<ul><li>A study introduces a schematic for translating between a given piecewise linear Morse function on a canonical polyhedral complex and a compatible discrete Morse function for ReLU neural networks.</li><li>The study expands computational tools for analyzing the topological properties of ReLU neural networks using discrete Morse theory.</li><li>An algorithm is introduced to determine if a given vertex in a canonical polyhedral complex corresponds to a piecewise linear Morse critical point.</li><li>New realizability results are provided for shallow ReLU neural networks with respect to sublevel set topology.</li></ul>

Combinatorial Regularity for Relatively Perfect Discrete Morse Gradient Vector Fields of ReLU Neural Networks

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