This document appears to be a seminar presentation about Hopfield networks. It introduces Hopfield networks as a form of recurrent neural network that can serve as associative memory and solve constraint satisfaction problems. It then discusses discrete Hopfield networks, which have binary neuron states and update asynchronously. The key properties and applications of discrete Hopfield networks are summarized, including how they can be used for content-addressable memory and determining if an input is a known or unknown pattern.

1. A Seminar Presentation for the degree of
Master of Technology
in
Computer Science and Engineering
PRESENTED BY:-
AKHIL UPADHYAY
M-TECH 3rd SEM CSE
ROLL NO.- 121140002
SUBMITED TO:-
MR. ROHIT MIRI
H.O.D. OF COMPUTER
SCIENCE DEPARTMENT

3. INTRODUCTION
 A Hopfield Networks is a form of recurrent artificial neural
Network popularized by John Hopfield in 1982, but described
earlier by Little in 1974
 Hopfield has developed a number of neural Networks based
on fixed weights and adaptive activations
 These Networks can serve as associative memory Networks
and can be used to solve constraint satisfaction problems such
as the "Travelling Salesman Problem
(Cont..)

4. Two types:
1. Discrete Hopfield Network.
2. Continuous Hopfield Network.
Discrete Hopfield Network
 Hopfield has proposed two basic models of associative
memories (Hopfield 1982, 1984).
(Cont..)

5. Discrete Hopfield Network
The first of these is a ‘DISCRETE MODEL’ while the
second is a ‘CONTINUOUS’ version of the same.
 The terms ‘DISCRETE’ or ‘CONTINUOUS’ refer to the
nature of the state variables and time, in these models.
 In the discrete Hopfield network, each neuron has a
binary state
𝑽𝒊 ∈{1,-1}
 The state of the network with N neurons is represented
by the vector
(Cont..)

6. Discrete Hopfield Network
V={ 𝑽 𝟏, … … . , 𝑽𝒊, … … . 𝑽 𝑵} 𝑻
 The network is fully-connected, i.e., each neuron
connected to all others.
 The weight from j’th neuron to i’th neuron is given by,
and weight matrix is given as
W={𝒘𝒊𝒋}
 Since the network has loops, computations are dynamic
and the network state evolves through time, which is a
discrete variable.
(Cont..)

7. Discrete Hopfield Network
 Hopfield net differ from iterative auto associative net in 2
things.
1. Only one unit updates its activation
at a time (based on the signal it receives from each other
unit)
2. Each unit continues to receive an
external signal in addition to the signal from the other units
in the net.
(Cont..)

8. Surprise
 The asynchronous updating of the units allows a function,
known as an energy function, to be found for the net.
 The existence of such a function enables us to prove that the
net will converge to a stable set of activations, rather than
oscillating.
 The original formulation of the discrete Hopfield net showed
the usefulness of the net as content-addressable memory.
(Cont..)

9. Discrete Hopfield Network
(Cont..)

10. Discrete Hopfield Network
Algorithm
There are several versions of the discrete Hopfield net.
 Binary Input Vectors
To store a set of binary patterns s ( p ) ,
p = 1 , . . . , P, where
))().....().....(()( 1 pspspsps ni
(Cont..)

11. Discrete Hopfield Network
 The weight matrix W = is given by}{ ijw
]12][12[ )()(   pj
p
piij ssw ji for
and
.0iiw
(Cont..)

12. Discrete Hopfield Network
 Bipolar Inputs
To store a set of binary patterns s ( p ) ,
p = 1 , . . . , P, where
))().....().....(()( 1 pspspsps ni
The weight matrix W = is given by,}{ ijw
)()( pj
p
piij ssw  ji for
and
0iiw
(Cont..)

13. PROPERTIES OF HOPFIELD NETWORK
A recurrent network with all nodes connected to all other
nodes.
Nodes have binary outputs (either 0,1 or -1,1).
Weights between the nodes are symmetric .
No connection from a node to itself is allowed.
Nodes are updated asynchronously ( i.e. nodes are selected at
random).
The network has no hidden nodes or layer.
(Cont..)

14. Discrete Hopfield Network
Applications:-
A binary Hopfield net can be used to determine whether an input
vector is a "known” or an "unknown" vector.
The net recognizes a "known" vector by producing a pattern of
activation on the units of the net that is the same as the vector
stored in the net.
If the input vector is an "unknown" vector, the activation vectors
produced as the net iterates will converge to an activation vector
that is not one of the stored patterns.

15. Thank You