Pruning a model is the process of sparsifying the weight matrices of the model’s layers, thereby reducing its storage size by packing weights more efficiently. Pruning sets a fraction of the values in the model’s weight matrices to zero.

Pruned weights can be represented more efficiently using a sparse representation rather than the typical dense representation. In a sparse representation, only non-zero values are stored, along with a bit mask, that takes the value 1 at the indices of the non-zero values. For example, if the weight values are {0, 7, 0, 0, 0, 0, 0, 56.3}, its sparse representation contains a bit mask with ones in the locations where the value is non-zero: 01000001b. This is accompanied by the non-zero data, which in the following example is a size-2 vector of value {7, 56.3}.

Creating a sparse representation

Creating a sparse representation.#

“Unstructured sparsity” is when weight values of lowest magnitude are set to zero from within the weight tensor as a whole, without adhering to any structure. On the other hand, certain constraints can be enforced while pruning, resulting in what is referred to as “structured sparsity”. A few of the common types include:

  • block sparsity: When weights are pruned in a grouped manner, such as in blocks of size 2, 4, and so on.

  • n:m sparsity: When weights are divided into blocks of size m and within each such block, n smallest values are chosen to be zero. For example, 3:4 sparsity would imply a 75% sparse level in which 3 values in each block of size 4 are set to zero.

While imposing more constraints, structured sparsity techniques could be advantageous for certain hardware in terms of latency performance.

Starting from iOS18/macOS15, the non zero float values in a sparse representation can be further compressed either using palettization or linear quantization, thereby providing further memory savings and improved runtime performance.

Feature Availability

Sparse weight representation for Core ML mlprogram models is available in iOS16/macOS13/watchOS9/tvOS16 and newer deployment target formats.