Using Early Exits for Fast Inference in
Automatic Modulation Classification

In wireless communications, the received signal $r(t)$ is the result of channel effects on the transmitted modulated signal $s(t)$ including distortions of signal’s amplitude and spectrum. Thus, the received signal in a wireless system is described by the following formula:

where $h(t)$ is the wireless channel frequency response and $n(t)$ is the additive noise.

Given the received signal at the receiver, the task of AMC is to identify the modulating type of the transmitted one. The problem then follows the definition of the maximum-a-posterior (MAP) criterion.

where $M=\{m_{i}\}_{i=1}^{N}$ and $N$ is the number of modulation techniques [13].

We use the recently released RML22 dataset [14] in our study. RML22 is an open-source dataset created based on the benchmark dataset RADIOML.2016.10A (RML16) and addresseses some of its shortcomings. Like RML16, the RML22 dataset is used as a synthetic dataset for different wireless problems including but not limited to AMC.

The dataset contains 420000 received baseband signals in 10 different modulation techniques: BPSK, QPSK, 8PSK, 16QAM, 64QAM, PAM4, CPFSK, GFSK, WBFM, AM-DSB. The dataset is evenly distributed among the 10 modulation techniques and 21 SNR levels from –20 dB to 20 dB in steps of 2 dB. Therefore, the dataset has 2000 data points (samples) per modulation type per SNR level. Each sample is in IQ format with a size of (2, 128). We use 10% of the dataset to test our AMC models, and 90% for model training and validation (10% of the 90% is used for validation). This comes to 340200 samples for training, 37800 for validation, and 42000 are allocated for testing.

To evaluate the effectiveness of early exiting in AMC, we first implemented a high-performing benchmark baseline network, based on the 1D-CNN architecture described in [14] and shown in Figure 2. The baseline backbone architecture leverages the benefits of CNNs, such as parameter sharing, translation invariance, and hierarchical representation [15]. Based on the network designed in [14] for the RML22 modulation classification dataset, our baseline model utilizes 1D convolutional layers for core feature extraction. The architecture, shown in Figure 2, consists of six consecutive 1D convolutional layers. Each convolutional layer in the baseline architecture extracts distinct features for accurate modulation classification. To enhance the network’s ability to capture complex representations, a Rectified Linear Unit (ReLU) activation function is applied after every convolutional layer. Additionally, max-pooling and batch normalization layers are inserted after some of these layers, facilitating dimension reduction and improving model convergence. The final stage consists of a max-pooling layer, 3 fully connected (FC) layers, and a SoftMax activation, producing an output of size (1, 10) representing the number of modulation types. The SoftMax layer ensures that each neuron’s output represents the probability of the input sample belonging to each class. To prevent overfitting, an implicit dropout layer with a dropout rate of 0.3 is included after each FC layer, except for the last layer.

The proposed early exiting architecture aims to achieve fast inference without compromising classification accuracy across all signal to noise ratios. The goal is to achieve a significant reduction in computations by exiting the backbone network early $-$ but to do so only when the received signal can be classified accurately with an early exit. To accomplish this, there are two main design aspects to be considered: 1) where the early exit branches off from the backbone network, and 2) the threshold value of the entropy confidence level that will terminate the inference path.

We therefore implement early exits at four different locations of the backbone network to investigate the impacts and trade-offs that each architecture provides. These EE architectures are illustrated in Figure 3 and are denoted with the naming convention (V0 to V3) based on their proximity to the input, with V0 being the closest and V3 being the farthest. All EE architectures maintain the same number and types of layers for the backbone architecture $-$ and the exit branches have identical intermediate classifier architectures. This allows for a comparative analysis of the impact of early exiting location on the overall performance of the network.

Early-exiting architectures have two or more branches that share a common set of network layers. As shown in Figure 3, the further away the exit or branch is from the input, the larger the number of shared network layers. Neural network training in EE architectures is therefore different from traditional networks since it has to incorporate a forward pass per branch and a resulting loss per branch.

In our proposed architectures, the training process involves two forward passes, as illustrated in Figure 3. The common network layers and the early exiting branch is referred to as Forward Pass 1 and full backbone branch is referred to as Forward Pass 2. Consequently, two losses are calculated: Loss 1 measures the cross-entropy between the output of Forward Pass 1 and the ground truth labels, while Loss 2 quantifies the cross-entropy between the output of Forward Pass 2 and the ground truth labels. To update the model’s parameters, Loss 1 is used for the backpropagation computations of gradients of the common layers and the early exit layers. On the other hand, Loss 2 is only used for the backpropagation computations of gradients for the main backbone network layers, excluding the common layers. In other words, Loss 2 only affects the layers starting from the branching location up to the end of the backbone network. This training procedure for the early exiting architectures is summarized in Algorithm 1.

The inference engine is responsible to execute the forward passes of the multi-branch architecture after training has converged and to determine whether an input sample can terminate at an early exit. The primary motive to use EE architectures in classification is to reduce the computational burden and inference time for input samples that can be correctly classified with an early exit or short branch.

