Towards this end, we adoptthe unconstrained-features model (UFM), a recent theoretical model for studying neural collapse, and introduce Simplex-Encoded-Labels Interpolation (SELI) as an invariant characterizationof theneuralcollapsephenomenon.

In this paper, we investigate the problem of cutting a tree originating from a pre-specified HC procedure through pairwise similarity queries generated by active learning algorithms.

The discovery of neural architectures from simple building blocks is a longstanding goal of Neural Architecture Search (NAS). Hierarchical search spaces are a promising step towards this goal but lack a unifying search space design framework and typically only search over some limited aspect of architectures. In this work, we introduce a unifying search space design framework based on context-free grammars that can naturally and compactly generate expressive hierarchical search spaces that are 100s of orders of magnitude larger than common spaces from the literature. By enhancing and using their properties, we effectively enable search over the complete architecture and can foster regularity. Further, we propose an efficient hierarchical kernel design for a Bayesian Optimization search strategy to efficiently search over such huge spaces.

The question of if and how rank collapse affects training is still largelyunanswered, anditsinvestigation isnecessary foramore comprehensive understanding ofthisarchitecture.

Recent work has shown that a much simpler model, simple graph convolution (SGC) (Wu et al., 2019),iscompetitivewithGCNs incommon graph machine learning benchmarks.

We also provide examples where biased estimators outperform their unbiased counterparts or where unbiased versions are simply not available. Finally, we demonstrate the effectiveness of our framework through experimental results that validate our theoretical findings.

However, a naive scheme to train such amodel results inadegenerate solution.