All it knows is that it had to preserve the program semantics from the perspective of the memory model. You might ask the question - why didn't the compiler perform this optimization itself? It turns out that it's an illegal optimization to make, considering that the compiler can't understand the semantics of the algorithm. We actually gained more time than we expected! This implementation took 1,070 ms to execute, which was 67% of the time it took to execute the original. Review of the mathematical operationīefore we focus on the code, let's review the basics. Also, a \(1x1\) convolution can be cast as a matrix multiplication even without im2col. However, this approach can be made efficient using implicit im2col, resulting in an implicit GEMM convolution, which is implemented in some of the cuDNN algorithms for NVIDIA GPUs. This is very inefficient, because the im2col matrix needs to be generated, and takes up a lot of extra memory and time. For example, a classic approach for this is to preprocess the input using im2col, do a matrix multiplication, and then apply col2im. At its core, the fully-connected layer is based on a generalized matrix multiplication ( GEMM).Ĭonvolutions can also be cast as matrix multiplications. Since this blog is about machine learning and mostly deep learning, the primary application of interest to the reader will most likely be the implementation of fully-connected layers in neural networks. solving the all-pairs shortest path (APSP) problem.finding the transitive closure in graphs.developing search result ranking algorithms (e.g.decompositions such as SVD (since \(M=U \Sigma V^*\)), which can be used e.g.characteristic equations in differential equations are based on eigenvalue decomposition.
linear regression (both the analytical and the iterative solution)
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