6.1 Shifter Problem
6.2 Single Shifter
6.3 Double Shifter

Shifter
 
 

6.1   Shifter Problem

All you do to solve a shifter-problem is to click a few buttons; however, first we will explain the problem.

The shifter problem generates a pattern, shifts the pattern in one of many possible ways and asks a neural network to identify the shifting.

This is obviously synthetic data instead of real data, such as a person's signature. The shifter problem is chosen because:

(1) the number of neurons is arbitrary, allowing you to work with many different sizes of neural networks;

(2) the amount of data is arbitrary, allowing you to study the relation between the amount of training data and the results;

(3) this is a very hard problem due to the large sample space.
 
 

Example 4-bit Shifter problem.

100             1100 1001         Left Shift, Wrap-around
001             1100 0110         Right Shift
010             1100 1100         No Shift
111             1111 0000         Not Valid

When you shift a pattern once, it is a single shifter; when you shift a pattern twice, it is a double shifter, ... Shifter data is used to train the neural network. Once training is finished, the network has to solve two types of problems: identify a shift or complete a shift.

6.2   Single Shifter

Two files are used: training, testing. You can choose the file names by clicking: "Data/Link". For the moment, we suggest you to use the default file names:
 

Training file: example1a.txt
Testing file: example1b.txt

Example/Shifter/Data.

This command will also open the two files and set up the neural network.

The default values (for the shifter problem) are:
 

15-bit Shifter (33 neurons),
250 training-patterns,
50 testing-patterns.

To change the default settings, click:

Example/Shifter/Parameter.

010                             means no shift;
000001000000010     is a 15-bit pattern; and
000001000000010     is generated by 'no shift'.

Use the command "Data/Symmetry" to read or set the symmetry parameters. In this problem, it indicates that the shifter has a 1-dimensional x-translation symmetry. This is very important for training the network.

Now that the network is initialized and the data is generated, it is ready to be trained and tested. Click Run/Classification. This command takes no time.

If you click Run/Distribution, the Boltzmann Machine will present you with a distribution, which is a set of possibilities and the probability for each possibility. The one with the largest number is the preferred answer. The following is an example of the output for a shifter problem:

xxx
    001101000101111
    100110100010111
Distribution begins:
    100     2
    001     50
End of the Distribution
001
    001101000101111
    100110100010111 50 1

xxx
    010000001111001
    100000011110010
Distribution begins:
    010     7
    100     440
    001     33
End of the Distribution
100
    010000001111001
    100000011110010 440 1

In each instance, the testing pattern is printed first. This is followed by all possible solutions and a relative probability for each possibility. In the first instance, 001 ( Right Shift ) is the answer; and in the second instance, 100 ( Left Shift ) is the answer. In both cases, the answers are correct.

The probabilities printed next to each possibility are relative probabilities. In the first example, the probabilities for 100, 010, and 001 are 2/52, 0, and 50/52, respectively. The probabilities are not normalized because they carry other information: the larger the number is, the more reliable the answer is.

In this example, 45 or so testing-patterns are recognized. If you are satisfied, copy the unrecognized patterns to the training file and run again (with xxx being replaced properly). Then you should get 100% correct classification. Alternatively, generate more training data by clicking:

Example/Shifter/Parameter,

And reset the number of training patterns.

Click commands "Run/Classification" or "Run/Distribution", you can expect three possibilities for each testing pattern:

6.3   Double Shifter

If you shift a pattern twice, you will get a double shifter. Here are two examples:

010001
        100100001000000
        100100001000000
        010010000100000

100010
        101000111110110
        010001111101101
        101000111110110.

The possible shifts are:
 

LL 100100
NL 010100
RL 001100
LN 100010
NN 010010
RN 001010
LR 100001
NR 010001
RR 001001

Where RL means Right-Left shifts. The testing patterns look like this:

xxxxxx
    100000000001011
    000000000010111
    000000000010111

The output data file for "Run/Distribution" looks like this:

xxxxxx
    100000000001011
    000000000010111
    000000000010111
Distribution begins:
    100100 260
    010100 128
    010010 32
    010001 32
    001100 80
    001001 32
End of the Distribution
100100
    100000000001011
    000000000010111
    000000000010111 260 1

The output data file contains the original vector, plus several possible shifts. Finally, the answer is printed. Each possibility is associated with a number:
 

for class 100100, the number is 260;
for class 010100, the number is 128;
for class 010010, the number is 32;
. . .

The predominate number here is 260, making the preferred answer 100100 (the left-left shift), which is the correct answer. These numbers are relative probabilities. Note, the probabilities printed next to each possibility are relative probabilities. The probabilities are not normalized because they carry other information: the larger the number is, the more reliable the answer is.

If you use "Run/Classification" instead of "Run/Distribution", then the results will look like this:

xxxxxx
    100000000001011
    000000000010111
    000000000010111

100100
    100000000001011
    000000000010111
    000000000010111 260 1
 
 

In the output data file, the original testing-vector is printed first, followed by the best match output-vector.