Sepp Hochreiter in his diploma thesis.[VAN1]

As a part of his thesis, Sepp implemented the Neural History Compressor above (see Sec. 1) and other RNN-based systems (see Sec. 11). However, he did much more: His work formally showed that deep NNs suffer from the now famous problem of vanishing or exploding gradients: in typical deep or recurrent networks, back-propagated error signals either shrink rapidly, or grow out of bounds. In both cases, learning fails. This analysis led to basic principles of what's now called LSTM (see Sec. 4).

Note that Sepp's thesis identified those problems of backpropagation in deep NNs two decades after another student with a similar first name (Seppo Linnainmaa) published modern backpropagation or the reverse mode of automatic differentiation in his own thesis of 1970.[BP1]

Interestingly, in 1994, others published results[VAN2] essentially identical to the 1991 vanishing gradient results of Sepp.[VAN1] Even after a common publication[VAN3] the first author of reference[VAN2] published papers[VAN4] that cited only their own 1994 paper but not Sepp's original work.

4. Long Short-Term Memory Recurrent Networks: Supervised Very Deep Learning

Recurrent Neural Networks, especially LSTM

The Long Short-Term Memory (LSTM) recurrent neural network[LSTM1-6] overcomes the Fundamental Deep Learning Problem identified by Sepp in his above-mentioned 1991 diploma thesis[VAN1] (see Sec. 3), which I consider one of the most important documents in the history of machine learning. It also provided essential insights for overcoming the problem, through basic principles (such as constant error flow) of what we called LSTM in a tech report of 1995.[LSTM0] This led to lots of follow-up work described below.

In 2020 we celebrated the quarter-century anniversary of LSTM's first failure to pass peer review. After the main peer-reviewed publication in 1997[LSTM1] (now the most cited article in the history of Neural Computation[25y97]), LSTM and its training procedures were further improved on my Swiss LSTM grants at IDSIA through the work of my later students Felix Gers, Alex Graves, and others. A milestone was the "vanilla LSTM architecture" with forget gate[LSTM2]—the LSTM variant of 1999-2000 that everybody is using today, e.g., in Google's Tensorflow. The LSTM forget gate is actually an end-to-end differentiable fast weight controller of the type we also introduced in 1991[FWP,FWP0] (see Sec. 8).

Our impact on the world's most valuable public companies (Google, Apple, Microsoft, Facebook, Amazon etc)

Alex was lead author of our first successful application of LSTM to speech (2004).[LSTM10] 2005 saw the first publication of LSTM with full backpropagation through time and of bi-directional LSTM[LSTM3] (now widely used). Another milestone of 2006 was the training method "Connectionist Temporal Classification" or CTC[CTC] for simultaneous alignment and recognition of sequences. Our team successfully applied CTC-trained LSTM to speech in 2007[LSTM4] (also with hierarchical LSTM stacks[LSTM14]). This was the first superior end-to-end neural speech recognition. It was very different from hybrid methods since the late 1980s which combined NNs and traditional approaches such as Hidden Markov Models (HMMs).[BW][BRI][BOU][HYB12][T22] In 2015, the CTC-LSTM combination dramatically improved Google's speech recognition on the Android smartphones.[GSR15][DL4][DLH]

The first superior end-to-end neural machine translation was also based on our LSTM. In 1995, we already had an excellent neural probabilistic text model.[SNT] In the early 2000s, we showed how LSTM can learn languages unlearnable by traditional models such as Hidden Markov Models.[LSTM13] This took a while to sink in, and compute still had to get 1000 times cheaper, but by 2016-17, both Google Translate[WU][GT16] and Facebook Translate[FB17] were based on two connected LSTMs,[S2S] one for the incoming text, one for the outgoing translation, much better than what they had before.[DL4]

In 2009, my PhD student Justin Bayer was lead author of a system that automatically designed LSTM-like architectures outperforming vanilla LSTM in certain applications.[LSTM7] In 2017, Google started using similar "neural architecture search."[NAS]

Winning Vision and Handwriting Recognition Competitions Through Purely Supervised Deep Learning Since 2009 Since 2006, we have worked with the software industry (e.g., LifeWare) to greatly improve handwriting recognition. In 2009, through the efforts of Alex, LSTM trained by CTC became the first RNN to win international competitions, namely, three ICDAR 2009 Connected Handwriting Competitions (French, Farsi, Arabic). This attracted enormous interest from industry. LSTM was soon used for everything that involves sequential data such as language and speech[LSTM10-11][LSTM4][DL1] and videos. By 2017, LSTM powered Facebook's machine translation (over 30 billion translations per week),[FB17][DL4] Apple's Quicktype on roughly 1 billion iPhones,[DL4] the voice of Amazon's Alexa,[DL4] Google's speech recognition (on Android smartphones since 2015)[GSR15][DL4] & image caption generation[DL4] & machine translation[GT16][DL4] & automatic email answering[DL4] etc. Business Week called LSTM "arguably the most commercial AI achievement."[AV1]

By 2016, more than a quarter of the awesome computational power for inference in Google's datacenters was used for LSTM (and 5% for another popular Deep Learning technique called CNNs—see Sec. 19).[JOU17] Google's new on-device speech recognition of 2019 (now on your phone, not on the server) is still based on LSTM.

Highway Networks:
First Working Feedforward Networks With Over 100 Layers

Through the work of my students Rupesh Kumar Srivastava and Klaus Greff, the LSTM principle also led to our Highway Networks[HW1] of May 2015, the first working very deep FNNs with hundreds of layers (previous NNs had at most a few tens of layers). Microsoft's popular ResNets[HW2] (which won the ImageNet 2015 contest) are a version thereof (ResNets are Highway Nets whose gates are always open). The earlier Highway Nets perform roughly as well as ResNets on ImageNet.[HW3] Highway layers are also often used for natural language processing, where the simpler residual layers do not work as well.[HW3]

Deep learning is all about NN depth.[DL1][DLH] LSTMs brought essentially unlimited depth to supervised recurrent NNs; Highway Nets brought it to feedforward NNs. Interestingly, LSTM has become the most cited NN of the 20th century; the Highway Net version called ResNet the most cited NN of the 21st.[MOST]

Deep Reinforcement Learning with Policy Gradients for Long Short-Term Memory (LSTM) )

We also trained LSTM through Reinforcement Learning (RL) for robotics without a teacher, e.g., with my postdoc Bram Bakker[LSTM-RL] (2002). And also through Neuroevolution and policy gradients, e.g., with my PhD student Daan Wierstra,[LSTM12][RPG07][RPG][LSTMPG] who later became employee number 1 of DeepMind, the company co-founded by his friend Shane Legg, another PhD student from my lab (Shane and Daan were the first persons at DeepMind with AI publications and PhDs in computer science). RL with LSTM has become important. For example, in 2019, DeepMind beat a pro player in the game of Starcraft, which is harder than Chess or Go[DM2] in many ways, using Alphastar whose brain has a deep LSTM core trained by RL.[DM3] An RL LSTM (with 84% of the model's total parameter count) also was the core of the famous OpenAI Five which learned to defeat human experts in the Dota 2 video game (2018).[OAI2] Bill Gates called this a "huge milestone in advancing artificial intelligence."[OAI2a]

AI v Covid-19. Juergen Schmidhuber

Essential foundations for all of this were laid in 1991. My team subsequently developed LSTM & CTC etc. with the help of basic funding from TU Munich and the (back then private) Swiss Dalle Molle Institute for AI (IDSIA), as well as public funding which I acquired from Switzerland, Germany, and EU during the "Neural Network Winter" of the 1990s and early 2000s, trying to keep the field alive when few were interested in NNs. I am especially thankful to Professors Kurt Bauknecht, Leslie Kaelbling, Ron Williams, and Ray Solomonoff whose positive reviews of my grant proposals have greatly helped to obtain financial support from SNF since the 1990s.

5. Artificial Curiosity / Generative Adversarial NNs (1990)

artificial curiosity through an adversarial unsupervised minimax game where one neural network minimizes the objective function maximized by another

As humans interact with the world, they learn to predict the consequences of their actions. They are also curious, designing experiments that lead to novel data from which they can learn more. To build curious artificial agents,[AC] I introduced a new type of active unsupervised or self-supervised learning in 1990.[AC90,AC90b] It is based on a minimax game where one NN minimizes the objective function maximized by another NN. Today, I refer to this duel between two unsupervised adversarial NNs as Adversarial Artificial Curiosity,[AC20] to distinguish it from our later types of Artificial Curiosity since 1991 (see Sec. 6).

How does Adversarial Curiosity work? The first NN is called the controller C. C (probabilistically) generates outputs that may influence an environment. The second NN is called the world model M. It predicts the environmental reactions to C's outputs. Using gradient descent, M minimizes its error, thus becoming a better predictor. But in a zero sum game, C tries to find outputs that maximize the error of M. M's loss is the gain of C.

That is, C is motivated to invent novel outputs or experiments that yield data that M still finds surprising, until the data becomes familiar and eventually boring. Compare more recent summaries and extensions of this principle.[AC09] A 2010 survey[AC10] summarised the work of 1990 as follows: a "neural network as a predictive world model is used to maximize the controller's intrinsic reward, which is proportional to the model's prediction errors."

So in 1990 we already had unsupervised or self-supervised neural nets that were both generative and adversarial (using much later terminology from 2014[GAN1]), generating experimental outputs yielding novel data, not only for stationary patterns but also for pattern sequences, and even for the general case of Reinforcement Learning (RL).

The popular Generative Adversarial Networks (GANs)[GAN0-1] (2010-2014) are an application of Adversarial Curiosity[AC90] where the environment simply returns whether C's current output is in a given set.[AC20][T22](Sec. XVII)

BTW, note that the closely related Adversarial Curiosity[AC90,AC90b] & GANs[GAN0-1] & Adversarial Predictability Minimization (see Sec. 7) are very different from other early adversarial machine learning settings[S59][H90] which neither involved unsupervised NNs nor were about modeling data nor used gradient descent.[AC20]

6. Artificial Curiosity Through NNs That Maximize Learning Progress (1991)

Artificial Curiosity & Creativity Since 1990-91

Numerous improvements of the original Adversarial Curiosity of 1990 (AC1990, Sec. 5) are summarized in more recent surveys.[AC06][AC09][AC10][AC] Here I focus on the first important improvement of 1991.[AC91][AC91b]

The errors of AC1990's world model M (to be minimized, Sec. 5) are the rewards of the controller C (to be maximized). This makes for a fine exploration strategy in many deterministic environments. In stochastic environments, however, this might fail. C might learn to focus on situations where M can always get high prediction errors due to randomness, or due to its computational limitations. For example, an agent controlled by C might get stuck in front of a TV screen showing highly unpredictable white noise.[AC10]

Therefore, as pointed out in 1991, in stochastic environments, C's reward should not be the errors of M, but (an approximation of) the first derivative of M's errors across subsequent training iterations, that is, M's improvements.[AC91][AC91b] As a consequence, despite its high errors in front of the noisy TV screen above, C won't get rewarded for getting stuck there. Both the totally predictable and the fundamentally unpredictable will get boring. This insight led to lots of follow-up work[AC10] on artificial scientists and artists.[AC09][AC]

Predictability Minimization: unsupervised minimax game where one neural network minimizes the objective function maximized by another 7. Adversarial Networks Create Disentangled Data Representations (1991)

Soon after my first work on adversarial generative networks in 1990 (see Sec. 5), I introduced a variation of the unsupervised adversarial minimax principle while I was a postdoc at the University of Colorado at Boulder. One of the most important NN tasks is to learn the statistics of given data such as images. To achieve this, I used again the principles of gradient descent/ascent in a minimax game where one NN minimizes the objective function maximized by another. This duel between two unsupervised adversarial NNs was called Predictability Minimization (PM, 1990s).[PM0-2] Contrary to later claims,[GAN1] PM is indeed a pure minimax game, e.g., Equation 2 of [PM2].[AC20][T20][T22]

The first toy experiments with PM[PM1] were conducted nearly three decades ago when compute was about a million times more expensive than today. When it had become about 10 times cheaper 5 years later, we could show that semi-linear PM variants applied to images automatically generate feature detectors well-known from neuroscience, such as on-center-off-surround detectors, off-center-on-surround detectors, and orientation-sensitive bar detectors.[PM2]

8. Fast Weight Programmers (1991). NNs Learn to Program NNs: Transformers with Linearized Self-Attention

26 March 1991: Neural nets learn to program neural nets with fast weights—like today's Transformer variants. 2021: New stuff!

A typical NN has many more connections than neurons. In traditional NNs, neuron activations change quickly, while connection weights change slowly. That is, the numerous weights cannot implement short-term memories or temporal variables, only the few neuron activations can. Non-traditional NNs with quickly changing "fast weights" overcome this limitation. Dynamic links or fast weights for NNs were introduced by Christoph v. d. Malsburg in 1981[FAST] and further studied by others.[FASTa,b] However, before 1991, no network learned by gradient descent to quickly compute the changes of the fast weight storage of another network or of itself.

Such end-to-end-differentiable Fast Weight Programmers (FWPs)[FWP] were published in 1991-93.[FWP0-2] There a slow NN learns to program the weights of a separate fast NN. That is, I separated storage and control like in traditional computers, but in a fully neural way (rather than in a hybrid fashion[PDA1-2][DNC]). FWPs embody the principles found in what is now called attention[ATT] and Transformers.[TR1-6][FWP] In fact, one of my 1991 FWPs is now called a Transformer with linearized self-attention.[TR5-6][FWP][ATT] See this tweet celebrating the 30-year anniversary of the 1992 journal publication.[FWP0-1]

Some of my FWPs used gradient descent-based, active control of fast weights through 2D tensors or outer product updates[FWP1-2] (compare our more recent work on this[FWP3-3a][FWP6-7]). One of the motivations[FWP2] was to get many more temporal variables under end-to-end differentiable control than what's possible in standard RNNs of the same size: O(H^2) instead of O(H), where H is the number of hidden units. A quarter century later, others followed this approach.[FWP4a][T22] The 1993 paper[FWP2] also explicitly introduced the "modern" terminology of learning internal spotlights of attention in end-to-end-differentiable networks. Compare Sec. 9 on learning attention.

metalearning machines that learn to learn (1987)

I also showed how FWPs can be used for meta-learning or learning to learn, one of my main research topics since 1987.[META1][META] In follow-up work[FWPMETA1-8] since 1992, the slow RNN and the fast RNN are identical: the initial weight of each connection in the net is trained by gradient descent, but during an episode, each connection can be addressed and read and modified by the net itself (through O(log n) special output units where n is the number of connections), and the connection's weight may rapidly change—the network becomes self-referential in the sense that it can in principle learn to run arbitrary computable weight change algorithms or learning algorithms (for all of its weights) on itself. This led to many follow-up papers in the 1990s and 2000s.

