Yunye Gong ^1* Michael Yao ² Ruyi Lian ² Xiao Lin ¹ Chao Chen ² Ajay Divakaran ¹ Yi Yao ¹

• ¹ SRI International, Menlo Park, United States
• ² Stony Brook University, Stony Brook, New York, United States

Manifold representation learning holds great promise for theoretical understanding and characterization of deep neural networks’ behaviors through the lens of geometries. However, data scarcity remains a major challenge in manifold analysis especially for data and applications with real-world complexity. To address this issue, we propose manifold representation meta-learning (MRML) based on autoencoders to recover the underlying manifold structures without uniformly or densely sampled data. Specifically, we adopt episodic training, following model agnostic meta-learning, to meta-learn autoencoders that are generalizable to unseen samples specifically corresponding to regions with low-sampling density. We demonstrate the effectiveness of MRML via empirical experiments on LineMOD, a dataset curated for 6-D object pose estimation. We also apply topological metrics based on persistent homology and neighborhood graphs for quantitative assessment of manifolds reconstructed by MRML. In comparison to state-of-the-art baselines, our proposed approach demonstrates improved manifold reconstruction better matching the data manifold by preserving prominent topological features and relative proximity of samples.