  Predictor-based methods have substantially enhanced Neural Architecture
Search (NAS) optimization. The efficacy of these predictors is largely
influenced by the method of encoding neural network architectures. While
traditional encodings used an adjacency matrix describing the graph structure
of a neural network, novel encodings embrace a variety of approaches from
unsupervised pretraining of latent representations to vectors of zero-cost
proxies. In this paper, we categorize and investigate neural encodings from
three main types: structural, learned, and score-based. Furthermore, we extend
these encodings and introduce \textit{unified encodings}, that extend NAS
predictors to multiple search spaces. Our analysis draws from experiments
conducted on over 1.5 million neural network architectures on NAS spaces such
as NASBench-101 (NB101), NB201, NB301, Network Design Spaces (NDS), and
TransNASBench-101. Building on our study, we present our predictor
\textbf{FLAN}: \textbf{Fl}ow \textbf{A}ttention for \textbf{N}AS. FLAN
integrates critical insights on predictor design, transfer learning, and
\textit{unified encodings} to enable more than an order of magnitude cost
reduction for training NAS accuracy predictors. Our implementation and
encodings for all neural networks are open-sourced at
\href{https://github.com/abdelfattah-lab/flan_nas}{https://github.com/abdelfattah-lab/flan\_nas}.
