Fast Task-Aware Architecture Inference

Fast Task-Aware Architecture Inference

Efi Kokiopoulou {efi,ahauth,sbaiz,agesmundo,bartok,jberent}@google.com Google AI Perception Anja Hauth Google AI Perception Luciano Sbaiz Google AI Perception Andrea Gesmundo Google AI Perception Gabor Bartok Google AI Perception Jesse Berent Google AI Perception
Abstract

Neural architecture search has been shown to hold great promise towards the automation of deep learning. However in spite of its potential, neural architecture search remains quite costly. To this point, we propose a novel gradient-based framework for efficient architecture search by sharing information across several tasks. We start by training many model architectures on several related (training) tasks. When a new unseen task is presented, the framework performs architecture inference in order to quickly identify a good candidate architecture, before any model is trained on the new task. At the core of our framework lies a deep value network that can predict the performance of input architectures on a task by utilizing task meta-features and the previous model training experiments performed on related tasks. We adopt a continuous parametrization of the model architecture which allows for efficient gradient-based optimization. Given a new task, an effective architecture is quickly identified by maximizing the estimated performance with respect to the model architecture parameters with simple gradient ascent. It is key to point out that our goal is to achieve reasonable performance at the lowest cost. We provide experimental results showing the effectiveness of the framework despite its high computational efficiency.

Figure 1: The proposed framework. (a) Offline phase. Several architectures are trained and their performances are stored in a database. The performances along with meta-features about the task are used to train a value network which estimates the performance. (b) Online phase. Given a new task and its meta-features, the system applies gradient ascent on the output of the value net.

1 Introduction

Designing high performing neural networks is a time consuming task that typically requires substantial human effort. In the past few years, neural architecture search and algorithmic solutions to model building have received growing research interest as they can automate the manual process of model design. Although they offer impressive results that compete with human-designed models [22], neural architecture search requires large amount of computational resources for each new task. For this reason, recent methods have been proposed that focus on reducing its cost (see e.g., [13, 15]). This very fact becomes a major limitation in those setups that impose strict resource constraints for model design. For example, in cloud machine learning services, the client uploads a new data set and an effective model should ideally be auto-designed in minutes (or seconds). In such settings architecture search has to be very efficient, which is the main motivation for this work.

At the same time, applying independently automated model building methods to each new task requires a lot of models to be trained as well as learning how to generate high performing models from scratch. Such an approach requires a formidable amount of computational resources and is far from being scalable. On the other hand, human experts can design state-of-the-art models using prior knowledge about how existing architectures perform across different data sets. Similar to human experts, we aim to cross learn from several task data sets and leverage prior knowledge.

In this paper, we present a framework that amortizes the cost of architecture search across several tasks and remains effective thanks to the knowledge transfer between tasks. Architecture search aims at learning a mapping from a data set to a high performing architecture. We propose to formulate architecture search as a structured prediction problem and build on top of previously proposed deep value networks [8]. Given a candidate model architecture and meta-features about the task, a deep value network provides a differentiable mapping whose output estimates the performance of the input architecture on the task data set. We also adopt a continuous parametrization of the model architecture which allows for efficient gradient-based optimization of the estimated performance. Also, in contrast to previous work, e.g., [5] that uses pre-computed meta-features for the task, we present a solution for learning the meta-features directly from the raw task samples as part of the deep value network weights.

The framework consists of an offline training phase and an online inference phase (see Fig. 1 for a conceptual illustration). Assuming that we have trained several model architectures on several related (training) tasks, when a new unseen task is presented, the framework performs fast architecture optimization in order to quickly identify a good candidate architecture, before any model training is performed. In particular, the best candidate architecture is efficiently identified by maximizing the estimated performance with respect to the model architecture parameters with simple gradient ascent. In summary, the paper contributions are the following:

  • Efficient architecture search using gradient-based architecture optimization.

  • Ability to learn the task meta-features directly from the raw task data samples.

  • Cross learning across many tasks (by leveraging information about how various architectures perform across many tasks data sets).

We provide experimental results showing the potential of the proposed framework. The rest of the paper is organized as follows. Section 2 formally defines the problem we are interested in. Next, in Section 3, we introduce the proposed framework and present it in details. Section 4 reviews related methods from the literature. We present experimental results in Section 5 and the conclusions and future work in Section 6.

2 Problem formulation

We are interested in task-aware efficient neural architecture search. Given a new (unseen) task data set, we would like to identify quickly an effective model architecture before any model is trained. We want to learn across datasets in order to amortize the cost of neural architecture search. In particular, we want to collectively learn from all the model training experiments and leverage this wealth of information. Instead of performing architecture search independently for each new data set, we would like to transfer the knowledge obtained from past training experiments on related tasks. In summary, the proposed framework should have the following properties:

  • High scalability in terms of computing resources.

