Does Unsupervised Architecture Representation Learning Help Neural Architecture Search?
Abstract
Existing Neural Architecture Search (NAS) methods either encode neural architectures using discrete encodings that do not scale well, or adopt supervised learningbased methods to jointly learn architecture representations and optimize architecture search on such representations which incurs search bias. Despite the widespread use, architecture representations learned in NAS are still poorly understood. We observe that the structural properties of neural architectures are hard to preserve in the latent space if architecture representation learning and search are coupled, resulting in less effective search performance. In this work, we find empirically that pretraining architecture representations using only neural architectures without their accuracies as labels improves the downstream architecture search efficiency. To explain this finding, we visualize how unsupervised architecture representation learning better encourages neural architectures with similar connections and operators to cluster together. This helps map neural architectures with similar performance to the same regions in the latent space and makes the transition of architectures in the latent space relatively smooth, which considerably benefits diverse downstream search strategies.
1 Introduction
Unsupervised representation learning has been successfully used in a wide range of domains including natural language processing Mikolov et al. (2013); Devlin et al. (2019); Radford et al. (2018), computer vision Oord et al. (2016); He et al. (2019), robotic learning Finn et al. (2016); Jang et al. (2018), and network analysis Perozzi et al. (2014); Grover and Leskovec (2016). Although differing in specific data type, the root cause of such success shared across domains is learning good data representations that are independent of the specific downstream task. In this work, we investigate unsupervised representation learning in the domain of neural architecture search (NAS), and demonstrate how NAS search spaces encoded through unsupervised representation learning could benefit the downstream search strategies.
Standard NAS methods encode the search space with the adjacency matrix and focus on designing different downstream search strategies based on reinforcement learning Williams (1992), evolutionary algorithm Real et al. (2017), and Bayesian optimization Falkner et al. (2018) to perform architecture search in discrete search spaces. Such discrete encoding scheme is a natural choice since neural architectures are discrete. However, the size of the adjacency matrix grows quadratically as search space scales up, making downstream architecture search less efficient in large search spaces Elsken et al. (2019a). To reduce the search cost, recent NAS methods employ dedicated networks to learn continuous representations of neural architectures and perform architecture search in continuous search spaces Luo et al. (2018); Liu et al. (2019); Xie et al. (2019); He et al. (2020). In these methods, architecture representations and downstream search strategies are jointly optimized in a supervised manner, guided by the accuracies of architectures selected by the search strategies. However, these supervised architecture representation learningbased methods are biased towards weightfree operations (e.g., skip connections, maxpooling) which are often preferred in the early stage of the search process, resulting in lower final accuracies Guo et al. (2019); Shu et al. (2020); Zela et al. (2020b, a).
In this work, we propose arch2vec, a simple yet effective neural architecture search method based on unsupervised architecture representation learning. As illustrated in Figure 1, compared to supervised architecture representation learningbased methods, arch2vec circumvents the bias caused by joint optimization through decoupling architecture representation learning and architecture search into two separate processes. To achieve this, arch2vec uses a variational graph isomorphism autoencoder to learn architecture representations using only neural architectures without their accuracies. As such, it injectively captures the local structural information of neural architectures and makes architectures with similar structures (measured by edit distance) cluster better and distribute more smoothly in the latent space, which facilitates the downstream architecture search. We visualize the learned architecture representations in §4.1. It shows that architecture representations learned by arch2vec can better preserve structural similarity of local neighborhoods than its supervised architecture representation learning counterpart. In particular, it is able to capture topology (e.g. skip connections or straight networks) and operation similarity, which helps cluster architectures with similar accuracy.
We follow the NAS best practices checklist Lindauer and Hutter (2019) to conduct our experiments. We validate the performance of arch2vec on three commonly used NAS search spaces NASBench101 Ying et al. (2019), NASBench201 Dong and Yang (2020) and DARTS Liu et al. (2019) and two search strategies based on reinforcement learning (RL) and Bayesian optimization (BO). Our results show that, with the same downstream search strategy, arch2vec consistently outperforms its discrete encoding and supervised architecture representation learning counterparts across all three search spaces.
Our contributions are summarized as follows:

We propose a neural architecture search method based on unsupervised representation learning that decouples architecture representation learning and architecture search.

We show that compared to supervised architecture representation learning, pretraining architecture representations without using their accuracies is able to better preserve the local structure relationship of neural architectures and helps construct a smoother latent space.

The pretrained architecture embeddings considerably benefit the downstream architecture search in terms of efficiency and robustness. This finding is consistent across three search spaces, two search strategies and two datasets, demonstrating the importance of unsupervised architecture representation learning for neural architecture search.
The implementation of arch2vec is available at https://github.com/MSUMLSysLab/arch2vec.
