Training artificial neural networks with constraints

A computer-implemented system comprising a machine learning model, the system comprising one or more microprocessors for:

• training the machine learning model using input data to derive a parametric function that minimizes error across output data associated with predicted output values,
• the machine learning model using a neural network constructed as a directed graph, the directed graph comprised of a plurality of nodes and edges that connect a source node to a destination node in the plurality of nodes, the edges including one or more conforming edges and non-conforming edges;
• adjusting weight parameters associated with the edges responsive to the input data, the output data, and the predicted output values, vis-à-vis a loss function associated with the predicted output values;
• determining that a first connection between two nodes in the plurality of nodes is either conforming or non-conforming based on a constraint formula related to the weight parameters;
• and
• sparsifying one or more edges by adjusting the corresponding weight parameters associated with the one or more edges towards a first value, in response to determining that the one or more edges are non-conforming edges,
• wherein the sparsifying is performed iteratively to meet one or more constraints associated with the weight parameters such that one or more constraint operators and a definition for a conforming edge and a non-conforming edge is applied (a) network-wide, (b) per-layer, or (c) per weight parameters for a node.