Artificial neural networks.

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Presentation transcript:

Artificial neural networks. COMP305. Part I. Artificial neural networks.

of the Artificial Neural Networks. Topic 3. Learning Rules of the Artificial Neural Networks.

Hebb’s rule (1949). Hebb conjectured that a particular type of use-dependent modification of the connection strength of synapses might underlie learning in the nervous system.

Hebb’s rule (1949). Hebb introduced a neurophysiological postulate : “…When an axon of cell A is near enough to excite a cell B and repeatedly and persistently tales part in firing it, some growth process or metabolic change takes place in one or both cells, such that A’s efficiency as one of the cells firing B, is increased.”

Hebb’s rule (1949). The simplest formalisation of Hebb’s rule is to increase weight of connection at every next instant in the way: (1) where (2)

Hebb’s rule (1949). where (2) here (1) where (2) here wjik is the weight of connection at instant k, wjik+1 is the weight of connection at the following instant k+1, Dwjik is increment by which the weight of connection is enlarged, C is positive coefficient which determines learning rate, aik is input value from the presynaptic neuron at instant k, Xjk is output of the postsynaptic neuron at the same instant k.

Hebb’s rule (1949). (1) where (2) Thus, the weight of connection changes at the next instant only if both preceding input via this connection and the resulting output simultaneously are not equal to 0.

Hebb’s rule (1949). (1) where (2) Equation (2) emphasises the correlation nature of a Hebbian synapse. It is sometimes referred to as the activity product rule.

Hebb’s rule (1949). (1) where (2) Hebb’s original learning rule (2) referred exclusively to excitatory synapses, and has the unfortunate property that it can only increase synaptic weights, thus washing out the distinctive performance of different neurons in a network, as the connections drive into saturation..

Hebb’s rule (1949). (1) where (2) However, when the Hebbian rule is augmented by a normalisation rule, e.g. keeping constant the total strength of synapses upon a given neuron, it tends to “sharpen” a neuron’s predisposition “without a teacher”, causing its firing to become better and better correlated with a cluster of stimulus patterns.

Normalised Hebb’s rule. (1) where (2) normalisation: (3) Hebb’s rule plays an important role in studies of ANN algorithms much “younger” than the rule itself, such as unsupervised learning or self-organisation.

Normalised Hebb in practice. Input unit No 1 2 3 4 a 1 w 1 w a 2 2 q X a w 3 3 w 4 a 4

Normalised Hebb in practice. Input unit No 1 2 3 4 t=0 C=1 w01 w02 w03 w04 1 1 1 q =1 X 1 1

Normalised Hebb in practice. Input unit No 1 2 3 4 t=0 C=1 w01 w02 w03 w04 1 1 1 q =1 X 1 1

Normalised Hebb in practice. Input unit No 1 2 3 4 t=0 C=1 w01 w02 w03 w04 1 1 1 q =1 X 1 1

Normalised Hebb in practice. Input unit No 1 2 3 4 t=0 C=1 w01 w02 w03 w04 0.5 0.5 0.5 q =1 X 0.5 0.5

Normalised Hebb in practice. Input unit No 1 2 3 4 t=0 C=1 a01 a02 a03 a04 1 w01 w02 w03 w04 0.5 1 0.5 0.5 q =1 X 1 0.5 0.5

Normalised Hebb in practice. Input unit No 1 2 3 4 t=0 C=1 a01 a02 a03 a04 1 w01 w02 w03 w04 0.5 1 0.5 0.5 q =1 X 1 0.5 0.5

Normalised Hebb in practice. Input unit No 1 2 3 4 t=0 C=1 a01 a02 a03 a04 1 w01 w02 w03 w04 0.5 1 0.5 0.5 q =1 1 1 0.5 0.5

Normalised Hebb in practice. Input unit No 1 2 3 4 t=0 C=1 a01 a02 a03 a04 1 w01 w02 w03 w04 0.5 1 0.5 0.5 q =1 1 1 0.5 0.5

Normalised Hebb in practice. Input unit No 1 2 3 4 a01 a02 a03 a04 1 t=1 C=1 w11 w12 w13 w14 1.5 0.5 1.5 0.5 q =1 X 1.5 0.5

