Convolution is one of the foundational operations in modern machine learning, but it is also a useful example of a broader engineering idea: many apparently specialized tensor operations can be reorganized into well-understood compute patterns that are easier to implement, optimize, and scale.

This article explains a practical way to implement 2D convolution by treating it as a structured form of matrix multiplication. The goal is not to promote a specific product or benchmark result, but to show a reusable optimization mindset for engineers building GPU compute kernels.

Key idea: A 1×1 convolution is effectively a matrix multiply, and larger K×K convolutions can be expressed as a sequence of matrix-like accumulations with careful attention to cache behavior and loop ordering.

Conv2D is everywhere in inference pipelines, image models, and feature extraction stages. Yet the implementation challenge is often less about the mathematical definition and more about the execution strategy: how data is laid out, how work is grouped, and how memory traffic is controlled.

A useful approach is to avoid treating convolution as a completely unique primitive. Instead, interpret it as a compute pattern closely related to matrix multiplication. This can reduce implementation complexity and create a clearer path for optimization.

A standard Conv2D operation can be described as applying a learned filter tensor across an input tensor to produce an output tensor.

Where: A is the input tensor of size N × H × W × C_in B is the weight tensor of size H_filter × W_filter × C_in × C_out C is the output tensor of size N × H_out × W_out × C_out

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