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 each task $i$ to an acceptable loss region modeled by a geodesic ball $B_{\bmΘ_i}(r_i(d))$ on $\mathbb{S}^{d-1}(\sqrt{d})$ centered at $\bmΘ_i$ with radius $r_i(d)$. To model task dependencies (similarities), task optima $\bmΘ_i$ are distributed by a Neyman-Scott clustered point process $Φ$. Cluster centers $\{\bm{Y}_j\}_{j=1}^{N_p}$ form a homogeneous Poisson point process on sphere, while intr...
| Authors | Nazanin Mirhosseini |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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