Long short-term memory
An LSTM is well-suited to learn from experience to classify, process and predict time series given time lags of unknown size and bound between important events. Relative insensitivity to gap length gives an advantage to LSTM over alternative RNNs, hidden Markov models and other sequence learning methods in numerous applications.
Among other successes, LSTM achieved record results in natural language text compression, unsegmented connected handwriting recognition and won the ICDAR handwriting competition (2009). LSTM networks were a major component of a network that achieved a record 17.7% phoneme error rate on the classic TIMIT natural speech dataset (2013).
As of 2016, major technology companies including Google, Apple, and Microsoft were using LSTM as fundamental components in new products. For example, Google used LSTM for speech recognition on the smartphone, for the smart assistant Allo and for Google Translate. Apple uses LSTM for the "Quicktype" function on the iPhone and for Siri. Amazon uses LSTM for Amazon Alexa.
A LSTM network contains LSTM units instead of, or in addition to, other network units. A LSTM unit remembers values for either long or short time periods. The key to this ability is that it uses no activation function within its recurrent components. Thus, the stored value is not iteratively modified and the gradient does not tend to vanish when trained with backpropagation through time.
LSTM units are often implemented in "blocks" containing several units. This design is typical with deep neural networks and facilitates implementations with parallel hardware. In the equations below, each variable in lowercase italics represents a vector with a length equal to the number of LSTM units in the block.
LSTM blocks contain three or four "gates" that control information flow. These gates are implemented using the logistic function to compute a value between 0 and 1. Multiplication is applied with this value to partially allow or deny information to flow into or out of the memory. For example, an "input" gate controls the extent to which a new value flows into the memory. A "forget" gate controls the extent to which a value remains in memory. An "output" gate controls the extent to which the value in memory is used to compute the output activation of the block. (In some implementations, the input and forget gates are merged into a single gate. The motivation for combining them is that the time to forget is when a new value worth remembering becomes available.)
The weights in a LSTM block ( and ) are used to direct the operation of the gates. These weights are applied to the values that feed into the block (including the input vector and the output from the previous time at step ) at each of the gates. Thus, the LSTM block determines how to maintain its memory as a function of those values, and training its weights causes the block to learn the function that minimizes loss.
Initial values: and . The operator denotes the Hadamard product (entry-wise product).
- : input vector
- : output vector
- : cell state vector
- , and : parameter matrices and vector
- , and : gate vectors
- : Forget gate vector. Weight of remembering old information.
- : Input gate vector. Weight of acquiring new information.
- : Output gate vector. Output candidate.
- : The original is a sigmoid function.
- : The original is a hyperbolic tangent.
- : The original is a hyperbolic tangent, but the peephole[clarification needed] LSTM paper suggests .
To minimize LSTM's total error on a set of training sequences, iterative gradient descent such as backpropagation through time can be used to change each weight in proportion to its derivative with respect to the error. A major problem with gradient descent for standard RNNs is that error gradients vanish exponentially quickly with the size of the time lag between important events. With LSTM blocks, however, when error values are back-propagated from the output, the error becomes trapped in the block's memory. This is referred to as an "error carousel" that continuously feeds error back to each of the gates until they become trained to cut off the value. Thus, regular backpropagation is effective at training an LSTM block to remember values for long durations.
LSTM can also be trained by a combination of artificial evolution for weights to the hidden units, and pseudo-inverse or support vector machines for weights to the output units. In reinforcement learning applications LSTM can be trained by policy gradient methods, evolution strategies or genetic algorithms.
Applications of LSTM include:
- Robot control
- Time series prediction
- Speech recognition
- Rhythm learning
- Music composition
- Grammar learning
- Handwriting recognition
- Human action recognition
- Protein Homology Detection
- Predicting subcellular localization of proteins
LSTM has Turing completeness in the sense that given enough network units it can compute any result that a conventional computer can compute, provided it has the proper weight matrix, which may be viewed as its program.
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- Recurrent Neural Networks with over 30 LSTM papers by Jürgen Schmidhuber's group at IDSIA
- Gers PhD thesis on LSTM networks.
- Fraud detection paper with two chapters devoted to explaining recurrent neural networks, especially LSTM.
- Paper on a high-performing extension of LSTM that has been simplified to a single node type and can train arbitrary architectures.
- Tutorial: How to implement LSTM in python with theano