  • Ability to scale and learn collectively across task data sets.

  • Ability to propose a good architecture for a new related task without training any model.

In the next section we propose a general framework that has these desired properties.

3 Proposed framework

Figure 2: Deep value network. (a) With pre-computed meta-features. (b) With learned meta-features. The value net consists of and .

We want to automatically discover the model architecture that achieves the best quality for a given data set. Essentially we are looking for learning a mapping from an input data set to a high performing model architecture. We propose to formalize the architecture search problem as a structured output prediction problem. The key intuition is that learning to criticize candidate architectures is easier than learning to directly predict the optimal architecture. In particular, the proposed framework builds on top of the Deep Value Networks (DVNs) [8] that were originally developed in the context of structured prediction applied to image segmentation. In our context, a deep value network acts as a meta-model that tunes the architecture of a child model. We consider child model families parametrized by , assuming for now that is a vector of continuous variables.

A deep value network in our context takes as input: (i) descriptive meta-features derived from a certain task data set and (ii) the child model architecture parameters , and predicts how well the architecture performs on the task data set described by . The performance metric can take various forms (e.g., accuracy, AUC) but the framework is agnostic to it. In this paper, we use the validation accuracy as performance metric. The deep value network is shown conceptually in Fig. 2. When training the value network, our hope is that it learns which type of child model architectures work well on certain types of data. This tries to mimic the human expert during manual architecture design. Human experts rely on intuition and prior knowledge when developing new candidate architectures. Here, our hope is that such an ‘intuition’ is encoded in the weights of the value network and that it is generally applicable and transferable across data sets.

In the following sections, we provide more details about the proposed framework. We discuss the meta-features of a task in Section 3.1. The framework has two phases: an off-line training phase and an online inference phase that are detailed below in Sections 3.2 and 3.3 respectively. Section 3.4 discusses the child model architecture parameters .

3.1 The meta-features of a task

The meta-features of a task describe its characteristics and statistics, and they are typically derived from the task data set itself. The meta-features may include the following: total number of samples, number of classes and their distribution, label entropy, total number of features and statistics about them (min, max, median), mutual information of the features with the label and task id. The latter can be used to learn an embedding for each data set. Similar data sets should get similar embeddings (see e.g., [20]).

Learning the meta-features.

On top of using pre-computed meta-features such as those listed above, one can also learn them directly from the task data set . In this case, the data set (or a large fraction of it) is given as input to the deep value network, and a task embedding is learned directly from the raw task data set samples. Note that we use both the features and the labels of the task data set samples towards learning the task embedding. This task embedding plays the role of the meta-features and is learned jointly together with the rest of the weights of the deep value network.

The task embedding should be invariant to the order of the samples in the task data set. According to [21], such a function can be decomposed in the form for suitable transformations and . The latter transformations are typically implemented by a few layers (e.g., fully connected, non-linearities etc.). The main idea is to transform each sample from the task data set using and then aggregate the transformed samples such that the task embedding becomes permutation invariant before it is fed into . This process is shown conceptually in Fig. 2, where the deep value network essentially consists of and that are jointly learned, i.e.,

(1)

We assume here that the data samples of different tasks are expressed in a common feature space that can be ingested by .

3.2 Off-line training phase

  Inputs:   Task datasets , see Eq. (2)   DVN training set , see Eq. (3)   kInnerIters, kOuterIters
  repeat
     Sample randomly a task .
     for  to kOuterIters  do
        Pick a mini-batch from with samples only from task .
        for  to kInnerIters  do
           Pick a large batch from the task dataset .
           Perform one step of Stochastic Gradient Descent step on the weights of the deep value network.
        end for
     end for
  until Convergence
Algorithm 1 Offline training phase

Assume we have tasks with corresponding data sets denoted:

(2)

where is the number of data samples in the -th task. is the i-the sample and its corresponding label in the -th task data set.

For each task data set, we generate child model architectures, train them and collect the model performances on the validation set in a life-long database of model training experiments (see Fig. 1). This database is used to generate the training set for the deep value network, which consists of triplets of the form:

(3)

where the value holds the child model performance obtained when training with the model architecture on the task data set with meta-features . In this paper, the model performance metric used is the validation accuracy. As more tasks are ingested in the database and more models get trained, the deep value network improves its predictions. In the Appendix we provide experimental results demonstrating this behaviour.