Compressed Network Search Finds Complex Neural Controllers with a Million Weights

Deep Reinforcement Learning (RL) without a teacher can also profit from fast weights even when the system's dynamics are not differentiable, as shown in 2005 by my former postdoc Faustino Gomez[FWP5] (now CEO of NNAISENSE) when affordable computers were about 1000 times faster than in the early 1990s.

Interestingly, our related work on Deep RL in the same year (but without fast weights) to my knowledge was the first machine learning publication with the word combination "learn deep" in the title[DL6-6a] (2005; soon afterwards many started talking about "Deep Learning").

15-year anniversary: 1st paper with

Over the decades we have published quite a few additional ways of learning to generate quickly numerous weights of large NNs through very compact codes.[KO0-2][CO1-3] Here we exploited that the Kolmogorov complexity or algorithmic information content of successful huge NNs may actually be rather small. In particular, in July 2013, Compressed Network Search[CO2] was the first Deep Learning model to successfully learn control policies directly from high-dimensional sensory input (video) using reinforcement learning, without any unsupervised pre-training (unlike in Sec. 1). Soon afterwards, DeepMind also had a Deep RL system for high-dimensional sensory input.[DM1-2]

Today, the most famous end-to-end differentiable fast weight-based NN[FWP0] may be our vanilla LSTM network of 2000[LSTM2] (Sec. 4), whose forget gates learn to control the fast weights on self-recurrent connections of internal LSTM cells. All the major IT companies are now massively using vanilla LSTMs.[DL4] The roots of this go back to 1991 (see Sec. 4 & Sec. 8).

The Fast Weight Programmers[FWP1-2] above, however, can also learn to memorize past data, e.g., by computing fast weight changes through additive outer products of self-invented activation patterns[FWP0-1] (now often called keys and values for self-attention[TR1-6]). The similar Transformers[TR1-2] combine this with projections and softmax and are now (2021) widely used in natural language processing (a traditional LSTM domain). For long input sequences, their efficiency was improved through Transformers with linearized self-attention[TR5-6][FWP][ATT] which are formally equivalent to my 1991 FWPs (apart from normalization). That is, these "modern" techniques also have their roots in my lab of 1991 at TUM.

9. Learning Sequential Attention with NNs (1990)

Learning Sequential Attention Through Neural Networks (1990)

Unlike traditional NNs, humans use sequential gaze shifts and selective attention to detect and recognize patterns. This can be much more efficient than the highly parallel approach of traditional FNNs. That's why we introduced sequential attention-learning NNs three decades ago (1990 and onwards).[ATT0-1] Shortly afterwards, I also explicitly addressed the learning of "internal spotlights of attention" in RNNs[FWP2] (see Sec. 8).

So back then we already had both of the now common types of neural sequential attention: end-to-end-differentiable "soft" attention (in latent space) through multiplicative units within NNs,[FWP][FWP2] and "hard" attention (in observation space) in the context of Reinforcement Learning (RL).[ATT0-1] This led to lots of follow-up work. Today, many are using sequential attention-learning NNs.

My overview paper for CMSS 1990[ATT2] summarised in Section 5 our early work on attention, to my knowledge the first implemented neural system for combining glimpses that jointly trains a recognition & prediction component with an attentional component (the fixation controller). As with the work of Sepp (see Sec. 3), this has often been misattributed. The reviewer of my 1990 paper wrote about his own work:[ATT3] "To our knowledge, this is the first implemented system for combining glimpses that jointly trains a recognition component ... with an attentional component (the fixation controller)"[T22] (see also Sec. 10).

Hierarchical Reinforcement Learning with neural subgoal generators(1990) 10. Gradient Descent Finds Subgoals for Hierarchical Reinforcement Learning (1990)

Traditional Reinforcement Learning (RL) without a teacher does not hierarchically decompose problems into easier subproblems.[HRLW] That's why in 1990 I introduced Hierarchical RL (HRL) with end-to-end differentiable NN-based subgoal generators,[HRL0] also with recurrent NNs that learn to generate sequences of subgoals.[HRL1-2][LEC] An RL machine gets extra inputs of the form (start, goal). An evaluator NN learns to predict the rewards/costs of going from start to goal. An (R)NN-based subgoal generator also sees (start, goal), and uses (copies of) the evaluator NN to learn by gradient descent a sequence of cost-minimising intermediate subgoals. The RL machine tries to use such subgoal sequences to achieve final goals. The system is learning action plans at multiple levels of abstraction and multiple time scales. At least in principle, it solves what was called an "open problem" in 2022.[LEC]

Our 1990-91 papers[HRL0-1] started a series of papers on HRL.(e.g., [HRL4]) The reviewer of my 1990 paper[ATT2] (which summarised in Section 6 our early work on HRL) was last author of a 1992 paper on HRL.[HRL3] Compare Sec. 9.

11. Planning with Recurrent World Models (1990)

1990: Planning & Reinforcement Learning with Recurrent World Models and Artificial Curiosity

In 1990, I introduced reinforcement learning (RL) and online planning based on a combination of two RNNs called the controller C and the world model M (see also Sec. 5). M learns to predict the consequences of C's actions. C learns to use M to plan ahead for several time steps, selecting action sequences that maximise predicted cumulative reward.[AC90] This led to lots of follow-up publications, also in recent years.[PLAN-PLAN6][LEC]

The 1990 FKI report[AC90] also introduced several other concepts that have become popular. See Sec. 12, Sec. 13, Sec. 14, Sec. 5, Sec. 20.

12. Goal-Defining Commands as Extra NN Inputs (1990)

One concept that is widely used in today's RL NNs are extra goal-defining input patterns that encode various tasks, such that the NN knows which task to execute next. We introduced this in 1990 in various contexts.[ATT0-1][HRL0-1] In [ATT0-1] a reinforcement learning neural controller learned to control a fovea through sequences of saccades to find particular objects in visual scenes, thus learning sequential attention (see Sec. 9). User-defined goals were provided to the system by special "goal input vectors" that remained constant (Sec. 3.2 of [ATT1]) while the system shaped its stream of visual inputs through fovea-shifting actions.

Hierarchical RL (HRL, Sec. 10) with end-to-end differentiable subgoal generators[HRL0-1][LEC] also uses an NN with task-defining inputs of the form (start, goal), learning to predict the costs of going from start to goal. (Compare my former student Tom Schaul's "universal value function approximator" at DeepMind a quarter century later.[UVF15])

PowerPlay: training an increasingly general problem solver by continually searching for the simplest still unsolvable problem

This led to lots of follow-up work. For example, our POWERPLAY RL system (2011)[PP][PP1] also uses task-defining inputs to distinguish between tasks, continually inventing on its own new goals and tasks, incrementally learning to become a more and more general problem solver in an active, partially unsupervised or self-supervised fashion. RL robots with high-dimensional video inputs and intrinsic motivation (like in PowerPlay) learned to explore in 2015.[PP2]

13. High-Dimensional Reward Signals As NN Inputs / General Value Functions (1990)

Traditional RL is based on one-dimensional reward signals. Humans, however, have millions of informative sensors for different types of pain and pleasure etc. To my knowledge, the 1990 tech report[AC90] was the first paper on RL with multi-dimensional, vector-valued pain and reward signals coming in through many different sensors, where cumulative values are predicted for all those sensors, not just for a single scalar overall reward. This later emerged again in RL in what we now call general value functions.[GVF] Unlike previous adaptive critics, the one of 1990[AC90] was multi-dimensional and recurrent. Unlike in traditional RL, those reward signals were also used as informative inputs to the controller NN learning to execute actions that maximise cumulative reward.[PLAN][LEC]

14. Deterministic Policy Gradients (1990)

The section "Augmenting the Algorithm by Temporal Difference Methods" of the 1990 paper[AC90] also combined the Dynamic Programming-based Temporal Difference method[TD] for predicting cumulative (possibly multi-dimensional, Sec. 13) rewards with a gradient-based predictive model of the world (see Sec. 11), to compute weight changes for the separate control network. See also Sec. 2.4 of the 1991 follow-up paper[PLAN3] (and compare [NAN1]). A quarter century later, a variant of this emerged as Deterministic Policy Gradient algorithm (DPG) at DeepMind.[DPG][DDPG]

15. Networks Adjust Networks / Synthetic Gradients (1990)

In 1990, I proposed various NNs that learn to adjust other NNs.[NAN1] Here I focus on the section "An Approach to Local Supervised Learning in Recurrent Networks".[NAN1] The global error measure to be minimized is the sum of all errors received at an RNN's output units over time. In conventional backpropagation through time (see surveys[BPTT1-2]), each unit needs a stack for remembering past activations which are used to compute contributions to weight changes during the error propagation phase. Instead of allowing unlimited storage capacities in the form of stacks, I introduced a second adaptive NN that learns to associate states of the RNN with corresponding error vectors. These locally estimated error gradients (rather than the true gradients) are used to adjust the RNN.[NAN1-4] Unlike standard backpropagation, the method is local in space and time.[BB1-2][NAN1] A quarter century later, DeepMind called this "Synthetic Gradients."[NAN5]

16. O(n3) Gradients for Online Recurrent NNs (1991)

The original 1987 fixed-size storage learning algorithm for fully recurrent continually running networks[ROB] requires O(n4) computations per time step, where n is the number of non-input units. I published a method which computes exactly the same gradient and requires fixed-size storage of the same order as the previous algorithm. But, the average time complexity per time step is only O(n3).[CUB1-2] However, this work does not really count, since the great RNN pioneer Ron Williams had derived this method first![CUB0]

1/3 century anniversary of 
Genetic Programming for code of unlimited size  (1987)

BTW, I committed a similar error in 1987 when I published what I thought was the first paper on Genetic Programming (GP), that is, on automatically evolving computer programs[GP1][GP] (authors in alphabetic order). At least our 1987 paper[GP1] seems to be the first on GP for codes with loops and codes of variable size, and the first on GP implemented in a Logic Programming language. Only later I found out that Nichael Cramer had published GP already in 1985[GP0] (and that Stephen F. Smith had proposed a related approach as part of a larger system[GPA] in 1980). Since then I have been trying to do the right thing and correctly attribute credit.

Neural Heat Exchanger (1990) 17. The Deep Neural Heat Exchanger (1990)

The Neural Heat Exchanger is supervised learning method for deep multi-layer NNs. It is inspired by the physical heat exchanger. Inputs "heat up" while being transformed through many successive layers, targets enter from the other end of the deep pipeline and "cool down." Unlike backpropagation, the method is entirely local in space and time.[BB1-2][NAN1] This makes its parallel implementation trivial. It was first presented during occasional talks at various universities since 1990,[NHE] and is closely related to the later Helmholtz Machine.[HEL] Again, experiments were conducted by my brilliant student Sepp Hochreiter (see Sec. 3, Sec. 4).

18. PhD Thesis (1990)

Neural Economy / Neural Bucket Brigade

My doctoral dissertation at TUM[PHD] also came out in 1991, summarising some of my earlier work since 1989, including the first Reinforcement Learning (RL) Neural Economy (the Neural Bucket Brigade),[BB1-2] learning algorithms for RNNs that are local in space and time,[BB1] hierarchical RL (HRL) with end-to-end differentiable subgoal generators (see Sec. 10), RL and planning through a combination of two RNNs called the controller C and the world model M (see Sec. 11), sequential attention-learning NNs (see Sec. 9), NNs that learn to adjust other NNs (including "synthetic gradients;" see Sec. 15), and unsupervised or self-supervised, generative, adversarial networks (see Sec. 5) for implementing curiosity.

Back then, much of the NN research by others was inspired by statistical mechanics.[L20][I25][K41][W45][AMH1-2] The works of 1990-91 (and my even earlier diploma thesis of 1987[META1]) embodied an alternative program-oriented view of Machine Learning.

Goedel Machine When Kurt Gödel laid the foundations of theoretical computer science in 1931,[GOD][GOD34][GOD21-21b] he represented both data (such as axioms and theorems) and programs (such as proof-generating sequences of operations on the data) in a universal coding language based on the integers. He famously used this language to construct formal statements that talk about the computation of other formal statements—especially self-referential statements which imply that they are not decidable, given a computational theorem prover that systematically enumerates all possible theorems from an enumerable set of axioms. Thus he identified fundamental limits of algorithmic theorem proving, computing, and any type of computation-based AI.

As I have frequently pointed out since 1990,[AC90] the weights of an NN should be viewed as its program. Some argue that the goal of a deep NN is to learn useful internal representations of observed data (there even is an international conference on learning representations called ICLR), but the NN's goal is actually to learn a program (the parameters) that computes such representations. Inspired by Gödel, I built NNs whose outputs are programs or weight matrices of other NNs (see Sec. 8), and even self-referential RNNs that can run and inspect their own weight change algorithms or learning algorithms (see Sec. 8). A difference to Gödel's work is that the universal programming language is not based on the integers, but on real values, such that the outputs of typical NNs are differentiable with respect to their programs. That is, a simple program generator (the efficient gradient descent procedure[BP1]) can compute a direction in program space where one may find a better program,[AC90] in particular, a better program-generating program (see Sec. 8). Much of my work since 1989 has exploited this fact.

19. From Unsupervised Pre-Training to Pure Supervised Learning (1991-95; 2006-11)

As mentioned in Sec. 1, my first Very Deep Learner was the RNN stack of 1991 which used unsupervised pre-training to learn problems of depth greater than 1000. Soon afterwards, however, we published more powerful ways of overcoming the Deep Learning Problem (see Sec. 3) without any unsupervised pre-training, replacing the unsupervised RNN stack[UN1-3] by the purely supervised Long Short-Term Memory (LSTM) (Sec. 4). That is, already in the previous millennium, unsupervised pre-training lost significance as LSTM did not require it. In fact, this shift from unsupervised pre-training to pure supervised learning started already in 1991.