To classify an input sample, it first traverses the initial common layers before reaching the first branch. The intermediate output of these layers, denoted as Q, is then saved and forwarded to the exit branch where the fully connected layers are executed. The EE resulting output, referred to as $z_{i}$ (where $i$ is the exit index), undergoes an entropy evaluation to determine the confidence level of this classification as follows:

This confidence level is then compared against a threshold value, $T$, which determines whether the classification $z_{i}$ will be accepted or rejected. If $E(z_{i})$ is less than or equal to $T$, the temporary classification $z_{i}$ becomes the model’s inference output. However, if $E(z_{i})$ exceeds $T$, the inference engine will redirect the input to the main backbone branch to be classified by Forward Pass 2. This inference procedure for our early exiting architectures is summarized in Algorithm. 2.

We first thoroughly study the effect of the location of the early exit (i.e., the architecture choice) on the classification accuracy, the frequency of exiting early, and the resulting inference time. These results are for a confidence threshold ($T=0.35$) that was shown to provide a good trade-off between accuracy and inference time. In the next subsection, we will discuss the effects of this threshold.

Classification Accuracy. Figure 4(a) shows the accuracy of the baseline backbone model and the four proposed EE architectures of Figure 3. The results follow the expected AMC trends where accuracy increases with increasing SNRs. All the models perform almost identically for low SNRs. Results vary amongst the models for higher SNR values ($>0$ dB) but we observe that $V0$, $V1$, and $V3$ perform very close to the baseline backbone model. To provide more insights on these results, we discuss the percentage of early inference exits next.

Frequency of Early Exits. Figure 4(b) shows the percentage of samples that were classified using the early exit branches for the different architectures. We observe two trends that validate our hypothesis that motivated the study of EE for AMC. The first that is indeed higher SNRs result in a higher percentage of samples that are successfully classified with the EE branches. It is therefore unnecessary to design very deep NN architectures when the SNR exceeds $0$ dB. This also indicates that the entropy measure in the inference engine captures the degree of classification certainty in AMC $-$ and that this certainty increases with increasing SNRs as one would expect. The second observation from Figure 4(b) is that when early exits happen very close to the input as in model $V0$, the entropy measure is too high and the percentage of successful classifications at this exit is low. This is expected since a very shallow architecture may not be sufficient. It is however worth noting that while $V0$ and $V1$ differ by a single 1D-Conv layer, this addition is enough to result in much larger %-age of exits.

A rather interesting result of Figure 4(b) is that $V2$ has a very high %-age of early exits, but Figure 4(a) indicates the accuracy of $V2$ has taken a small hit compared to the rest of the architectures. To investigate if this was due to the mis-classifications of the $V2$ early exit, we plot the EE accuracies for $V1$ and $V2$ in Figure 5. The figure shows that indeed exits at $V2$ have a considerably higher percentage of incorrectly classified modulations, and this has resulted in the accuracy drop observed in Figure 4(a). As such, careful considerations should be made to the location of the EE branch since it can have an impact on the resulting performance.

Inference Time. In order to show the benefits of the proposed EE strategies, we plot the resulting inference times of the different architectures in Figure 4(c). Architectures $V0$ and $V3$ do not provide inference time gains except at very high SNRs and this is expected due to different reasons. $V0$ is a very shallow architecture and most of the samples are not classified after traversing the EE branch due to a high entropy. This results in an additional delay incurred by using this branch. $V3$ is a very long architecture and despite that, at low to medium SNR values, the entropy values are not low enough for a successful exit. The entropy calculation itself introduces additional inference delays for even cases where EE is successful. Both $V0$ and $V3$ were designed as extreme branching locations and are provided mainly to validate and gauge the relative behavior of EE architectures in AMC.

Figure 4(c) shows that $V1$ and $V2$ have considerably lower inference times than the baseline architecture for positive SNR values. This demonstrates the value of EE-based designs for AMC. Further optimizations are also possible. For example, the entropy calculation does not need to happen at every signal sample once a signals SNR is deemed suitable for the early exit. To reduce the inference time of the SNR signals, they may be explicitly directed toward the back-bone branch and EE may be disabled based on their SNR value. Adaptive entropy thresholds can also be introduced for low SNR signals to allow them to exit early despite a high entropy. This is because they are unlikely to be classified accurately even by the long branch. Inference time can also be further reduced by calibrating the entropy threshold as discussed next.

Using a higher entropy threshold (lower confidence level) will result in more frequent early exits for all architectures. This is illustrated in Figure 6(a) that shows the considerable decrease in inference time, particularly for $V1$ amongst all the architectures due to its shallow but effective architecture. This inference time reduction does however compromise the accuracy as shown in Figure 6(c). It is worth noting that $V3$ does not undergo the same accuracy reduction since it has a far EE and most inputs are classified correctly. This comes at the cost of a much larger inference time.

Results for reducing the entropy threshold are also provided in Figure 6(b) and Figure 6(d). The inference time is now increased since most inputs will not successfully exit the branches with this threshold and will be redirected to traverse the full backbone path as well. These results demonstrate the importance of calibrating the entropy threshold to achieve the desired accuracy-inference time trade-offs.