It's not an activation function, because it has the learnable weights of a linear projection (mat vec multiplication) and the clamping properties of an activation function all in one.
My personal issue with the proposal is that it essentially doubles the amount of memory needed on-chip.
Yat-Product GEMMV now needs to store the running total of the inner product and the norm of the input vectors. That's a big cost increase for something that might not improve performance all that much.
one simple usecase for them is physics-informed neural networks and neural ODEs, where using activation functions is discouraged, mainly because they aren't infinitly differentiable, and they use the tanh or the sin most of the time, this kernel i introduced works better then the neurons followed with a tanh to solve different PDEs
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
mlnomadpy•6mo ago
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.
MiniGPT with huggingface datasets streaming: https://www.kaggle.com/code/skywolfmo/yat-nnx-minigpt-finewe...
rytill•6mo ago
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.
russfink•6mo ago
julius•6mo ago
"The dot product itself is a geometrically impoverished measure, primarily capturing alignment while conflating magnitude with direction and often obscuring more complex structural and spatial relationships [10, 11, 4, 61, 17]. Furthermore, the way current activation functions achieve non-linearity can exacerbate this issue. For instance, ReLU (f (x) = max(0, x)) maps all negative pre-activations, which can signify a spectrum of relationships from weak dissimilarity to strong anti-alignment, to a single zero output. This thresholding, while promoting sparsity, means the network treats diverse inputs as uniformly orthogonal or linearly independent for onward signal propagation. Such a coarse-graining of geometric relationships leads to a tangible loss of information regarding the degree and nature of anti-alignment or other neg- ative linear dependencies. This information loss, coupled with the inherent limitations of the dot product, highlights a fundamental challenge."
mlnomadpy•6mo ago
mlnomadpy•6mo ago
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