Highway Networks (1505.00387v2)

Abstract: There is plenty of theoretical and empirical evidence that depth of neural networks is a crucial ingredient for their success. However, network training becomes more difficult with increasing depth and training of very deep networks remains an open problem. In this extended abstract, we introduce a new architecture designed to ease gradient-based training of very deep networks. We refer to networks with this architecture as highway networks, since they allow unimpeded information flow across several layers on "information highways". The architecture is characterized by the use of gating units which learn to regulate the flow of information through a network. Highway networks with hundreds of layers can be trained directly using stochastic gradient descent and with a variety of activation functions, opening up the possibility of studying extremely deep and efficient architectures.

• The paper introduces gating mechanisms in highway networks that enable efficient training of extremely deep neural architectures.
• It employs transform and carry gates with a negative bias initialization strategy to facilitate unimpeded information flow across layers.
• Empirical results on MNIST and CIFAR-10 reveal that highway networks achieve superior performance and depth-invariant optimization compared to plain networks.

Highway Networks: Enhancing Training of Extremely Deep Neural Networks

In the "Highway Networks" paper by Srivastava, Greff, and Schmidhuber from IDSIA, the authors propose a novel neural network architecture designed to significantly improve the optimization of very deep networks. This architecture, dubbed "highway networks," addresses the well-documented difficulties in training deep networks by incorporating learned gating mechanisms, thereby facilitating unimpeded information flow across multiple layers.

Key Architectural Innovations

Highway networks introduce two critical non-linear transforms: the transform gate (T) and the carry gate (C). These gates are designed to modulate the flow of information through the network. The highway network layer output $\mathbf{y}$ is mathematically defined as:

$$\mathbf{y} = H(\mathbf{x}, \mathbf{W_H}) \cdot T(\mathbf{x}, \mathbf{W_T}) + \mathbf{x} \cdot (1 - T(\mathbf{x}, \mathbf{W_T})),$$

where $H$ represents the typical non-linear layer transformation, and $\mathbf{x}$ is the input to the layer. The carry gate $C(\mathbf{x}, \mathbf{W_C})$ is simplified to $1 - T(\mathbf{x}, \mathbf{W_T})$, ensuring that the dimensionality matches across the operations.

The initialization scheme for the transform gate utilizes a negative bias value, which biases the network initially towards carry behavior. This strategy draws inspiration from Long Short-Term Memory (LSTM) networks and assists in bridging dependencies across many layers early during training. This initialization, along with stochastic gradient descent (SGD) with momentum, allows for effective training of networks with hundreds of layers.

Empirical Results

The empirical evaluations demonstrate the highway networks' capability to train very deep architectures efficiently. The authors conducted extensive experiments on the MNIST and CIFAR-10 datasets. Key results include:

• Optimization Performance: Highway networks, even as deep as 100 layers, show robust optimization properties, achieving an order of magnitude better performance than traditional networks at similar depths on the MNIST dataset.
• Comparison to Plain Networks: Plain networks exhibit significant degradation in performance as depth increases, whereas highway networks maintain strong performance metrics, indicating their depth-invariant optimization capability.
• Fitnet Comparison: On the CIFAR-10 dataset, highway networks not only train directly using backpropagation but also deliver competitive or superior accuracy compared to Fitnets trained using a two-stage hint-based method. Highway networks with up to 19 layers achieve an accuracy of 92.24%, surpassing Fitnet-based models of similar configurations.

Analysis

The internal analysis of highway networks reveals the functional behavior of the transform gates and information flow within the network. The observations indicate that the transform gates increasingly become selective as training progresses, thereby effectively utilizing the carry behavior to pass information through many layers without significant transformation, forming architectures resembling "information highways."

Implications and Future Directions

The proposed highway networks hold substantial implications for both theoretical and practical advancements in deep learning. The ability to reliably train networks with hundreds of layers opens avenues for exploring more complex and deeper models in various application domains, from vision to natural language processing. The flexibility in activation function choice without requiring specialized initialization schemes further broadens the scope of neural network architectures amenable to deep learning.

Future research could focus on fine-tuning the gating mechanisms, better understanding the dynamics of deep network training, and exploring different application domains to exploit the full potential of highway networks. Additionally, investigating the interplay between architecture depth and other optimization techniques may yield insights that can further mitigate the challenges associated with training extremely deep neural networks.

In conclusion, the "Highway Networks" paper introduces a significant architectural innovation that addresses one of the core challenges in deep learning—optimizing deeply layered networks. Through their innovative use of gating mechanisms and empirical validations, Srivastava, Greff, and Schmidhuber provide a robust foundation for future exploration and application of deep neural networks.