Long short-term memory explained

Long short-term memory (LSTM) is a type of recurrent neural network (RNN) aimed at dealing with the vanishing gradient problem present in traditional RNNs. Its relative insensitivity to gap length is its advantage over other RNNs, hidden Markov models and other sequence learning methods. It aims to provide a short-term memory for RNN that can last thousands of timesteps, thus "long short-term memory". The name is made in analogy with long-term memory and short-term memory and their relationship, studied by cognitive psychologists since early 20th century.

It is applicable to classification, processing and predicting data based on time series, such as in handwriting, speech recognition,^{[1] [2]} machine translation, speech activity detection,^[3] robot control, video games, and healthcare.

A common LSTM unit is composed of a cell, an input gate, an output gate^[4] and a forget gate. The cell remembers values over arbitrary time intervals and the three gates regulate the flow of information into and out of the cell. Forget gates decide what information to discard from the previous state by mapping the previous state and the current input to a value between 0 and 1. A (rounded) value of 1 means to keep the information, and a value of 0 means to discard it. Input gates decide which pieces of new information to store in the current cell state, using the same system as forget gates. Output gates control which pieces of information in the current cell state to output by assigning a value from 0 to 1 to the information, considering the previous and current states. Selectively outputting relevant information from the current state allows the LSTM network to maintain useful, long-term dependencies to make predictions, both in current and future time-steps.

Motivation

In theory, classic RNNs can keep track of arbitrary long-term dependencies in the input sequences. The problem with classic RNNs is computational (or practical) in nature: when training a classic RNN using back-propagation, the long-term gradients which are back-propagated can "vanish", meaning they can tend to zero due to very small numbers creeping into the computations, causing the model to effectively stop learning. RNNs using LSTM units partially solve the vanishing gradient problem, because LSTM units allow gradients to also flow with little to no attenuation. However, LSTM networks can still suffer from the exploding gradient problem.^[5]

The intuition behind the LSTM architecture is to create an additional module in a neural network that learns when to remember and when to forget pertinent information. In other words, the network effectively learns which information might be needed later on in a sequence and when that information is no longer needed. For instance, in the context of natural language processing, the network can learn grammatical dependencies. An LSTM might process the sentence "Dave, as a result of his controversial claims, is now a pariah" by remembering the (statistically likely) grammatical gender and number of the subject Dave, note that this information is pertinent for the pronoun his and note that this information is no longer important after the verb is.

Variants

In the equations below, the lowercase variables represent vectors. Matrices

W _{q} and U _{q} contain, respectively, the weights of the input and recurrent connections, where the subscript _{q} can either be the input gate i , output gate o , the forget gate f or the memory cell c , depending on the activation being calculated. In this section, we are thus using a "vector notation". So, for example, c _{t} \in R ^{h} is not just one unit of one LSTM cell, but contains h LSTM cell's units.

LSTM with a forget gate

The compact forms of the equations for the forward pass of an LSTM cell with a forget gate are:^[6]

\begin{align} f _{t} & = \sigma _{g(W} _{f} x _{t} + U _{f} h _{t-1} + b _{f)} \\ i _{t} & = \sigma _{g(W} _{i} x _{t} + U _{i} h _{t-1} + b _{i)} \\ o _{t} & = \sigma _{g(W} _{o} x _{t} + U _{o} h _{t-1} + b _{o)} \\ \tilde{c} _{t} & = \sigma _{c(W} _{c} x _{t} + U _{c} h _{t-1} + b _{c)} \\ c _{t} & = f _{t} \odot c _{t-1} + i _{t} \odot \tilde{c} _{t} \\ h _{t} & = o _{t} \odot \sigma _{h(c} _{t) \end{align}}

where the initial values are

c _{0} = 0 and h _{0} = 0 and the operator \odot denotes the Hadamard product (element-wise product). The subscript t indexes the time step.

Variables

Letting the superscripts

d and h refer to the number of input features and number of hidden units, respectively:x _{t} \in R ^{d}

input vector to the LSTM unit

f _{t} \in {( 0 , 1 )} ^{h}

forget gate's activation vector

i _{t} \in {( 0 , 1 )} ^{h}

input/update gate's activation vector

o _{t} \in {( 0 , 1 )} ^{h}

output gate's activation vector

h _{t} \in {( -1 , 1 )} ^{h}

hidden state vector also known as output vector of the LSTM unit

\tilde{c} _{t} \in {( -1 , 1 )} ^{h}

cell input activation vector

c _{t} \in R ^{h}

cell state vector

W \in R ^{h} , U \in R ^{h} and b \in R ^{h} : weight matrices and bias vector parameters which need to be learned during training

Activation functions

\sigma _{g} : sigmoid function.\sigma _{c} : hyperbolic tangent function.\sigma _{h} : hyperbolic tangent function or, as the peephole LSTM paper suggests, \sigma _{h(x)} = x .