2 Related Work
Unsupervised Representation Learning of Graphs. Our work is closely related to unsupervised representation learning of graphs. In this domain, some methods have been proposed to learn representations using local random walk statistics and matrix factorizationbased learning objectives Perozzi et al. (2014); Grover and Leskovec (2016); Tang et al. (2015); Wang et al. (2016); some methods either reconstruct a graph’s adjacency matrix by predicting edge existence Kipf and Welling (2016); Hamilton et al. (2017) or maximize the mutual information between local node representations and a pooled graph representation Veličković et al. (2019). The expressiveness of Graph Neural Networks (GNNs) is studied in Xu et al. (2019) in terms of their ability to distinguish any two graphs. It also introduces Graph Isomorphism Networks (GINs), which is proved to be as powerful as the WeisfeilerLehman test Weisfeiler and Lehman (1968) for graph isomorphism. Zhang et al. (2019) proposes an asynchronous message passing scheme to encode DAG computations using RNNs. In contrast, we injectively encode architecture structures using GINs, and we show a strong pretraining performance based on its highly expressive aggregation scheme. You et al. (2020) focuses on network generators that output relational graphs, and the predictive performance highly depends on the structure measures of the relational graphs. In contrast, we encode structural information of neural networks into compact continuous embeddings, and the predictive performance depends on how well the structure is injected into the embeddings.
Regularized Autoencoders. Autoencoders can be seen as energybased models trained with reconstruction energy LeCun et al. (2006). Our goal is to encode neural architectures with similar performance into the same regions of the latent space, and to make the transition of architectures in the latent space relatively smooth. To prevent degenerated mapping where latent space is free of any structure, there is a rich literature on restricting the lowenergy area for data points on the manifold Kavukcuoglu et al. (2010); Vincent et al. (2008); Kingma and Welling (2014); Makhzani et al. (2016); Ghosh et al. (2020). Here we adopt the popular variational autoencoder framework Kingma and Welling (2014); Kipf and Welling (2016) to optimize the variational lower bound w.r.t. the variational parameters, which as we show in our experiments acts as an effective regularization. While Simonovsky and Komodakis (2018); Wang et al. (2020) use graph VAE for the generative problems, we focus on mapping the finite discrete neural architectures into the continuous latent space regularized by KLdivergence such that each architecture is encoded into a unique area in the latent space.
Neural Architecture Search (NAS). As mentioned in §1, early NAS methods are built upon discrete encodings Zoph and Le (2017); Baker et al. (2017); Falkner et al. (2018); Real et al. (2019); Kandasamy et al. (2018), which face the scalability challenge Elsken et al. (2019b); Ren et al. (2020) in large search spaces. To address this challenge, recent NAS methods shift from conducting architecture search in discrete spaces to continuous spaces using different architecture encoders such as SRM Baker et al. (2018), MLP White et al. (2019), LSTM Luo et al. (2018) or GCN Shi et al. (2019); Wen et al. (2019). However, what lies in common under these methods is that the architecture representation and search direction are jointly optimized by the supervision signal (e.g., accuracies of the selected architectures), which could bias the architecture representation learning and search direction. White et al. (2020) emphasizes the importance of studying architecture encodings, and we focus on encoding adjacency matrixbased architectures into lowdimensional embeddings in the continuous space. Liu et al. (2020) shows that architectures searched without using labels are competitive to their counterparts searched with labels. Different from their approach which performs pretext tasks using image statistics, we use architecture reconstruction objective to preserve the local structure relationship in the latent space.
3 arch2vec
In this section, we describe the details of arch2vec, followed by two downstream architecture search strategies we use in this work.
3.1 Variational Graph Isomorphism Autoencoder
Preliminaries
We restrict our search space to the cellbased architectures. Following the configuration in NASBench101 Ying et al. (2019), each cell is a labeled DAG , with as a set of nodes and as a set of edges. Each node is associated with a label chosen from a set of predefined operations. A natural encoding scheme of cellbased neural architectures is an upper triangular adjacency matrix and an onehot operation matrix . This discrete encoding is not unique, as permuting the adjacency matrix and the operation matrix would lead to the same graph, which is known as graph isomorphism Weisfeiler and Lehman (1968).
Encoder
To learn a continuous representation that is invariant to isomorphic graphs, we leverage Graph Isomorphism Networks (GINs) Xu et al. (2019) to encode the graphstructured architectures given its better expressiveness. We augment the adjacency matrix as to transfer original directed graphs into undirected graphs, allowing bidirectional information flow. Similar to Kipf and Welling (2016), the inference model, i.e. the encoding part of the model, is defined as:
(1) 
We use the layer GIN to get the node embedding matrix :
(2) 
where , is a trainable bias, and MLP is a multilayer perception where each layer is a linearbatchnormReLU triplet. The node embedding matrix is then fed into two fullyconnected layers to obtain the mean and the variance of the posterior approximation in Eq. (1). During the inference, the architecture representation is derived by summing the representation vectors of all the nodes.