10-year anniversary of supervised deep learning breakthrough (2010)

A very similar shift took place much later between 2006 and 2010, this time for the less general feedforward NNs (FNNs) rather than recurrent NNs (RNNs). Again, my little lab played a central role in this transition. In 2006, supervised learning in FNNs was facilitated by unsupervised pre-training of stacks of FNNs[UN4] (see Sec. 1). But in 2010, our team with my outstanding Romanian postdoc Dan Ciresan[MLP1-2] showed that deep FNNs can be trained by plain backpropagation and do not at all require unsupervised pre-training for important applications.[MLP2] Our system set a new performance record[MLP1] on the back then famous and widely used image recognition benchmark called MNIST. This was achieved by greatly accelerating traditional FNNs on highly parallel graphics processing units called GPUs. A reviewer called this a "wake-up call to the machine learning community."

In 2011, DanNet triggered the deep convolutional neural network (CNN) revolution

My team at the Swiss AI Lab IDSIA further improved the above-mentioned work (2010) on purely supervised Deep Learning in FNNs[MLP1-2] by replacing the traditional FNNs through another old NN type called convolutional NNs or CNNs, invented and developed by others since the 1970s.[CNN1-5] Our supervised fast deep CNN called DanNet (Ciresan et al., 2011)[GPUCNN1] was a practical breakthrough (much faster than early work on accelerating CNNs[GPUCNN]). DanNet was the first pure CNN to win international computer vision competitions, and won 4 of them in a row between May 15, 2011, and September 10, 2012.[GPUCNN5] (All of this happened before a similar GPU-CNN by others won ImageNet 2012.[GPUCNN5]) In particular, DanNet was the first deep CNN to win a Chinese handwriting contest (ICDAR 2011), the first to achieve superhuman visual pattern recognition in any international contest (IJCNN 2011), the first to win an image segmentation contest (ISBI, May 2012), and the first to win a contest on object detection in large images (ICPR, 10 Sept 2012), at the same time the first to win a medical imaging contest (on cancer detection).[GPUCNN5]

History of computer vision contests won by deep CNNs since 2011

One year later, our team also won the MICCAI Grand Challenge on mitosis detection.[MGC][GPUCNN5-8] Our fast CNN image scanners were over 1000 times faster than previous methods.[SCAN] This Deep Learning approach has transformed medical imaging.

DanNet more than halved the error rate for object recognition in a contest already in 2011, 20 years after our Annus Mirabilis.[GPUCNN2] Soon afterwards, others applied similar approaches in image recognition contests.[GPUCNN5][MOST]

IJCNN 2011 on-site Traffic Sign Recognition Competition (1st rank, 2 August 2011, 0.56% error rate, the only method better than humans, who achieved 1.16% on average; 3rd place for 1.69%) (Juergen Schmidhuber)

Like our LSTM results of 2009 (see Sec. 4), the above-mentioned results with feedforward NNs of 2010-11 attracted enormous interest from industry. For example, in 2010, we introduced our deep and fast GPU-based NNs to Arcelor Mittal, the world's largest steel maker, and were able to greatly improve steel defect detection.[ST] This may have been the first Deep Learning breakthrough in heavy industry. Today, most AI startups and major IT firms as well as many other famous companies are using such supervised fast GPU-NNs.

Let me emphasize, however, that the above-mentioned supervised deep learning revolutions of the early 1990s (for recurrent NNs) and of 2010 (for feedforward NNs)[MLP1-2] did not at all kill unsupervised learning. For example, pre-trained language models are now heavily used by Transformers (see Sec. 8) which excel at the traditional LSTM domain of Natural Language Processing[TR1-6] (although there are still many language tasks that LSTM can rapidly learn to solve quickly[LSTM13] while plain Transformers can't). Remarkably, Transformers with linearized self-attention were also first published[FWP0-7] in our Annus Mirabilis of 1990-1991,[MOST] together with unsupervised pre-training for deep learning.[UN-UN3] And our unsupervised generative adversarial NNs since 1990[AC90-AC20][PLAN][AC] are still used to endow agents with artificial curiosity (see Sec. 5 & Sec. 6)—see also a version of our adversarial NNs[AC90b] called GANs.[AC20][R2][PLAN][MOST][T22](Sec. XVII) Unsupervised learning still has a bright future!

20. The Amazing FKI Tech Report Series on Artificial Intelligence in the 1990s

In hindsight, many of the later widely used basic ideas of "modern" Deep Learning were published in our Miraculous Year 1990-1991 at TU Munich, soon after the fall of the Berlin Wall: unsupervised or self-supervised, data-generating, adversarial networks (for artificial curiosity and related concepts; see Sec. 5; see also follow-up work at CU in Sec. 7), the Fundamental Deep Learning Problem (vanishing / exploding gradients; see Sec. 3) and its solutions through (a) unsupervised pre-training for very deep (recurrent) networks (see Sec. 1) and (b) basic insights leading to LSTM (see Sec. 4, Sec. 8). We also introduced sequential attention-learning NNs back then—another concept that has become popular (see Sec. 9 on both hard and soft attention, in observation space and in latent space), as well as NNs that learn to program the fast weights of another NN, and even their own weights. In particular, we already had what's now called Transformers with linearized self-attention (see Sec. 8). Plus all the other things mentioned above, from Hierarchical Reinforcement Learning (see Sec. 10) to planning with recurrent neural world models (see Sec. 11). Of course, one had to wait for faster computers to commercialize such algorithms. By the mid 2010s, however, our stuff was massively used by Apple, Google, Facebook, Amazon, Samsung, Baidu, Microsoft, etc, many billions of times per day on billions of computers.[DL4]

Learning & Planning with Recurrent World Models; Adversarial Generative Nets for Artificial Curiosity and related concepts (1990) Most of the results above were actually first published in TU Munich's FKI Tech Report series, for which I drew many illustrations by hand, some of them shown in the present page (see Sec. 10, Sec. 11, Sec. 13, Sec. 18). The FKI series now plays an important role in the history of Artificial Intelligence, as it introduced several important concepts: unsupervised pre-training for very Deep Learning (FKI-148-91;[UN0] see Sec. 1), compressing / distilling one NN into another (FKI-148-91;[UN0] see Sec. 2), Long Short-Term Memory (FKI-207-95;[LSTM0] see Sec. 4, Sec. 8), Artificial Curiosity through NNs that maximize learning progress (FKI-149-91;[AC91] see Sec. 6), end-to-end-differentiable Fast Weight Programmers that learn to program other NNs (separating storage and control for NNs like in traditional computers; see FKI-147-91[FWP0] and Sec. 8—the outer product version of 1991 is a Transformer with linearized self-attention), learning of sequential attention with NNs (FKI-128-90;[ATT0] see Sec. 9), goal-defining commands as extra NN inputs (FKI-128-90,[ATT0] FKI-129-90;[HRL0] see Sec. 12), end-to-end-differentiable Hierarchical Reinforcement Learning (FKI-129-90;[HRL0] see Sec. 10), NNs adjusting NNs / synthetic gradients (FKI-125-90;[NAN2] see Sec. 15). (Cubic gradient computation for online recurrent NNs also was published as FKI-151-91,[CUB1] but this one does not really count; see Sec. 16.) In particular, the report FKI-126-90[AC90] introduced a whole bunch of concepts that are now widely used: planning with recurrent world models (see Sec. 11), high-dimensional reward signals as extra NN inputs / general value functions (see Sec. 13), deterministic policy gradients (see Sec. 14), NNs that are both generative and adversarial (see Sec. 5; see also Sec. 7), for Artificial Curiosity and related concepts. Later remarkable FKI Tech Reports from the 1990s describe ways of greatly compressing NNs[KO0][FM] to improve their generalisation capability.

Peer-reviewed versions came out soon after the tech reports. For example, in 1992, I had a fun contest with the great David MacKay as to who'd have more publications within a single year in Neural Computation, back then the leading journal of our field. By the end of 1992, both of us had four. But David won, because his publications (mostly on Bayesian approaches for NNs) were much longer than mine :-) Disclaimer: Of course, silly measures like number of publications and h-index etc should not matter in science.[NAT1]

Juergen Schmidhuber painted by deepart.io in the style of van Gogh 21. Concluding Remarks

When only consulting surveys from the Anglosphere, it is not always clear[DLC] that Deep Learning was first conceived outside of it.[DLH] It started in 1965 in the Ukraine (back then the USSR) with the first nets of arbitrary depth that really learned[DEEP1-2] (see Sec. 1). A few years later, stochastic gradient descent was successfully applied in Japan to learn internal representations in deep multi-layer perceptrons.[GD1-2a][DLH][T22] Soon afterwards, modern backpropagation was published in Finland (1970)[BP1] (see Sec. 0). The basic deep convolutional NN architecture (now widely used) was invented in the 1970s in Japan[CNN1] where NNs with convolutions were later (1987) also combined with "weight sharing" and backpropagation.[CNN1a] Unsupervised or self-supervised adversarial networks that duel each other in a minimax game to implement Artificial Curiosity etc (now widely used) originated in Munich (1990, Sec. 5) (also the birthplace of the first truly self-driving cars in the 1980s—in highway traffic by 1994). The principle of Transformers with linearized self-attention[FWP,FWP0] (see Sec. 8) and the fundamental problem of backpropagation-based Deep Learning[VAN1] (1991, see Sec. 3) were also discovered in Munich. So were the first "modern" Deep Learners to overcome this problem, through (1) unsupervised pre-training[UN1-2] (1991, see Sec. 1), and (2) Long Short-Term Memory,[LSTM0-7] "arguably the most commercial AI achievement"[AV1] (see Sec. 4). LSTM was further developed in Switzerland (see Sec. 4), which is also home of the first image recognition contest-winning deep GPU-based CNNs (2011, Sec. 19—everybody in computer vision is using this approach now), the first superhuman visual pattern recognition (2011), and the first very deep, working feedforward NNs with more than a hundred layers[HW1] (see Sec. 4). Around 1990, Switzerland also became origin of the World Wide Web, which allowed for quickly spreading AI around the globe. As of 2017, Switzerland is still leading the world in AI research in terms of citation impact, though China is now the nation that produces the most papers on AI.[THE17]

Self-referential problem-solving robot thinking about itself Of course, Deep Learning is just a small part of AI, mostly limited to passive pattern recognition. We view it as a by-product of our research on more general AI through meta-learning or "learning to learn learning algorithms" (publications since 1987), systems with artificial curiosity and creativity that invent their own problems and set their own goals (since 1990), evolutionary computation (since 1987) and RNN evolution and compressed network search, reinforcement learning (RL) for agents in realistic partially observable environments where traditional RL (for board games etc) does not work (since 1989), general artificial intelligence, optimal universal learning machines such as the Gödel machine (2003-), optimal search for programs running on general purpose computers such as RNNs, etc.

And of course, AI itself is just part of a grander scheme driving the universe from simple initial conditions to more and more unfathomable complexity.[SA17] Finally, even this awesome process may be just a tiny part of the even grander, optimally efficient computation of all logically possible universes.[ALL1-3]


Creative Commons License Thanks to several expert reviewers for useful comments. (Let me know under juergen@idsia.ch if you can spot any remaining error.) The present article[MIR] had an impact on later posts which contain additional relevant references. It also influenced some of the most popular posts and comments of 2019 at reddit/ML: at the time the largest machine learning forum with over 800k subscribers.[R2-R8] The contents of this article may be used for educational and non-commercial purposes, including articles for Wikipedia and similar sites. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.


[25y97] In 2022, we are celebrating the following works from a quarter-century ago. 1. Journal paper on Long Short-Term Memory, the most cited neural network (NN) of the 20th century (and basis of the most cited NN of the 21st). 2. First paper on physical, philosophical and theological consequences of the simplest and fastest way of computing all possible metaverses (= computable universes). 3. Implementing artificial curiosity and creativity through generative adversarial agents that learn to design abstract, interesting computational experiments. 4. Journal paper on meta-reinforcement learning. 5. Journal paper on hierarchical Q-learning. 6. First paper on reinforcement learning to play soccer: start of a series. 7. Journal papers on flat minima & low-complexity NNs that generalize well. 8. Journal paper on Low-Complexity Art, the Minimal Art of the Information Age. 9. Journal paper on probabilistic incremental program evolution.

[AC] J.  Schmidhuber (AI Blog, 2021). 3 decades of artificial curiosity & creativity. Our artificial scientists not only answer given questions but also invent new questions. They achieve curiosity through: (1990) the principle of generative adversarial networks, (1991) neural nets that maximise learning progress, (1995) neural nets that maximise information gain (optimally since 2011), (1997) adversarial design of surprising computational experiments, (2006) maximizing compression progress like scientists/artists/comedians do, (2011) PowerPlay... Since 2012: applications to real robots.

[AC90] J.  Schmidhuber. Making the world differentiable: On using fully recurrent self-supervised neural networks for dynamic reinforcement learning and planning in non-stationary environments. Technical Report FKI-126-90, TUM, Feb 1990, revised Nov 1990. PDF. The first paper on planning with reinforcement learning recurrent neural networks (NNs) (more) and on generative adversarial networks where a generator NN is fighting a predictor NN in a minimax game (more).

[AC90b] J.  Schmidhuber. A possibility for implementing curiosity and boredom in model-building neural controllers. In J. A. Meyer and S. W. Wilson, editors, Proc. of the International Conference on Simulation of Adaptive Behavior: From Animals to Animats, pages 222-227. MIT Press/Bradford Books, 1991. PDF. HTML.

[AC91] J. Schmidhuber. Adaptive confidence and adaptive curiosity. Technical Report FKI-149-91, Inst. f. Informatik, Tech. Univ. Munich, April 1991. PDF.

[AC91b] J.  Schmidhuber. Curious model-building control systems. In Proc. International Joint Conference on Neural Networks, Singapore, volume 2, pages 1458-1463. IEEE, 1991. PDF.

