I was able to create a new kernel that allows you to learn non-linearity without using activation functions, making the models whitebox, and without any information loss.
they are one of the reasons neural networks are blackbox,
we lose information about the data manifold the deeper we go in the network, making it impossible to trace back the output
this preprint is not coming from a standpoint of optimizing the inference/compute, but from trying to create models that we can interpret in the future and control
I misread this as if "there is no non-linearity". there is still non-linearity, it is just renamed and reshuffled into new operators. basically renaming apples into oranges.
basicly the real "non-linearity" in deep learning have always been the orthogonality, squashing functions make it easy for the neurons to tap into the orthogonality, while most of the activation functions "lie" about their orthogonality by setting the dot product score to "0", and a dot product of 0 between two vectors means they are orthogonal (linear indep)
what i did was rely on both the angular information and spatial information between the input x and the weight w to measure how "similar" they are.
the lower bound of the yat-product is 0, and it is achieved only when two vectors are orthogonal and away
One interesting thing to notice is how you can remodel xor into being a linear function by using u + v as input 1 and u * v as input 2 which means it can be represented in a NN without a hidden layer. And not only xor, it keeps all other logic gates simple. So only by transforming inputs one can reduce network complexity. Perhaps a field ripe for research.
indeed,
there is an extensive work done in kernel learning that is facinating
and one of the applications that still do these transformations are satellite imagery/multispectral imagery, you can get more information just from calculating the ndvi from the different bands of your image, which make it easy for your models to make decisions
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[ 3.4 ms ] story [ 24.6 ms ] threadI was able to create a new kernel that allows you to learn non-linearity without using activation functions, making the models whitebox, and without any information loss.
MiniGPT with huggingface datasets streaming: https://www.kaggle.com/code/skywolfmo/yat-nnx-minigpt-finewe...
To my knowledge they’re a negligible portion of the total compute during training or inference and work well to provide non-linearity.
Very open to learning more.
this preprint is not coming from a standpoint of optimizing the inference/compute, but from trying to create models that we can interpret in the future and control
what i did was rely on both the angular information and spatial information between the input x and the weight w to measure how "similar" they are.
the lower bound of the yat-product is 0, and it is achieved only when two vectors are orthogonal and away