A liquid state machine (LSM) is a type of
reservoir computer that uses a
spiking neural network
Spiking neural networks (SNNs) are artificial neural networks that more closely mimic natural neural networks. In addition to neuronal and synaptic state, SNNs incorporate the concept of time into their operating model. The idea is that neuron ...
. An LSM consists of a large collection of units (called ''nodes'', or ''neurons''). Each node receives time varying input from external sources (the inputs) as well as from other nodes. Nodes are
randomly connected to each other. The
recurrent nature of the connections turns the time varying input into a
spatio-temporal pattern
Spatiotemporal patterns are patterns that occur in a wide range of natural phenoma and are characterized by a spatial and a temporal patterning. The general rules of pattern formation hold. In contrast to "static", pure spatial patterns, the ...
of activations in the network nodes. The spatio-temporal patterns of activation are read out by
linear discriminant units.
The soup of recurrently connected nodes will end up computing a large variety of
nonlinear function
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
s on the input. Given a
large enough variety of such nonlinear functions, it is theoretically possible to obtain linear combinations (using the read out units) to perform whatever mathematical operation is needed to perform a certain task, such as
speech recognition
Speech recognition is an interdisciplinary subfield of computer science and computational linguistics that develops methodologies and technologies that enable the recognition and translation of spoken language into text by computers with the m ...
or
computer vision
Computer vision is an interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate tasks that the hum ...
.
The word
liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
in the name comes from the analogy drawn to dropping a stone into a still body of water or other liquid. The falling stone will generate
ripples
Ripple may refer to:
Science and technology
* Capillary wave, commonly known as ripple, a wave traveling along the phase boundary of a fluid
** Ripple, more generally a disturbance, for example of spacetime in gravitational waves
* Ripple (electri ...
in the liquid. The input (motion of the falling stone) has been converted into a spatio-temporal pattern of liquid displacement (ripples).
LSMs have been put forward as a way to explain the operation of
brain
A brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a v ...
s. LSMs are argued to be an improvement over the theory of artificial neural networks because:
#Circuits are not hard coded to perform a specific task.
#Continuous time inputs are handled "naturally".
#Computations on various time scales can be done using the same network.
#The same network can perform multiple computations.
Criticisms of LSMs as used in
computational neuroscience
Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to u ...
are that
#LSMs don't actually explain how the brain functions. At best they can replicate some parts of brain functionality.
#There is no guaranteed way to dissect a working network and figure out how or what computations are being performed.
#Very little control over the process.
Universal function approximation
If a reservoir has fading memory and input separability, with help of a readout, it can be proven the liquid state machine is a universal function approximator using
Stone–Weierstrass theorem
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function. Because polynomials are among the si ...
.
See also
*
Echo state network
An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer (with typically 1% connectivity). The connectivity and weights of hidden neurons are fixed and randomly assig ...
: similar concept in
recurrent neural network
A recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes can create a cycle, allowing output from some nodes to affect subsequent input to the same nodes. This allows it to exhibit temporal dynamic ...
*
Reservoir computing
Reservoir computing is a framework for computation derived from recurrent neural network theory that maps input signals into higher dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir. After the in ...
: the conceptual framework
*
Self-organizing map
A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher dimensional data set while preserving the to ...
Libraries
* LiquidC#: Implementation of topologically robust liquid state machine
with a neuronal network detector
References
*
*{{citation
, author1=Wolfgang Maass , author2=Thomas Natschläger , author3=Henry Markram , title = Computational Models for Generic Cortical Microcircuits
, journal = In Computational Neuroscience: A Comprehensive Approach, Ch 18
, volume = 18
, pages = 575–605
, date = 2004
, url = https://igi-web.tugraz.at/PDF/149-v05.pdf
Artificial neural networks