Lightning Talks
summary
Models that accept variable sizes generalize across sizes only when two concrete conditions hold: task-model alignment (the target function is uniformly continuous under the model’s hidden pseudo metric) and the training and test distributions are close under that metric. Universal approximation for these architectures means continuity w.r.t specific metrics (e.g., normalized DeepSet ≈ Wasserstein, PointNet ≈ Hausdorff, plain DeepSet ≈ ℓ1), which explains why mean/moment tasks transfer under normalized DeepSet but diameter only under PointNet; simulations match these predictions.
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