Decoder
Our decoder is a generative model aiming at reconstructing and from the latent variables :
(3) 
(4) 
where is the sigmoid activation, softmax(·) is the softmax activation applied rowwise, and indicates the operation selected from the predifined set of opreations at the n node. and are learnable weights and biases of the decoder.
3.2 Training Objective
In practice, our variational graph isomorphism autoencoder consists of a fivelayer GIN and a onelayer MLP. The details of the model architecture are described in §4. The dimensionality of the embedding is set to 16. During training, model weights are learned by iteratively maximizing a tractable variational lower bound:
(5) 
where as we assume that the adjacency matrix and the operation matrix are conditionally independent given the latent variable . The second term on the right hand side of Eq. (5) denotes the KullbackLeibler divergence Kullback and Leibler (1951) which is used to measure the difference between the posterior distribution and the prior distribution . Here we choose a Gaussian prior due to its simplicity. We use reparameterization trick Kingma and Welling (2014) for training since it can be thought of as injecting noise to the code layer. The random noise injection mechanism has been proved to be effective on the regularization of neural networks Sietsma and Dow (1991); An (1996); Kingma and Welling (2014). The loss is optimized using minibatch gradient descent over neural architectures.
3.3 Architecture Search Strategies
We use reinforcement learning (RL) and Bayesian optimization (BO) as two representative search algorithms to evaluate arch2vec on the downstream architecture search.
Reinforcement Learning (RL)
We use REINFORCE Williams (1992) as our RLbased search strategy as it has been shown to converge better than more advanced RL methods such as PPO Schulman et al. (2017) for neural architecture search. For RL, the pretrained embeddings are passed to the Policy LSTM to sample the action and obtain the next state (valid architecture embedding) using nearestneighborhood retrieval based on L2 distance to maximize accuracy as reward. We use a singlelayer LSTM as the controller and output a 16dimensional output as the mean vector to the Gaussian policy with a fixed identity covariance matrix. The controller is optimized using Adam optimizer Kingma and Ba (2015) with a learning rate of . The number of sampled architectures in each episode is set to 16 and the discount factor is set to 0.8. The baseline value is set to 0.95. The maximum estimated wallclock time for each run is set to seconds.
Bayesian Optimization (BO)
We use DNGO Snoek et al. (2015) as our BObased search strategy. We use a onelayer adaptive basis regression network with hidden dimension 128 to model distributions over functions. It serves as an alternative to Gaussian process in order to avoid cubic scaling Garnett et al. (2014). We use expected improvement (EI) Mockus (1977) as the acquisition function which is widely used in NAS Kandasamy et al. (2018); White et al. (2019); Shi et al. (2019). The best function value of EI is set to 0.95. During the search process, the pretrained embeddings are passed to DNGO to select the top5 architectures in each round of search, which are then added to the pool. The network is retrained for 100 epochs in the next round using the selected architectures in the updated pool. This process is iterated until the maximum estimated wallclock time is reached.
4 Experimental Results
We validate arch2vec on three commonly used NAS search spaces. The details of the hyperparameters we used for searching in each search space are included in Appendix .
NASBench101. NASBench101 Ying et al. (2019) is the first rigorous NAS dataset designed for benchmarking NAS methods. It targets the cellbased search space used in many popular NAS methods Zoph et al. (2018); Liu et al. (2018, 2019) and contains unique neural architectures. Each architecture comes with precomputed validation and test accuracies on CIFAR10. The cell consists of 7 nodes and can take on any DAG structure from the input to the output with at most 9 edges, with the first node as input and the last node as output. The intermediate nodes can be either 11 convolution, 33 convolution or 33 max pooling. We split the dataset into 90% training and 10% heldout test sets for arch2vec pretraining.
NASBench201. Different from NASBench101, the cellbased search space in NASBench201 Dong and Yang (2020) is represented as a DAG with nodes representing sum of feature maps and edges associated with operation transforms. Each DAG is generated by 4 nodes and 5 associated operations: 11 convolution, 33 convolution, 33 average pooling, skip connection and zero, resulting in a total of unique neural architectures. The training details for each architecture candidate are provided for three datasets: CIFAR10, CIFAR100 and ImageNet16120 Chrabaszcz et al. (2017). We use the same data split as used in NASBench101.
DARTS search space. The DARTS search space Liu et al. (2019) is a popular search space for largescale NAS experiments. The search space consists of two cells: a convolutional cell and a reduction cell, each with six nodes. For each cell, the first two nodes are the outputs from the previous two cells. The next four nodes contain two edges as input, creating a DAG. The network is then constructed by stacking the cells. Following Liu et al. (2018), we use the same cell for both normal and reduction cell, allowing roughly DAGs without considering graph isomorphism. We randomly sample 600,000 unique architectures in this search space following the mobile setting Liu et al. (2019). We use the same data split as used in NASBench101.
