Providing flexible matrix processors for performing neural network convolution in matrix-processor-based devices is disclosed. In this regard, a matrix-processor-based device provides a central processing unit (CPU) and a matrix processor. The matrix processor reorganizes a plurality of weight matrices and a plurality of input matrices into swizzled weight matrices and swizzled input matrices, respectively, that have regular dimensions natively supported by the matrix processor. The matrix-processor-based device then performs a convolution operation using the matrix processor to perform matrix multiplication/accumulation operations for the regular dimensions of the weight matrices and the input matrices, and further uses the CPU to execute instructions for handling the irregular dimensions of the weight matrices and the input matrices (e.g., by executing a series of nested loops, as a non-limiting example). The matrix-processor-based device thus provides efficient hardware acceleration by taking advantage of dimensional regularity, while maintaining the flexibility to handle different variations of convolution.