Peephole LSTM

The figure on the right is a graphical representation of an LSTM unit with peephole connections (i.e. a peephole LSTM). Peephole connections allow the gates to access the constant error carousel (CEC), whose activation is the cell state.

h _{t-1} is not used, c _{t-1} is used instead in most places.\begin{align} f _{t} & = \sigma _{g(W} _{f} x _{t} + U _{f} c _{t-1} + b _{f)} \\ i _{t} & = \sigma _{g(W} _{i} x _{t} + U _{i} c _{t-1} + b _{i)} \\ o _{t} & = \sigma _{g(W} _{o} x _{t} + U _{o} c _{t-1} + b _{o)} \\ c _{t} & = f _{t} \odot c _{t-1} + i _{t} \odot \sigma _{c(W} _{c} x _{t} + b _{c)} \\ h _{t} & = o _{t} \odot \sigma _{h(c} _{t) \end{align}}

Each of the gates can be thought as a "standard" neuron in a feed-forward (or multi-layer) neural network: that is, they compute an activation (using an activation function) of a weighted sum.

i _{t,} o _{t} and f _{t} represent the activations of respectively the input, output and forget gates, at time step t .

The 3 exit arrows from the memory cell

c to the 3 gates i, o and f represent the peephole connections. These peephole connections actually denote the contributions of the activation of the memory cell c at time step t -1 , i.e. the contribution of c _{t-1} (and not c _{t} , as the picture may suggest). In other words, the gates i, o and f calculate their activations at time step t (i.e., respectively, i _{t,} o _{t} and f _{t} ) also considering the activation of the memory cell c at time step t - 1 , i.e. c _{t-1} .

The single left-to-right arrow exiting the memory cell is not a peephole connection and denotes

c _{t} .

The little circles containing a

x symbol represent an element-wise multiplication between its inputs. The big circles containing an S-like curve represent the application of a differentiable function (like the sigmoid function) to a weighted sum.

Peephole convolutional LSTM

Peephole convolutional LSTM.^[7] The

* denotes the convolution operator.

Training

An RNN using LSTM units can be trained in a supervised fashion on a set of training sequences, using an optimization algorithm like gradient descent combined with backpropagation through time to compute the gradients needed during the optimization process, in order to change each weight of the LSTM network in proportion to the derivative of the error (at the output layer of the LSTM network) with respect to corresponding weight.

A problem with using gradient descent for standard RNNs is that error gradients vanish exponentially quickly with the size of the time lag between important events. This is due to

\lim _{n} W ^{n} = 0 if the spectral radius of W is smaller than 1.^[8]

However, with LSTM units, when error values are back-propagated from the output layer, the error remains in the LSTM unit's cell. This "error carousel" continuously feeds error back to each of the LSTM unit's gates, until they learn to cut off the value.

CTC score function

Many applications use stacks of LSTM RNNs^[9] and train them by connectionist temporal classification (CTC)^[10] to find an RNN weight matrix that maximizes the probability of the label sequences in a training set, given the corresponding input sequences. CTC achieves both alignment and recognition.

Alternatives

Sometimes, it can be advantageous to train (parts of) an LSTM by neuroevolution or by policy gradient methods, especially when there is no "teacher" (that is, training labels).

Success

There have been several successful stories of training, in a non-supervised fashion, RNNs with LSTM units.

In 2018, Bill Gates called it a "huge milestone in advancing artificial intelligence" when bots developed by OpenAI were able to beat humans in the game of Dota 2.^[11] OpenAI Five consists of five independent but coordinated neural networks. Each network is trained by a policy gradient method without supervising teacher and contains a single-layer, 1024-unit Long-Short-Term-Memory that sees the current game state and emits actions through several possible action heads.

In 2018, OpenAI also trained a similar LSTM by policy gradients to control a human-like robot hand that manipulates physical objects with unprecedented dexterity.^[12]

In 2019, DeepMind's program AlphaStar used a deep LSTM core to excel at the complex video game Starcraft II.^[13] This was viewed as significant progress towards Artificial General Intelligence.

Applications

Applications of LSTM include:

• Robot control^[14]
• Time series prediction^[15]
• Speech recognition^{[16] [17] [18]}
• Rhythm learning^[19]
• Hydrological rainfall–runoff modeling^[20]
• Music composition^[21]
• Grammar learning^{[22] [23] [24]}
• Handwriting recognition^{[25] [26]}
• Human action recognition^[27]
• Sign language translation^[28]
• Protein homology detection^[29]
• Predicting subcellular localization of proteins^[30]
• Time series anomaly detection^[31]
• Several prediction tasks in the area of business process management^[32]
• Prediction in medical care pathways^[33]
• Semantic parsing^[34]
• Object co-segmentation^{[35] [36]}
• Airport passenger management^[37]
• Short-term traffic forecast^[38]
• Drug design^[39]
• Market Prediction^[40]
• Activity Classification in Video

Timeline of development

1989: Mike Mozer's work on "focused back-propagation"^[41] anticipates aspects of LSTM, which the LSTM paper cites.