For pretraining, we use a fivelayer Graph Isomorphism Network (GIN) with hidden sizes of {128, 128, 128, 128, 16} as the encoder and a onelayer MLP with a hidden dimension of 16 as the decoder. The adjacency matrix is preprocessed as an undirected graph to allow bidirectional information flow. After forwarding the inputs to the model, the reconstruction error is minimized using Adam optimizer Kingma and Ba (2015) with a learning rate of . We train the model with batch size 32 and the training loss is able to converge well after 8 epochs on NASBench101, and 10 epochs on NASBench201 and DARTS. After training, we extract the architecture embeddings from the encoder for the downstream architecture search.
In the following, we first evaluate the pretraining performance of arch2vec (§4.1) and then the neural architecture search performance based on its pretrained representations (§4.2).
4.1 Pretraining Performance
Observation (1): We compare arch2vec with two popular baselines GAE Kipf and Welling (2016) and VGAE Kipf and Welling (2016) using three metrics suggested by Zhang et al. (2019): 1) Reconstruction Accuracy (reconstruction accuracy of the heldout test set), 2) Validity (how often a random sample from the prior distribution can generate a valid architecture), and 3) Uniqueness (unique architectures out of valid generations). As shown in Table 1, arch2vec outperforms both GAE and VGAE, and achieves the highest reconstruction accuracy, validity, and uniqueness across all the three search spaces. This is because encoding with GINs outperforms GCNs in reconstruction accuracy due to its better neighbor aggregation scheme; the KL term effectively regularizes the mapping from the discrete space to the continuous latent space, leading to better generative performance measured by validity and uniqueness. Given its superior performance, we stick to arch2vec for the remainder of our evaluation.
Observation (2):
We compare arch2vec with its supervised architecture representation learning counterpart on the predictive performance of the latent representations. This metric measures how well the latent representations can predict the performance of the corresponding architectures.
Being able to accurately predict the performance of the architectures based on the latent representations makes it easier to search for the highperformance points in the latent space.
Specifically, we train a Gaussian Process model with 250 sampled architectures to predict the performance of the other architectures, and report the predictive performance across 10 different seeds. We use RMSE and the Pearson correlation coefficient (Pearson’s r) to evaluate points with test accuracy higher than 0.8.
Figure 2 compares the predictive performance between arch2vec and its supervised counterpart on NASBench101.
As shown, arch2vec outperforms its supervised counterpart
Observation (3): In Figure 4, we plot the relationship between the L2 distance in the latent space and the edit distance of the corresponding DAGs between two architectures. As shown, for arch2vec, the L2 distance grows monotonically with increasing edit distance. This result indicates that arch2vec is able to preserve the closeness between two architectures measured by edit distance, which potentially benefits the effectiveness of the downstream search. In contrast, such closeness is not well captured by supervised architecture representation learning.
Observation (4): In Figure 4, we visualize the latent spaces of NASBench101 learned by arch2vec (left) and its supervised counterpart (right) in the 2dimensional space generated using tSNE. We overlaid the original colorscale with red (>92% accuracy) and black (<82% accuracy) for highlighting purpose. As shown, for arch2vec, the architecture embeddings span the whole latent space, and architectures with similar accuracies are clustered together. Conducting architecture search on such smooth performance surface is much easier and is hence more efficient. In contrast, for the supervised counterpart, the embeddings are discontinuous in the latent space, and the transition of accuracy is nonsmooth. This indicates that joint optimization guided by accuracy cannot injectively encode architecture structures. As a result, architecture does not have its unique embedding in the latent space, which makes the task of architecture search more challenging.
Observation (5): To provide a closer look at the learned latent space, Figure 5 visualizes the architecture cells decoded from the latent space of arch2vec (upper) and supervised architecture representation learning (lower). For arch2vec, the adjacent architectures change smoothly and embrace similar connections and operations. This indicates that unsupervised architecture representation learning helps model a smoothlychanging structure surface. As we show in the next section, such smoothness greatly helps the downstream search since architectures with similar performance tend to locate near each other in the latent space instead of locating randomly. In contrast, the supervised counterpart does not group similar connections and operations well and has much higher edit distances between adjacent architectures. This biases the search direction since dependencies between architecture structures are not well captured.
4.2 Neural Architecture Search (NAS) Performance
NAS results on NASBench101.
For fair comparison, we reproduced the NAS methods which use the adjacency matrixbased encoding in Ying et al. (2019)
As shown in Figure 6, BOHB and RE are the two bestperforming methods using the adjacency matrixbased encoding. However, they perform slightly worse than supervised architecture representation learning because the highdimensional input may require more observations for the optimization. In contrast, supervised architecture representation learning focuses on lowdimensional continuous optimization and thus makes the search more efficient. As shown in Figure 6 (left), arch2vec considerably outperforms its supervised counterpart and the adjacency matrixbased encoding after wall clock seconds. Figure 6 (right) further shows that arch2vec is able to robustly achieve the lowest final test regret after seconds across 500 independent runs.
