To validate the effectiveness of SHOT, we conduct empirical tests on standard few-shot learning tasks and qualitatively analyze its dynamics.

Bounding and predicting the generalization gap of overparameterized neural networks remains a central open problem in theoretical machine learning. There is a recent and growing body of literature that proposes the framework of fractals to model optimization trajectories of neural networks, motivating generalization bounds and measures based on the fractal dimension of the trajectory. Notably, the persistent homology dimension has been proposed to correlate with the generalization gap.

Offline model-based optimization seeks to optimize against a learned surrogate model without querying the true oracle objective function during optimization.

For example, while prior work has suggested that theglobally optimal VAEsolution canlearn thecorrect manifold dimension, anecessary (butnotsufficient)condition forproducing samplesfrom the true data distribution, this has never been rigorously proven. Moreover, it remains unclear how such considerations would change when various types of conditioning variablesare introduced, or when the data support is extended to a union of manifolds (e.g., as is likely the case for MNIST digits and related). In this work, we address these points by first proving that VAE global minima are indeed capable of recovering the correct manifold dimension.

We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks.

We genuinely appreciate all three reviewers' (#1,#2,#3,#4) valuable suggestions to strengthen our paper. More details are referred to Reviewer #3's Q2. We sincerely appreciate your suggestion and will revise the caption in figure 4 for better readability. Reply: It is a great observation. Thus, IL appears to be a main contributor for L2O generalizing across different optimizees.