About the softmax layer of the model architecture

[sunshineYin]

Hello, I am also a researcher on GIScience and human mobility, and I have read your paper about "DeepGravity" published on Nature Communications. It's an excellent and innovative work. And I am trying to reproduce it for other similar tasks. But I have some questions about your source code and am grateful for your help.

In your paper, there is a model architecture in Figure 1, you design a feed-forward neural network with 15 hidden layers. And input all the three-tuple (xi, xj, rij) into it (which is the same feed-forward network) for training, right? And the output of each three-tuple should be a score sij. And then, you apply a softmax layer to normalize it as probability pij, which indicates the probability of interaction between location i and j. So, my question is how this softmax layer is implemented. Because for each OD-specific three-tuple, the output is a value, not a vector, so how to use softmax for a single value? And besides, because the softmax layer is to get the probability of going to each destination with a fixed origin, right? It is necessary to ensure that the origins of the same batch of OD samples that are input into the softmax layer are the same, so that it makes sense, and I do not find the corresponding implementation part in the source code.

Thank you first and hope to hear from you as soon as possible.

[sunshineYin]

Any reply? Thanks.

[MassimilianoLuca]

Dear sunshineYin, I am sorry for the late reply.
Actually, the probabilities of the model are computed within the GLM_multinomialRegression class we implemented in the file od_models.py. In particular, there is the function predict_proba that uses a softmax to actually compute the probability of a vector x passed to the model. Note that everything is invocated from the get_cpc function (same file) when we call average_OD_model

Please, let me know if it is more clear and it there is something else we can do

[sunshineYin]

Dear Luca,

Yeah, I have found your code based on your reply. But I still have some questions.

In your predict_proba function of od_models.py,

DeepGravity/deepgravity/models/od_models.py

Line 77 in 8693536

probs = sm(torch.squeeze(self.forward(x), dim=-1))

Your input to the softmax is from self.forward(x) , right? But the forward function is a single linear layer, as follows:

DeepGravity/deepgravity/models/od_models.py

Line 36 in 8693536

out = self.linear1(vX)

The linear layer is as follows, the output dim is 1, right?

DeepGravity/deepgravity/models/od_models.py

Line 33 in 8693536

self.linear1 = torch.nn.Linear(dim_w, 1)

So my question is: how to use softmax for a single value (1-dim), because it is not a vector? I still don't know how it works :)

Thanks again for your kindness and hope to get your reply soon!