Concentration of measure for non-linear random matrices with applications to neural networks and non-commutative polynomials

Key Points

• Concentration inequalities are established for non-linear random matrices, providing new insights into their statistical properties.
• Estimates are derived for linear spectral statistics of the conjugate kernel, with applications to both neural networks and polynomials.
• The analysis includes models of dependent random matrices, which enhances the understanding of their behavior under various conditions.
• This work highlights the relevance of these inequalities in fields like machine learning and theoretical computer science, pointing to broader applications.