Table 2 shows the search performance comparison in terms of number of architecture queries. While RLbased search using discrete encoding suffers from the scalability issue, arch2vec encodes architectures into a lower dimensional continuous space and is able to achieve competitive RLbased search performance with only a simple onelayer LSTM controller. For NAO Luo et al. (2018), its performance is inferior to arch2vec as it entangles structure reconstruction and accuracy prediction together, which inevitably biases the architecture representation learning.
NAS results on NASBench201. For CIFAR10, we follow the same implementation established in NASBench201 by searching based on the validation accuracy obtained after 12 training epochs with converged learning rate scheduling. The search budget is set to seconds. The NAS experiments on CIFAR100 and ImageNet16120 are conducted with a budget that corresponds to the same number of queries used in CIFAR10. As listed in Table 3, searching with arch2vec leads to better validation and test accuracy as well as reduced variability among different runs on all datasets.
NAS results on DARTS search space.
Similar to White et al. (2019), we set the budget to 100 queries in this search space. In each query, a sampled architecture is trained for 50 epochs and the average validation error of the last 5 epochs is computed. To ensure fair comparison with the same hyparameters setup, we retrained the architectures from works that exactly
5 Conclusion
arch2vec is a simple yet effective neural architecture search method based on unsupervised architecture representation learning. By learning architecture representations without using their accuracies, it constructs a more smoothlychanging architecture performance surface in the latent space compared to its supervised architecture representation learning counterpart. We have demonstrated its effectiveness on benefiting different downstream search strategies in three NAS search spaces. We suggest that it is desirable to take a closer look at architecture representation learning for neural architecture search. It is also possible that designing neural architecture search method using arch2vec with a better search strategy in the continuous space will produce better results.
6 Acknowledgement
We would like to thank the anonymous reviewers for their helpful comments. This work was partially supported by NSF Awards CNS1617627, CNS1814551, and PFI:BIC1632051.
Broader Impact
In this paper, we challenge the common practice in neural architecture search and ask the question: does unsupervised architecture representation learning help neural architecture search? We approach this question through two sets of experiments: 1) the predictive performance comparison and 2) the neural architecture search efficiency and robustness comparison of the learned architecture representations using supervised and unsupervised learning. In both experiments, we found unsupervised architecture representation learning performs reasonably well. Current NAS methods are typically restricted to some small search blocks such as Inception cell or ResNet block, and most of them perform equally well with enough human expertise under this setup. With the drastically increased computational power, the design of the search space will be more complex Radosavovic et al. (2020) and therefore hugely increases the search complexity. In such case, unsupervised architecture representation learning may benefit many downstream applications where the search space contains billions of network architectures, with only a few of them trained with annotated data to obtain the accuracy. Supervised optimization in such large search spaces might be less effective . In the future, we suggest more work to be done to investigate unsupervised neural architecture search with different meaningful pretext tasks on larger search spaces. A better pretraining strategy for neural architectures leveraging graph neural networks seems to be a promising direction, as the unsupervised learning method introduced in our paper has already shown its simplicity and effectiveness.
Appendix A Pretraining and search details on each search space
As described in §3, we use adjacency matrix and operation matrix as inputs to our neural architecture encoder (§3.1). In this section, we present the search details for NASBench101 [65], NASBench201 [8] and DARTS [32] search spaces.
a.1 NASBench101
We followed the encoding scheme in NASBench101 [65]. Specifically, a cell in NASBench101 is represented as a directed acyclic graph (DAG) where nodes represent operations and edges represent data flow. A uppertriangular binary matrix is used to encode edges. A operation matrix is used to encode operations, input, and output, with the order as {input, 1 1 conv, 3 3 conv, 3 3 maxpool (MP), output}. For cells with less than nodes, their adjacency and operator matrices are padded with trailing zeros. Figure 7 shows an example of a 7node cell in NASBench101 search space and its corresponding adjacency and operation matrices.
For RLbased search, we use REINFORCE [62] as the search strategy. We use a onelayer LSTM with hidden dimension 128 as the controller and output a 16dimensional output as the mean vector to the Gaussian policy with a fixed identity covariance matrix. The controller is optimized using Adam optimizer [23] with learning rate . The number of sampled architectures in each episode is set to 16 and the discount factor is set to 0.8. The baseline value is set to 0.95. The maximum estimated wallclock time for each run is set to seconds.
