andy
4cc2e79866
Affected files: .obsidian/global-search.json .obsidian/workspace.json Health/Alexithymia.md Health/BWS.md STEM/AI/Neural Networks/Activation Functions.md STEM/AI/Neural Networks/Architectures.md STEM/AI/Neural Networks/CNN/CNN.md STEM/AI/Neural Networks/MLP/Back-Propagation.md STEM/AI/Neural Networks/Transformers/Attention.md STEM/CS/Calling Conventions.md STEM/CS/Languages/Assembly.md
69 lines
1.5 KiB
Markdown
69 lines
1.5 KiB
Markdown
- Limits output values
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- Squashing function
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# Threshold
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- For binary functions
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- Not differentiable
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- Sharp rise
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- *Heaviside function*
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- Unipolar
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- 0 <-> +1
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- Bipolar
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- -1 <-> +1
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# Sigmoid
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- Logistic function
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- Normalises
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- Introduces non-linearity
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- Alternative is $tanh$
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- -1 <-> +1
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- Easy to take derivative
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$$\frac d {dx} \sigma(x)=
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\frac d {dx} \left[
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\frac 1 {1+e^{-x}}
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\right]
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=\sigma(x)\cdot(1-\sigma(x))$$
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### Derivative
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$$y_j(n)=\varphi_j(v_j(n))=
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\frac 1 {1+e^{-v_j(n)}}$$
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$$\frac{\partial y_j(n)}{\partial v_j(n)}=
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\varphi_j'(v_j(n))=
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\frac{e^{-v_j(n)}}{(1+e^{-v_j(n)})^2}=
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y_j(n)(1-y_j(n))$$
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- Nice derivative
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- Max value of $\varphi_j'(v_j(n))$ occurs when $y_j(n)=0.5$
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- Min value of 0 when $y_j=0$ or $1$
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- Initial [weights](Weight%20Init.md) chosen so not saturated at 0 or 1
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If $y=\frac u v$
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Where $u$ and $v$ are differential functions
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$$\frac{dy}{dx}=\frac d {dx}\left(\frac u v\right)$$
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$$\frac{dy}{dx}=
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\frac {v \frac d {dx}(u) - u\frac d {dx}(v)} {v^2}$$
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# ReLu
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Rectilinear
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- For deep networks
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- $y=max(0,x)$
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- CNNs
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- Breaks associativity of successive [convolutions](../../Signal%20Proc/Convolution.md)
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- Critical for learning complex functions
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- Sometimes small scalar for negative
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- Leaky ReLu
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# SoftMax
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- Output is per-class vector of likelihoods
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- Should be normalised into probability vector
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## AlexNet
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$$f(x_i)=\frac{\text{exp}(x_i)}{\sum_{j=1}^{1000}\text{exp}(x_j)}$$ |