Effect of Spherical Parameter Space on Number of Non-Forgetting Tasks and Capacity of Continual Learning

We propose a continuous learning formulation for $T$ non-forgetting tasks with the spherical parameter space $\mathbb{S}^{d-1}(\sqrt{d})$ in asymptotic regime $d\rightarrow \infty$. Each task $i$ has an optimum $\bmΘ_i$, minimizing its corresponding loss function $R_i(\bm{w})$ on sphere. We reduce e