Normalised Hebb in practice. Input unit No 1 2 3 4 t=1 C=1 w11 w12 w13 w14 1.5 0.5 1.5 0.5 q =1 X 1.5 0.5

Normalised Hebb in practice. Input unit No 1 2 3 4 t=1 C=1 w11 w12 w13 w14 1.5 0.5 1.5 0.5 q =1 X 1.5 0.5

Normalised Hebb in practice. Input unit No 1 2 3 4 t=1 C=1 w11 w12 w13 w14 0.67 0.22 0.67 0.22 q =1 X 0.67 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 t=1 C=1 w11 w12 w13 w14 0.67 0.22 0.67 0.22 q =1 X 0.67 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 w01 w02 w03 w04 0.5 t=1 C=1 w11 w12 w13 w14 0.67 0.22 0.67 0.22 q =1 X 0.67 Continue… 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 t=1 C=1 a11 a12 a13 a14 1 w11 w12 w13 w14 0.67 0.22 1 0.67 0.22 q =1 X 1 0.67 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 t=1 C=1 a11 a12 a13 a14 1 w11 w12 w13 w14 0.67 0.22 1 0.67 0.22 q =1 1 1 0.67 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 t=1 C=1 a11 a12 a13 a14 1 w11 w12 w13 w14 0.67 0.22 1 0.67 0.22 q =1 1 1 0.67 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 t=2 C=1 w21 w22 w23 w24 1.67 0.22 1.67 0.22 q =1 X 1.67 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 t=2 C=1 w21 w22 w23 w24 1.67 0.22 1.67 0.22 q =1 X 1.67 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 t=2 C=1 w21 w22 w23 w24 1.67 0.22 1.67 0.22 q =1 X 1.67 0.22

Normalised Hebb in practice. Input unit No 1 2 3 4 t=2 C=1 w21 w22 w23 w24 0.70 0.09 0.70 0.09 q =1 X 0.70 0.09

Normalised Hebb in practice. Input unit No 1 2 3 4 t=2 C=1 w21 w22 w23 w24 0.70 0.09 0.70 0.09 q =1 X 0.70 0.09

Normalised Hebb in practice. Input unit No 1 2 3 4 w11 w12 w13 w14 0.67 0.22 t=2 C=1 w21 w22 w23 w24 0.70 0.09 0.70 0.09 q =1 X 0.70 0.09 Continue…

Normalised Hebb in practice. Input unit No 1 2 3 4 t=2 C=1 a21 a22 a23 a24 1 w21 w22 w23 w24 0.70 0.09 1 0.70 0.09 q =1 X 1 0.70 0.09

Normalised Hebb in practice. Input unit No 1 2 3 4 t=2 C=1 a21 a22 a23 a24 1 w21 w22 w23 w24 0.70 0.09 1 0.70 0.09 q =1 1 1 0.70 0.09

Normalised Hebb in practice. Input unit No 1 2 3 4 t=2 C=1 a21 a22 a23 a24 1 w21 w22 w23 w24 0.70 0.09 1 0.70 0.09 q =1 1 1 0.70 0.09

Normalised Hebb in practice. Input unit No 1 2 3 4 a21 a22 a23 a24 1 t=3 C=1 w31 w32 w33 w34 1.70 0.09 1.70 0.09 q =1 X 1.70 0.09

Normalised Hebb in practice. Input unit No 1 2 3 4 t=3 C=1 w31 w32 w33 w34 1.70 0.09 1.70 0.09 q =1 X 1.70 0.09

Normalised Hebb in practice. Input unit No 1 2 3 4 t=3 C=1 w31 w32 w33 w34 1.70 0.09 1.70 0.09 q =1 X 1.70 0.09

Normalised Hebb in practice. Input unit No 1 2 3 4 t=3 C=1 w31 w32 w33 w34 0.71 0.04 0.71 0.04 q =1 X 0.71 0.04

Normalised Hebb in practice. Input unit No 1 2 3 4 w21 w22 w23 w24 0.70 0.09 t=3 C=1 w31 w32 w33 w34 0.71 0.04 0.71 0.04 q =1 X 0.71 0.04 Continue…