Once the child model training experiments have been collected in the database, we can start training the deep value network. Algorithm 1 shows the main steps of this offline training phase.

3.3 Online inference phase

  Inputs:   New Task dataset   Trained DVN model   kNumStartingPoints, kMaxIters
  Compute the meta-features
  Form an empty set of solutions
  for  to kNumStartingPoints  do
     Pick an initial guess ,
     repeat
        
        
     until Convergence (or kMaxIters)
      where is the found solution and its corresponding value.
  end for
  Output: .
Algorithm 2 Online inference phase

After training the deep value network , the model weights are kept fixed. At inference time, given a new task dataset, we first extract its meta-features . At this point we can employ the value network in two ways. First, if we have a candidate architecture we can evaluate it by simply doing a forward pass on the deep value net and get the estimated child model performance. Alternatively, we can compute the gradient of with respect to and perform simple gradient-based optimization to get a good candidate architecture that maximizes the estimated child model performance.

In practice, we noticed that the gradient ascent is sensitive to initialization. Hence, we run the process several times with different initial guesses and at the end pick the one that resulted in the maximum estimated performance. Note also that in order to be able to perform gradient-based inference we need to relax the model architecture parameters to live in a continuous space. Section 3.4 below discusses this parametrization in details. The main steps of the online phase are shown in Algorithm 2. This online process is also illustrated conceptually in Fig. 1.

3.4 Architecture parametrization

We discuss in this section the parametrization of the child model architectures. Previous work [13, 18] has shown that relaxing the parametrization from discrete to continuous space allows for efficient gradient-based optimization schemes while still providing competitive model performances. Our approach goes along the lines of this previous work. The main idea is that in order to make the architecture space continuous we move away from the categorical nature of design choices to a parametrized softmax over all possible choices. We provide below a few examples where this is applied.

Continuous parametrization for one layer

Assume that we have implemented a basis set consisting of base layers corresponding to different sizes and different activation functions. We associate a weight with each base layer and we define a new parametrized layer as follows

(4)

The values allow the final parametrized layer to ‘morph’ from one size to another and/or from one activation function to another. We use zero padding whenever needed to resolve the dimension mismatch among base layers of different sizes.

Continuous parametrization for a child network

Leveraging on the continuous parametrization for one layer introduced above, we can put several parametrized layers together. We attach a superscript to the layer parameters to denote the layer where they belong to i.e., is the parameter that multiplies the output of the -th base layer in the -th parametrized layer of the final network. We also add the ability for each layer to be enabled or disabled independently from the other layers. For this, we add extra parameters that control the presence or absence of each layer. This is shown conceptually in Fig. 3 below.

Figure 3: Continuous parametrization of the child models.

Putting everything together, we consider child models that are standard Feedforward Neural Networks (FFNNs) composed of an embedding module followed by several parametrized layers and a final softmax classification layer. The reason for using an embedding module is that it speeds up the training time for the child models and improves their quality especially when the training set is small. The embedding module is soft-selected by an input set of pre-trained embedding modules111The pre-trained modules are available via the Tensorflow Hub service (https://www.tensorflow.org/hub). Please refer to the Appendix for more details about them. using the same softmax trick analogous to Eq. (4) where we denote by the corresponding parameters of the softmax. After this relaxation, architecture search reduces to learning the continuous variables . We refer to as the encoding of the model architecture. Finally, we would like to emphasize that this parametrization is just one example among many possible options. Any parametrization will work with the proposed framework as long as it is continuous.

4 Related work

Automated model building is an important challenging research problem and several related methods have been proposed in the past few years. In general, previous works can be broadly categorized into the following classes:

  • Bayesian optimization methods [19, 14, 9, 6] build a probabilistic model of the performance of the network as a function of its hyperparameters and then decide which candidate point in the search space to evaluate next.

  • Methods based on Reinforcement Learning (RL) [22, 20, 15, 12] evaluate candidate child model architectures on-the-fly, by training and evaluating on a validation set. Using the validation accuracy as the reward signal, these methods use RL to optimize the child model architecture.

  • Evolutionary methods such as [17] form a population of model architectures. The population is evolved over time by picking individuals and mutating them (e.g., inserting a new layer). The quality of the population improves over time as the individuals with poor performance are removed.

  • Morphing methods [7, 3] start with an initial model architecture and they iteratively refine the architecture during training until a certain objective is hit (e.g., model size or flops per inference).

  • Performance prediction methods [10, 4, 2, 12]. Given a candidate model architecture, these methods forecast its performance without training. In order to train the performance predictor a database of previous trainings of various model architectures is typically built.