1991: Sepp Hochreiter analyzed the vanishing gradient problem and developed principles of the method in his German diploma thesis,^[42] which was considered highly significant by his supervisor Jürgen Schmidhuber.^[43]

1995: "Long Short-Term Memory (LSTM)" is published in a technical report by Sepp Hochreiter and Jürgen Schmidhuber.

1996: LSTM is published at NIPS'1996, a peer-reviewed conference.

1997: The main LSTM paper is published in the journal Neural Computation.^[44] By introducing Constant Error Carousel (CEC) units, LSTM deals with the vanishing gradient problem. The initial version of LSTM block included cells, input and output gates.^[45]

1999: Felix Gers, Jürgen Schmidhuber, and Fred Cummins introduced the forget gate (also called "keep gate") into the LSTM architecture,^[46] enabling the LSTM to reset its own state.^[45]

2000: Gers, Schmidhuber, and Cummins added peephole connections (connections from the cell to the gates) into the architecture.^{[23] [19]} Additionally, the output activation function was omitted.^[45]

2001: Gers and Schmidhuber trained LSTM to learn languages unlearnable by traditional models such as Hidden Markov Models.

Hochreiter et al. used LSTM for meta-learning (i.e. learning a learning algorithm).^[47]

2004: First successful application of LSTM to speech Alex Graves et al.^{[48] [49]}

2005: First publication (Graves and Schmidhuber) of LSTM with full backpropagation through time and of bi-directional LSTM.

2005: Daan Wierstra, Faustino Gomez, and Schmidhuber trained LSTM by neuroevolution without a teacher.^[15]

2006: Graves, Fernandez, Gomez, and Schmidhuber introduce a new error function for LSTM: Connectionist Temporal Classification (CTC) for simultaneous alignment and recognition of sequences. CTC-trained LSTM led to breakthroughs in speech recognition.

Mayer et al. trained LSTM to control robots.

2007: Wierstra, Foerster, Peters, and Schmidhuber trained LSTM by policy gradients for reinforcement learning without a teacher.^[50]

Hochreiter, Heuesel, and Obermayr applied LSTM to protein homology detection the field of biology.

2009: An LSTM trained by CTC won the ICDAR connected handwriting recognition competition. Three such models were submitted by a team led by Alex Graves.^[51] One was the most accurate model in the competition and another was the fastest.^[52] This was the first time an RNN won international competitions.

2009: Justin Bayer et al. introduced neural architecture search for LSTM.^[53]

2013: Alex Graves, Abdel-rahman Mohamed, and Geoffrey Hinton used LSTM networks as a major component of a network that achieved a record 17.7% phoneme error rate on the classic TIMIT natural speech dataset.

2014: Kyunghyun Cho et al. put forward a simplified variant of the forget gate LSTM called Gated recurrent unit (GRU).^[54]

2015: Google started using an LSTM trained by CTC for speech recognition on Google Voice.^{[55] [56]} According to the official blog post, the new model cut transcription errors by 49%.^[57]

2015: Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used LSTM principles to create the Highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks.^{[58] [59] [60]} 7 months later, Kaiming He, Xiangyu Zhang; Shaoqing Ren, and Jian Sun won the ImageNet 2015 competition with an open-gated or gateless Highway network variant called Residual neural network.^[61] This has become the most cited neural network of the 21st century.

2016: Google started using an LSTM to suggest messages in the Allo conversation app.^[62] In the same year, Google released the Google Neural Machine Translation system for Google Translate which used LSTMs to reduce translation errors by 60%.^{[63] [64] [65]}

Apple announced in its Worldwide Developers Conference that it would start using the LSTM for quicktype^{[66] [67] [68]} in the iPhone and for Siri.^{[69] [70]}

Amazon released Polly, which generates the voices behind Alexa, using a bidirectional LSTM for the text-to-speech technology.^[71]

2017: Facebook performed some 4.5 billion automatic translations every day using long short-term memory networks.^[72]

Researchers from Michigan State University, IBM Research, and Cornell University published a study in the Knowledge Discovery and Data Mining (KDD) conference.^{[73] [74] [75]} Their Time-Aware LSTM (T-LSTM) performs better on certain data sets than standard LSTM.

Microsoft reported reaching 94.9% recognition accuracy on the Switchboard corpus, incorporating a vocabulary of 165,000 words. The approach used "dialog session-based long-short-term memory".^[76]

2018: OpenAI used LSTM trained by policy gradients to beat humans in the complex video game of Dota 2, and to control a human-like robot hand that manipulates physical objects with unprecedented dexterity.

