## 3 Method
### PrimeNet  
In the proposed PrimeNet framework, the shallow, deep learning structures work as a catalyst in the overall learning of the primary discriminative network. The capsule-like shallow structures present multiscale feature representations, and the dynamic selection logic encourages the representations with immediate minimum local loss. The learned feature representation is dynamically added to the secondary classifier network, which benefits the model into faster convergence. To design the PrimeNet block, we first set up the conditional computation model with multiple intermediate classifiers. Each classifier in this arrangement operates on a different feature scale. The shallow _Local Loss Block_ layer order ( \(CONV\to BN\to LReLU\to FC\to SOFTMAX\)) from Figure 1 is followed to compute local loss from each intermediate classifier. From Figure 2, it can be seen that larger filter sizes (namely \(5\times 5\) and \(7\times 7\)) are used, which will result in an increased number of parameters and require more computation power. A \(1\times 1\) convolution layer is used just after the input for dimensionality reduction, while retaining the salient features from the input. The memory and computational savings by dimensionality reduction allowed us to use a \(3\times 3\) projection further to pool features across the channels and increase feature maps. _Translation invariant feature projection:_ The convolution layer feature maps, unlike dense layers, are inherently insensitive to the location of the features in the input [2; 30; 31]. There may be chances that the loss-based conditional computation may always choose and concentrate in a particular local region. Moreover, the proposed multiscale feature abstraction process distills the most prominent visual indicators set, and the remaining features of the other layers are soft pruned. Sometimes, soft pruning could also result in the loss of essential features, which is a problem known as extreme compression. The translation invariance in CNN is achieved by combining the convolution and maxpooling layer operations. The convolution layer convolves through an image patch and abstracts the features with their respective position. After that, max-pooling filters out the max value of the feature from the convolved output and reduces the dimension and complexity. By obtaining the max-value, it inherently discards the positional information of the features, which makes it translation invariant. In the proposed research, we innovatively used the translation invariance of the input, projected with input features of the same image. This helped our adaptive convolution design to avoid the correlated units being concentrated in the same region. The projection layer also reduces the effect of extreme compression caused by soft pruning and presents a normalized local translation invariant feature presentation of the same input. To implement the adaptive convolution strategy, we set up our conditional computation block as a primary external network which consists of four intermediate classifiers respective to each feature scale. Each intermediate classifier (named a capsule network) implements the shared input for the same target output. The proposed PrimeNet architecture multiscale micro-network operates to perform intermediate classifications. Local loss is computed for each scale convolution, and the adaptive convolution is performed. The other layers with higher losses are soft pruned, and their weights are locally updated. \[[y_{1},y_{2},y_{3},y_{4}]=f(x;\theta)=[f_{1}(x;\theta_{1}),...,f_{4}(x;\theta _{4})], \tag{2}\]  
Figure 1: The backward-locking free, custom convolution block that updates the layer-wise local loss instead of sending the gradients back through backpropagation. Redrawn from figure source in Reference [4]. Figure 2: The proposed PrimeNet architecture. Multi-scale micro-network operates to perform intermediate classifications. Local loss is computed for each scale convolution, and the adaptive convolution is performed.