The proposed framework also belongs to the last category of performance prediction methods. However, our deep value network is task-aware and takes-in not only the architecture but also meta-features about the task, with the extra ability of learning them directly from the raw task samples. Hence, the proposed framework in its current form is novel (to the best of our knowledge). However, it shares connections and similarities with existing works that we outline below. The previously proposed SMAC method [9] for general algorithm configuration also uses a history of past configuration experiments as well as descriptive features for the problem instances. However, this method uses an expensive Bayesian optimization process as opposed to the efficient gradient-based architecture search that this framework proposes (implied by the structured prediction formulation).

The TAPAS system proposed in [10] also uses a history of past configuration experiments stored in a database of experiments. The paper proposes a performance predictor that takes as input the difficulty of the dataset as well as a candidate network architecture. However, they use only pre-computed meta-features and their architecture parametrization is not differentiable.

The paper in [20] proposes a multi-task training of RL-based architecture search methods. For each task, it learns a task embedding that captures the task similarity. The task embedding is provided as input to the controller at each time step. In contrast to our work where the task embedding is derived directly from the data samples of the task, the task embedding in [20] is derived from the task id. Also, this method still requires some child model trainings and evaluations on the test task as opposed to our method that requires no child model trainings.


Data set Train Examples Val. Examples Test Examples Classes Reference
Airline 11712 1464 1464 3 crowdflower.com
Corporate Messaging 2494 312 312 4 crowdflower.com
Emotion 32000 4000 4000 13 crowdflower.com
Disasters 8688 1086 1086 2 crowdflower.com
Global Warming 3380 422 423 2 crowdflower.com
Political Bias 4000 500 500 2 crowdflower.com
Political Message 5000 500 500 9 crowdflower.com
Progressive Opinion 927 116 116 3 crowdflower.com
Progressive Stance 927 116 116 4 crowdflower.com
US Economic Performance 3961 495 496 2 crowdflower.com
Table 1: Statistics for the NLP classification data sets. Number of examples in the training set, validation set and test set, number of classes and reference.

5 Experiments

The framework has been implemented in TensorFlow222We plan to make the code publicly available. [1]. For the experimental results we use publicly available NLP data sets whose main characteristics are shown in Table 1. We have performed several leave-one-out experiments, where each task in our set is considered to be a test task and the rest of the tasks are used as the training tasks. Then for each such leave-one-out experiment, we train a DVN, we study its predictive performance and use it for fast architecture inference. More details are provided below.

5.1 Setup

Child models

The child models have been implemented using the parametrization discussed in Section 3.4. The sizes of the base layers in a single parametrized layer are and each one of them is combined with two distinct activation functions (relu and tanh). Hence a single parametrized layer is composed of twelve base layers and each child model has seven such parametrized layers. The child models have been trained using Adam optimizer [11] with a learning rate of for 20 training epochs.

Deep value network

The value network was trained on the child model training experiments stored in the database, which was populated with about 500 child model architectures per task (generated by random one-hot architecture encodings). We used a simple value network consisting of two fully connected layers of size 50 each for the task meta-features tower (aka in Fig. 2) and two fully connected layers of sizes 50 and 10 for the tower that produces the final prediction (aka in Fig. 2). The value network used standard L2 loss for regression and was trained using Stochastic Gradient Descent with momentum [16] (using 0.5 as default parameter). The learning rate was set to . We set kOuterIters to 1 and kInnerIters to 2 in Algorithm 1. When training the value network we normalized the child performances using the mean and standard deviation of the population of child performances for a certain task . Each task has its own level of difficulty and we noticed that this normalization step factors out the difficulty of the task and improves the performance of the value network.

5.2 Predicting the model performance


Task name Without Meta-features With Meta-Features
airline 0.8003 0.0180 0.8260 0.0125
emotion 0.8269 0.0138 0.8523 0.0088
global warming 0.8072 0.0116 0.8179 0.0076
corporate messaging 0.8090 0.0067 0.8527 0.0076
disasters 0.8066 0.0053 0.7933 0.0121
political message 0.4915 0.0114 0.5078 0.0091
political bias 0.5408 0.0138 0.5210 0.0111
progressive opinion 0.8164 0.0130 0.8338 0.0063
progressive stance 0.7244 0.0212 0.7883 0.0200
us economic performance 0.3051 0.0103 0.2851 0.0114
Table 2: Spearman’s rank correlations between the actual performances and the predicted performances provided by the value network; breakdown by task. The higher the better. The meta-features seem to help in the majority of tasks.

