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Jürgen Schmidhuber is a computer scientist whose research includes learning architectures for recurrent neural networks. He coauthored the1997long short-term memory paper with Sepp Hochreiter and the2000adaptive-forgetting paper with Felix A. Gers and Fred Cummins. These are team contributions documented by the original bylines.^{[ref] [ref] [ref]}

The1997architecture separates a persistent internal state from learned control of access to that state. A LSTM input gate controls new input, while a LSTM output gate controls how stored information influences output. This arrangement was designed to reduce the vanishing gradient problem that makes distant events difficult to associate during learning.^[ref]

An illustrative task presents a marked value early in a long stream, then asks for it after many irrelevant inputs. A network needs both a way to retain the relevant information and a way to protect it from later interference. The paper tested artificial long-delay tasks; success on those experiments is evidence about the architecture and learning procedure under specified conditions, not a guarantee of unlimited or error-free memory.

Long short-term memory, usually abbreviated LSTM, is a recurrent neural network architecture that carries an explicit memory state through a sequence and learns when to write, retain and expose its contents. It addresses the vanishing gradient problem: in ordinary recurrence, repeated multiplication by small derivatives can make a distant input have almost no effect on the gradient used for learning. Sepp Hochreiter and Jürgen Schmidhuber's 1997 architecture provided a memory-cell path designed to preserve error flow, with gates controlling access.^[ref]

A common simplified modern form, omitting peephole connections, isHere $x_t$ is the input, $c_t$ the memory, $h_t$ the exposed state, $\sigma$ the logistic sigmoid function, $\tanh$ the hyperbolic tangent, and $\odot$ componentwise multiplication. The learned matrices and biases determine an input gate in long short-term memory $i_t$, a forget gate in long short-term memory $f_t$, and an output gate in long short-term memory $o_t$. LSTM: A Search Space Odyssey by Klaus Greff and others gives a more general baseline with peephole connections; the equations above deliberately show the simpler variant.^[ref]

For a scalar memory with writing switched off in the idealized limit and constant retention $f$, $c_n=f^n{c}_0$. Over 100 steps, $f=0.99$ retains about $0.366c_0$, while $f=0.999$ retains about $0.905c_0$. This illustrates how a learned gate can select a retention timescale. Exactly zero or one are limiting idealizations for a finite-input logistic sigmoid function. The product of forget gates describes the direct memory path; it is not the entire recurrent derivative, because gates also depend on earlier states.

The forget gate in long short-term memory was introduced after the original architecture, in Learning to Forget: Continual Prediction with LSTM by Felix A. Gers, Jürgen Schmidhuber and Fred Cummins, to allow old contents to be reset during continuing input streams. Training still uses methods such as backpropagation through time. Artificial delayed-dependency tasks in the original paper demonstrated learning across more than 1,000 time steps in particular experiments; this does not imply unlimited memory or guaranteed success on every long sequence.^[ref][ref]

Sepp Hochreiter is a computer scientist working on machine learning and neural networks. His institutional profile identifies long short-term memory among his research topics. The1997paper with Jürgen Schmidhuber connects his earlier analysis of decaying learning signals to a recurrent architecture designed to preserve useful error flow.^{[ref] [ref]}

A toy chain rule calculation explains the motivation. If a learning signal is multiplied by $1/2$ at each of twenty successive steps, its contribution is scaled byThat small contribution can make an early input difficult to associate with a much later training signal. The example illustrates the vanishing gradient problem; it is not a measurement of every recurrent neural network.

The long short-term memory design introduced a controlled internal path with constant error flow, while multiplicative gates regulate access. Its artificial-data experiments included successful learning across delays exceeding1000discrete steps. The reported capability belongs to those experiments and their architecture-specific learning rules, rather than implying that any trained instance will remember every input indefinitely.^[ref]