Training Very Deep Networks (1507.06228v2)

Abstract: Theoretical and empirical evidence indicates that the depth of neural networks is crucial for their success. However, training becomes more difficult as depth increases, and training of very deep networks remains an open problem. Here we introduce a new architecture designed to overcome this. Our so-called highway networks allow unimpeded information flow across many layers on information highways. They are inspired by Long Short-Term Memory recurrent networks and use adaptive gating units to regulate the information flow. Even with hundreds of layers, highway networks can be trained directly through simple gradient descent. This enables the study of extremely deep and efficient architectures.

• The paper presents highway networks that use adaptive transform and carry gates to effectively address the vanishing gradient problem in deep architectures.
• Empirical results on datasets like MNIST and CIFAR showcase that highway networks maintain stable performance even in networks with up to 100 layers.
• Lesioning experiments and theoretical insights demonstrate that adaptive gating enables dynamic information flow, guiding future research in deep network design.

Training Very Deep Networks: An Overview

The paper "Training Very Deep Networks" by Rupesh Kumar Srivastava, Klaus Greff, and Jürgen Schmidhuber presents a novel architecture called highway networks, aimed at addressing the difficulties associated with training very deep neural networks. This essay provides an insightful overview of the paper's content, focusing on the proposed solutions, empirical validations, and theoretical contributions.

Introduction and Background

Deep neural networks (DNNs) have shown remarkable success in various supervised learning tasks, leveraging their depth to represent complex functions efficiently. However, the training process becomes progressively challenging with increasing depth, primarily due to poor propagation of gradients and activations. Traditional feed-forward networks tend to suffer from vanishing gradients, making it difficult to investigate the benefits of very deep networks thoroughly.

Several strategies have been proposed to address these issues, including improved optimizers, well-designed initialization strategies, novel activation functions, and architectures with skip connections. Despite these efforts, the efficient training of extremely deep networks remains an open problem. The authors propose highway networks inspired by Long Short-Term Memory (LSTM) recurrent networks, utilizing adaptive gating units to facilitate unimpeded information flow across many layers.

Highway Networks: Architecture and Training

The core idea behind highway networks is to introduce adaptive gating mechanisms that allow the network to regulate the information flow between layers. This is achieved through two key mechanisms: transform gates ($T$) and carry gates ($C$). The highway layer output $\mathbf{y}$ is 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 $H$ is a non-linear transformation function, and $\mathbf{x}$ is the input to the layer. The gates $T$ and $C$ determine how much of the input is transformed and how much is carried forward directly.

Empirical Validation

The empirical results demonstrate the effectiveness of highway networks in training extremely deep architectures. Key findings include:

1. Optimization Comparison: As shown in Figure 1, plain networks exhibit significant degradation in performance with increasing depth. In contrast, highway networks maintain stable training advantages with up to 100 layers.
2. MNIST Classification: Highway networks achieved competitive performance on the MNIST dataset using fewer parameters compared to state-of-the-art methods, highlighting their efficiency.
3. CIFAR-10 and CIFAR-100 Results: Highway networks matched or exceeded the accuracy of fitnets, and were trained in a single stage without the need for hints from a pre-trained teacher network.
4. Layer Analysis: Lesioning experiments reveal that in highway networks, early layers tend to perform substantial computation, while later layers maintain information flow. For complex datasets like CIFAR-100, deeper layers contribute progressively to the computation.

Theoretical Contributions and Future Directions

Highway networks offer several theoretical and practical implications. The adaptive gating mechanisms facilitate dynamic routing of information, enabling the network to learn efficient pathways for different inputs. This structural flexibility allows for the blending of depth and computational bottlenecks, mitigating issues like gradient vanishing.

Theoretically, the work opens up new avenues for investigating the depths required for specific tasks. Practically, highway networks enable the construction of efficient deep architectures capable of handling complex tasks without compromising ease of training or generalization ability. Future developments could explore extending these principles to recurrent and convolutional architectures, refining initialization strategies, and evaluating other non-linear transformations within the highway framework.

Conclusion

The introduction of highway networks marks a significant advancement in the training of very deep networks. By overcoming the propagation challenges through adaptive gating mechanisms, the paper demonstrates the feasibility of training deep architectures efficiently using simple gradient descent methods. The empirical results validate the theoretical underpinnings, and the structural insights provided could guide future research in optimizing and understanding deep neural networks.