2019: DeepMind used LSTM trained by policy gradients to excel at the complex video game of Starcraft II.

2021: According to Google Scholar, in 2021, LSTM was cited over 16,000 times within a single year. This reflects applications of LSTM in many different fields including healthcare.^[77]

2024: An evolution of LSTM called xLSTM is published by a team leaded by Sepp Hochreiter.^[78]

See also

• Attention (machine learning)
• Deep learning
• Differentiable neural computer
• Gated recurrent unit
• Highway network
• Long-term potentiation
• Prefrontal cortex basal ganglia working memory
• Recurrent neural network
• Seq2seq
• Time aware long short-term memory
• Transformer (machine learning model)
• Time series

References

^[79]

Further reading

• A generalized LSTM-like training algorithm for second-order recurrent neural networks . Derek D. . Monner . James A. . Reggia . Neural Networks . 2010 . 25 . 1 . 70–83 . 10.1016/j.neunet.2011.07.003 . 21803542 . 3217173 . High-performing extension of LSTM that has been simplified to a single node type and can train arbitrary architectures .
• Learning precise timing with LSTM recurrent networks . Gers . Felix A. . Nicol N. . Schraudolph . Jürgen . Schmidhuber . Journal of Machine Learning Research . 3 . Aug 2002 . 115–143 .
• Web site: Long Short-Term Memory in Recurrent Neural Networks . PhD thesis . Gers . Felix . 2001 .
• Data Mining, Fraud Detection and Mobile Telecommunications: Call Pattern Analysis with Unsupervised Neural Networks . 11394/249 . Abidogun . Olusola Adeniyi . Master's Thesis . live . May 22, 2012 . https://web.archive.org/web/20120522234026/http://etd.uwc.ac.za/usrfiles/modules/etd/docs/etd_init_3937_1174040706.pdf . 2005 . University of the Western Cape . Thesis .
  • original with two chapters devoted to explaining recurrent neural networks, especially LSTM.

External links

• Recurrent Neural Networks with over 30 LSTM papers by Jürgen Schmidhuber's group at IDSIA
• Web site: LSTM Networks – A Detailed Explanation . Article . R . Dolphin . 12 November 2021 .
• Web site: How to implement LSTM in Python with Theano . Tutorial . Christian . Herta .

