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The prohibitive energy cost of running high-performance Convolutional Neural Networks (CNNs) has been limiting their deployment on resource-constrained platforms including mobile and wearable devices.
We propose a CNN for energy-aware dynamic routing, called the EnergyNet, that achieves adaptive-complexity inference based on the inputs, leading to an overall reduction of run time energy cost without noticeably losing (or even improving) accuracy.
That is achieved by proposing an energy loss that captures both computational and data movement costs.
We combine it with the accuracy-oriented loss, and learn a dynamic routing policy for skipping certain layers in the networks, that optimizes the hybrid loss.
Our empirical results demonstrate that, compared to the baseline CNNs, EnergyNetcan trim down the energy cost up to 40% and 65%, during inference on the CIFAR10 and Tiny ImageNet testing sets, respectively, while maintaining the same testing accuracies.
It is further encouraging to observe that the energy awareness might serve as a training regularization and can even improve prediction accuracy:  our models can achieve 0.7% higher top-1 testing accuracy than the baseline on CIFAR-10 when saving up to 27% energy, and 1.0% higher top-5 testing accuracy on Tiny ImageNet when saving up to 50% energy, respectively.
While deep learning-powered Internet of Things (IoT) devices promise to dramatically revolutionize the way we live and work by enhancing our ability to recognize, analyze, and classify the world around us, this revolution has yet to be unleashed due to many fundamental challenges.
Edge devices, such as smart phones, smart sensors, drones and robots, have limited energy and computation resources since they are battery-powered and have a small form factor.
On the other hand, high-performance Convolutional Neural Networks (CNNs) come at a cost of prohibitive energy consumption BID0 .
The CNNs with the highest accuracy have hundreds of layers and tens of millions of parameters.
When deployed in practice, such networks drain the battery very quickly BID1 .
Recently, there have been a number of methods proposed to reduce energy cost in CNNs, while not hampering their predictive power.
Most of them aim to reduce the model size or the number of computations BID2 BID3 BID4 BID5 BID6 BID7 BID8 BID9 BID10 BID11 .
However, BID1 shows that a smaller model size and fewer operations might not necessarily lead to a lower energy cost.
BID1 uses energy cost to guide the pruning process, where the layer with the highest energy cost is pruned first.
BID12 formulates the CNN training process as an optimization problem under a certain energy budget constraint.
While both methods BID1 BID12 show promising results towards pursuing more energy-efficient CNN models, they do not incorporate energy costs into the training loss function to explicitly learn a more energy-efficient model.
Furthermore, once their model structures are learned from training, it can only be fixed during the inference time, and there is no room for input-dependent adaptivity.
This paper proposes a new CNN model that combines energy cost with a dynamic routing strategy to enable adaptive energy-efficient inference.
Our proposed model, termed as EnergyNet, is a gated CNN architecture which employs conditional computing to route the input data through the network Figure 1 : EnergyNet Structure: each green circle G indicates an RNN gate and each blue square under G indicates one block of layers in the base model.
To reduce the energy cost, the RNN gates generate routing strategies dynamically for different input images.
By sharing the parameters between all RNN gates, they will have only 0.04% of the energy cost of the base CNN model, which is negligible.
In this specific example, only the first and third blocks get executed.in an efficient path.
Built on a base network (such as ResNet-34 or ResNet-50 BID13 ), EnergyNet uses an additional gating network BID10 to decide whether the current input should skip certain layers in the network or not.
It optimizes a weighted combination of an accuracy loss and an energy loss which captures both the computational and memory data movement costs, under which EnergyNet is trained to find the optimal routing policy to reduce the energy cost of the model without degrading the prediction accuracy.
Our empirical results demonstrate that, compared to the base network without gating nor dynamic inference, EnergyNet can trim down the energy cost up to 40% and 65%, during inference on the CIFAR10 and Tiny ImageNet testing sets, respectively, while maintaining almost the same testing accuracy.
Interestingly enough, we find the energy-aware EnergyNet can even achieve win-win, by simultaneously improving the prediction accuracy and saving energy, potentially due to its equivalent effect as a training regularization to avoid overfitting.
For example, our models achieve 0.7% higher top-1 testing accuracy than the baseline on CIFAR-10 when saving up to 27% energy, and 1.0% higher top-5 accuracy on Tiny ImageNet when saving up to 50% energy, respectively.
Overview: EnergyNet implements an effective dynamic routing algorithm using a set of gating networks, which shares similar ideas with BID10 , as depicted in Figure 1 .
Each gating network associates with a block of layers in the EnergyNet.
Given an input image, the gating networks decide if the corresponding block should be skipped or not.
The input to each block is first sent to the gating network G, whose output is either 0 or 1.
If it is 0, the block will be skipped; otherwise, it will process the input normally as in the base model.
