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
1.5 KiB
1.5 KiB
- Limits output values
- Squashing function
Threshold
- For binary functions
- Not differentiable
- Sharp rise
- Heaviside function
- Unipolar
- 0 <-> +1
- Bipolar
- -1 <-> +1
Sigmoid
- Logistic function
- Normalises
- Introduces non-linearity
- Alternative is
tanh
- -1 <-> +1
- Easy to take derivative
\frac d {dx} \sigma(x)=
\frac d {dx} \left[
\frac 1 {1+e^{-x}}
\right]
=\sigma(x)\cdot(1-\sigma(x))$$
![sigmoid](../../img/sigmoid.png)
### Derivative
$$y_j(n)=\varphi_j(v_j(n))=
\frac 1 {1+e^{-v_j(n)}}$$
$$\frac{\partial y_j(n)}{\partial v_j(n)}=
\varphi_j'(v_j(n))=
\frac{e^{-v_j(n)}}{(1+e^{-v_j(n)})^2}=
y_j(n)(1-y_j(n))$$
- Nice derivative
- Max value of $\varphi_j'(v_j(n))$ occurs when $y_j(n)=0.5$
- Min value of 0 when $y_j=0$ or $1$
- Initial [weights](Weight%20Init.md) chosen so not saturated at 0 or 1
If $y=\frac u v$
Where $u$ and $v$ are differential functions
$$\frac{dy}{dx}=\frac d {dx}\left(\frac u v\right)$$
$$\frac{dy}{dx}=
\frac {v \frac d {dx}(u) - u\frac d {dx}(v)} {v^2}$$
# ReLu
Rectilinear
- For deep networks
- $y=max(0,x)$
- CNNs
- Breaks associativity of successive [convolutions](../../Signal%20Proc/Convolution.md)
- Critical for learning complex functions
- Sometimes small scalar for negative
- Leaky ReLu
![relu](../../img/relu.png)
# SoftMax
- Output is per-class vector of likelihoods
- Should be normalised into probability vector
## AlexNet
$$f(x_i)=\frac{\text{exp}(x_i)}{\sum_{j=1}^{1000}\text{exp}(x_j)}$$