Notes and References

1. Web site: Long Short-Term Memory recurrent neural network architectures for large scale acoustic modeling. Sak. Hasim. Senior. Andrew. 2014. https://web.archive.org/web/20180424203806/https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/43905.pdf. 2018-04-24. dead. Beaufays. Francoise.
2. Li. Xiangang. Wu. Xihong. 2014-10-15. Constructing Long Short-Term Memory based Deep Recurrent Neural Networks for Large Vocabulary Speech Recognition. 1410.4281. cs.CL.
3. Sahidullah . Md . Patino . Jose . Cornell . Samuele . Yin . Ruiking . Sivasankaran . Sunit . Bredin . Herve . Korshunov . Pavel . Brutti . Alessio . Serizel . Romain . Vincent . Emmanuel . Evans . Nicholas . Marcel . Sebastien . Squartini . Stefano . Barras . Claude . 2019-11-06 . The Speed Submission to DIHARD II: Contributions & Lessons Learned . eess.AS . 1911.02388 .
4. Hochreiter . Sepp . Schmidhuber . Juergen . LSTM can solve hard long time lag problems . Advances in Neural Information Processing Systems . https://neurips.cc . 1996 .
5. Book: Calin . Ovidiu . Deep Learning Architectures . 14 February 2020 . Springer Nature . Cham, Switzerland . 978-3-030-36720-6 . 555.
6. Felix A. Gers . Jürgen Schmidhuber . Fred Cummins . Learning to Forget: Continual Prediction with LSTM . . 12 . 10 . 2451–2471 . 2000 . 10.1162/089976600300015015. 11032042 . 10.1.1.55.5709 . 11598600 .
7. Xingjian Shi . Zhourong Chen . Hao Wang . Dit-Yan Yeung . Wai-kin Wong . Wang-chun Woo . Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting . Proceedings of the 28th International Conference on Neural Information Processing Systems . 802–810 . 2015 . 1506.04214 . 2015arXiv150604214S .
8. Book: https://www.researchgate.net/publication/2839938. Gradient Flow in Recurrent Nets: the Difficulty of Learning Long-Term Dependencies (PDF Download Available). Hochreiter. S.. Y. . Bengio. P. . Frasconi . J. . Schmidhuber. S. C. . Kremer and . J. F. . Kolen . A Field Guide to Dynamical Recurrent Neural Networks.. 2001. IEEE Press.
9. Fernández . Santiago . Graves . Alex . Schmidhuber . Jürgen . 2007 . Sequence labelling in structured domains with hierarchical recurrent neural networks . 10.1.1.79.1887 . Proc. 20th Int. Joint Conf. On Artificial Intelligence, Ijcai 2007 . 774–779.
10. Graves . Alex . Fernández . Santiago . Gomez . Faustino . Schmidhuber . Jürgen . 2006 . Connectionist temporal classification: Labelling unsegmented sequence data with recurrent neural networks . 10.1.1.75.6306 . In Proceedings of the International Conference on Machine Learning, ICML 2006 . 369–376.
11. News: The Science Behind OpenAI Five that just Produced One of the Greatest Breakthrough in the History of AI. Rodriguez. Jesus. July 2, 2018. https://web.archive.org/web/20191226222000/https://towardsdatascience.com/the-science-behind-openai-five-that-just-produced-one-of-the-greatest-breakthrough-in-the-history-b045bcdc2b69?gi=24b20ef8ca3f. 2019-12-26. dead. Towards Data Science. 2019-01-15.
12. News: Learning Dexterity. July 30, 2018. OpenAI. 2023-06-28.
13. News: DeepMind's AI, AlphaStar Showcases Significant Progress Towards AGI. Stanford. Stacy. January 25, 2019. Medium ML Memoirs. 2019-01-15.
14. Book: Mayer. H.. Gomez. F.. Wierstra. D.. Nagy. I.. Knoll. A.. Schmidhuber. J.. 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems . A System for Robotic Heart Surgery that Learns to Tie Knots Using Recurrent Neural Networks . October 2006. 543–548. 10.1109/IROS.2006.282190. 978-1-4244-0258-8. 10.1.1.218.3399. 12284900.
15. Wierstra. Daan. Schmidhuber. J.. Gomez. F. J.. 2005. Evolino: Hybrid Neuroevolution/Optimal Linear Search for Sequence Learning. Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), Edinburgh. 853–858.
16. Graves . A. . Schmidhuber . J. . 2005 . Framewise phoneme classification with bidirectional LSTM and other neural network architectures . Neural Networks . 18 . 5–6. 602–610 . 10.1016/j.neunet.2005.06.042. 16112549 . 10.1.1.331.5800 . 1856462 .
17. Fernández. S.. Graves. A.. Schmidhuber. J.. 9 September 2007. 28 December 2023. An Application of Recurrent Neural Networks to Discriminative Keyword Spotting. Proceedings of the 17th International Conference on Artificial Neural Networks. ICANN'07. Berlin, Heidelberg. Springer-Verlag. 220–229. 978-3540746935.
