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How to calculate a meaningful distance between multidimensional tensors

You could try an earthmovers distance (https://en.m.wikipedia.org/wiki/Earth_mover%27s_distance) in 2d or 3d over the image? For example you could do this, but call sequentially (https://discuss....
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Should I need to interpret the word "metric" in "performance metric" rigorously?

"Metric" should be understood as "a function of the trained model and of a dataset which returns a number". For example, in reinforcement learning, one can use as an evaluation ...
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What inherent quality of a function makes it treated as either loss or evaluation metric?

Common loss functions, like the cross-entropy or mean squared error, are chosen because, if you minimize them, you are actually maximizing the likelihood of the parameters given the observed data. In ...
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Compare the efficiency of a trained ML model with a non-learning-based method for solving the same problem

The most generic answer to this question is: the same metrics you use to evaluate the quality of your model during training or in test phase. (Plus the timing of inference if you're referring to ...
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Does it make sense to use BLEU or ROUGE for any machine translation task?

Yes - and no. The important distinction is whether your data contains proper word boundaries and rigorous translation references. BLEU and ROGUE both work by comparing a candidate (ie, model output) ...
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