Leabra

Leabra stands for "Local, Error-driven and Associative, Biologically Realistic Algorithm". It is a model of learning which is a balance between Hebbian and error-driven learning with other network-derived characteristics. This model is used to mathematically predict outcomes based on inputs and previous learning influences. This model is heavily influenced by and contributes to neural network designs and models. This algorithm is the default algorithm in Emergent (successor of PDP++) when making a new project, and is extensively used in various simulations.

Hebbian learning is performed using conditional principal components analysis (CPCA) algorithm with correction factor for sparse expected activity levels.

Error-driven learning is performed using GeneRec, which is a generalization of the Recirculation algorithm, and approximates Almeida-Pineda recurrent backpropagation. The symmetric, midpoint version of GeneRec is used, which is equivalent to the contrastive Hebbian learning algorithm (CHL). See O'Reilly (1996; Neural Computation) for more details.

The activation function is a point-neuron approximation with both discrete spiking and continuous rate-code output.

Layer or unit-group level inhibition can be computed directly using a k-winners-take-all (KWTA) function, producing sparse distributed representations.

The net input is computed as an average, not a sum, over connections, based on normalized, sigmoidaly transformed weight values, which are subject to scaling on a connection-group level to alter relative contributions. Automatic scaling is performed to compensate for differences in expected activity level in the different projections.

Documentation about this algorithm can be found in the book "Computational Explorations in Cognitive Neuroscience: Understanding the Mind by Simulating the Brain" published by MIT press. and in the Emergent Documentation

Overview of the Leabra Algorithm
The pseudocode for Leabra is given here, showing exactly how the pieces of the algorithm described in more detail in the subsequent sections fit together.

Special algorithms

 * Temporal Differences and General Da (dopamine) Modulation. Temporal differences (TD) is widely used as a model of midbrain dopaminergic firing.
 * Primary value learned value (PVLV). PVLV simulates behavioral and neural data on Pavlovian conditioning and the midbrain dopaminergic neurons that fire in proportion to unexpected rewards (an alternative to TD).
 * Prefrontal Cortex Basal Ganglia Working Memory (PBWM). PBWM uses PVLV to train Prefrontal cortex working memory updating system, based on the biology of the prefrontal cortex and basal ganglia.