[AC06] J.  Schmidhuber. Developmental Robotics, Optimal Artificial Curiosity, Creativity, Music, and the Fine Arts. Connection Science, 18(2): 173-187, 2006. PDF.

[AC09] J. Schmidhuber. Art & science as by-products of the search for novel patterns, or data compressible in unknown yet learnable ways. In M. Botta (ed.), Et al. Edizioni, 2009, pp. 98-112. PDF. (More on artificial scientists and artists.)

[AC10] J. Schmidhuber. Formal Theory of Creativity, Fun, and Intrinsic Motivation (1990-2010). IEEE Transactions on Autonomous Mental Development, 2(3):230-247, 2010. IEEE link. PDF.

[AC20] J. Schmidhuber. Generative Adversarial Networks are Special Cases of Artificial Curiosity (1990) and also Closely Related to Predictability Minimization (1991). Neural Networks, Volume 127, p 58-66, 2020. Preprint arXiv/1906.04493.

[ALL1] A Computer Scientist's View of Life, the Universe, and Everything. LNCS 201-288, Springer, 1997 (submitted 1996). PDF. More.

[ALL2] Algorithmic theories of everything (2000). ArXiv: quant-ph/ 0011122. See also: International Journal of Foundations of Computer Science 13(4):587-612, 2002: PDF. See also: Proc. COLT 2002: PDF. More.

[ALL3] J. Schmidhuber. The Fastest Way of Computing All Universes. In H. Zenil, ed., A Computable Universe. World Scientific, 2012. PDF of preprint. More.

[AMH1] S. I. Amari (1972). Learning patterns and pattern sequences by self-organizing nets of threshold elements. IEEE Transactions, C 21, 1197-1206, 1972. PDF. First publication of what was later sometimes called the Hopfield network,[AMH2] based on the Lenz-Ising recurrent architecture.[L20][I25][T22]

[AMH2] J. J. Hopfield (1982). Neural networks and physical systems with emergent collective computational abilities. Proc. of the National Academy of Sciences, vol. 79, pages 2554-2558, 1982. The Hopfield network or Amari-Hopfield Network was published in 1972 by Amari.[AMH1]

[ATT] J. Schmidhuber (AI Blog, 2020). 30-year anniversary of end-to-end differentiable sequential neural attention. Plus goal-conditional reinforcement learning. We had both hard attention[ATT0-2] (1990) and soft attention (1991-93).[FWP] Today, both types are very popular.

[ATT0] J. Schmidhuber and R. Huber. Learning to generate focus trajectories for attentive vision. Technical Report FKI-128-90, Institut für Informatik, Technische Universität München, 1990. PDF.

[ATT1] J. Schmidhuber and R. Huber. Learning to generate artificial fovea trajectories for target detection. International Journal of Neural Systems, 2(1 & 2):135-141, 1991. Based on TR FKI-128-90, TUM, 1990. PDF. More.

[ATT2] J.  Schmidhuber. Learning algorithms for networks with internal and external feedback. In D. S. Touretzky, J. L. Elman, T. J. Sejnowski, and G. E. Hinton, editors, Proc. of the 1990 Connectionist Models Summer School, pages 52-61. San Mateo, CA: Morgan Kaufmann, 1990. PS. (PDF.)

[ATT3] H. Larochelle, G. E. Hinton. Learning to combine foveal glimpses with a third-order Boltzmann machine. NIPS 2010. This work is very similar to [ATT0-2] which the authors did not cite. In fact, the 2nd author was the reviewer of a 1990 paper[ATT2] which summarised in its Section 5 Schmidhuber's early work on attention: the first implemented neural system for combining glimpses that jointly trains a recognition & prediction component with an attentional component (the fixation controller). Two decades later, he wrote about his own work:[ATT3] "To our knowledge, this is the first implemented system for combining glimpses that jointly trains a recognition component ... with an attentional component (the fixation controller)." See [MIR](Sec. 9)[R4].

[AV1] A. Vance. Google Amazon and Facebook Owe Jürgen Schmidhuber a Fortune—This Man Is the Godfather the AI Community Wants to Forget. Business Week, Bloomberg, May 15, 2018.

[BB1] J.  Schmidhuber. A local learning algorithm for dynamic feedforward and recurrent networks. Technical Report FKI-124-90, Institut für Informatik, Technische Universität München, 1990. PDF.

[BB2] J. Schmidhuber. A local learning algorithm for dynamic feedforward and recurrent networks. Connection Science, 1(4):403-412, 1989. (The Neural Bucket Brigade—figures omitted!). PDF. HTML. Compare TR FKI-124-90, TUM, 1990. PDF. Proposal of a biologically more plausible deep learning algorithm that—unlike backpropagation—is local in space and time. Based on a "neural economy" for reinforcement learning.

[BP1] S. Linnainmaa. The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors. Master's Thesis (in Finnish), Univ. Helsinki, 1970. See chapters 6-7 and FORTRAN code on pages 58-60. PDF. See also BIT 16, 146-160, 1976. Link. The first publication on "modern" backpropagation, also known as the reverse mode of automatic differentiation.

[BP2] P. J. Werbos. Applications of advances in nonlinear sensitivity analysis. In R. Drenick, F. Kozin, (eds): System Modeling and Optimization: Proc. IFIP, Springer, 1982. PDF. First application of backpropagation[BP1] to NNs (concretizing thoughts in Werbos' 1974 thesis).

[BP4] J. Schmidhuber (AI Blog, 2014; updated 2020). Who invented backpropagation? More.[DL2]

[BP5] A. Griewank (2012). Who invented the reverse mode of differentiation? Documenta Mathematica, Extra Volume ISMP (2012): 389-400.

[BP6] S. I. Amari (1977). Neural Theory of Association and Concept Formation. Biological Cybernetics, vol. 26, p. 175-185, 1977. See Section 3.1 on using gradient descent for learning in multilayer networks.

[BPA] H. J. Kelley. Gradient Theory of Optimal Flight Paths. ARS Journal, Vol. 30, No. 10, pp. 947-954, 1960. Precursor of modern backpropagation.[BP1-4]

[BPB] A. E. Bryson. A gradient method for optimizing multi-stage allocation processes. Proc. Harvard Univ. Symposium on digital computers and their applications, 1961.

[BPC] S. E. Dreyfus. The numerical solution of variational problems. Journal of Mathematical Analysis and Applications, 5(1): 30-45, 1962.

[BPTT1] P. J. Werbos. Backpropagation through time: what it does and how to do it. Proceedings of the IEEE 78.10, 1550-1560, 1990.

[BPTT2] R. J. Williams and D. Zipser. Gradient-based learning algorithms for recurrent networks. In: Backpropagation: Theory, architectures, and applications, p 433, 1995.

[BOU] H Bourlard, N Morgan (1993). Connectionist speech recognition. Kluwer, 1993.

[BRI] Bridle, J.S. (1990). Alpha-Nets: A Recurrent "Neural" Network Architecture with a Hidden Markov Model Interpretation, Speech Communication, vol. 9, no. 1, pp. 83-92.

[BW] H. Bourlard, C. J. Wellekens (1989). Links between Markov models and multilayer perceptrons. NIPS 1989, p. 502-510.

[CNN1] K. Fukushima: Neural network model for a mechanism of pattern recognition unaffected by shift in position—Neocognitron. Trans. IECE, vol. J62-A, no. 10, pp. 658-665, 1979. The first deep convolutional neural network architecture, with alternating convolutional layers and downsampling layers. In Japanese. English version: [CNN1+]. More in Scholarpedia.

[CNN1+] K. Fukushima: Neocognitron: a self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biological Cybernetics, vol. 36, no. 4, pp. 193-202 (April 1980). Link.

[CNN1a] A. Waibel. Phoneme Recognition Using Time-Delay Neural Networks. Meeting of IEICE, Tokyo, Japan, 1987. First application of backpropagation[BP1][BP2] and weight-sharing to a convolutional architecture.

[CNN1b] A. Waibel, T. Hanazawa, G. Hinton, K. Shikano and K. J. Lang. Phoneme recognition using time-delay neural networks. IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 3, pp. 328-339, March 1989. Based on [CNN1a].

[CNN1c] Bower Award Ceremony 2021: Jürgen Schmidhuber lauds Kunihiko Fukushima. YouTube video, 2021.

[CNN2] Y. LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, L. D. Jackel: Backpropagation Applied to Handwritten Zip Code Recognition, Neural Computation, 1(4):541-551, 1989. PDF.

[CNN3a] K. Yamaguchi, K. Sakamoto, A. Kenji, T. Akabane, Y. Fujimoto. A Neural Network for Speaker-Independent Isolated Word Recognition. First International Conference on Spoken Language Processing (ICSLP 90), Kobe, Japan, Nov 1990. An NN with convolutions using Max-Pooling instead of Fukushima's Spatial Averaging.[CNN1]

[CNN3] Weng, J., Ahuja, N., and Huang, T. S. (1993). Learning recognition and segmentation of 3-D objects from 2-D images. Proc. 4th Intl. Conf. Computer Vision, Berlin, Germany, pp. 121-128. A 2D CNN whose downsampling layers use Max-Pooling (which has become very popular) instead of Fukushima's Spatial Averaging.[CNN1]

[CNN4] M. A. Ranzato, Y. LeCun: A Sparse and Locally Shift Invariant Feature Extractor Applied to Document Images. Proc. ICDAR, 2007

[CNN5a] S. Behnke. Learning iterative image reconstruction in the neural abstraction pyramid. International Journal of Computational Intelligence and Applications, 1(4):427-438, 1999.

[CNN5b] S. Behnke. Hierarchical Neural Networks for Image Interpretation, volume LNCS 2766 of Lecture Notes in Computer Science. Springer, 2003.

[CNN5c] D. Scherer, A. Mueller, S. Behnke. Evaluation of pooling operations in convolutional architectures for object recognition. In Proc. International Conference on Artificial Neural Networks (ICANN), pages 92-101, 2010.

[CO1] J. Koutnik, F. Gomez, J. Schmidhuber (2010). Evolving Neural Networks in Compressed Weight Space. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2010), Portland, 2010. PDF.

[CO2] J. Koutnik, G. Cuccu, J. Schmidhuber, F. Gomez. Evolving Large-Scale Neural Networks for Vision-Based Reinforcement Learning. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), Amsterdam, July 2013. PDF.

[CO3] R. K. Srivastava, J. Schmidhuber, F. Gomez. Generalized Compressed Network Search. Proc. GECCO 2012. PDF.

[CTC] A. Graves, S. Fernandez, F. Gomez, J. Schmidhuber. Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks. ICML 06, Pittsburgh, 2006. PDF.

[CUB0] R. J. Williams. Complexity of exact gradient computation algorithms for recurrent neural networks. Technical Report NU-CCS-89-27, Northeastern University, College of Computer Science, 1989.

[CUB1] An O(n3) learning algorithm for fully recurrent neural networks. Technical Report FKI-151-91, Institut für Informatik, Technische Universität München, 1991. PDF.

[CUB2] J. Schmidhuber. A fixed size storage O(n3) time complexity learning algorithm for fully recurrent continually running networks. Neural Computation, 4(2):243-248, 1992. PDF.

[CW] J. Koutnik, K. Greff, F. Gomez, J. Schmidhuber. A Clockwork RNN. Proc. 31st International Conference on Machine Learning (ICML), p. 1845-1853, Beijing, 2014. Preprint arXiv:1402.3511 [cs.NE].

[DAN] J. Schmidhuber (AI Blog, 2021). 10-year anniversary. In 2011, DanNet triggered the deep convolutional neural network (CNN) revolution. Named after Schmidhuber's outstanding postdoc Dan Ciresan, it was the first deep and fast CNN to win international computer vision contests, and had a temporary monopoly on winning them, driven by a very fast implementation based on graphics processing units (GPUs). 1st superhuman result in 2011.[DAN1] Now everybody is using this approach.

[DAN1] J. Schmidhuber (AI Blog, 2011; updated 2021 for 10th birthday of DanNet): First superhuman visual pattern recognition. At the IJCNN 2011 computer vision competition in Silicon Valley, the artificial neural network called DanNet performed twice better than humans, three times better than the closest artificial competitor (from LeCun's team), and six times better than the best non-neural method.

[DEC] J. Schmidhuber (AI Blog, 02/20/2020, updated 2021, 2022). The 2010s: Our Decade of Deep Learning / Outlook on the 2020s. The recent decade's most important developments and industrial applications based on our AI, with an outlook on the 2020s, also addressing privacy and data markets.

[DEEP1] Ivakhnenko, A. G. and Lapa, V. G. (1965). Cybernetic Predicting Devices. CCM Information Corporation. First working Deep Learners with many layers, learning internal representations.

[DEEP1a] Ivakhnenko, Alexey Grigorevich. The group method of data of handling; a rival of the method of stochastic approximation. Soviet Automatic Control 13 (1968): 43-55.

[DEEP2] Ivakhnenko, A. G. (1971). Polynomial theory of complex systems. IEEE Transactions on Systems, Man and Cybernetics, (4):364-378.

[DIST2] O. Vinyals, J. A. Dean, G. E. Hinton. Distilling the Knowledge in a Neural Network. Preprint arXiv:1503.02531 [stat.ML], 2015. The authors did not cite the original 1991 NN distillation procedure,[UN0-2][MIR](Sec. 2) not even in the later patent application US20150356461A1.

[DL1] J. Schmidhuber, 2015. Deep learning in neural networks: An overview. Neural Networks, 61, 85-117. More. Got the first Best Paper Award ever issued by the journal Neural Networks, founded in 1988.

[DL2] J. Schmidhuber, 2015. Deep Learning. Scholarpedia, 10(11):32832.

[DL4] J. Schmidhuber (AI Blog, 2017). Our impact on the world's most valuable public companies: Apple, Google, Microsoft, Facebook, Amazon... By 2015-17, neural nets developed in Schmidhuber's labs were on over 3 billion devices such as smartphones, and used many billions of times per day, consuming a significant fraction of the world's compute. Examples: greatly improved (CTC-based) speech recognition on all Android phones, greatly improved machine translation through Google Translate and Facebook (over 4 billion LSTM-based translations per day), Apple's Siri and Quicktype on all iPhones, the answers of Amazon's Alexa, etc. Google's 2019 on-device speech recognition (on the phone, not the server) is still based on LSTM.

