Training network to minimize worst-case error

1. A method for training a classification network that classifies inputs into a plurality of different categories, the method comprising:

propagating a set of inputs through the classification network to generate a set of output probability distributions, the generated output probability distribution for each input providing a probability of the input belonging to each of the categories, each input having a corresponding expected output probability distribution that specifies a particular one of the categories to which the input belongs;

calculating a value of a continuously-differentiable loss function comprising a term that approximates a maximum of entropy calculations for each of the different categories; and

using the calculated continuously-differentiable loss function value to train weights of the classification network, wherein the term that approximates the maximum of the entropy calculations biases the training of the weights towards reducing a difference between the expected output probability distributions and the generated output probability distributions for inputs belonging to a category with the largest entropy calculations.

2. The method of claim 1 , wherein calculating the value of the continuously-differentiable loss function comprises calculating the entropy for each of the different categories.

3. The method of claim 2 , wherein calculating the entropy for each of the different categories comprises, for each of the categories:

calculating an average of the generated output probability distributions for the inputs belonging to the category; and

calculating the entropy of the average of the generated output probability distributions for the inputs belonging to the category.

4. The method of claim 2 , wherein calculating the entropy for each of the different categories comprises using a log-sum-exponent formulation that highlights inputs with the largest divergence between expected output probability distributions and generated output probability distributions.

5. The method of claim 4 , wherein the term that approximates the maximum of the entropy calculations is a log-sum-exponent term that uses the log-sum-exponent formulation of the entropy as its exponent.

6. The method of claim 5 , wherein:

the summation in the log-sum-exponent term is a summation over the plurality of different categories; and

the summation in the log-sum-exponent formulation of the entropy calculation for a particular category is a summation over the inputs belonging to the particular category.

7. The method of claim 1 , wherein:

the set of inputs comprises a plurality of inputs for each of the categories; and

for each category, the expected output probability distribution for each input belonging to the category is 1 for the category to which the input belongs and 0 for each other category.

8. The method of claim 1 , wherein using the calculated continuously-differentiable loss function value to train the weights of the classification network comprises:

back-propagating the calculated loss function value to determine, for each of a plurality of the weights of the classification network, a rate of change in the calculated loss function value relative to a rate of change in the weight; and

modifying each respective weight of the plurality of weights according to the respective rate of change determined for the weight.

9. The method of claim 1 , wherein the classification network is for embedding into a device after the classification network is trained.

10. The method of claim 1 , wherein the inputs are images and the plurality of categories are different types of objects represented in the images.

11. A non-transitory machine-readable medium storing a program which when executed by at least one processing unit trains a classification network that classifies inputs into a plurality of different categories, the program comprising sets of instructions for:

propagating a set of inputs through the classification network to generate a set of output probability distributions, the generated output probability distribution for each input providing a probability of the input belonging to each of the categories, each input having a corresponding expected output probability distribution that specifies a particular one of the categories to which the input belongs;

calculating a value of a continuously-differentiable loss function comprising a term that approximates a maximum of entropy calculations for each of the different categories; and

using the calculated continuously-differentiable loss function value to train weights of the classification network, wherein the term that approximates the maximum of the entropy calculations biases the training of the weights towards reducing a difference between the expected output probability distributions and the generated output probability distributions for inputs belonging to a category with the largest entropy calculations.

12. The non-transitory machine-readable medium of claim 11 , wherein the set of instructions for calculating the value of the continuously-differentiable loss function comprises a set of instructions for calculating the entropy for each of the different categories.

13. The non-transitory machine-readable medium of claim 12 , wherein the set of instructions for calculating the entropy for each of the different categories comprises sets of instructions for, for each of the categories:

calculating an average of the generated output probability distributions for the inputs belonging to the category; and

calculating the entropy of the average of the generated output probability distributions for the inputs belonging to the category.

14. The non-transitory machine-readable medium of claim 12 , wherein the set of instructions for calculating the entropy for each of the different categories comprises a set of instructions for using a log-sum-exponent formulation that highlights inputs with the largest divergence between expected output probability distributions and generated output probability distributions.

15. The non-transitory machine-readable medium of claim 14 , wherein the term that approximates the maximum of the entropy calculations is a log-sum-exponent term that uses the log-sum-exponent formulation of the entropy as its exponent.

16. The non-transitory machine-readable medium of claim 15 , wherein:

the summation in the log-sum-exponent term is a summation over the plurality of different categories; and

the summation in the log-sum-exponent formulation of the entropy calculation for a particular category is a summation over the inputs belonging to the particular category.

17. The non-transitory machine-readable medium of claim 11 , wherein:

the set of inputs comprises a plurality of inputs for each of the categories; and

for each category, the expected output probability distribution for each input belonging to the category is 1 for the category to which the input belongs and 0 for each other category.

18. The non-transitory machine-readable medium of claim 11 , wherein the set of instructions for using the calculated continuously-differentiable loss function value to train the weights of the classification network comprises sets of instructions for:

back-propagating the calculated loss function value to determine, for each of a plurality of the weights of the classification network, a rate of change in the calculated loss function value relative to a rate of change in the weight; and

modifying each respective weight of the plurality of weights according to the respective rate of change determined for the weight.

19. The non-transitory machine-readable medium of claim 11 , wherein the classification network is for embedding into a device after the classification network is trained.

20. The non-transitory machine-readable medium of claim 11 , wherein the inputs are images and the plurality of categories are different types of objects represented in the images.