For BObased search, we use DNGO [51] as the search strategy. We use a onelayer fully connected network with hidden dimension 128 to perform adaptive basis function regression. We randomly sample 16 architectures at the beginning, and select the top 5 bestperforming architectures and then add them to the architecture pool in each architecture sampling iteration. The network is optimized using selected architecture samples in the pool using Adam optimizer with learning rate and trained for 100 epochs in each architecture sampling iteration. The best function value of expected improvement (EI) is set to 0.95. We use the same time budget used in RLbased search.
a.2 NASBench201
Different from NASBench101, NASBench201 [8] employs a fixed cellbased DAG representation of neural architectures, where nodes represent the sum of feature maps and edges are associated with operations that transform the feature maps from the source node to the destination node. To represent the architectures in NASBench201 with discrete encoding that is compatible with our neural architecture encoder, we first transform the original DAG in NASBench201 into a DAG with nodes representing operations and edges representing data flow as the ones in NASBench101. We then use the same discrete encoding scheme in NASBench101 to encode each cell into an adjacency matrix and operation matrix. An example is shown in Figure 8. The hyperparameters we used for pretraining on NASBench201 are the same as described in §4.
For RLbased search, the search is stopped when it reaches the time budget , , seconds for CIFAR10, CIFAR100, and ImageNet16200, respectively. For CIFAR10, we follow the same implementation established in NASBench201 by searching based on the validation accuracy obtained after 12 training epochs with converged learning rate scheduling. The discount factor and the baseline value is set to 0.4. All the other hyperparameters are the same as described in §A.1.
For BObased search, we initially sample 16 architectures and select the bestperforming architecture to the pool in each iteration. The best function value of EI is set to 1.0 for all datasets. We use the same search budget as used in RLbased search. All the other hyperparameters are the same as described in §A.1.
a.3 DARTS Search Space
The cell in the DARTS search space has the following property: two input nodes are from the output of two previous cells; each intermediate node is connected by two predecessors, with each connection associated with one operation; the output node is the concatenation of all of the intermediate nodes within the cell [32].
Based on these properties, a uppertriangular binary matrix is used to encode edges and a operation matrix is used to encode operations, with the order as {, , zero, 3 3 maxpool, 3 3 averagepool, identity, 3 3 separable conv, 5 5 separable conv, 3 3 dilated conv, 5 5 dilated conv, }. An example is shown in Figure 9. Following [31], we use the same cell for both normal and reduction cell, allowing roughly DAGs without considering graph isomorphism. We randomly sample 600,000 unique architectures in this search space following the mobile setting [32]. The hyperparameters we used for pretraining on DARTS search space are the same as described in §4.
We set the computational budget to 100 architecture queries in this search space. In each query, a sampled architecture is trained for 50 epochs and the average validation accuracy of the last 5 epochs is computed. All the other hyperparamers we used for RLbased search and BObased search are the same as described in §A.1.
Appendix B More details on pretraining evaluation metrics
We split the the dataset into 90% training and 10% heldout test sets for arch2vec pretraining on each search space. In §4.1, we evaluate the pretraining performance of arch2vec using three metrics suggested by [69]: 1) Reconstruction Accuracy (reconstruction accuracy of the heldout test set) which measures how well the embeddings can errorlessly remap to the original structures; 2) Validity (how often a random sample from the prior distribution can generate a valid architecture) which measures the generative ability the model; and 3) Uniqueness (unique architectures out of valid generations) which measures the smoothness and diversity of the generated samples.
To compute Reconstruction Accuracy, we report the proportion of the decoded neural architectures of the heldout test set that are identical to the inputs. To compute Validity, we randomly pick 10,000 points generated by the Gaussian prior and then apply std() + mean(), where are the encoded means of the training data. It scales the sampled points and shifts them to the center of the embeddings of the training set. We report the proportion of the decoded architectures that are valid in the search space. To compute Uniqueness, we report the proportion of the unique architectures out of valid decoded architectures.
The validity check criteria varies across different search spaces. For NASBench101 and NASBench201, we use the NASBench101
Appendix C Best found cells and transfer learning results on ImageNet
Figure 10 shows the best cell found by arch2vec using RLbased and BObased search strategy. As observed in [41], the shapes of normalized empirical distribution functions (EDFs) for NAS design spaces on ImagetNet [6] match their CIFAR10 counterparts. This suggests that NAS design spaces developed on CIFAR10 are transferable to ImageNet [41]. Therefore, we evaluate the performance of the best cell found on CIFAR10 using arch2vec for ImageNet. In order to compare in a fair manner, we consider the mobile setting [71, 43, 32] where the number of multiplyadd operations of the model is restricted to be less than 600M. We follow [28] to use the exactly same training hyperparameters used in the DARTS paper [32]. Table 5 shows the transfer learning results on ImageNet. With comparable computational complexity, arch2vecRL and arch2vecBO outperform DARTS [32] and SNAS [63] methods in the DARTS search space, and is competitive among all cellbased NAS methods under this setting.
