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Title: CrescendoNet: A Simple Deep Convolutional Neural Network with Ensemble Behavior

Paper content:
We introduce a new deep convolutional neural network, CrescendoNet, by stacking simple building blocks without residual connections.
Each Crescendo block contains independent convolution paths with increased depths.
The numbers of convolution layers and parameters are only increased linearly in Crescendo blocks.
In experiments, CrescendoNet with only 15 layers outperforms almost all networks without residual connections on benchmark datasets, CIFAR10, CIFAR100, and SVHN.
Given sufficient amount of data as in SVHN dataset, CrescendoNet with 15 layers and 4.1M parameters can match the performance of DenseNet-BC with 250 layers and 15.3M parameters.
CrescendoNet provides a new way to construct high performance deep convolutional neural networks without residual connections.
Moreover, through investigating the behavior and performance of subnetworks in CrescendoNet, we note that the high performance of CrescendoNet may come from its implicit ensemble behavior, which differs from the FractalNet that is also a deep convolutional neural network without residual connections.
Furthermore, the independence between paths in CrescendoNet allows us to introduce a new path-wise training procedure, which can reduce the memory needed for training.
Deep convolutional neural networks (CNNs) have significantly improved the performance of image classification BID3 BID25 .
However, training a CNN also becomes increasingly difficult with the network deepening.
One of important research efforts to overcome this difficulty is to develop new neural network architectures BID6 BID14 .Recently
, residual network BID3 and its variants BID8 have used residual connections among layers to train very deep CNN. The residual
connections promote the feature reuse, help the gradient flow, and reduce the need for massive parameters. The ResNet BID3
and DenseNet BID8 achieved state-of-the-art accuracy on benchmark datasets. Alternatively,
FractalNet BID14 expanded the convolutional layers in a fractal form to generate deep CNNs. Without residual
connections BID3 and manual deep supervision BID15 , FractalNet achieved high performance on image classification based on network structural design only.Many studies tried to understand reasons behind the representation view of deep CNNs. BID27 showed that
residual network can be seen as an ensemble of relatively shallow effective paths. However, BID2 argued
that ensembles of shallow networks cannot explain the experimental results of lesioning, layer dropout, and layer reshuffling on ResNet. They proposed that residual
connections have led to unrolled iterative estimation in ResNet. Meanwhile, BID14 speculated
that the high performance of FractalNet was due to the unrolled iterative estimation of features of the longest path using features of shorter paths. Although unrolled iterative
estimation model can explain many experimental results, it is unclear how it helps improve the classification performance of ResNet and FractalNet. On the other hand, the ensemble
model can explain the performance improvement easily.In this work, we propose CrescendoNet, a new deep convolutional neural network with ensemble behavior. Same as other deep CNNs, CrescendoNet
is created by stacking simple building blocks, called Crescendo blocks FIG0 ). Each Crescendo block comprises a set
of independent feed-forward paths with increased number of convolution and batch-norm layers (Ioffe & Szegedy, 2015a). We only use the identical size, 3 ×
3, for all convolutional filters in the entire network. Despite its simplicity, CrescendoNet
shows competitive performance on benchmark CIFAR10, CI-FAR100, and SVHN datasets.Similar to FractalNet, CrescendoNet does not include residual connections. The high performance of CrescendoNet
also comes completely from its network structural design. Unlike the FractalNet, in which the
numbers of convolutional layers and associated parameters are increased exponentially, the numbers of convolutional layers and parameters in Crescendo blocks are increased linearly.CrescendoNet shows clear ensemble behavior (Section 3.4). In CrescendoNet, although the longer
paths have better performances than those of shorter paths, the combination of different length paths have even better performance. A set of paths generally outperform
its subsets. This is different from FractalNet,
in which the longest path alone achieves the similar performance as the entire network does, far better than other paths do.Furthermore, the independence between paths in CrescendoNet allows us to introduce a new pathwise training procedure, in which paths in each building block are trained independently and sequentially. The path-wise procedure can reduce
the memory needed for training. Especially, we can reduce the amortized
memory used for training CrescendoNet to about one fourth.We summarize our contribution as follows:• We propose the Crescendo block with linearly increased convolutional and batch-norm layers. The CrescendoNet generated by stacking
Crescendo blocks further demonstrates that the high performance of deep CNNs can be achieved without explicit residual learning.• Through our analysis and experiments,
we discovered an emergent behavior which is significantly different from which of FractalNet. The entire CrescendoNet outperforms any
subset of it can provide an insight of improving the model performance by increasing the number of paths by a pattern.• We introduce a path-wise training approach
for CrescendoNet, which can lower the memory requirements without significant loss of accuracy given sufficient data.
CNN has shown excellent performance on image recognition tasks.
However, it is still challenging to tune, modify, and design an CNN.
We propose CrescendoNet, which has a simple convolutional neural network architecture without residual connections BID3 .
Crescendo block uses convolutional layers with same size 3 × 3 and joins feature maps from each branch by the averaging operation.
The number of convolutional layers grows linearly in CrescendoNet while exponentially in FractalNet BID14 .
This leads to a significant reduction of computational complexity.Even with much fewer layers and a simpler structure, CrescendoNet matches the performance of the original and most of the variants of ResNet on CIFAR10 and CIFAR100 classification tasks.
Like FractalNet BID14 , we use dropout and drop-path as regularization mechanisms, which can train CrescendoNet to be an anytime classifier, namely, CrescendoNet can perform inference with any combination of the branches according to the latency requirements.
Our experiments also demonstrated that CrescendoNet synergized well with Adam optimization, especially when the training data is sufficient.
In other words, we can avoid scheduling the learning rate which is usually performed empirically for training existing CNN architectures.CrescendoNet shows a different behavior from FractalNet in experiments on CIFAR10/100 and SVHN.
In FractalNet BID14 , the longest path alone achieves the similar performance as the entire network, far better than other paths, which shows the student-teacher effect.
The whole FractalNet except the longest path acts as a scaffold for the training and becomes dispensable later.
On the other hand, CrescendoNet shows that the whole network significantly outperforms any set of it.
This fact sheds the light on exploring the mechanism which can improve the performance of deep CNNs by increasing the number of paths.

assistant: text: We introduce CrescendoNet, a deep CNN architecture by stacking simple building blocks without residual connections.