18. Book: Mohamed. Abdel-rahman. Hinton. Geoffrey. 2013. 6645–6649. Graves. Alex. 2013 IEEE International Conference on Acoustics, Speech and Signal Processing . Speech recognition with deep recurrent neural networks . 10.1109/ICASSP.2013.6638947. 978-1-4799-0356-6. 1303.5778. 206741496.
19. Gers . F. . Schraudolph . N. . Schmidhuber . J. . 2002 . Learning precise timing with LSTM recurrent networks . Journal of Machine Learning Research . 3 . 115–143 .
20. Kratzert . Frederik . Klotz . Daniel . Shalev . Guy . Klambauer . Günter . Hochreiter . Sepp . Nearing . Grey . 2019-12-17 . Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets . Hydrology and Earth System Sciences. 23 . 12 . 5089–5110 . 10.5194/hess-23-5089-2019 . 1907.08456 . 2019HESS...23.5089K . 1027-5606 . free .
21. Book: Eck. Douglas. Schmidhuber. Jürgen. Artificial Neural Networks — ICANN 2002 . Learning the Long-Term Structure of the Blues . 2002-08-28. 2415. Springer, Berlin, Heidelberg. 284–289. 10.1007/3-540-46084-5_47. 978-3540460848. Lecture Notes in Computer Science. 10.1.1.116.3620.
22. Schmidhuber . J. . Gers . F. . Eck . D. . Schmidhuber . J. . Gers . F. . 2002 . Learning nonregular languages: A comparison of simple recurrent networks and LSTM . Neural Computation . 14 . 9. 2039–2041 . 10.1162/089976602320263980. 12184841 . 10.1.1.11.7369 . 30459046 .
23. Gers . F. A. . Schmidhuber . J. . 2001 . [ftp://ftp.idsia.ch/pub/juergen/L-IEEE.pdf LSTM Recurrent Networks Learn Simple Context Free and Context Sensitive Languages ]. IEEE Transactions on Neural Networks . 12 . 6. 1333–1340 . 10.1109/72.963769. 18249962 . 10192330 .
24. Perez-Ortiz . J. A. . Gers . F. A. . Eck . D. . Schmidhuber . J. . 2003 . Kalman filters improve LSTM network performance in problems unsolvable by traditional recurrent nets . Neural Networks . 16 . 2. 241–250 . 10.1016/s0893-6080(02)00219-8. 12628609 . 10.1.1.381.1992 .
25. A. Graves, J. Schmidhuber. Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks. Advances in Neural Information Processing Systems 22, NIPS'22, pp 545–552, Vancouver, MIT Press, 2009.
26. Graves. A.. Fernández. S.. Liwicki. M.. Bunke. H.. Schmidhuber. J.. 3 December 2007. 28 December 2023. Unconstrained Online Handwriting Recognition with Recurrent Neural Networks. Proceedings of the 20th International Conference on Neural Information Processing Systems. NIPS'07. USA. Curran Associates Inc.. 577–584. 9781605603520.
27. Book: M. . Baccouche . F. . Mamalet . C. . Wolf . C. . Garcia . A. . Baskurt . Sequential Deep Learning for Human Action Recognition . 2nd International Workshop on Human Behavior Understanding (HBU) . A. A. . Salah . B. . Lepri . Amsterdam, Netherlands . 29–39 . Lecture Notes in Computer Science . 7065 . Springer . 2011 . 978-3-642-25445-1. 10.1007/978-3-642-25446-8_4 .
28. Huang . Jie . Zhou . Wengang . Zhang . Qilin . Li . Houqiang . Li . Weiping . Video-based Sign Language Recognition without Temporal Segmentation . 2018-01-30 . cs.CV . 1801.10111 .
29. Hochreiter . S. . Heusel . M. . Obermayer . K. . 10.1093/bioinformatics/btm247 . Fast model-based protein homology detection without alignment . Bioinformatics . 23 . 14 . 1728–1736 . 2007 . 17488755. free .
30. Thireou . T. . Reczko . M. . 2007 . Bidirectional Long Short-Term Memory Networks for predicting the subcellular localization of eukaryotic proteins . IEEE/ACM Transactions on Computational Biology and Bioinformatics . 4 . 3. 441–446 . 10.1109/tcbb.2007.1015. 17666763 . 11787259 .
31. Malhotra. Pankaj. Vig. Lovekesh. Shroff. Gautam. Agarwal. Puneet. April 2015. Long Short Term Memory Networks for Anomaly Detection in Time Series. European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning — ESANN 2015. 2018-02-21. 2020-10-30. https://web.archive.org/web/20201030224634/https://www.elen.ucl.ac.be/Proceedings/esann/esannpdf/es2015-56.pdf. dead.
32. Book: Tax. N. . Verenich . I. . La Rosa . M. . Dumas . M. . Advanced Information Systems Engineering . Predictive Business Process Monitoring with LSTM Neural Networks . 2017 . 10253 . 477–492. 10.1007/978-3-319-59536-8_30. 1612.02130 . Lecture Notes in Computer Science . 978-3-319-59535-1 . 2192354 .
33. Choi. E. . Bahadori. M.T. . Schuetz . E. . Stewart. W. . Sun. J. . JMLR Workshop and Conference Proceedings . 2016 . Doctor AI: Predicting Clinical Events via Recurrent Neural Networks . 56 . 301–318. 28286600 . 5341604 . 2015arXiv151105942C . 1511.05942 .
