Which Format is Faster, Matlab (.mat) or NumPy (.npy)? I am working on a deep learning problem to detect cancer in images of size 250 x 250. I have hardware limitations and I have been running out of memory. 

I decided to convert my images to Matlab formatted files (".mat"), with some improvement; however, I still run out of memory. I have explored some resources that highly recommend using NumPy files (".npy").

It would be costly to convert my images to NumPy files, so I would like to make sure that converting will make a difference. I am not asking for memory enhancement algorithms (e.g. batching), just the memory difference between ".mat" and ".npy" files.
From my research:


both can store data in binary format
both store the data type of the data
I am unsure about compression ratios and load time, which seems to be the subtext of your question.


One thing you don't seem to address is what you are loading the data into, or whether you are considering moving from a MATLAB environment to Python environment or visa-versa.

That said, I found this post useful and thought it may be helpful to you if you have not seen it already.  https://stackoverflow.com/a/10997335/3259054 Perhaps you could write a small script to sample some files and see the difference.

Have you considered the HDF5 format?  If you are looking to make a change, you might as well test other options too and HDF5 has a lot of momentum towards becoming the de facto standard for scientific computing.

Finally, purely out of a desire to learn, why are you concerned about the file format if you have memory constraints?