Introduction to Deep Learning with PyTorch
Chapter 3: PyTorch Tensors
Quick exercises
Here are some quick exercises to apply what you have just read!
Exercise 1: Logistic Function
We define the logistic function \sigma(\cdot) as: \sigma (x) = \dfrac{1}{1 + e^{-x}}
This function presents relevant properties:
- \forall x, \: 0 < \sigma (x) < 1
- \lim_{x \rightarrow -\infty} \sigma (x) = 0
- \lim_{x \rightarrow +\infty} \sigma (x) = 1
Those properties make it suitable to model probabilities.
Implement a function logistic, applying the above function to all elements of a tensor.
def logistic(tensor):
"""
Args:
tensor (torch.Tensor)
Return:
logistic_tensor (torch.Tensor) : resulting tensor after having applied the logistic function to all elements of tensor.
"""
return ????
def logistic(tensor):
"""
Args:
tensor (torch.Tensor)
Return:
logistic_tensor (torch.Tensor) : resulting tensor after having applied the logistic function to all elements of tensor.
"""
return 1 / (1 + torch.exp(-1 * tensor))
Exercise 2: Mean of Tensors
Implement a function mean_tensors that takes as input a list of tensors and returns the mean of all those tensors.
def mean_tensors(tensors_list):
"""
Args:
tensors_list (List[torch.Tensor]) list of tensors of the same shape
Return:
mean_tensors (torch.Tensor) : resulting tensor after having calculated the mean of all tensors passed as input.
"""
One solution would be:
def mean_tensors(tensors_list):
"""
Args:
tensors_list (List[torch.Tensor]) list of tensors of the same shape
Return:
mean_tensors (torch.Tensor) : resulting tensor after having calculated the mean of all tensors passed as input.
"""
assert len(tensors_list) > 0
sum_tensors = tensors_list[0]
for tensor in tensors_list[1:]:
sum_tensors += tensor
mean = sum_tensors / len(tensors_list)
return mean
Or if you want to be more concise:
def mean_tensors(tensors_list):
"""
Args:
tensors_list (List[torch.Tensor]) list of tensors of the same shape
Return:
mean_tensors (torch.Tensor) : resulting tensor after having calculated the mean of all tensors passed as input.
"""
assert len(tensors_list) > 0
mean = sum(tensors_list) / len(tensors_list)
return mean