Task name Without Meta-features With Meta-Features
airline 0.7709 0.0143 0.8294 0.0174
emotion 0.7570 0.0164 0.8011 0.0116
global warming 0.7002 0.0102 0.7403 0.0138
corporate messaging 0.7218 0.0102 0.7746 0.0099
disasters 0.7805 0.0120 0.8039 0.0143
political message 0.7345 0.0124 0.7451 0.0138
political bias 0.1718 0.0148 0.1382 0.0148
progressive opinion 0.4473 0.0060 0.4720 0.0092
progressive stance 0.4189 0.0112 0.4614 0.0138
us economic performance 0.6886 0.0164 0.6970 0.0146
Table 3: R2 values between the actual performances and the predicted performances provided by the value network; breakdown by task. The higher the better. The meta-features seem to help in the majority of tasks.

We study the predictive performance of the value network in each one of the leave-one-out experiments. In particular, given the predicted performances and their corresponding actual performances, we quantify the predictive performance in terms of the Spearman’s rank correlation coefficient as well as the standard R2 metric for regression. In order to get more accurate results we repeat this process ten times and we report the statistics of the obtained performances. Table 2 shows the obtained Spearman’s rank correlations for each task and Table 3 shows the corresponding R2 metric values. Notice that in most cases, the Spearman’s rank correlations lie around 0.8, which seems rather satisfactory for a method that does not use any child model trainings on the test task.

We have also studied experimentally the effect of the meta-features and report the predictive performances with and without meta-features. The results in both tables suggest that the meta-features are helpful, as expected, since both metrics increase. The meta-features provide task-specific information to the value network that helps towards estimating the relative performance of various architectures for the task at hand.

5.3 Architecture search


Task name First10 NAS Num Child models Proposed
airline 0.7904 0.0366 0.83197 751 0.8222 0.0129
global warming 0.7806 0.0249 0.79196 1927 0.8017 0.0108
disasters 0.8193 0.0105 0.83425 1283 0.8235 0.0119
political bias 0.7770 0.0151 0.778 1989 0.7686 0.0108
progressive opinion 0.6750 0.0428 0.73276 1505 0.7052 0.0381
progressive stance 0.4181 0.0645 0.57759 1635 0.4724 0.0537
us economic performance 0.7494 0.0112 0.76411 1966 0.7498 0.0132
corporate messaging 0.8006 0.0492 0.85897 968 0.8247 0.0387
emotion 0.2998 0.0278 0.35425 1779 0.3397 0.0238
political message 0.4230 0.0075 0.414 1974 0.4214 0.0061
Table 4: Comparison with NAS in terms of test accuracy. The table shows the test accuracy achieved by the top model according to the validation accuracy that NAS found. The number of child models that NAS trained in order to achieve this test accuracy is also reported. For the sake of completeness, we report the statistics of the test accuracy obtained by the first 10 models that NAS tried. Notice that the proposed method (without any child model training on the test task) achieves test accuracy which is close to that of NAS in the majority of cases.

In this section we look into the performance of the child model architectures suggested by our method and we report their test accuracy. When we apply our algorithm we set kNumStartingPoints to 10 and kMaxIters to 1000 in Algorithm 2. For each task we run our method ten times in order to get more accurate statistics on the performances.

We compare against the NAS method for architecture search using Reinforcement Learning [22]. In particular, we applied NAS on the same child models as our method. Table 4 shows for each task the test accuracy of the child model that NAS found as having the best validation accuracy. We report also the number of trained child models that were needed for achieving this accuracy. For the sake of completeness, the table also includes the performances of the first 10 models that NAS tried.

Notice that the performance of the proposed method is not too far from that of NAS. This is very promising given that the proposed method requires no child model training in its online phase and is very efficient.

Note finally that the experiments above have been all performed in the continuous architecture space. However, we acknowledge that inference with continuous child model architectures can be expensive for some applications, since it involves computations over all possible design choices. In such cases, one may want to prune the architecture (in order to make inference faster) but still keep the same model quality. This will be the subject of a forthcoming study.

6 Conclusions and future work

We presented a framework for efficient architecture inference that cross learns from several tasks. This is feasible thanks to a deep value network that predicts the performance of a candidate architecture on a certain task based on learned meta-features derived from the raw data. Given a new task, the proposed method uses simple gradient ascent to infer a candidate architecture for it and experimental results confirm that the performance of the found architecture is relatively close to that of the very expensive baseline. In our future work, we plan to explore different child model parametrizations, study the effect of pruning the architecture and apply the method to other data modalities beyond text (e.g., images).

Acknowledgements

The authors would like to thank Thomas Deselaers for his valuable comments, fruitful discussions and support.

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