# Entropy of a Multidimensional Tensor

I’m looking to compute the discrete entropy (not cross-entropy) of a multidimensional tensor in my loss function. Consider the tensor to have shape `BATCH_S x D`, where each data point is a `D` dimensional vector, and I have `BATCH_S` of them. The formula requires me to compute the probability of seeing each data point, and I can’t seem to find a way to do this while retaining the ability to do a backward pass. To do so, all I need is the frequency of each element because I can divide that by the sum of the frequencies.

There’s torch.histc, but that doesn’t work for multidimensional data, and neither does torch.bincount. There’s also torch.unique which has the `return_count` optional param, but that’s has no `grad_fn`.

Any help is appreciated! Thanks

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did you find a solution to this? I have the same question

No they are inherently non-differentiable functions as they require binning (and uses an indicator function). Take a look at this paper which looks at a continuous approximation of mutual information, which is a function of entropy. You can approximate the indicator function (required for binning) with a triangular kernel function, but you will need to derive your own backward function.