Analysis of kinetic models for label switching and stochastic gradient descent

Figure 1.  Solutions with fixed label and convergence in semilogarithmic scale towards stationary states given by $ d = 1 $ with quadratic potentials $ f(x, s) = \frac s2|x - s|^2 $ and $ f(x, s) = sx^2 $, $ S = \left\{ {1, 2} \right\}$ and $ \mu = Bern(p) $ compared with the estimate provided by theorem 3.2

Figure 2.  Stationary state of example 4 with $ v = (0, 1) $ and $ p = 0.7 $. The red dots represent the support of this state

Figure 3.  Stationary state of example 4 with v = (1; 1) and p = 0:7. The red dots represent the support of this state

Figure 4.  Solutions for a fixed label to equation (2) with $ f(x, s) = \frac s2|x - s|^2 $: in the first two figures the solutions with $ K = 10 $ and $ K = 10^9 $, in the figure below the corresponding solution of the gradient flow as discussed in subsection 5.1

Figure 5.  Convergence in semilogarithmic scale given by $ d = 1 $ with quadratic potentials $ f(x, s) = \frac s2|x - s|^2 $ and $ f(x, s) = sx^2 $, $ K(t) = 1 + t $, $ S = \left\{ {1, 2} \right\} $ and $ \mu = Bern(0.5) $ towards $ \delta_{5/3} $ and $ \delta_0 $ compared with the theoretical estimate of subsection 5.3