|
347 | 347 | "cell_type": "markdown", |
348 | 348 | "metadata": {}, |
349 | 349 | "source": [ |
350 | | - "This particular activation function is of course not differentiable, and it remains to be shown that the weights can be learned, but nevertheless, a single unit can be identified that solves the XOR problem.\n", |
| 350 | + "![Indicator function not differentiable](img/non-differentiable-function_1_0.png \"\")" |
| 351 | + ] |
| 352 | + }, |
| 353 | + { |
| 354 | + "cell_type": "markdown", |
| 355 | + "metadata": {}, |
| 356 | + "source": [ |
| 357 | + "This particular activation function is of course not differentiable, which means that we cannot compute the gradient in this case at $x=0.5,ドル and thus we cannot compute the gradient descent necessary for weight optimization in backpropagation. It remains to be shown that the weights can be learned. Nevertheless, a single unit can be identified that solves the XOR problem, if the decision function is not binary or piecewise linear.\n", |
351 | 358 | "\n", |
352 | | - "The difference between Minsky and Papert's (1969) definition of a perceptron and this unit is that - as Julia Hockenmaier pointed out - a perceptron is defined to have a decision function that would be binary and piecewise linear. This means that the unit that solves the XOR problem is not compatible with the definition of perceptron as in Minsky and Papert (1969) (p.c. Julia Hockenmaier)." |
| 359 | + "The difference between Minsky and Papert's (1969) definition of a perceptron and this unit is that - as Julia Hockenmaier pointed out - a perceptron is defined to have a decision function that would be binary and piecewise linear. This means that the unit above that solves the XOR problem is not compatible with the definition of perceptron as in Minsky and Papert (1969) (p.c. Julia Hockenmaier)." |
353 | 360 | ] |
354 | 361 | }, |
355 | 362 | { |
|
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