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Title: DARTS: Differentiable Architecture Search

Paper content:
This paper addresses the scalability challenge of architecture search by formulating the task in a differentiable manner.
Unlike conventional approaches of applying evolution or reinforcement learning over a discrete and non-differentiable search space, our method is based on the continuous relaxation of the architecture representation, allowing efficient search of the architecture using gradient descent.
Extensive experiments on CIFAR-10, ImageNet, Penn Treebank and WikiText-2 show that our algorithm excels in discovering high-performance convolutional architectures for image classification and recurrent architectures for language modeling, while being orders of magnitude faster than state-of-the-art non-differentiable techniques.
Discovering state-of-the-art neural network architectures requires substantial effort of human experts.
Recently, there has been a growing interest in developing algorithmic solutions to automate the manual process of architecture design.
The automatically searched architectures have achieved highly competitive performance in tasks such as image classification BID35 BID36 BID13 a; BID26 and object detection BID36 .The
best existing architecture search algorithms are computationally demanding despite their remarkable performance. For
example, obtaining a state-of-the-art architecture for CIFAR-10 and ImageNet required 2000 GPU days of reinforcement learning (RL) BID36 or 3150 GPU days of evolution BID26 . Several
approaches for speeding up have been proposed, such as imposing a particular structure of the search space BID13 a) , weights or performance prediction for each individual architecture (Brock et al., 2018; Baker et al., 2018) and weight sharing/inheritance across multiple architectures BID0 BID24 Cai et al., 2018; Bender et al., 2018) , but the fundamental challenge of scalability remains. An inherent
cause of inefficiency for the dominant approaches, e.g. based on RL, evolution, MCTS BID20 , SMBO BID12 or Bayesian optimization BID9 , is the fact that architecture search is treated as a black-box optimization problem over a discrete domain, which leads to a large number of architecture evaluations required.In this work, we approach the problem from a different angle, and propose a method for efficient architecture search called DARTS (Differentiable ARchiTecture Search). Instead of
searching over a discrete set of candidate architectures, we relax the search space to be continuous, so that the architecture can be optimized with respect to its validation set performance by gradient descent. The data efficiency
of gradient-based optimization, as opposed to inefficient black-box search, allows DARTS to achieve competitive performance with the state of the art using orders of magnitude less computation resources. It also outperforms
another recent efficient architecture search method, ENAS BID24 . Notably, DARTS is simpler
than many existing approaches as it does not involve controllers BID35 Baker et al., 2017; BID36 BID24 BID33 , hypernetworks (Brock et al., 2018) or performance predictors BID12 ), yet it is generic enough handle both convolutional and recurrent architectures.The idea of searching architectures within a continuous domain is not new BID27 Ahmed & Torresani, 2017; BID30 BID28 , but there are several major distinctions. While prior works seek to
fine-tune a specific aspect of an architecture, such as filter shapes or branching patterns in a convolutional network, DARTS is able to learn high-performance architecture building blocks with complex graph topologies within a rich search space. Moreover, DARTS is not restricted
to any specific architecture family, and is applicable to both convolutional and recurrent networks.In our experiments (Sect. 3) we show that DARTS is able to design a convolutional cell that achieves 2.76 ± 0.09% test error on CIFAR-10 for image classification using 3.3M parameters, which is competitive with the state-of-the-art result by regularized evolution BID26 obtained using three orders of magnitude more computation resources. The same convolutional cell also
achieves 26.7% top-1 error when transferred to ImageNet (mobile setting), which is comparable to the best RL method BID36 . On the language modeling task, DARTS
efficiently discovers a recurrent cell that achieves 55.7 test perplexity on Penn Treebank (PTB), outperforming both extensively tuned LSTM BID17 and all the existing automatically searched cells based on NAS BID35 and ENAS BID24 .Our contributions can be summarized as
follows:• We introduce a novel algorithm for differentiable network architecture search based on bilevel optimization, which is applicable to both convolutional and recurrent architectures.• Through extensive experiments on image
classification and language modeling tasks we show that gradient-based architecture search achieves highly competitive results on CIFAR-10 and outperforms the state of the art on PTB. This is a very interesting result, considering
that so far the best architecture search methods used non-differentiable search techniques, e.g. based on RL BID36 or evolution BID26 BID13 ).• We achieve remarkable efficiency improvement
(reducing the cost of architecture discovery to a few GPU days), which we attribute to the use of gradient-based optimization as opposed to non-differentiable search techniques.• We show that the architectures learned by DARTS
on CIFAR-10 and PTB are transferable to ImageNet and WikiText-2, respectively.The implementation of DARTS is available at https://github.com/quark0/darts 2 DIFFERENTIABLE ARCHITECTURE SEARCH We describe our search space in general form in Sect. 2.1, where the computation procedure for an architecture
(or a cell in it) is represented as a directed acyclic graph. We then introduce a simple continuous relaxation scheme
for our search space which leads to a differentiable learning objective for the joint optimization of the architecture and its weights (Sect. 2.2). Finally, we propose an approximation technique to make
the algorithm computationally feasible and efficient (Sect. 2.3).
