Evaluating machine learning models requires evaluation data.

Figure 1: ( A) Protein backbone residue with three backbone atoms represented by a coordinate frame.

Given a convex body, generate samples from the body according to structured densities is a fundamental problem in computer science and machine learning.

Recent studies have revealed that properties of training trajectories can be indicative of generalization.

Eqn. 3) is equivalent to optimizing CL (InfoNCE, cf. To complete the proof, we start with giving some important notations and theorem. Here we simply disregard the constant term present in Eqn. 4 as it does not impact optimization, and From the Thm.3.2, we have the equivalence between InfoNCE and CL-DRO. By using McDiarmid's inequality in Thm A.4,for any ϵ, we have: While Corollary 3.4 has already been proven in [ We start with introducing a useful lemma. Then the CL-DRO objective is the tight variational estimation of ϕ -divergence.

Substituting this value of into Theorem D.1, we get that the sampler A

We propose new width-based planning and learning algorithms inspired from a careful analysis of the design decisions made by previous width-based planners.