Appendix D More visualization results of each search space
NASBench101. In Figure 11, we visualize three randomly selected pairs of sequences of architecture cells decoded from the learned latent space of arch2vec (upper) and supervised architecture representation learning (lower) on NASBench101. Each pair starts from the same point, and each architecture is the closest point of the previous one in the latent space excluding previously visited ones. As shown, architecture representations learned by arch2vec can better capture topology and operation similarity than its supervised architecture representation learning counterpart. In particular, Figure 11 (a) and (b) show that arch2vec is able to better cluster straight networks, while supervised learning encodes straight networks and networks with skip connections together in the latent space.
NASBench201. Similarly, Figure 12 shows the visualization of five randomly selected pairs of sequences of decoded architecture cells using arch2vec (upper) and supervised architecture representation learning (lower) on NASBench201. The red mark denotes the change of operations between consecutive samples. Note that the edge flow in NASBench201 is fixed; only the operator associated with each edge can be changed. As shown, arch2vec leads to a smoother local change of operations than its supervised architecture representation learning counterpart.
DARTS Search Space. For the DARTS search space, we can only visualize the decoded architecture cells using arch2vec since there is no architecture accuracy recorded in this largescale search space. Figure 13 shows an example of the sequence of decoded neural architecture cells using arch2vec. As shown, the edge connections of each cell remain unchanged in the decoded sequence, and the operation associated with each edge is gradually changed. This indicates that arch2vec preserves the local structural similarity of neighborhoods in the latent space.
Footnotes
 The RMSE and Pearson’s r are: 0.0380.025 / 0.530.09 for the supervised architecture representation learning, and 0.0180.001 / 0.670.02 for arch2vec. A smaller RMSE and a larger Pearson’s r indicates a better predictive performance.
 https://github.com/automl/nas_benchmarks
 https://github.com/quark0/darts/blob/master/cnn/train.py
 https://github.com/googleresearch/nasbench/blob/master/nasbench/api.py
 https://github.com/DXY/NASBench201/blob/v1.1/nas_201_api/api.py
References
 (1996) The effects of adding noise during backpropagation training on a generalization performance. In Neural Computation, Cited by: §3.2.
 (2017) Designing neural network architectures using reinforcement learning. In ICLR, Cited by: §2.
 (2018) Accelerating neural architecture search using performance prediction. In ICLR Workshop, Cited by: §2.
 (2012) Random search for hyperparameter optimization. In JMLR, Cited by: §4.2, Table 3.
 (2017) A downsampled variant of imagenet as an alternative to the cifar datasets. In arXiv:1707.08819, Cited by: §4.
 (2009) ImageNet: A LargeScale Hierarchical Image Database. In CVPR, Cited by: Appendix C, §4.2.
 (2019) Bert: pretraining of deep bidirectional transformers for language understanding. In ACL, Cited by: §1.
 (2020) NASBench201: extending the scope of reproducible neural architecture search. In ICLR, Cited by: §A.2, Appendix A, §1, §4.
 (2019) Neural architecture search: a survey. In JMLR, Cited by: §1.
 (2019) Neural architecture search: a survey. In JMLR, Cited by: §2.
 (2018) BOHB: robust and efficient hyperparameter optimization at scale. In ICML, Cited by: §1, §2, §4.2, Table 3.
 (2016) Unsupervised learning for physical interaction through video prediction. In NeurIPS, Cited by: §1.
 (2014) Active learning of linear embeddings for gaussian processes. In UAI, Cited by: §3.3.2.
 (2020) From variational to deterministic autoencoders. In ICLR, Cited by: §2.
 (2016) Node2vec: scalable feature learning for networks. In ACM SIGKDD, Cited by: §1, §2.
 (2019) Single path oneshot neural architecture search with uniform sampling. In arXiv:1904.00420, Cited by: §1.
 (2017) Inductive representation learning on large graphs. In NeurIPS, Cited by: §2.
 (2020) MiLeNAS: efficient neural architecture search via mixedlevel reformulation. In CVPR, Cited by: §1.
 (2019) Momentum contrast for unsupervised visual representation learning. In arXiv:1911.05722, Cited by: §1.
 (2018) Grasp2vec: learning object representations from selfsupervised grasping. In arXiv:1811.06964, Cited by: §1.
 (2018) Neural architecture search with bayesian optimisation and optimal transport. In NeurIPS, Cited by: §2, §3.3.2.
 (2010) Learning convolutional feature hierarchies for visual recognition. In NeurIPS, Cited by: §2.
 (2015) Adam: a method for stochastic optimization. In ICLR, Cited by: §A.1, §3.3.1, §4.
 (2014) Autoencoding variational bayes. In ICLR, Cited by: §2, §3.2.
 (2016) Variational graph autoencoders. In NeurIPS Workshop, Cited by: §2, §2, §3.1.2, §4.1, Table 1.
 (1951) On information and sufficiency. In Annals of Mathematical Statistics, Cited by: §3.2.
 (2006) A tutorial on energybased learning. In Predicting Structured Data, Cited by: §2.
 (2019) Random search and reproducibility for neural architecture search. In UAI, Cited by: Appendix C, Table 4.
