- 86 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Simple Perceptrons' - gretel

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Simple Perceptrons

Or one-layer feed-forward networks

Equation governing comp of simple perceptron

activation function, usually nonlinear, e.g. step function or sigmoid

ksi

Threshold or no threshold?

with threshold

without threshold; threshold simulated with connections to an input terminal permanently tied to -1

The General Association (Matching) Task:

Is to ask for: actual output pattern = target pattern

Threshold Units

- Start with simplest threshold unit, practical for 1-level perceptrons

- Also assume the targets have plus/minus 1 values and no values in between those extremes, that is,

- Then all that matter is that for each input pattern, the net input (weighted sum) h to each output unit has the same sign as the target zeta

A Notational Simplification

- To simplify notation, note that the output units are independent
- [In a multilayer nn, however, the hidden (non-output) layers aren’t independent]
- So let’s consider only one output at a time
- Drop the i subscripts

Weights and each input pattern live in the same space.

Advantage: can geometrically represent these two vectors together.

New Form for General Association Task: geometric interpretation

Another form:

A simple learning algorithm interpretation

- Also called the Perceptron Rule
- Go through the input patterns one by one
- For each pattern go through the output units one by one, asking whether output is the desired one.
- If so, leave the weight into that unit alone
- Else in the spirit of Hebb add to each connection something proportional to product of the input and desired output

Simplified Simple Learning Algorithm interpretation(for one neuron case)

- Start with w = 0 (not necessary)
- Cycle through the learning patterns
- For each pattern ksi
- If the output (O) != desired output (zeta), add product of the desired output and the input to w. (i.e., w = w + z*x)

- For each pattern ksi
- Keep cycling through the patterns until done.
- Convergence is guaranteed provided the two classes of input points are linearly separable.
- Perceptron convergence theorem guarantees this

Weight Update Formula, interpretation“Hebbian” from blue book, too complicated

Download Presentation

Connecting to Server..