receive a shard input matrix comprising a number of non-zero values equal to or less than a predetermined maximum non-zero threshold and having a dimension equal to or less than a predetermined dimension threshold, the non-zero threshold corresponding to a number of multiplier circuits of the sparse shard and the dimension threshold corresponding to a maximum matrix input size that the sparse shard can process;

receive a shard input vector comprising a plurality of vector values;

receive, for each of the multiplier circuits, a respective non-zero value of the shard input matrix;

generate, by the plurality of multiplier circuits, one or more products of vector values multiplied with the respective non-zero values of the shard input matrix; and

generate, as output to the sparse shard and using the one or more products, a shard output vector that is the product of applying the shard input vector to the shard input matrix.