Basic Hebbian plasticity rule implementation.

This module implements the classic Hebbian learning rule, often summarized as "neurons that fire together wire together."

Theory

Hebbian learning was proposed by Donald Hebb in 1949 as a model for how neural connections are strengthened through experience. The basic rule is:

Δw_ij = η × pre_i × post_j

Where: - Δw_ij is the weight change from neuron i to j - η (eta) is the learning rate - pre_i is the presynaptic (input) activation - post_j is the postsynaptic (output) activation

Variants Implemented

1. **Basic Hebbian** (default): Δw = η × pre × post

2. **Bounded Hebbian** (with weight clamping): Δw = η × pre × post, clamped to [-1, 1]

3. **Oja's Rule** (with normalization): Δw = η × post × (pre - post × w) This prevents unbounded weight growth.

Usage

Weight = {0.5, 0.0, 0.01, []}, % Initial weight spec PreActivity = 0.8, PostActivity = 0.6, Reward = 0.0, % Not used in basic Hebbian

NewWeight = plasticity_hebbian:apply_rule(Weight, PreActivity, PostActivity, Reward). %% => {0.5048, 0.0048, 0.01, []}

Configuration

The learning rate is stored in the weight_spec tuple (3rd element). Additional parameters can be stored in the parameter list (4th element):

- {bounded, Min, Max}` - Clamp weights to [Min, Max] - `{oja, true}` - Use Ojas normalized rule - {decay, Rate}` - Apply weight decay: w = w × (1 - decay)

References

[1] Hebb, D.O. (1949). The Organization of Behavior. Wiley. [2] Oja, E. (1982). "A simplified neuron model as a principal component analyzer." Journal of Mathematical Biology.