 (2019) Best practices for scientific research on neural architecture search. In arXiv:1909.02453, Cited by: §1.
 (2020) Are labels necessary for neural architecture search?. In arXiv:2003.12056, Cited by: §2.
 (2018) Progressive neural architecture search. In ECCV, Cited by: §A.3, §4, §4.
 (2019) DARTS: differentiable architecture search. In ICLR, Cited by: §A.3, §A.3, Appendix A, Table 5, Appendix C, §1, §1, Table 4, §4, §4.
 (2018) Neural architecture optimization. In NeurIPS, Cited by: §1, §2, §4.2, Table 2.
 (2016) Adversarial autoencoders. In ICLR, Cited by: §2.
 (2013) Distributed representations of words and phrases and their compositionality. In NeurIPS, Cited by: §1.
 (1977) On bayesian methods for seeking the extremum and their application.. In IFIP Congress, Cited by: §3.3.2.
 (2016) Conditional image generation with pixelcnn decoders. In NeurIPS, Cited by: §1.
 (2014) DeepWalk: online learning of social representations. In ACM SIGKDD, Cited by: §1, §2.
 (2018) Efficient neural architecture search via parameter sharing. In ICML, Cited by: Table 4.
 (2018) Improving language understanding by generative pretraining. In OpenAI Blog, Cited by: §1.
 (2019) On network design spaces for visual recognition. In ICCV, Cited by: Appendix C.
 (2020) Designing network design spaces. In CVPR, Cited by: Broader Impact.
 (2019) Regularized evolution for image classifier architecture search. In AAAI, Cited by: Table 5, Appendix C, §2, §4.2, Table 3.
 (2017) Largescale evolution of image classifiers. In ICML, Cited by: §1.
 (2020) A comprehensive survey of neural architecture search: challenges and solutions. In arXiv:2006.02903, Cited by: §2.
 (2017) Proximal policy optimization algorithms. In arXiv:1707.06347, Cited by: §3.3.1.
 (2019) Efficient samplebased neural architecture search with learnable predictor. In arXiv:1911.09336, Cited by: §2, §3.3.2.
 (2020) Understanding architectures learnt by cellbased neural architecture search. In ICLR, Cited by: §1.
 (1991) Creating artificial neural networks that generalize. In Neural Networks, Cited by: §3.2.
 (2018) GraphVAE: towards generation of small graphs using variational autoencoders. In arXiv:1802.03480, Cited by: §2.
 (2015) Scalable bayesian optimization using deep neural networks. In ICML, Cited by: §A.1, §3.3.2.
 (2015) LINE: largescale information network embedding.. In WWW, Cited by: §2.
 (2008) Visualizing data using tSNE. In JMLR, Cited by: Figure 4.
 (2019) Deep Graph Infomax. In ICLR, Cited by: §2.
 (2008) Extracting and composing robust features with denoising autoencoders. In ICML, Cited by: §2.
 (2016) Structural deep network embedding. In KDD, Cited by: §2.
 (2020) Graphdriven generative models for heterogeneous multitask learning. In AAAI, Cited by: §2.
 (1968) A reduction of a graph to a canonical form and an algebra arising during this reduction.. In NauchnoTechnicheskaya Informatsia, Cited by: §2, §3.1.1.
 (2019) Neural predictor for neural architecture search. In arXiv:1912.00848, Cited by: §2.
 (2020) A study on encodings for neural architecture search. In NeurIPS, Cited by: §2.
 (2019) BANANAS: bayesian optimization with neural architectures for neural architecture search. In arXiv:1910.11858, Cited by: §2, §3.3.2, §4.2, Table 2, Table 4.
 (1992) Simple statistical gradientfollowing algorithms for connectionist reinforcement learning. In Machine Learning, Cited by: §A.1, §1, §3.3.1, §4.2, Table 3.
 (2019) SNAS: stochastic neural architecture search. In ICLR, Cited by: Table 5, Appendix C, §1, Table 4.
 (2019) How powerful are graph neural networks?. In ICLR, Cited by: §2, §3.1.2.
 (2019) NASBench101: towards reproducible neural architecture search. In ICML, Cited by: §A.1, Appendix A, §1, §3.1.1, §4.2, Table 2, §4.
 (2020) Graph structure of neural networks. In ICML, Cited by: §2.
 (2020) Understanding and robustifying differentiable architecture search. In ICLR, Cited by: §1.
 (2020) NASbench1shot1: benchmarking and dissecting oneshot neural architecture search. In ICLR, Cited by: §1.
 (2019) Dvae: a variational autoencoder for directed acyclic graphs. In NeurIPS, Cited by: Appendix B, §2, §4.1.
 (2017) Neural architecture search with reinforcement learning. In ICLR, Cited by: §2.
 (2018) Learning transferable architectures for scalable image recognition. In CVPR, Cited by: Table 5, Appendix C, §4.