<ul><li>Non-linear versions of log-Sobolev inequalities provide global exponential long-time convergence to free energy minimizers.</li><li>These versions do not hold when the free energy has critical points that are not global minimizers.</li><li>The research extends the arguments and establishes local log-Sobolev inequalities for the granular media equation in certain cases.</li><li>The analysis shows exponential convergence to stationary solutions in both mean-field and kinetic equations.</li></ul>

Research on Convergence rates in Machine Learning research part3

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