## softmax()


Apply the softmax function to a list of logits.


Usage


``` python
softmax(logits)
```


Converts a vector of raw scores (logits) into a probability distribution where each element is in (0, 1) and all elements sum to 1.


## Parameters


`logits: list`  
A list of numeric values (raw scores).


## Returns


`list`  
A list of probabilities summing to 1.0.


## Notes

Applies the softmax function:

 \sigma(z)\_i = \frac{e^{z_i}}{\sum\_{j=1}^{K} e^{z_j}} 

For numerical stability, the implementation subtracts the maximum logit value before exponentiation:

 \sigma(z)\_i = \frac{e^{z_i - \max(z)}}{\sum\_{j=1}^{K} e^{z_j - \max(z)}} 

This prevents overflow when logit values are large.


## Examples

``` python
>>> result = softmax([1.0, 2.0, 3.0])
>>> round(sum(result), 5)
```

1.0

``` python
>>> softmax([0.0, 0.0])
```

\[0.5, 0.5\]