34. Jia . Robin . Liang . Percy . 2016 . 1606.03622 . Data Recombination for Neural Semantic Parsing . cs.CL .
35. Wang . Le . Duan . Xuhuan . Zhang . Qilin . Niu . Zhenxing . Hua . Gang . Zheng . Nanning . Segment-Tube: Spatio-Temporal Action Localization in Untrimmed Videos with Per-Frame Segmentation . Sensors . 18 . 5 . 2018-05-22 . 1424-8220 . 10.3390/s18051657 . 29789447 . 5982167 . 1657 . 2018Senso..18.1657W . free .
36. Duan . Xuhuan . Wang . Le . Zhai . Changbo . Zheng . Nanning . Zhang . Qilin . Niu . Zhenxing . Hua . Gang . 2018 25th IEEE International Conference on Image Processing (ICIP) . Joint Spatio-Temporal Action Localization in Untrimmed Videos with Per-Frame Segmentation . 25th IEEE International Conference on Image Processing (ICIP). 2018 . 918–922 . 978-1-4799-7061-2 . 10.1109/icip.2018.8451692 .
37. Neural networks trained with WiFi traces to predict airport passenger behavior . Orsini . F. . Gastaldi . M. . Mantecchini . L. . Rossi . R. . 2019 . IEEE . Krakow . 6th International Conference on Models and Technologies for Intelligent Transportation Systems . 8883365 . 10.1109/MTITS.2019.8883365 . 1910.14026.
38. Zhao . Z. . Chen . W. . Wu . X. . Chen . P.C.Y. . Liu . J. . 2017 . LSTM network: A deep learning approach for Short-term traffic forecast . IET Intelligent Transport Systems . 11 . 2 . 68–75 . 10.1049/iet-its.2016.0208 . 114567527 .
39. Gupta A, Müller AT, Huisman BJH, Fuchs JA, Schneider P, Schneider G. Generative Recurrent Networks for De Novo Drug Design. . Mol Inform . 2018 . 37 . 1–2 . 29095571 . 10.1002/minf.201700111 . 5836943 .
40. 2020-10-26. Foreign Exchange Currency Rate Prediction using a GRU-LSTM Hybrid Network. Soft Computing Letters. en. 100009. 10.1016/j.socl.2020.100009. 2666-2221. free. Saiful Islam. Md.. Hossain. Emam. 3.
41. Mozer. Mike. A Focused Backpropagation Algorithm for Temporal Pattern Recognition. Complex Systems. 1989.
42. Untersuchungen zu dynamischen neuronalen Netzen. diploma . Sepp. Hochreiter. Technical University Munich, Institute of Computer Science. 1991.
43. Schmidhuber. Juergen. Juergen Schmidhuber. 2022. Annotated History of Modern AI and Deep Learning . cs.NE. 2212.11279.
44. Sepp Hochreiter . Jürgen Schmidhuber . Long short-term memory . . 9 . 8 . 1735–1780 . 1997 . 10.1162/neco.1997.9.8.1735 . 9377276. 1915014 . Jürgen Schmidhuber . Sepp Hochreiter .
45. Klaus Greff . Rupesh Kumar Srivastava . Jan Koutník . Bas R. Steunebrink . Jürgen Schmidhuber . 1503.04069 . LSTM: A Search Space Odyssey . IEEE Transactions on Neural Networks and Learning Systems . 28 . 10 . 2222–2232 . 2015 . 10.1109/TNNLS.2016.2582924 . 27411231 . 2015arXiv150304069G . 3356463 .
46. Book: 10.1049/cp:19991218. Learning to forget: Continual prediction with LSTM. 9th International Conference on Artificial Neural Networks: ICANN '99. 1999. 850–855. 1999. Gers. Felix. Schmidhuber. Jürgen. Cummins. Fred. 0-85296-721-7.
47. Book: Hochreiter. S.. Younger. A. S.. Conwell. P. R. . Artificial Neural Networks — ICANN 2001 . Learning to Learn Using Gradient Descent . 2130. 2001. 87–94. 0302-9743. 10.1007/3-540-44668-0_13. Lecture Notes in Computer Science. 978-3-540-42486-4. 10.1.1.5.323. 52872549 .
48. Graves . Alex . Beringer . Nicole . Eck . Douglas . Schmidhuber . Juergen . Biologically Plausible Speech Recognition with LSTM Neural Nets. . Workshop on Biologically Inspired Approaches to Advanced Information Technology, Bio-ADIT 2004, Lausanne, Switzerland . 175–184 . 2004 .
49. Schmidhuber, Juergen . Deep Learning: Our Miraculous Year 1990-1991 . 10 May 2021 . 2005.05744 . cs.NE.
50. Wierstra. Daan. Foerster. Alexander. Schmidhuber. Juergen. Peters. Jan. 2005. Solving Deep Memory POMDPs with Recurrent Policy Gradients. International Conference on Artificial Neural Networks ICANN'07.
51. Graves. A.. Liwicki. M.. Fernández. S.. Bertolami. R.. Bunke. H.. Schmidhuber. J.. May 2009. A Novel Connectionist System for Unconstrained Handwriting Recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence. 31. 5. 855–868. 10.1.1.139.4502. 10.1109/tpami.2008.137. 0162-8828. 19299860. 14635907.
52. Book: Märgner. Volker. Abed. Haikal El. 2009 10th International Conference on Document Analysis and Recognition . ICDAR 2009 Arabic Handwriting Recognition Competition . July 2009. 1383–1387. 10.1109/ICDAR.2009.256. 978-1-4244-4500-4. 52851337.