We presented DARTS, a simple yet efficient architecture search algorithm for both convolutional and recurrent networks.
By searching in a continuous space, DARTS is able to match or outperform the state-of-the-art non-differentiable architecture search methods on image classification and language modeling tasks with remarkable efficiency improvement by several orders of magnitude.There are many interesting directions to improve DARTS further.
For example, the current method may suffer from discrepancies between the continuous architecture encoding and the derived discrete architecture.
This could be alleviated, e.g., by annealing the softmax temperature (with a suitable schedule) to enforce one-hot selection.
It would also be interesting to explore performance-aware architecture derivation schemes based on the one-shot model learned during the search process.A EXPERIMENTAL DETAILS A.1
ARCHITECTURE SEARCH A.1.1 CIFAR-10Since the architecture will be varying throughout the search process, we always use batch-specific statistics for batch normalization rather than the global moving average.
Learnable affine parameters in all batch normalizations are disabled during the search process to avoid rescaling the outputs of the candidate operations.To carry out architecture search, we hold out half of the CIFAR-10 training data as the validation set.
A small network of 8 cells is trained using DARTS for 50 epochs, with batch size 64 (for both the training and validation sets) and the initial number of channels 16.
The numbers were chosen to ensure the network can fit into a single GPU.
We use momentum SGD to optimize the weights w, with initial learning rate η w = 0.025 (annealed down to zero following a cosine schedule without restart BID14 ), momentum 0.9, and weight decay 3 × 10 −4 .
We use zero initialization for architecture variables (the α's in both the normal and reduction cells), which implies equal amount of attention (after taking the softmax) over all possible ops.
At the early stage this ensures weights in every candidate op to receive sufficient learning signal (more exploration).
We use Adam BID10 as the optimizer for α, with initial learning rate η α = 3 × 10 −4 , momentum β = (0.5, 0.999) and weight decay 10 −3 .
The search takes one day on a single GPU 3 .A.1.2
PTB For architecture search, both the embedding and the hidden sizes are set to 300. The linear
transformation parameters across all incoming operations connected to the same node are shared (their shapes are all 300 × 300), as the algorithm always has the option to focus on one of the predecessors and mask away the others. Tying the
weights leads to memory savings and faster computation, allowing us to train the continuous architecture using a single GPU. Learnable
affine parameters in batch normalizations are disabled, as we did for convolutional cells. The network
is then trained for 50 epochs using SGD without momentum, with learning rate η w = 20, batch size 256, BPTT length 35, and weight decay 5 × 10 −7 . We apply variational
dropout BID3 of 0.2 to word embeddings, 0.75 to the cell input, and 0.25 to all the hidden nodes. A dropout of 0.75 is
also applied to the output layer. Other training settings
are identical to those in BID18 ; BID31 . Similarly to the convolutional
architectures, we use Adam for the optimization of α (initialized as zeros), with initial learning rate η α = 3 × 10 −3 , momentum β = (0.9, 0.999) and weight decay 10 −3 . The search takes 6 hours on a
single GPU.

assistant: text: We propose a differentiable architecture search algorithm for both convolutional and recurrent networks, achieving competitive performance with the state of the art using orders of magnitude less computation resources.