[DL6] F. Gomez and J. Schmidhuber. Co-evolving recurrent neurons learn deep memory POMDPs. In Proc. GECCO'05, Washington, D. C., pp. 1795-1802, ACM Press, New York, NY, USA, 2005. PDF.

[DL6a] J. Schmidhuber (AI Blog, Nov 2020). 15-year anniversary: 1st paper with "learn deep" in the title (2005). Our deep reinforcement learning & neuroevolution solved problems of depth 1000 and more.[DL6] Soon after its publication, everybody started talking about "deep learning." Causality or correlation?

[DLC] J. Schmidhuber (AI Blog, June 2015). Critique of Paper by self-proclaimed[DLC1-2] "Deep Learning Conspiracy" (Nature 521 p 436). The inventor of an important method should get credit for inventing it. She may not always be the one who popularizes it. Then the popularizer should get credit for popularizing it (but not for inventing it).

[DLC1] Y. LeCun. IEEE Spectrum Interview by L. Gomes, Feb 2015. Quote: "A lot of us involved in the resurgence of Deep Learning in the mid-2000s, including Geoff Hinton, Yoshua Bengio, and myself—the so-called 'Deep Learning conspiracy' ..."

[DLC2] M. Bergen, K. Wagner (2015). Welcome to the AI Conspiracy: The 'Canadian Mafia' Behind Tech's Latest Craze. Vox recode, 15 July 2015. Quote: "... referred to themselves as the 'deep learning conspiracy.' Others called them the 'Canadian Mafia.'"

[DLH] J. Schmidhuber (AI Blog, 2022). Annotated History of Modern AI and Deep Learning. Technical Report IDSIA-22-22, IDSIA, Lugano, Switzerland, 2022. Preprint arXiv:2212.11279.

[DM1] V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, M. Riedmiller. Playing Atari with Deep Reinforcement Learning. Tech Report, 19 Dec. 2013, arxiv:1312.5602.

[DM2] V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, D. Hassabis. Human-level control through deep reinforcement learning. Nature, vol. 518, p 1529, 26 Feb. 2015. Link. DeepMind's first famous paper. Its abstract claims: "While reinforcement learning agents have achieved some successes in a variety of domains, their applicability has previously been limited to domains in which useful features can be handcrafted, or to domains with fully observed, low-dimensional state spaces." It also claims to bridge "the divide between high-dimensional sensory inputs and actions." Similarly, the first sentence of the abstract of the earlier tech report version[DM1] of [DM2] claims to "present the first deep learning model to successfully learn control policies directly from high-dimensional sensory input using reinforcement learning." However, the first such system (requiring no unsupervised pre-training) was created earlier by Jan Koutnik et al. in Schmidhuber's lab.[CO2] DeepMind was co-founded by Shane Legg, a PhD student from this lab; he and Daan Wierstra (another PhD student of Schmidhuber and DeepMind's 1st employee) were the first persons at DeepMind who had AI publications and PhDs in computer science. More.

[DM3] S. Stanford. DeepMind's AI, AlphaStar Showcases Significant Progress Towards AGI. Medium ML Memoirs, 2019. Alphastar has a "deep LSTM core."

[DNC] A. Graves, G. Wayne, M. Reynolds, T. Harley, I. Danihelka, A. Grabska-Barwinska, S. G. Colmenarejo, E. Grefenstette, T. Ramalho, J. Agapiou, A. P. Badia, K. M. Hermann, Y. Zwols, G. Ostrovski, A. Cain, H. King, C. Summerfield, P. Blunsom, K. Kavukcuoglu, D. Hassabis. Hybrid computing using a neural network with dynamic external memory. Nature, 538:7626, p 471, 2016. This work of DeepMind did not cite the original work of the early 1990s on neural networks learning to control dynamic external memories.[PDA1-2][FWP0-1]

[DDPG] T. P. Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y. Tassa, D. Silver, D. Wierstra. Continuous control with deep reinforcement learning. Preprint arXiv:1509.02971, 2015.

[DPG] D. Silver, G. Lever, N. Heess, T. Degris, D. Wierstra, M. Riedmiller. Deterministic policy gradient algorithms. Proceedings of ICML'31, Beijing, China, 2014. JMLR: W&CP volume 32.

[Drop1] S. J. Hanson (1990). A Stochastic Version of the Delta Rule, PHYSICA D,42, 265-272. What's now called "dropout" is a variation of the stochastic delta rule—compare preprint arXiv:1808.03578, 2018.

[Drop2] N. Frazier-Logue, S. J. Hanson (2020). The Stochastic Delta Rule: Faster and More Accurate Deep Learning Through Adaptive Weight Noise. Neural Computation 32(5):1018-1032.

[Drop3] J. Hertz, A. Krogh, R. Palmer (1991). Introduction to the Theory of Neural Computation. Redwood City, California: Addison-Wesley Pub. Co., pp. 45-46.

[Drop4] N. Frazier-Logue, S. J. Hanson (2018). Dropout is a special case of the stochastic delta rule: faster and more accurate deep learning. Preprint arXiv:1808.03578, 2018.

[FAST] C. v.d. Malsburg. Tech Report 81-2, Abteilung f. Neurobiologie, Max-Planck Institut f. Biophysik und Chemie, Goettingen, 1981. First paper on fast weights or dynamic links.

[FASTa] J. A. Feldman. Dynamic connections in neural networks. Biological Cybernetics, 46(1):27-39, 1982. 2nd paper on fast weights.

[FASTb] G. E. Hinton, D. C. Plaut. Using fast weights to deblur old memories. Proc. 9th annual conference of the Cognitive Science Society (pp. 177-186), 1987. 3rd paper on fast weights (two types of weights with different learning rates).

[FB17] By 2017, Facebook used LSTM to handle over 4 billion automatic translations per day (The Verge, August 4, 2017); see also Facebook blog by J.M. Pino, A. Sidorov, N.F. Ayan (August 3, 2017)

[FM] S. Hochreiter and J. Schmidhuber. Flat minimum search finds simple nets. Technical Report FKI-200-94, Fakultät für Informatik, Technische Universität München, December 1994. PDF.

[FWP] J.  Schmidhuber (AI Blog, 26 March 2021, updated 2022). 26 March 1991: Neural nets learn to program neural nets with fast weights—like Transformer variants. 2021: New stuff! 30-year anniversary of a now popular alternative[FWP0-1] to recurrent NNs. A slow feedforward NN learns by gradient descent to program the changes of the fast weights[FAST,FASTa] of another NN, separating memory and control like in traditional computers. Such Fast Weight Programmers[FWP0-6,FWPMETA1-8] can learn to memorize past data, e.g., by computing fast weight changes through additive outer products of self-invented activation patterns[FWP0-1] (now often called keys and values for self-attention[TR1-6]). The similar Transformers[TR1-2] combine this with projections and softmax and are now widely used in natural language processing. For long input sequences, their efficiency was improved through Transformers with linearized self-attention[TR5-6] which are formally equivalent to Schmidhuber's 1991 outer product-based Fast Weight Programmers (apart from normalization). In 1993, he introduced the attention terminology[FWP2] now used in this context,[ATT] and extended the approach to RNNs that program themselves. See tweet of 2022.

[FWP0] J.  Schmidhuber. Learning to control fast-weight memories: An alternative to recurrent nets. Technical Report FKI-147-91, Institut für Informatik, Technische Universität München, 26 March 1991. PDF. First paper on fast weight programmers that separate storage and control: a slow net learns by gradient descent to compute weight changes of a fast net. The outer product-based version (Eq. 5) is now known as a "Transformer with linearized self-attention."[FWP]

[FWP1] J. Schmidhuber. Learning to control fast-weight memories: An alternative to recurrent nets. Neural Computation, 4(1):131-139, 1992. Based on [FWP0]. PDF. HTML. Pictures (German). See tweet of 2022 for 30-year anniversary.

[FWP2] J. Schmidhuber. Reducing the ratio between learning complexity and number of time-varying variables in fully recurrent nets. In Proceedings of the International Conference on Artificial Neural Networks, Amsterdam, pages 460-463. Springer, 1993. PDF. First recurrent NN-based fast weight programmer using outer products, introducing the terminology of learning "internal spotlights of attention."

[FWP3] I. Schlag, J. Schmidhuber. Gated Fast Weights for On-The-Fly Neural Program Generation. Workshop on Meta-Learning, @N(eur)IPS 2017, Long Beach, CA, USA.

[FWP3a] I. Schlag, J. Schmidhuber. Learning to Reason with Third Order Tensor Products. Advances in Neural Information Processing Systems (N(eur)IPS), Montreal, 2018. Preprint: arXiv:1811.12143. PDF.

[FWP4a] J. Ba, G. Hinton, V. Mnih, J. Z. Leibo, C. Ionescu. Using Fast Weights to Attend to the Recent Past. NIPS 2016. PDF. Similar to [FWP0-2], in both motivation [FWP2] and execution.

[FWP4b] D. Bahdanau, K. Cho, Y. Bengio. Neural Machine Translation by Jointly Learning to Align and Translate. 2014-16. Preprint arXiv/1409.0473, 2014-16. This work on soft "attention" did not cite Schmidhuber's much earlier original work of 1991-1993 on soft attention and Transformers with linearized self-attention.[FWP,FWP0-2,6][ATT]

[FWP4d] Y. Tang, D. Nguyen, D. Ha (2020). Neuroevolution of Self-Interpretable Agents. Preprint: arXiv:2003.08165.

[FWP5] F. J. Gomez and J. Schmidhuber. Evolving modular fast-weight networks for control. In W. Duch et al. (Eds.): Proc. ICANN'05, LNCS 3697, pp. 383-389, Springer-Verlag Berlin Heidelberg, 2005. PDF. HTML overview. Reinforcement-learning fast weight programmer.

[FWP6] I. Schlag, K. Irie, J. Schmidhuber. Linear Transformers Are Secretly Fast Weight Memory Systems. 2021. Preprint: arXiv:2102.11174.

[FWP7] K. Irie, I. Schlag, R. Csordas, J. Schmidhuber. Going Beyond Linear Transformers with Recurrent Fast Weight Programmers. Preprint: arXiv:2106.06295 (June 2021).

[FWPMETA1] J. Schmidhuber. Steps towards `self-referential' learning. Technical Report CU-CS-627-92, Dept. of Comp. Sci., University of Colorado at Boulder, November 1992. PDF.

[FWPMETA2] J. Schmidhuber. A self-referential weight matrix. In Proceedings of the International Conference on Artificial Neural Networks, Amsterdam, pages 446-451. Springer, 1993. PDF.

[FWPMETA3] J. Schmidhuber. An introspective network that can learn to run its own weight change algorithm. In Proc. of the Intl. Conf. on Artificial Neural Networks, Brighton, pages 191-195. IEE, 1993.

[FWPMETA4] J.  Schmidhuber. A neural network that embeds its own meta-levels. In Proc. of the International Conference on Neural Networks '93, San Francisco. IEEE, 1993.

[FWPMETA5] J. Schmidhuber. Habilitation thesis, TUM, 1993. PDF. A recurrent neural net with a self-referential, self-reading, self-modifying weight matrix can be found here.

[FWPMETA6] L. Kirsch and J. Schmidhuber. Meta Learning Backpropagation & Improving It. Advances in Neural Information Processing Systems (NeurIPS), 2021. Preprint arXiv:2012.14905 [cs.LG], 2020.

[FWPMETA7] I. Schlag, T. Munkhdalai, J. Schmidhuber. Learning Associative Inference Using Fast Weight Memory. Report arXiv:2011.07831 [cs.AI], 2020.

[FWPMETA8] K. Irie, I. Schlag, R. Csordas, J. Schmidhuber. A Modern Self-Referential Weight Matrix That Learns to Modify Itself. International Conference on Machine Learning (ICML), 2022. Preprint: arXiv:2202.05780.

[FWPMETA9] L. Kirsch and J. Schmidhuber. Self-Referential Meta Learning. First Conference on Automated Machine Learning (Late-Breaking Workshop), 2022.

[G63] R. J Glauber (1963). Time-dependent statistics of the Ising model. Journal of Mathematical Physics, 4(2):294-307, 1963.

[GAN0] O. Niemitalo. A method for training artificial neural networks to generate missing data within a variable context. Blog post, Internet Archive, 2010

[GAN1] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio. Generative adversarial nets. NIPS 2014, 2672-2680, Dec 2014. A description of GANs that does not cite Schmidhuber's original GAN principle of 1990[AC][AC90,AC90b][AC20][R2][T22] (also containing wrong claims about Schmidhuber's adversarial NNs for Predictability Minimization[PM0-2][AC20][T22]).

[GDa] Y. Z. Tsypkin (1966). Adaptation, training and self-organization automatic control systems, Avtomatika I Telemekhanika, 27, 23-61. On gradient descent-based on-line learning for non-linear systems.

[GDb] Y. Z. Tsypkin (1971). Adaptation and Learning in Automatic Systems, Academic Press, 1971. On gradient descent-based on-line learning for non-linear systems.

[GD1] S. I. Amari (1967). A theory of adaptive pattern classifier, IEEE Trans, EC-16, 279-307 (Japanese version published in 1965). PDF. Probably the first paper on using stochastic gradient descent[STO51-52] for learning in multilayer neural networks (without specifying the specific gradient descent method now known as reverse mode of automatic differentiation or backpropagation[BP1]).

[GD2] S. I. Amari (1968). Information Theory—Geometric Theory of Information, Kyoritsu Publ., 1968 (in Japanese). OCR-based PDF scan of pages 94-135 (see pages 119-120). Contains computer simulation results for a five layer network (with 2 modifiable layers) which learns internal representations to classify non-linearily separable pattern classes.

[GD2a] H. Saito (1967). Master's thesis, Graduate School of Engineering, Kyushu University, Japan. Implementation of Amari's 1967 stochastic gradient descent method for multilayer perceptrons.[GD1] (S. Amari, personal communication, 2021.)

[GOD] K. Gödel. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38:173-198, 1931. In the early 1930s, Gödel founded theoretical computer science. He identified fundamental limits of mathematics and theorem proving and computing and Artificial Intelligence.

