Connectionism

In most connectionist models, networks change over time. A closely related and very common aspect of connectionist models is activation. At any time, a unit in the network has an activation, which is a numerical value intended to represent some aspect of the unit. For example, if the units in the model are neurons, the activation could represent the probability that the neuron would generate an action potential spike. Activation typically spreads to all the other units connected to it. Spreading activation is always a feature of neural network models, and it is very common in connectionist models used by cognitive psychologists.

Neural networks are by far the most commonly used connectionist model today. Though there are a large variety of neural network models, they almost always follow two basic principles regarding the mind:

1. Any mental state can be described as an (N)-dimensional vector of numeric activation values over neural units in a network.
2. Memory is created by modifying the strength of the connections between neural units. The connection strengths, or "weights", are generally represented as an N×N matrix.

Most of the variety among neural network models comes from:

• Interpretation of units: Units can be interpreted as neurons or groups of neurons.
• Definition of activation: Activation can be defined in a variety of ways. For example, in a Boltzmann machine, the activation is interpreted as the probability of generating an action potential spike, and is determined via a logistic function on the sum of the inputs to a unit.
• Learning algorithm: Different networks modify their connections differently. In general, any mathematically defined change in connection weights over time is referred to as the "learning algorithm".

Connectionists are in agreement that recurrent neural networks (directed networks wherein connections of the network can form a directed cycle) are a better model of the brain than feedforward neural networks (directed networks with no cycles, called DAG). Many recurrent connectionist models also incorporate dynamical systems theory. Many researchers, such as the connectionist Paul Smolensky, have argued that connectionist models will evolve toward fully continuous, high-dimensional, non-linear, dynamic systems approaches.

Connectionist work in general does not need to be biologically realistic and therefore suffers from a lack of neuroscientific plausibility.[4][5][6][7][8][9][10] However, the structure of neural networks is derived from that of biological neurons, and this parallel in low-level structure is often argued to be an advantage of connectionism in modeling cognitive structures compared with other approaches.[3] One area where connectionist models are thought to be biologically implausible is with respect to error-propagation networks that are needed to support learning,[11][12] but error propagation can explain some of the biologically-generated electrical activity seen at the scalp in event-related potentials such as the N400 and P600,[13] and this provides some biological support for one of the key assumptions of connectionist learning procedures.

The weights in a neural network are adjusted according to some learning rule or algorithm, such as Hebbian learning. Thus, connectionists have created many sophisticated learning procedures for neural networks. Learning always involves modifying the connection weights. In general, these involve mathematical formulas to determine the change in weights when given sets of data consisting of activation vectors for some subset of the neural units. Several studies have been focused on designing teaching-learning methods based on connectionism.[14]

By formalizing learning in such a way, connectionists have many tools. A very common strategy in connectionist learning methods is to incorporate gradient descent over an error surface in a space defined by the weight matrix. All gradient descent learning in connectionist models involves changing each weight by the partial derivative of the error surface with respect to the weight. Backpropagation (BP), first made popular in the 1980s, is probably the most commonly known connectionist gradient descent algorithm today.[12]

Connectionism can be traced to ideas more than a century old, which were little more than speculation until the mid-to-late 20th century.

The prevailing connectionist approach today was originally known as parallel distributed processing (PDP). It was an artificial neural network approach that stressed the parallel nature of neural processing, and the distributed nature of neural representations. It provided a general mathematical framework for researchers to operate in. The framework involved eight major aspects:

• A set of processing units, represented by a set of integers.
• An activation for each unit, represented by a vector of time-dependent functions.
• An output function for each unit, represented by a vector of functions on the activations.
• A pattern of connectivity among units, represented by a matrix of real numbers indicating connection strength.
• A propagation rule spreading the activations via the connections, represented by a function on the output of the units.
• An activation rule for combining inputs to a unit to determine its new activation, represented by a function on the current activation and propagation.
• A learning rule for modifying connections based on experience, represented by a change in the weights based on any number of variables.
• An environment that provides the system with experience, represented by sets of activation vectors for some subset of the units.

A lot of the research that led to the development of PDP was done in the 1970s, but PDP became popular in the 1980s with the release of the books Parallel Distributed Processing: Explorations in the Microstructure of Cognition - Volume 1 (foundations) and Volume 2 (Psychological and Biological Models), by James L. McClelland, David E. Rumelhart and the PDP Research Group. The books are now considered seminal connectionist works, and it is now common to fully equate PDP and connectionism, although the term "connectionism" is not used in the books. Following the PDP model, researchers have theorized systems based on the principles of perpendicular distributed processing (PDP).

PDP's direct roots were the perceptron theories of researchers such as Frank Rosenblatt from the 1950s and 1960s. But perceptron models were made very unpopular by the book Perceptrons by Marvin Minsky and Seymour Papert, published in 1969. It demonstrated the limits on the sorts of functions that single-layered (no hidden layer) perceptrons can calculate, showing that even simple functions like the exclusive disjunction (XOR) could not be handled properly. The PDP books overcame this limitation by showing that multi-level, non-linear neural networks were far more robust and could be used for a vast array of functions.[15]

Many earlier researchers advocated connectionist style models, for example in the 1940s and 1950s, Warren McCulloch and Walter Pitts (MP neuron), Donald Olding Hebb, and Karl Lashley. McCulloch and Pitts showed how neural systems could implement first-order logic: Their classic paper "A Logical Calculus of Ideas Immanent in Nervous Activity" (1943) is important in this development here. They were influenced by the important work of Nicolas Rashevsky in the 1930s. Hebb contributed greatly to speculations about neural functioning, and proposed a learning principle, Hebbian learning, that is still used today. Lashley argued for distributed representations as a result of his failure to find anything like a localized engram in years of lesion experiments.

Though PDP is the dominant form of connectionism, other theoretical work should also be classified as connectionist.

Many connectionist principles can be traced to early work in psychology, such as that of William James.[16] Psychological theories based on knowledge about the human brain were fashionable in the late 19th century. As early as 1869, the neurologist John Hughlings Jackson argued for multi-level, distributed systems. Following from this lead, Herbert Spencer's Principles of Psychology, 3rd edition (1872), and Sigmund Freud's Project for a Scientific Psychology (composed 1895) propounded connectionist or proto-connectionist theories. These tended to be speculative theories. But by the early 20th century, Edward Thorndike was experimenting on learning that posited a connectionist type network.

Friedrich Hayek independently conceived the Hebbian synapse learning model in a paper presented in 1920 and developed that model into global brain theory constituted of networks Hebbian synapses building into larger systems of maps and memory network . Hayek's breakthrough work was cited by Frank Rosenblatt in his perceptron paper.

Another form of connectionist model was the relational network framework developed by the linguist Sydney Lamb in the 1960s. Relational networks have been only used by linguists, and were never unified with the PDP approach. As a result, they are now used by very few researchers.

There are also hybrid connectionist models, mostly mixing symbolic representations with neural network models. The hybrid approach has been advocated by some researchers (such as Ron Sun).