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| data_mining:neural_network:perceptron [2017/02/03 22:59] – [What perceptrons can't do] phreazer | data_mining:neural_network:perceptron [2017/02/03 23:21] (current) – [What perceptrons can't do] phreazer | ||
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| ==== What perceptrons can't do ==== | ==== What perceptrons can't do ==== | ||
| - | Separate feature unit for each of the many binary vectors => any possible discrimination. | + | Separate feature unit for each of the many binary vectors => any possible discrimination. |
| This type of table look-up won't generalize. (guess due to the binary encoding). | This type of table look-up won't generalize. (guess due to the binary encoding). | ||
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| - Weight plane is perpendicular to the weight vector and misses the origin by a distance equal to the threshold. | - Weight plane is perpendicular to the weight vector and misses the origin by a distance equal to the threshold. | ||
| - | Pos and neg cases can not be seperated by a plane. | + | Pos and neg cases can not be seperated by a plane => not linearly separable. |
| + | === Discriminate patterns under translation with wrap-around === | ||
| + | |||
| + | Binary threshold neuron can't discriminate between different patterns that have same number of on pixels (if pattern can translate with wrap-around). | ||
| + | |||
| + | Proof: | ||
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| + | Pattern A on all possible translations (4 on pixels). | ||
| + | Total Input will be 4x sum of all the weights. | ||
| + | |||
| + | Pattern B on all possible translations (4 on pixels) | ||
| + | Total Input will be 4x sum of all the weights. | ||
| + | |||
| + | But every single case of pattern A must provide more import than all single cases of pattern B. | ||
| Case: | Case: | ||
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| Any example with 3 pixels on: activation = -0.5 | Any example with 3 pixels on: activation = -0.5 | ||
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| Any example with 1 pixel on: activation = -2.5 | Any example with 1 pixel on: activation = -2.5 | ||
| + | |||
| Any example with 4 pixel on: acitvation = 0.5 | Any example with 4 pixel on: acitvation = 0.5 | ||
| => correctly classified. | => correctly classified. | ||
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| + | Whole point of pattern recognition is to recognize patterns despite transformations like translation. Minksy and Paper (" | ||
| + | - Translation with **wrap-around** form a group. | ||
| + | To deal with such transf. tricky part of recognition must be solved by hand-coded **feature detectors** (not learning procedure). | ||
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| + | Conclusion (after 20 yrs): Neuronal Network has to learn the feature detectors (not only weights). | ||
| + | * More layers of linear units do not help (still linear). | ||
| + | * Fixed output non-linearities are not enough. | ||
| + | |||
| + | => Need multiple layers of **adaptive**, | ||
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| + | * Efficient way of adapting all the weights. | ||
| + | * Learning weights going into hidden units is equivalent to learning features. | ||
| + | * No one is telling us what the feature vectors should be. | ||
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