[GOD21] J. Schmidhuber (AI Blog, 2021). 90th anniversary celebrations: 1931: Kurt Gödel, founder of theoretical computer science, shows limits of math, logic, computing, and artificial intelligence. This was number 1 on Hacker News.

[GOD21a] J. Schmidhuber (2021). Als Kurt Gödel die Grenzen des Berechenbaren entdeckte. (When Kurt Gödel discovered the limits of computability.) Frankfurter Allgemeine Zeitung, 16/6/2021.

[GOD21b] J. Schmidhuber (AI Blog, 2021). 80. Jahrestag: 1931: Kurt Gödel, Vater der theoretischen Informatik, entdeckt die Grenzen des Berechenbaren und der künstlichen Intelligenz.

[GOD34] K. Gödel (1934). On undecidable propositions of formal mathematical systems. Notes by S. C. Kleene and J. B. Rosser on lectures at the Institute for Advanced Study, Princeton, New Jersey, 1934, 30 pp. (Reprinted in M. Davis, (ed.), The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions, Raven Press, Hewlett, New York, 1965.) Gödel introduced a universal coding language.

[GP] J. Schmidhuber (AI Blog, 2020). Genetic Programming for code of unlimited size (1987).

[GP0] N. Cramer. A Representation for the Adaptive Generation of Simple Sequential Programs, Proc. of an Intl. Conf. on Genetic Algorithms and their Applications, Carnegie-Mellon University, July 24-26, 1985.

[GP1] D. Dickmanns, J. Schmidhuber, and A. Winklhofer. Der genetische Algorithmus: Eine Implementierung in Prolog. Fortgeschrittenenpraktikum, Institut für Informatik, Lehrstuhl Prof. Radig, Technische Universität München, 1987. Probably the first work on Genetic Programming for evolving programs of unlimited size written in a universal coding language. Based on work I did since 1985 on a Symbolics Lisp Machine of SIEMENS AG. Authors in alphabetical order. More.

[GPA] S. F. Smith. A Learning System Based on Genetic Adaptive Algorithms, PhD Thesis, Univ. Pittsburgh, 1980.

[GPUNN] Oh, K.-S. and Jung, K. (2004). GPU implementation of neural networks. Pattern Recognition, 37(6):1311-1314. Speeding up traditional NNs on GPU by a factor of 20.

[GPUCNN] K. Chellapilla, S. Puri, P. Simard. High performance convolutional neural networks for document processing. International Workshop on Frontiers in Handwriting Recognition, 2006. Speeding up shallow CNNs on GPU by a factor of 4.

[GPUCNN1] D. C. Ciresan, U. Meier, J. Masci, L. M. Gambardella, J. Schmidhuber. Flexible, High Performance Convolutional Neural Networks for Image Classification. International Joint Conference on Artificial Intelligence (IJCAI-2011, Barcelona), 2011. PDF. ArXiv preprint. Speeding up deep CNNs on GPU by a factor of 60. Used to win four important computer vision competitions 2011-2012 before others won any with similar approaches.

[GPUCNN2] D. C. Ciresan, U. Meier, J. Masci, J. Schmidhuber. A Committee of Neural Networks for Traffic Sign Classification. International Joint Conference on Neural Networks (IJCNN-2011, San Francisco), 2011. PDF. HTML overview. First superhuman performance in a computer vision contest, with half the error rate of humans, and one third the error rate of the closest competitor.[DAN1] This led to massive interest from industry.

[GPUCNN3] D. C. Ciresan, U. Meier, J. Schmidhuber. Multi-column Deep Neural Networks for Image Classification. Proc. IEEE Conf. on Computer Vision and Pattern Recognition CVPR 2012, p 3642-3649, July 2012. PDF. Longer TR of Feb 2012: arXiv:1202.2745v1 [cs.CV]. More.

[GPUCNN4] A. Krizhevsky, I. Sutskever, G. E. Hinton. ImageNet Classification with Deep Convolutional Neural Networks. NIPS 25, MIT Press, Dec 2012. PDF. This paper describes AlexNet, which is similar to the earlier DanNet,[DAN,DAN1][R6] the first pure deep CNN to win computer vision contests in 2011[GPUCNN2-3,5] (AlexNet and VGG Net[GPUCNN9] followed in 2012-2014). [GPUCNN4] emphasizes benefits of Fukushima's ReLUs (1969)[RELU1] and dropout (a variant of Hanson 1990 stochastic delta rule)[Drop1-4] but neither cites the original work[RELU1][Drop1] nor the basic CNN architecture (Fukushima, 1979).[CNN1]

[GPUCNN5] J. Schmidhuber (AI Blog, 2017; updated 2021 for 10th birthday of DanNet): History of computer vision contests won by deep CNNs since 2011. DanNet was the first CNN to win one, and won 4 of them in a row before the similar AlexNet/VGG Net and the Resnet (a Highway Net with open gates) joined the party. Today, deep CNNs are standard in computer vision.

[GPUCNN6] J. Schmidhuber, D. Ciresan, U. Meier, J. Masci, A. Graves. On Fast Deep Nets for AGI Vision. In Proc. Fourth Conference on Artificial General Intelligence (AGI-11), Google, Mountain View, California, 2011. PDF.

[GPUCNN7] D. C. Ciresan, A. Giusti, L. M. Gambardella, J. Schmidhuber. Mitosis Detection in Breast Cancer Histology Images using Deep Neural Networks. MICCAI 2013. PDF.

[GPUCNN8] J. Schmidhuber (AI Blog, 2017; updated 2021 for 10th birthday of DanNet). First deep learner to win a contest on object detection in large images— first deep learner to win a medical imaging contest (2012). Link. How the Swiss AI Lab IDSIA used GPU-based CNNs to win the ICPR 2012 Contest on Mitosis Detection and the MICCAI 2013 Grand Challenge.

[GPUCNN9] K. Simonyan, A. Zisserman. Very deep convolutional networks for large-scale image recognition. Preprint arXiv:1409.1556 (2014).

[GSR15] Dramatic improvement of Google's speech recognition through LSTM: Alphr Technology, Jul 2015, or 9to5google, Jul 2015

[GT16] Google's dramatically improved Google Translate of 2016 is based on LSTM, e.g., WIRED, Sep 2016, or siliconANGLE, Sep 2016

[GVF] R. Sutton, J. Modayil, M. Delp, T. De-gris, P. M. Pilarski, A. White, AD. Precup. Horde: A scalable real-time architecture for learning knowledge from unsupervised sensorimotor interaction. 10th International Conference on Autonomous Agents and Multiagent Systems-Volume 2, pp.761-768, 2011.

[H86] J. L. van Hemmen (1986). Spin-glass models of a neural network. Phys. Rev. A 34, 3435, 1 Oct 1986.

[H88] H. Sompolinsky (1988). Statistical Mechanics of Neural Networks. Physics Today 41, 12, 70, 1988.

[H90] W. D. Hillis. Co-evolving parasites improve simulated evolution as an optimization procedure. Physica D: Nonlinear Phenomena, 42(1-3):228-234, 1990.

[HB96] S. El Hihi, Y. Bengio. Hierarchical recurrent neural networks for long-term dependencies. NIPS, 1996.

[HEL] P. Dayan, G. E. Hinton, R. M. Neal, and R. S. Zemel. The Helmholtz machine. Neural Computation, 7:889-904, 1995. An unsupervised learning algorithm related to Schmidhuber's supervised Neural Heat Exchanger.[NHE]

[HIN] J. Schmidhuber (AI Blog, 2020). Critique of 2019 Honda Prize. Science must not allow corporate PR to distort the academic record.

[HRLW] C. Watkins (1989). Learning from delayed rewards.

[HRL0] J.  Schmidhuber. Towards compositional learning with dynamic neural networks. Technical Report FKI-129-90, Institut für Informatik, Technische Universität München, 1990. PDF. An RL machine gets extra command inputs of the form (start, goal). An evaluator NN learns to predict the current rewards/costs of going from start to goal. An (R)NN-based subgoal generator also sees (start, goal), and uses (copies of) the evaluator NN to learn by gradient descent a sequence of cost-minimising intermediate subgoals. The RL machine tries to use such subgoal sequences to achieve final goals. The system is learning action plans at multiple levels of abstraction and multiple time scales and solves what Y. LeCun called an "open problem" in 2022.[LEC]

[HRL1] J. Schmidhuber. Learning to generate sub-goals for action sequences. In T. Kohonen, K. Mäkisara, O. Simula, and J. Kangas, editors, Artificial Neural Networks, pages 967-972. Elsevier Science Publishers B.V., North-Holland, 1991. PDF. Extending TR FKI-129-90, TUM, 1990. HTML & images in German.

[HRL2] J.  Schmidhuber and R. Wahnsiedler. Planning simple trajectories using neural subgoal generators. In J. A. Meyer, H. L. Roitblat, and S. W. Wilson, editors, Proc. of the 2nd International Conference on Simulation of Adaptive Behavior, pages 196-202. MIT Press, 1992. PDF. HTML & images in German.

[HRL3] P. Dayan and G. E. Hinton. Feudal Reinforcement Learning. Advances in Neural Information Processing Systems 5, NIPS, 1992.

[HRL4] M. Wiering and J. Schmidhuber. HQ-Learning. Adaptive Behavior 6(2):219-246, 1997. PDF.

[HW1] R. K. Srivastava, K. Greff, J. Schmidhuber. Highway networks. Preprints arXiv:1505.00387 (May 2015) and arXiv:1507.06228 (July 2015). Also at NIPS 2015. The first working very deep feedforward nets with over 100 layers (previous NNs had at most a few tens of layers). Let g, t, h, denote non-linear differentiable functions. Each non-input layer of a highway net computes g(x)x + t(x)h(x), where x is the data from the previous layer. (Like LSTM with forget gates[LSTM2] for RNNs.) Resnets[HW2] are a version of this where the gates are always open: g(x)=t(x)=const=1. Highway Nets perform roughly as well as ResNets[HW2] on ImageNet.[HW3] Variants of highway gates are also used for certain algorithmic tasks, where the simpler residual layers do not work as well.[NDR] More.

[HW1a] R. K. Srivastava, K. Greff, J. Schmidhuber. Highway networks. Presentation at the Deep Learning Workshop, ICML'15, July 10-11, 2015. Link.

[HW2] He, K., Zhang, X., Ren, S., Sun, J. Deep residual learning for image recognition. Preprint arXiv:1512.03385 (Dec 2015). Residual nets are a special case of Highway Nets[HW1] where the gates are always open: g(x)=1 (a typical highway net initialization) and t(x)=1. More.

[HW3] K. Greff, R. K. Srivastava, J. Schmidhuber. Highway and Residual Networks learn Unrolled Iterative Estimation. Preprint arxiv:1612.07771 (2016). Also at ICLR 2017.

[HYB12] Hinton, G. E., Deng, L., Yu, D., Dahl, G. E., Mohamed, A., Jaitly, N., Senior, A., Vanhoucke, V., Nguyen, P., Sainath, T. N., and Kingsbury, B. (2012). Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal Process. Mag., 29(6):82-97.

[I24] E. Ising (1925). Beitrag zur Theorie des Ferro- und Paramagnetismus. Dissertation, 1924.

[I25] E. Ising (1925). Beitrag zur Theorie des Ferromagnetismus. Z. Phys., 31 (1): 253-258, 1925. The first non-learning recurrent NN architecture (the Ising model or Lenz-Ising model) was introduced and analyzed by physicists Ernst Ising and Wilhelm Lenz in the 1920s.[L20][I25][K41][W45][T22] It settles into an equilibrium state in response to input conditions, and is the foundation of the first published learning RNNs.[AMH1-2]

[JOU17] Jouppi et al. (2017). In-Datacenter Performance Analysis of a Tensor Processing Unit. Preprint arXiv:1704.04760

[K41] H. A. Kramers and G. H. Wannier (1941). Statistics of the Two-Dimensional Ferromagnet. Phys. Rev. 60, 252 and 263, 1941.

[K56] S.C. Kleene. Representation of Events in Nerve Nets and Finite Automata. Automata Studies, Editors: C.E. Shannon and J. McCarthy, Princeton University Press, p. 3-42, Princeton, N.J., 1956.

[KO0] J.  Schmidhuber. Discovering problem solutions with low Kolmogorov complexity and high generalization capability. Technical Report FKI-194-94, Fakultät für Informatik, Technische Universität München, 1994. PDF.

[KO1] J.  Schmidhuber. Discovering solutions with low Kolmogorov complexity and high generalization capability. In A. Prieditis and S. Russell, editors, Machine Learning: Proceedings of the Twelfth International Conference (ICML 1995), pages 488-496. Morgan Kaufmann Publishers, San Francisco, CA, 1995. PDF.

[KO2] J. Schmidhuber. Discovering neural nets with low Kolmogorov complexity and high generalization capability. Neural Networks, 10(5):857-873, 1997. PDF.

[L20] W. Lenz (1920). Beitraege zum Verständnis der magnetischen Eigenschaften in festen Körpern. Physikalische Zeitschrift, 21: 613-615.

[LEC] J. Schmidhuber (AI Blog, 2022). LeCun's 2022 paper on autonomous machine intelligence rehashes but does not cite essential work of 1990-2015. Years ago, Schmidhuber's team published most of what Y. LeCun calls his "main original contributions:" neural nets that learn multiple time scales and levels of abstraction, generate subgoals, use intrinsic motivation to improve world models, and plan (1990); controllers that learn informative predictable representations (1997), etc. This was also discussed on Hacker News, reddit, and in the media. See tweet1. LeCun also listed the "5 best ideas 2012-2022" without mentioning that most of them are from Schmidhuber's lab, and older. See tweet2.

[LSTM0] S. Hochreiter and J. Schmidhuber. Long Short-Term Memory. TR FKI-207-95, TUM, August 1995. PDF.

[LSTM1] S. Hochreiter, J. Schmidhuber. Long Short-Term Memory. Neural Computation, 9(8):1735-1780, 1997. PDF. Based on [LSTM0]. More.

[LSTM2] F. A. Gers, J. Schmidhuber, F. Cummins. Learning to Forget: Continual Prediction with LSTM. Neural Computation, 12(10):2451-2471, 2000. PDF. The "vanilla LSTM architecture" with forget gates that everybody is using today, e.g., in Google's Tensorflow.