Normalised Hebb in practice. Input unit No 1 2 3 4 t=3 C=1 a31 a32 a33 a34 1 w31 w32 w33 w34 0.71 0.04 1 0.71 0.04 q =1 X 1 0.71 0.04

Normalised Hebb in practice. Input unit No 1 2 3 4 t=3 C=1 a31 a32 a33 a34 1 w31 w32 w33 w34 0.71 0.04 1 0.71 0.04 q =1 1 1 0.71 0.04

Normalised Hebb in practice. Input unit No 1 2 3 4 t=3 C=1 a31 a32 a33 a34 1 w31 w32 w33 w34 0.71 0.04 1 0.71 0.04 q =1 1 1 0.71 0.04

Normalised Hebb in practice. Input unit No 1 2 3 4 a31 a32 a33 a34 1 t=3 C=1 w31 w32 w33 w34 1.71 0.04 1 1.71 0.04 q =1 1 1 1.71 0.04

Normalised Hebb in practice. Input unit No 1 2 3 4 t=4 C=1 w41 w42 w43 w44 1.71 0.04 1.71 0.04 q =1 X 1.71 0.04

Normalised Hebb in practice. Input unit No 1 2 3 4 t=4 C=1 w41 w42 w43 w44 1.71 0.04 1.71 0.04 q =1 X 1.71 0.04

Normalised Hebb in practice. Input unit No 1 2 3 4 t=4 C=1 w41 w42 w43 w44 0.71 0.02 0.71 0.02 q =1 X 0.71 0.02

Normalised Hebb in practice. Input unit No 1 2 3 4 w31 w32 w33 w34 0.71 0.04 t=4 C=1 w41 w42 w43 w44 0.71 0.02 0.71 0.02 q =1 X 0.71 0.02 Continue…

Normalised Hebb in practice. Input unit No 1 2 3 4 t=4 C=1 a41 a42 a43 a44 1 w41 w42 w43 w44 0.71 0.02 1 0.71 0.02 q =1 X 1 0.71 0.02

Normalised Hebb in practice. Input unit No 1 2 3 4 t=4 C=1 a41 a42 a43 a44 1 w41 w42 w43 w44 0.71 0.02 1 0.71 0.02 q =1 1 1 0.71 0.02

Normalised Hebb in practice. Input unit No 1 2 3 4 t=4 C=1 a41 a42 a43 a44 1 w41 w42 w43 w44 0.71 0.02 1 0.71 0.02 q =1 1 1 0.71 0.02

Normalised Hebb in practice. Input unit No 1 2 3 4 a41 a42 a43 a44 1 t=4 C=1 w51 w52 w53 w54 1.71 0.02 1 1.71 0.02 q =1 1 1 1.71 0.02

Normalised Hebb in practice. Input unit No 1 2 3 4 t=5 C=1 w51 w52 w53 w54 1.71 0.02 1.71 0.02 q =1 X 1.71 0.02

Normalised Hebb in practice. Input unit No 1 2 3 4 t=5 C=1 w51 w52 w53 w54 1.71 0.02 1.71 0.02 q =1 X 1.71 0.02

Normalised Hebb in practice. Input unit No 1 2 3 4 t=5 C=1 w51 w52 w53 w54 0.71 0.01 0.71 0.01 q =1 X 0.71 0.01

Normalised Hebb in practice. Input unit No 1 2 3 4 w41 w42 w43 w44 0.71 0.02 t=5 C=1 w51 w52 w53 w54 0.71 0.01 0.71 0.01 q =1 X 0.71 0.01 STOP!!!!

Normalised Hebb in practice. Input unit No 1 2 3 4 w 1.0 w 1,3 0.5 0.71 w Iteration N 2,4 0.01 0.0 1 2 3 4 5 q =1 0.3 X 0.71 0.2 0.1 0.01 Iteration N 0.0 1 2 3 4 5

Normalised Hebb in practice. Input unit No 1 2 3 4 Test a1 a2 a3 a4 1 w1 w2 w3 w4 0.71 0.01 1 0.71 0.01 1 q =1 X 0.71 I do not know you… 0.01