Sequential Euclidean connections with exponential memory: distributional performance and adversarial robustness

Points in the unit ball of $\mathbb R^d$ are processed sequentially. Each new point $p_i$ is connected to a state $x_{i-1}$ that summarizes earlier observations, after which $x_i=γx_{i-1}+(1-γ)p_i$, with $0\leqγ\leq1$. The cost is the sum of the $α$-powers of the connection lengths. This constant-ga