[LSTM3] A. Graves, J. Schmidhuber. Framewise phoneme classification with bidirectional LSTM and other neural network architectures. Neural Networks, 18:5-6, pp. 602-610, 2005. PDF.

[LSTM4] S. Fernandez, A. Graves, J. Schmidhuber. An application of recurrent neural networks to discriminative keyword spotting. Intl. Conf. on Artificial Neural Networks ICANN'07, 2007. PDF.

[LSTM5] A. Graves, M. Liwicki, S. Fernandez, R. Bertolami, H. Bunke, J. Schmidhuber. A Novel Connectionist System for Improved Unconstrained Handwriting Recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 5, 2009. PDF.

[LSTM6] A. Graves, J. Schmidhuber. Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks. NIPS'22, p 545-552, Vancouver, MIT Press, 2009. PDF.

[LSTM7] J. Bayer, D. Wierstra, J. Togelius, J. Schmidhuber. Evolving memory cell structures for sequence learning. Proc. ICANN-09, Cyprus, 2009. PDF.

[LSTM8] A. Graves, A. Mohamed, G. E. Hinton. Speech Recognition with Deep Recurrent Neural Networks. ICASSP 2013, Vancouver, 2013. PDF.

[LSTM9] O. Vinyals, L. Kaiser, T. Koo, S. Petrov, I. Sutskever, G. Hinton. Grammar as a Foreign Language. Preprint arXiv:1412.7449 [cs.CL].

[LSTM10] A. Graves, D. Eck and N. Beringer, J. Schmidhuber. Biologically Plausible Speech Recognition with LSTM Neural Nets. In J. Ijspeert (Ed.), First Intl. Workshop on Biologically Inspired Approaches to Advanced Information Technology, Bio-ADIT 2004, Lausanne, Switzerland, p. 175-184, 2004. PDF.

[LSTM11] N. Beringer and A. Graves and F. Schiel and J. Schmidhuber. Classifying unprompted speech by retraining LSTM Nets. In W. Duch et al. (Eds.): Proc. Intl. Conf. on Artificial Neural Networks ICANN'05, LNCS 3696, pp. 575-581, Springer-Verlag Berlin Heidelberg, 2005.

[LSTM12] D. Wierstra, F. Gomez, J. Schmidhuber. Modeling systems with internal state using Evolino. In Proc. of the 2005 conference on genetic and evolutionary computation (GECCO), Washington, D. C., pp. 1795-1802, ACM Press, New York, NY, USA, 2005. Got a GECCO best paper award.

[LSTM13] F. A. Gers and J. Schmidhuber. LSTM Recurrent Networks Learn Simple Context Free and Context Sensitive Languages. IEEE Transactions on Neural Networks 12(6):1333-1340, 2001. PDF.

[LSTM14] S. Fernandez, A. Graves, J. Schmidhuber. Sequence labelling in structured domains with hierarchical recurrent neural networks. In Proc. IJCAI 07, p. 774-779, Hyderabad, India, 2007 (talk). PDF.

[LSTM15] A. Graves, J. Schmidhuber. Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks. Advances in Neural Information Processing Systems 22, NIPS'22, p 545-552, Vancouver, MIT Press, 2009. PDF.

[LSTM16] M. Stollenga, W. Byeon, M. Liwicki, J. Schmidhuber. Parallel Multi-Dimensional LSTM, With Application to Fast Biomedical Volumetric Image Segmentation. Advances in Neural Information Processing Systems (NIPS), 2015. Preprint: arxiv:1506.07452.

[LSTM17] J. A. Perez-Ortiz, F. A. Gers, D. Eck, J. Schmidhuber. Kalman filters improve LSTM network performance in problems unsolvable by traditional recurrent nets. Neural Networks 16(2):241-250, 2003. PDF.

[LSTMGRU] J. Chung, C. Gulcehre, K. Cho, Y. Bengio (2014). Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling. Preprint arXiv:1412.3555 [cs.NE]. The so-called gated recurrent units (GRU) are actually a variant of the vanilla LSTM architecture[LSTM2] (2000) which the authors did not cite although this work[LSTM2] was the one that introduced gated recurrent units. Furthermore, Schmidhuber's team automatically evolved lots of additional LSTM variants and topologies already in 2009[LSTM7] without changing the name of the basic method. (Margin note: GRU cells lack an important gate and can neither learn to count[LSTMGRU2] nor learn simple non-regular languages;[LSTMGRU2] they also do not work as well for challenging translation tasks, according to Google Brain.[LSTMGRU3])

[LSTMGRU2] G. Weiss, Y. Goldberg, E. Yahav. On the Practical Computational Power of Finite Precision RNNs for Language Recognition. Preprint arXiv:1805.04908.

[LSTMGRU3] D. Britz et al. (2017). Massive Exploration of Neural Machine Translation Architectures. Preprint arXiv:1703.03906

[LSTMPG] J. Schmidhuber (AI Blog, Dec 2020). 10-year anniversary of our journal paper on deep reinforcement learning with policy gradients for LSTM (2007-2010). Recent famous applications of policy gradients to LSTM: DeepMind's Starcraft player (2019) and OpenAI's dextrous robot hand & Dota player (2018)—Bill Gates called this a huge milestone in advancing AI.

[LSTM-RL] B. Bakker, F. Linaker, J. Schmidhuber. Reinforcement Learning in Partially Observable Mobile Robot Domains Using Unsupervised Event Extraction. In Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2002), Lausanne, 2002. PDF.

[MC43] W. S. McCulloch, W. Pitts. A Logical Calculus of Ideas Immanent in Nervous Activity. Bulletin of Mathematical Biophysics, Vol. 5, p. 115-133, 1943.

[META] J. Schmidhuber (AI Blog, 2020). 1/3 century anniversary of first publication on metalearning machines that learn to learn (1987). For its cover I drew a robot that bootstraps itself. 1992-: gradient descent-based neural metalearning. 1994-: Meta-Reinforcement Learning with self-modifying policies. 1997: Meta-RL plus artificial curiosity and intrinsic motivation. 2002-: asymptotically optimal metalearning for curriculum learning. 2003-: mathematically optimal Gödel Machine. 2020: new stuff!

[META1] J.  Schmidhuber. Evolutionary principles in self-referential learning, or on learning how to learn: The meta-meta-... hook. Diploma thesis, Institut für Informatik, Technische Universität München, 1987. Searchable PDF scan (created by OCRmypdf which uses LSTM). HTML. For example, Genetic Programming (GP) is applied to itself, to recursively evolve better GP methods through Meta-Evolution. More.

[MGC] MICCAI 2013 Grand Challenge on Mitosis Detection, organised by M. Veta, M.A. Viergever, J.P.W. Pluim, N. Stathonikos, P. J. van Diest of University Medical Center Utrecht.

[MIR] J. Schmidhuber (AI Blog, Oct 2019, updated 2021, 2022). Deep Learning: Our Miraculous Year 1990-1991. Preprint arXiv:2005.05744, 2020. The deep learning neural networks of our team have revolutionised pattern recognition and machine learning, and are now heavily used in academia and industry. In 2020-21, we celebrated that many of the basic ideas behind this revolution were published within fewer than 12 months in our "Annus Mirabilis" 1990-1991 at TU Munich.

[MLP1] D. C. Ciresan, U. Meier, L. M. Gambardella, J. Schmidhuber. Deep Big Simple Neural Nets For Handwritten Digit Recognition. Neural Computation 22(12): 3207-3220, 2010. ArXiv Preprint. Showed that plain backprop for deep standard NNs is sufficient to break benchmark records, without any unsupervised pre-training.

[MLP2] J. Schmidhuber (AI Blog, Sep 2020). 10-year anniversary of supervised deep learning breakthrough (2010). No unsupervised pre-training. By 2010, when compute was 100 times more expensive than today, both our feedforward NNs[MLP1] and our earlier recurrent NNs were able to beat all competing algorithms on important problems of that time. This deep learning revolution quickly spread from Europe to North America and Asia. The rest is history.

[MOST] J.  Schmidhuber (AI Blog, 2021). The most cited neural networks all build on work done in my labs. Foundations of the most popular NNs originated in my labs at TU Munich and IDSIA. Here I mention: (1) Long Short-Term Memory (LSTM), (2) ResNet (which is our earlier Highway Net with open gates), (3) AlexNet and VGG Net (both building on our similar earlier DanNet: the first deep convolutional NN to win image recognition competitions), (4) Generative Adversarial Networks (an instance of my earlier Adversarial Artificial Curiosity), and (5) variants of Transformers (Transformers with linearized self-attention are formally equivalent to my earlier Fast Weight Programmers). Most of this started with our Annus Mirabilis of 1990-1991.[MIR]

[NAN1] J.  Schmidhuber. Networks adjusting networks. In J. Kindermann and A. Linden, editors, Proceedings of `Distributed Adaptive Neural Information Processing', St.Augustin, 24.-25.5. 1989, pages 197-208. Oldenbourg, 1990. Extended version: TR FKI-125-90 (revised), Institut für Informatik, TUM. PDF. Includes the proposal of a biologically more plausible deep learning algorithm that—unlike backpropagation—is local in space and time. Based on neural nets learning to estimate gradients for other neural nets.

[NAN2] J.  Schmidhuber. Networks adjusting networks. Technical Report FKI-125-90, Institut für Informatik, Technische Universität München. Revised in November 1990. PDF.

[NAN3] Recurrent networks adjusted by adaptive critics. In Proc. IEEE/INNS International Joint Conference on Neural Networks, Washington, D. C., volume 1, pages 719-722, 1990.

[NAN4] J. Schmidhuber. Additional remarks on G. Lukes' review of Schmidhuber's paper `Recurrent networks adjusted by adaptive critics'. Neural Network Reviews, 4(1):43, 1990.

[NAN5] M. Jaderberg, W. M. Czarnecki, S. Osindero, O. Vinyals, A. Graves, D. Silver, K. Kavukcuoglu. Decoupled Neural Interfaces using Synthetic Gradients. Preprint arXiv:1608.05343, 2016. This work of DeepMind is similar to [NAN1-2].

[NAS] B. Zoph, Q. V. Le. Neural Architecture Search with Reinforcement Learning. Preprint arXiv:1611.01578 (PDF), 2017.

[NAT1] J. Schmidhuber. Citation bubble about to burst? Nature, vol. 469, p. 34, 6 January 2011. HTML.

[NDR] R. Csordas, K. Irie, J. Schmidhuber. The Neural Data Router: Adaptive Control Flow in Transformers Improves Systematic Generalization. Proc. ICLR 2022. Preprint arXiv/2110.07732.

[NHE] J. Schmidhuber. The Neural Heat Exchanger. Oral presentations since 1990 at various universities including TUM and the University of Colorado at Boulder. Also in In S. Amari, L. Xu, L. Chan, I. King, K. Leung, eds., Proceedings of the Intl. Conference on Neural Information Processing (1996), pages 194-197, Springer, Hongkong. Link. Proposal of a biologically more plausible deep learning algorithm that—unlike backpropagation—is local in space and time. Inspired by the physical heat exchanger: inputs "heat up" while being transformed through many successive layers, targets enter from the other end of the deep pipeline and "cool down."

[OAI1] G. Powell, J. Schneider, J. Tobin, W. Zaremba, A. Petron, M. Chociej, L. Weng, B. McGrew, S. Sidor, A. Ray, P. Welinder, R. Jozefowicz, M. Plappert, J. Pachocki, M. Andrychowicz, B. Baker. Learning Dexterity. OpenAI Blog, 2018.

[OAI1a] OpenAI, M. Andrychowicz, B. Baker, M. Chociej, R. Jozefowicz, B. McGrew, J. Pachocki, A. Petron, M. Plappert, G. Powell, A. Ray, J. Schneider, S. Sidor, J. Tobin, P. Welinder, L. Weng, W. Zaremba. Learning Dexterous In-Hand Manipulation. arxiv:1312.5602 (PDF).

[OAI2] OpenAI et al. (Dec 2019). Dota 2 with Large Scale Deep Reinforcement Learning. Preprint arxiv:1912.06680. An LSTM composes 84% of the model's total parameter count.

[OAI2a] J. Rodriguez. The Science Behind OpenAI Five that just Produced One of the Greatest Breakthrough in the History of AI. Towards Data Science, 2018. An LSTM was the core of OpenAI Five.

[PDA1] G.Z. Sun, H.H. Chen, C.L. Giles, Y.C. Lee, D. Chen. Neural Networks with External Memory Stack that Learn Context—Free Grammars from Examples. Proceedings of the 1990 Conference on Information Science and Systems, Vol.II, pp. 649-653, Princeton University, Princeton, NJ, 1990.

[PDA2] M. Mozer, S. Das. A connectionist symbol manipulator that discovers the structure of context-free languages. Proc. NIPS 1993.

[PLAN] J. Schmidhuber (AI Blog, 2020). 30-year anniversary of planning & reinforcement learning with recurrent world models and artificial curiosity (1990). This work also introduced high-dimensional reward signals, deterministic policy gradients for RNNs, the GAN principle (widely used today). Agents with adaptive recurrent world models even suggest a simple explanation of consciousness & self-awareness.

[PLAN2] J.  Schmidhuber. An on-line algorithm for dynamic reinforcement learning and planning in reactive environments. Proc. IEEE/INNS International Joint Conference on Neural Networks, San Diego, volume 2, pages 253-258, 1990. Based on TR FKI-126-90 (1990).[AC90] More.

[PLAN3] J.  Schmidhuber. Reinforcement learning in Markovian and non-Markovian environments. In D. S. Lippman, J. E. Moody, and D. S. Touretzky, editors, Advances in Neural Information Processing Systems 3, NIPS'3, pages 500-506. San Mateo, CA: Morgan Kaufmann, 1991. PDF. Partially based on [AC90].

[PLAN4] J. Schmidhuber. On Learning to Think: Algorithmic Information Theory for Novel Combinations of Reinforcement Learning Controllers and Recurrent Neural World Models. Report arXiv:1210.0118 [cs.AI], 2015.

[PLAN5] One Big Net For Everything. Preprint arXiv:1802.08864 [cs.AI], Feb 2018.

