A convolutional neural network is implemented on a graphics processing unit. The network is then trained through a series of forward and backward passes, with convolutional kernels and bias matrices modified on each backward pass according to a gradient of an error function. The implementation takes advantage of parallel processing capabilities of pixel shader units on a GPU, and utilizes a set of start-to-finish formulas to program the computations on the pixel shaders. Input and output to the program is done through textures, and a multi-pass summation process is used when sums are needed across pixel shader unit registers.