53. Bayer. Justin. Wierstra. Daan. Schmidhuber. Juergen. Togelius. Julian. 2009. Evolving memory cell structures for sequence learning. International Conference on Artificial Neural Networks ICANN'09, Cyprus.
54. Cho . Kyunghyun. van Merrienboer. Bart. Gulcehre. Caglar. Bahdanau. Dzmitry. Bougares. Fethi. Schwenk. Holger. Bengio. Yoshua. 2014 . Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation . 1406.1078. cs.CL.
55. News: Beaufays. Françoise. The neural networks behind Google Voice transcription. August 11, 2015. Research Blog. 2017-06-27.
56. News: Sak. Haşim. Google voice search: faster and more accurate. September 24, 2015. Research Blog. 2017-06-27. Senior. Andrew. en-US. Rao. Kanishka. Beaufays. Françoise. Schalkwyk. Johan.
57. Web site: Neon prescription... or rather, New transcription for Google Voice. Official Google Blog. 23 July 2015. en. 2020-04-25.
58. Srivastava. Rupesh Kumar. Greff. Klaus. Schmidhuber. Jürgen. Highway Networks. 1505.00387. 2 May 2015. cs.LG.
59. Srivastava. Rupesh K. Greff. Klaus. Schmidhuber. Juergen. Training Very Deep Networks. Advances in Neural Information Processing Systems . 2015. 28. 2377–2385. Curran Associates, Inc..
60. News: Schmidhuber . Jürgen . The most cited neural networks all build on work done in my labs. 2021. AI Blog. IDSIA, Switzerland . 2022-04-30.
61. He. Kaiming. Zhang. Xiangyu. Ren. Shaoqing. Sun. Jian. 2016. Deep Residual Learning for Image Recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA. IEEE. 770–778. 1512.03385. 10.1109/CVPR.2016.90. 978-1-4673-8851-1.
62. News: Khaitan. Pranav. Chat Smarter with Allo. May 18, 2016. Research Blog. 2017-06-27.
63. 1609.08144. cs.CL. Yonghui. Wu. Mike. Schuster. Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation. 2016-09-26. Krikun. Le. Quoc V.. Norouzi. Mohammad. Macherey. Gao. Zhifeng. Maxim. Yuan. Qin. Cao. Chen. Wolfgang.
64. Metz. Cade. September 27, 2016. An Infusion of AI Makes Google Translate More Powerful Than Ever WIRED. Wired. 2017-06-27.
65. Web site: A Neural Network for Machine Translation, at Production Scale. Google AI Blog. 27 September 2016 . en. 2020-04-25.
66. Web site: Apple's Machines Can Learn Too. Efrati. Amir. June 13, 2016. The Information. 2017-06-27.
67. News: Ranger. Steve. June 14, 2016. iPhone, AI and big data: Here's how Apple plans to protect your privacy. ZDNet. 2017-06-27.
68. Web site: Can Global Semantic Context Improve Neural Language Models? – Apple. Apple Machine Learning Journal. en-US. 2020-04-30.
69. Web site: iOS 10: Siri now works in third-party apps, comes with extra AI features. Smith. Chris. 2016-06-13. BGR. 2017-06-27.
70. Capes. Tim. Coles. Paul. Conkie. Alistair. Golipour. Ladan. Hadjitarkhani. Abie. Hu. Qiong. Huddleston. Nancy. Hunt. Melvyn. Li. Jiangchuan. Neeracher. Matthias. Prahallad. Kishore. 2017-08-20. Siri On-Device Deep Learning-Guided Unit Selection Text-to-Speech System. Interspeech 2017. en. ISCA. 4011–4015. 10.21437/Interspeech.2017-1798.
71. Web site: Bringing the Magic of Amazon AI and Alexa to Apps on AWS. – All Things Distributed. Vogels. Werner. 30 November 2016. www.allthingsdistributed.com. 2017-06-27.
72. Web site: Facebook's translations are now powered completely by AI. Ong. Thuy. 4 August 2017. www.allthingsdistributed.com. 2019-02-15.
73. Web site: Patient Subtyping via Time-Aware LSTM Networks . msu.edu . 21 Nov 2018.
74. Web site: Patient Subtyping via Time-Aware LSTM Networks . Kdd.org . 24 May 2018.
75. Web site: SIGKDD . Kdd.org . 24 May 2018.
76. Web site: Microsoft's speech recognition system is now as good as a human. Haridy. Rich. August 21, 2017. newatlas.com. 2017-08-27.
77. News: Schmidhuber . Jürgen . The 2010s: Our Decade of Deep Learning / Outlook on the 2020s. 2021. AI Blog. IDSIA, Switzerland . 2022-04-30.
78. Beck . Maximilian . xLSTM: Extended Long Short-Term Memory . 2024-05-07 . 2405.04517 . Pöppel . Korbinian . Spanring . Markus . Auer . Andreas . Prudnikova . Oleksandra . Kopp . Michael . Klambauer . Günter . Brandstetter . Johannes . Hochreiter . Sepp. cs.LG .
79. Abbey Martin, Andrew J. Hill, Konstantin M. Seiler & Mehala Balamurali (2023) Automatic excavator action recognition and localisation for untrimmed video using hybrid LSTM-Transformer networks, International Journal of Mining, Reclamation and Environment, DOI: 10.1080/17480930.2023.2290364