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 are celebrating 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 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 for Unsupervised Data Modeling (1991)

Sec. 8: Fast Weight Programmers Learn to Program NNs (1991), Like Transformer Variants

Sec. 9: Learning Sequential Attention with NNs (1990)

Sec. 10: 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 Adjusting Networks / Synthetic Gradients (1990)

Sec. 16: O(n^{3}) Gradient Computation for Online Recurrent NNs (1991)

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

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)

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]}

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]} 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]}

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,
first informally proposed in 1945,^{[MC43]}
then formalised in 1956^{[K56][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 Pre-Training (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. (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]}

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.^{[UN0-3]} 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 (1991)

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]} or "cloning" the behavior of a teacher net into a student net.

##
**3. The Fundamental Deep Learning Problem: Vanishing / Exploding Gradients (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

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*), 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^{[FWP0]} (see Sec. 8).

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]}
In 2015, the CTC-LSTM combination dramatically improved
Google's speech recognition on the Android smartphones.^{[GSR15][DL4]}

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]}

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.

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. Microsoft's popular ResNets^{[HW2]} (which won the
ImageNet 2015 contest) are a special case 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]}

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]} 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]}

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 Through Adversarial Generative NNs (1990)**

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, 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]}

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)**

Numerous improvements of the original Adversarial Curiosity of 1990 (AC1990, Sec. 5)
are summarized in more recent surveys.^{[AC06][AC09][AC10]} 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]}

##
**7. Adversarial Networks for Unsupervised Data Modeling (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]}
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: NNs Learn to Program NNs (1991), Like Today's Transformer Variants

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 certain types of what is now called
attention^{[ATT]}
and *Transformers*.^{[TR1-6][FWP]}

Some of my Fast Weight Programmers 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]}).
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]}
The 1993 paper^{[FWP2]} also explicitly addressed the learning of internal spotlights of attention in end-to-end-differentiable networks. Compare Sec. 9 on
learning attention.

I also showed how fast weights can be used for meta-learning or
learning to learn, one of my main research topics
since 1987.^{[META1]}
In follow-up work^{[FWPMETA1-5]} 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.

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").

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]} is actually 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
*linear* Transformers or Performers^{[TR5-6]}
which are *formally equivalent* to my 1991 Fast Weight Programmers (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)

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)"*
(see also Sec. 10).

##
10. 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]}
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.
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)

In 1990, I introduced reinforcement learning (RL) and 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.^{[PLAN2-6]}
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]} 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]})

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.
##
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 Adjusting 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][NAN1]}
A quarter century later, DeepMind called this "Synthetic Gradients."^{[NAN5]}
##
16. O(n^{3}) Gradients for Online Recurrent NNs (1991)

The original 1987 fixed-size storage learning algorithm for
fully recurrent continually running networks^{[ROB]}
requires O(n^{4}) 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(n^{3}).^{[CUB1-2]} *However, this work does not really count,
since the great RNN pioneer Ron Williams had derived this method first!*^{[CUB0]}

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]} (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.

##
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. 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)

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][HOP]}
The works of 1990-91 (and my even earlier diploma thesis of 1987^{[META1]})
embodied an alternative *program-oriented* view of Machine Learning.

When Kurt Gödel
laid the foundations of theoretical computer science in 1931,^{[GOD][GOD34]}
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.

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."

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.^{[CNN1-4]}
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]}) and
won 4 important computer vision competitions 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]}

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]}

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.

##
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 the principle of what's now called linear Transformers (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]}
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
formally equivalent to linear Transformers),
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]}

##

##
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.
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). Five years later, modern backpropagation was published "next door" 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
linear Transformers^{[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]}

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]}

##
Acknowledgments

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.

##
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College of Computer Science, 1989.

[CUB1]
An O(n^{3}) 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(n^{3}) 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 (2021).
10-year anniversary. In 2011, DanNet triggered the deep convolutional neural network (CNN) revolution. *Named after my 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 (2011; updated 2021 for 10th birthday of DanNet): First superhuman visual pattern recognition.
*At the IJCNN 2011 computer vision competition in Silicon Valley,
our artificial neural network called DanNet performed twice better than humans, three times better than the closest artificial competitor, and six times better than the best non-neural method.*

[DEC] J. Schmidhuber (02/20/2020). 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.

[DL1] J. Schmidhuber, 2015.
Deep Learning in neural networks: An overview. Neural Networks, 61, 85-117.
More.