[PLAN6] D. Ha, J. Schmidhuber. Recurrent World Models Facilitate Policy Evolution. Advances in Neural Information Processing Systems (NIPS), Montreal, 2018. (Talk.) Preprint: arXiv:1809.01999. Github: World Models.

[PG] R. J. Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning 8.3-4: 229-256, 1992.

[PHD] J.  Schmidhuber. Dynamische neuronale Netze und das fundamentale raumzeitliche Lernproblem (Dynamic neural nets and the fundamental spatio-temporal credit assignment problem). Dissertation, Institut für Informatik, Technische Universität München, 1990. PDF. HTML.

[PM0] J. Schmidhuber. Learning factorial codes by predictability minimization. TR CU-CS-565-91, Univ. Colorado at Boulder, 1991. PDF. More.

[PM1] J. Schmidhuber. Learning factorial codes by predictability minimization. Neural Computation, 4(6):863-879, 1992. Based on [PM0], 1991. PDF. More.

[PM2] J. Schmidhuber, M. Eldracher, B. Foltin. Semilinear predictability minimzation produces well-known feature detectors. Neural Computation, 8(4):773-786, 1996. PDF. More.

[PP] J. Schmidhuber. POWERPLAY: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem. Frontiers in Cognitive Science, 2013. ArXiv preprint (2011): arXiv:1112.5309 [cs.AI]

[PP1] R. K. Srivastava, B. Steunebrink, J. Schmidhuber. First Experiments with PowerPlay. Neural Networks, 2013. ArXiv preprint (2012): arXiv:1210.8385 [cs.AI].

[PP2] V. Kompella, M. Stollenga, M. Luciw, J. Schmidhuber. Continual curiosity-driven skill acquisition from high-dimensional video inputs for humanoid robots. Artificial Intelligence, 2015.

[R1] Reddit/ML, 2019. Hinton, LeCun, Bengio receive ACM Turing Award. This announcement contains more comments about Schmidhuber than about any of the awardees.

[R2] Reddit/ML, 2019. J. Schmidhuber really had GANs in 1990.

[R3] Reddit/ML, 2019. NeurIPS 2019 Bengio Schmidhuber Meta-Learning Fiasco. Schmidhuber started metalearning (learning to learn—now a hot topic) in 1987[META1][META] long before Bengio who suggested in public at N(eur)IPS 2019 that he did it before Schmidhuber.

[R4] Reddit/ML, 2019. Five major deep learning papers by G. Hinton did not cite similar earlier work by J. Schmidhuber.

[R5] Reddit/ML, 2019. The 1997 LSTM paper by Hochreiter & Schmidhuber has become the most cited deep learning research paper of the 20th century.

[R6] Reddit/ML, 2019. DanNet, the CUDA CNN of Dan Ciresan in J. Schmidhuber's team, won 4 image recognition challenges prior to AlexNet.

[R7] Reddit/ML, 2019. J. Schmidhuber on Seppo Linnainmaa, inventor of backpropagation in 1970.

[R8] Reddit/ML, 2019. J. Schmidhuber on Alexey Ivakhnenko, godfather of deep learning 1965.

[R11] Reddit/ML, 2020. Schmidhuber: Critique of Honda Prize for Dr. Hinton

[R12] Reddit/ML, 2020. J. Schmidhuber: Critique of Turing Award for Drs. Bengio & Hinton & LeCun

[R15] Reddit/ML, 2021. J. Schmidhuber's work on fast weights from 1991 is similar to linearized variants of Transformers

[RCNN] R. Girshick, J. Donahue, T. Darrell, J. Malik. Rich feature hierarchies for accurate object detection and semantic segmentation. Preprint arXiv/1311.2524, Nov 2013.

[RCNN2] R. Girshick. Fast R-CNN. Proc. of the IEEE international conference on computer vision, p. 1440-1448, 2015.

[RCNN3] K. He, G. Gkioxari, P. Dollar, R. Girshick. Mask R-CNN. Preprint arXiv/1703.06870, 2017.

[RELU1] K. Fukushima (1969). Visual feature extraction by a multilayered network of analog threshold elements. IEEE Transactions on Systems Science and Cybernetics. 5 (4): 322-333. doi:10.1109/TSSC.1969.300225. This work introduced rectified linear units or ReLUs, now widely used.

[RELU2] C. v. d. Malsburg (1973). Self-Organization of Orientation Sensitive Cells in the Striate Cortex. Kybernetik, 14:85-100, 1973. See Table 1 for rectified linear units or ReLUs. Possibly this was also the first work on applying an EM algorithm to neural nets.

[ROB] A. J. Robinson and F. Fallside. The utility driven dynamic error propagation network. Technical Report CUED/F-INFENG/TR.1, Cambridge University Engineering Department, 1987.

[RPG] D. Wierstra, A. Foerster, J. Peters, J. Schmidhuber (2010). Recurrent policy gradients. Logic Journal of the IGPL, 18(5), 620-634.

[RPG07] D. Wierstra, A. Foerster, J. Peters, J. Schmidhuber. Solving Deep Memory POMDPs with Recurrent Policy Gradients. Intl. Conf. on Artificial Neural Networks ICANN'07, 2007. PDF.

[S2S] I. Sutskever, O. Vinyals, Quoc V. Le. Sequence to sequence learning with neural networks. In: Advances in Neural Information Processing Systems (NIPS), 2014, 3104-3112.

[S59] A. L. Samuel. Some studies in machine learning using the game of checkers. IBM Journal on Research and Development, 3:210-229, 1959.

[S93] D. Sherrington (1993). Neural networks: the spin glass approach. North-Holland Mathematical Library, vol 51, 1993, p. 261-291.

[SNT] J. Schmidhuber, S. Heil (1996). Sequential neural text compression. IEEE Trans. Neural Networks, 1996. PDF. A probabilistic language model based on predictive coding; an earlier version appeared at NIPS 1995.

[SK75] D. Sherrington, S. Kirkpatrick (1975). Solvable Model of a Spin-Glass. Phys. Rev. Lett. 35, 1792, 1975.

[STO51] H. Robbins, S. Monro (1951). A Stochastic Approximation Method. The Annals of Mathematical Statistics. 22(3):400, 1951.

[STO52] J. Kiefer, J. Wolfowitz (1952). Stochastic Estimation of the Maximum of a Regression Function. The Annals of Mathematical Statistics. 23(3):462, 1952.

[TD] R. Sutton. Learning to predict by the methods of temporal differences. Machine Learning. 3 (1): 9-44, 1988.

[UN] J. Schmidhuber (AI Blog, 2021). 30-year anniversary. 1991: First very deep learning with unsupervised pre-training. Unsupervised hierarchical predictive coding finds compact internal representations of sequential data to facilitate downstream learning. The hierarchy can be distilled into a single deep neural network (suggesting a simple model of conscious and subconscious information processing). 1993: solving problems of depth >1000.

[UN0] J.  Schmidhuber. Neural sequence chunkers. Technical Report FKI-148-91, Institut für Informatik, Technische Universität München, April 1991. PDF. Unsupervised/self-supervised learning and predictive coding is used in a deep hierarchy of recurrent neural networks (RNNs) to find compact internal representations of long sequences of data, across multiple time scales and levels of abstraction. Each RNN tries to solve the pretext task of predicting its next input, sending only unexpected inputs to the next RNN above. The resulting compressed sequence representations greatly facilitate downstream supervised deep learning such as sequence classification. By 1993, the approach solved problems of depth 1000 [UN2] (requiring 1000 subsequent computational stages/layers—the more such stages, the deeper the learning). A variant collapses the hierarchy into a single deep net. It uses a so-called conscious chunker RNN which attends to unexpected events that surprise a lower-level so-called subconscious automatiser RNN. The chunker learns to understand the surprising events by predicting them. The automatiser uses a neural knowledge distillation procedure to compress and absorb the formerly conscious insights and behaviours of the chunker, thus making them subconscious. The systems of 1991 allowed for much deeper learning than previous methods. More.

[UN1] J. Schmidhuber. Learning complex, extended sequences using the principle of history compression. Neural Computation, 4(2):234-242, 1992. Based on TR FKI-148-91, TUM, 1991.[UN0] PDF. First working Deep Learner based on a deep RNN hierarchy (with different self-organising time scales), overcoming the vanishing gradient problem through unsupervised pre-training and predictive coding (with self-supervised target generation). Also: compressing or distilling a teacher net (the chunker) into a student net (the automatizer) that does not forget its old skills—such approaches are now widely used. More.

[UN2] J. Schmidhuber. Habilitation thesis, TUM, 1993. PDF. An ancient experiment on "Very Deep Learning" with credit assignment across 1200 time steps or virtual layers and unsupervised pre-training for a stack of recurrent NN can be found here (depth > 1000).

[UN3] J.  Schmidhuber, M. C. Mozer, and D. Prelinger. Continuous history compression. In H. Hüning, S. Neuhauser, M. Raus, and W. Ritschel, editors, Proc. of Intl. Workshop on Neural Networks, RWTH Aachen, pages 87-95. Augustinus, 1993.

[UN4] G. E. Hinton, R. R. Salakhutdinov. Reducing the dimensionality of data with neural networks. Science, Vol. 313. no. 5786, pp. 504—507, 2006. PDF. This work describes unsupervised pre-training of stacks of feedforward NNs (FNNs) called Deep Belief Networks (DBNs). It did not cite the much earlier 1991 unsupervised pre-training of stacks of more general recurrent NNs (RNNs)[UN0-3] which introduced the first NNs shown to solve very deep problems. The 2006 justification of the authors was essentially the one Schmidhuber used for the 1991 RNN stack: each higher level tries to reduce the description length (or negative log probability) of the data representation in the level below.[HIN][T22][MIR] This can greatly facilitate very deep downstream learning.[UN0-3]

[UN5] Y. Bengio, P. Lamblin, D. Popovici, H. Larochelle. Greedy layer-wise training of deep networks. Proc. NIPS 06, pages 153-160, Dec. 2006. The comment under reference[UN4] applies here as well.

[UVF15] T. Schaul, D. Horgan, K. Gregor, D. Silver. Universal value function approximators. Proc. ICML 2015, pp. 1312-1320, 2015.

[SA17] J. Schmidhuber. Falling Walls: The Past, Present and Future of Artificial Intelligence. Scientific American, Observations, Nov 2017.

[SCAN] J. Masci, A. Giusti, D. Ciresan, G. Fricout, J. Schmidhuber. A Fast Learning Algorithm for Image Segmentation with Max-Pooling Convolutional Networks. ICIP 2013. Preprint arXiv:1302.1690.

[ST] J. Masci, U. Meier, D. Ciresan, G. Fricout, J. Schmidhuber Steel Defect Classification with Max-Pooling Convolutional Neural Networks. Proc. IJCNN 2012. PDF.

[T20] J. Schmidhuber (AI Blog, 25 June 2020). Critique of 2018 Turing Award for Deep Learning.

[T22] J. Schmidhuber (AI Blog, 2022). Scientific Integrity and the History of Deep Learning: The 2021 Turing Lecture, and the 2018 Turing Award. Technical Report IDSIA-77-21, IDSIA, Lugano, Switzerland, 2022.

[THE17] S. Baker (2017). Which countries and universities are leading on AI research? Times Higher Education World University Rankings, 2017. Link.

[TR1] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, I. Polosukhin (2017). Attention is all you need. NIPS 2017, pp. 5998-6008. This paper introduced the name "Transformers" for a now widely used NN type. It did not cite the 1991 publication on what's now called "Transformers with linearized self-attention."[FWP0-6][TR5-6] Schmidhuber also introduced the now popular attention terminology in 1993.[ATT][FWP2][R4] See tweet of 2022 for 30-year anniversary.

[TR2] J. Devlin, M. W. Chang, K. Lee, K. Toutanova (2018). Bert: Pre-training of deep bidirectional Transformers for language understanding. Preprint arXiv:1810.04805.

[TR3] K. Tran, A. Bisazza, C. Monz. The Importance of Being Recurrent for Modeling Hierarchical Structure. EMNLP 2018, p 4731-4736. ArXiv preprint 1803.03585.

[TR4] M. Hahn. Theoretical Limitations of Self-Attention in Neural Sequence Models. Transactions of the Association for Computational Linguistics, Volume 8, p.156-171, 2020.

[TR5] A. Katharopoulos, A. Vyas, N. Pappas, F. Fleuret. Transformers are RNNs: Fast autoregressive Transformers with linear attention. In Proc. Int. Conf. on Machine Learning (ICML), July 2020.

[TR6] K. Choromanski, V. Likhosherstov, D. Dohan, X. Song, A. Gane, T. Sarlos, P. Hawkins, J. Davis, A. Mohiuddin, L. Kaiser, et al. Rethinking attention with Performers. In Int. Conf. on Learning Representations (ICLR), 2021.

[VAN1] S. Hochreiter. Untersuchungen zu dynamischen neuronalen Netzen. Diploma thesis, TUM, 1991 (advisor J. Schmidhuber). PDF. More on the Fundamental Deep Learning Problem.

[VAN2] Y. Bengio, P. Simard, P. Frasconi. Learning long-term dependencies with gradient descent is difficult. IEEE TNN 5(2), p 157-166, 1994. Results are essentially identical to those of Schmidhuber's diploma student Sepp Hochreiter (1991).[VAN1] Even after a common publication,[VAN3] the first author of [VAN2] published papers[VAN4] that cited only their own [VAN2] but not the original work.

[VAN3] S. Hochreiter, Y. Bengio, P. Frasconi, J. Schmidhuber. Gradient flow in recurrent nets: the difficulty of learning long-term dependencies. In S. C. Kremer and J. F. Kolen, eds., A Field Guide to Dynamical Recurrent Neural Networks. IEEE press, 2001. PDF.

[VAN4] Y. Bengio. Neural net language models. Scholarpedia, 3(1):3881, 2008. Link.

[W45] G. H. Wannier (1945). The Statistical Problem in Cooperative Phenomena. Rev. Mod. Phys. 17, 50.

[WU] Y. Wu et al. Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation. Preprint arXiv:1609.08144 (PDF), 2016.


Our impact on the world's most valuable public companies (Google, Apple, Microsoft, Facebook, mazon etc)