If the input and output of the block have different dimensions, then we can perform a linear projection using a shortcut connection to match the dimensions as in BID13 .
The core innovation in EnergyNet is the adoption of a new energy-aware loss function for learning the gating (skipping) policy, whose details we defer to the next subsection.
In our implementation, we adopt the recurrent gates (RNNGates) as in BID10 (see FIG1 ).
Gate-I (b) FFGate-II It is composed of a global average pooling followed by a linear projection that reduces the features to a 10-dimensional vector.
A Long Short Term Memory (LSTM) BID14 network that contains a single layer of dimension 10 is applied to generate a binary scalar.
As mentioned in BID10 , this RNNGate design incurs a negligible overhead compared to its feed-forward counterpart (0.04% vs. 12.5% of the computation of the residual blocks when the baseline architecture is a ResNet).
In order to further reduce the energy cost due to loading parameters into the memory, all RNNGates in the EnergyNet share the same weights.
Energy-aware Learning for Dynamic Routing: The dynamic routing in EnergyNet is learned by minimizing an energy cost together with the accuracy loss.
In particular, the learning goal in the EnergyNet is defined as: min DISPLAYFORM0 Here, α is a weighting coefficient of the energy loss, and W and G denote the parameters of the base model and the gating network, respectively.
Also, L(W, G) denotes the prediction loss, and E(W, G) denotes the energy cost of the CNN model associated with W and G, which is calculated by accumulating the energy cost of the layers that are not skipped.
In order to compute the energy cost of each layer, we adopt the following energy model: DISPLAYFORM1 where e i and e M AC denote the energy costs of accessing the i-th memory hierarchy and one multiplyand-accumulate (MAC) operation BID15 , respectively, while # M AC and # acci denote the total number of MAC operations and accesses to the i-th memory hierarchy, respectively.
Note that state-of-the-art CNN accelerators commonly employ such a hierarchical memory architecture for minimizing the dominant memory access and data movement costs.
In this work, we consider the most commonly used design of three memory hierarchies including the main memory, the cache memory, and local register files BID15 , and employ a state-of-the-art simulation tool called "SCALE-Sim" BID16 to calculate the number of memory accesses # acci and the total number of MACs # M AC .
Summary: We show that EnergyNet saves more energy than the baseline ResNet after training on CIFAR10 and Tiny ImageNet BID17 .
In particular, compared to the baseline ResNet, EnergyNet saves up to 40% and 65% energy cost without degrading the prediction accuracy, when processing CIFAR10 and TinyImageNet images, respectively.
More encouragingly, our models can achieve 0.7% higher top-1 testing accuracy than the baseline on CIFAR-10 when saving up to 27% energy, and 1.0% higher top-5 testing accuracy on Tiny ImageNet when saving up to 50% energy, respectively.
We use the ResNet-38 and ResNet-50 in BID13 as the baseline models for constructing and evaluating EnergyNet models on CIFAR-10 and Tiny ImageNet, with the resulting models denoted as EnergyNet-38 and EnergyNet-50, respectively.
The training process contains three steps.
In step I, we set the weighting coefficient α to a small value (e.g., 0.1), which helps the model converge to the baseline accuracy first.
In step II, we increase α to a larger value (e.g., 0.9) and retrain the model obtained from step I. For step III , it is only triggered if the model sees an accuracy loss larger than a threshold (default 0.1%) from step II: we then set α to a small value (e.g., 0.1) again to retrain the resulting model from step II for restoring the accuracy.
Such a three-step strategy proves to help stabilize training and gain better performance.
Discussion: We use energy savings as a metric to quantify the resulting energy efficiency improvement of EnergyNet.
The energy savings is defined as E s /E total , where E total and E s are the energy cost of the baseline model and the skipped layers due to EnergyNet.
From FIG2 , we can conclude that EnergyNet achieves the goal of reducing energy cost while preserving or even improving the prediction accuracy.
In particular, the accuracy of EnergyNet-38 and EnergyNet-50 will not drop when the energy savings is as high as 40% and 65%, respectively.
To confirm that these experimental results are not just a coincidence, we performed 20 trials of experiments using EnergyNet-38 and observed that the confidence interval with a 95% confidence level for the mean of the prediction accuracy and the energy savings are [92.47%, 92.58%] and [39.55%, 40.52%], respectively, verifying the reproducibility of EnergyNet's prediction accuracy and resulting energy savings.
We observe that EnergyNet can achieve a higher accuracy than the original ResNet model.
We conjecture that this is because EnergyNet can overcome overfitting when performing the dynamic routing for energy savings.
Further EnergyNet can aggressively reduce energy cost by about 4×, over both the ResNet-38 and ResNet-50 baselines, at the cost of 3% and 4% testing accuracy losses , respectively.
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assistant: text: This paper proposes a new CNN model that combines energy cost with a dynamic routing strategy to enable adaptive energy-efficient inference.