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

[DL4] J. Schmidhuber, 2017. Our impact on the world's most valuable public companies: 1. Apple, 2. Alphabet (Google), 3. Microsoft, 4. Facebook, 5. Amazon ...
HTML.

[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 (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, 2015. Critique of Paper by "Deep Learning Conspiracy" (Nature 521 p 436). June 2015.
HTML.

[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.

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

[DNC] Hybrid computing using a neural network with dynamic external memory.
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.
Nature, 538:7626, p 471, 2016.

[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.

[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.
*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 (26 March 2021).
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 of
another NN.
Such *Fast Weight Programmers* 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
*linear* Transformers or Performers^{[TR5-6]}
which are *formally equivalent* to the 1991 Fast Weight Programmers (apart from normalization).
In 1993, I introduced
the attention terminology^{[FWP2]} now used
in this context,^{[ATT]} and
extended the approach to
RNNs that program themselves.

[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: a slow net learns by gradient descent to compute weight changes of a fast net (like in linear Transformers*^{[FWP]}).

[FWP1] J. Schmidhuber. Learning to control fast-weight memories: An alternative to recurrent nets. Neural Computation, 4(1):131-139, 1992.
PDF.
HTML.
Pictures (German).

[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 fast weight programmer based on outer products. Introduced 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.

[FWP4b]
D. Bahdanau, K. Cho, Y. Bengio (2014).
Neural Machine Translation by Jointly Learning to Align and Translate. Preprint arXiv:1409.0473 [cs.CL].

[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.

[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.
*First recurrent fast weight programmer that can learn
to run a learning algorithm or weight change algorithm on itself.*

[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. Metalearning Workshop at NeurIPS, 2020.
Preprint arXiv:2012.14905 [cs.LG], 2020.

[FWPMETA7]
I. Schlag, T. Munkhdalai, J. Schmidhuber.
Learning Associative Inference Using Fast Weight Memory.
To appear at ICLR 2021.
Report arXiv:2011.07831 [cs.AI], 2020.

[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.

[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.*

[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 the first universal coding language.*

[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.
HTML.

[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.

[GPUCNN5]
J. Schmidhuber (2017; updated 2021 for 10th birthday of DanNet): History of computer vision contests won by deep CNNs since 2011. DanNet won 4 of them in a row before the similar AlexNet 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. First deep learner to win a contest on object detection in large images—
first deep learner to win a medical imaging contest (2012). HTML.
*How IDSIA used GPU-based CNNs to win the
ICPR 2012 Contest on Mitosis Detection
and the
MICCAI 2013 Grand Challenge.*

[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.

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

[HOP]
J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the USA, vol. 79 no. 8 pp. 2554-2558, 1982.

[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.

[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 special case 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]} Highway layers are also often used for natural language processing, where the simpler residual layers do not work as well.^{[HW3]}
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.

[I25]
E. Ising (1925). Beitrag zur Theorie des Ferromagnetismus. Z. Phys., 31 (1): 253-258, 1925.

[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.

[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].

[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 (Dec 2020). 10-year anniversary of our deep reinforcement learning with policy gradients for LSTM (2007-2010). Recent famous applications: 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.

[META1]
J. Schmidhuber.
Evolutionary principles in self-referential learning, or on learning
how to learn: The meta-meta-... hook. Diploma thesis, Tech Univ. Munich,
1987. HTML.

[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 (2019). Deep Learning: Our Miraculous Year 1990-1991. Preprint
arXiv:2005.05744, 2020.
*The Deep Learning neural networks of our team have revolutionized pattern recognition and machine learning, and are now heavily used in academia and industry. In 2020-21, we celebrate 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
(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.

[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.

[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.

[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.

[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.

[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 (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.
In *Proc. IEEE/INNS International Joint Conference on Neural
Networks, San Diego*, volume 2, pages 253-258, 1990.
Based on.^{[AC90]}

[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.

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

[R3] Reddit/ML, 2019. NeurIPS 2019 Bengio Schmidhuber Meta-Learning Fiasco.

[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

[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.

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

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

[UN]
J. Schmidhuber (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.

[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.
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.

[UN5]
Y. Bengio, P. Lamblin, D. Popovici, H. Larochelle.
Greedy layer-wise training of deep networks.
Proc. NIPS 06, pages 153-160, Dec. 2006.

[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 (2020). Critique of 2018 Turing Award for Drs. Bengio & Hinton & LeCun. Link.

[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. Preprint: arXiv:1706.03762

[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

[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.

.