This paper introduces a scheme that predicts the difficulty of classifying an image, reduces the image size according to the prediction, and speeds up the inference time. We observe that models such as ResNet-50 and EfficientNet can classify specific images correctly even after downsizing. We consider these correctly classified images as easy images and others as complex images. Then we collect images with different difficulties and train a difficulty model that classifies the difficulty of an image and determines whether we should downsize an image. In addition, we use an inference model that consists of multiple models for classifying images of different image sizes, and each model is trained with specific datasets to increase its accuracy for the particular image sizes. Finally, we concatenate the difficulty and inference models to get the hybrid model. Our experiments use MobileNetV3-small as the lightweight difficulty model, and ResNet- 50 and EfficientNet-B4 as the inference models. Experimental results indicate a trade-off between the inference time and the image classification accuracy, and the confidence threshold of the difficulty model affects this trade-off. If the confidence threshold of the difficulty model is high/low, the inference time and the image classification accuracy increase/decrease. As a result, the user can control the behavior of the hybrid model by adjusting the confidence threshold of the difficulty model and finding a customized balance between the inference time and the classification accuracy.

Deep Neural Networks (DNNs) are very popular in many machine learning domains. To achieve higher accuracy, DNNs have become deeper and larger. However, the improvement in accuracy comes with the price of the longer inference time and energy consumption. The marginal cost to increase a unit of accuracy has become higher as the accuracy itself is rising.The Branchynet, known as early exits, is an architecture to address increasing marginal cost for improving accuracy. The Branchynet adds extra side classifiers to a DNN model. The inference on a significant portion of the samples can exit from the network earlier via these side branches if they already have high confidence in the results.The Branchynet requires manually tuning the learning hyperparameters, e.g., the locations of branches and the confidence threshold for early exiting. The effectiveness of this manual tuning dramatically impacts the efficiency of the tuned networks. To the best of our knowledge, there are no efficient algorithms to find the best branch location, which is a trade-off between the accuracy and inference time on the Branchynet.We propose an algorithm to find the optimal branch locations for the Branchynet. We formulate the problem of finding the optimal branch location for the branchynet as an optimization problem, and prove that the branch placement problem is an NPcomplete problem. We then derive dynamic programming that runs in pseudo-polynomial time and solves the branch placement problem optimally.We also implement our algorithm and solve the branch placement problems on four types of VGG networks. The experiment results indicate that our dynamic programming can find the optimal branch locations for generating the maximum number of correct classifications within a given time budget. We also run the four VGG models on a GeForce RTX-3090 GPU with the branch combination found by the dynamic programming. The experiment results show that our dynamic programming accurately predicts the number of correct classifications and the execution time on the GPU.