Can a Neural Network be Trained to Output a Smaller Neural Network?

The question of whether we can train a neural network to output a smaller neural network has been an intriguing challenge in the field of deep learning. This technique would enable us to automatically generate specialized sub-networks, potentially leading to more efficient and adaptable models. This article explores the feasibility and challenges of this idea, focusing on backpropagation, regularization techniques, and an alternative approach involving contrastive restricted Boltzmann machines (CRBMs).

Approach via Backpropagation

The initial approach might involve training a larger neural network to output a smaller network. To achieve this, we would need a mechanism to represent a neural network within another neural network. Here’s how you might go about it:

Step 1: Generate Random Networks

First, generate a bunch of random architectures, represented by a set of As and Bs. For example, A might represent activation functions, and B might represent connection weights.

Step 2: Train Smaller Networks

For each of the generated networks, train a smaller neural network via backpropagation. Optimized methods like L-BFGS can be used for better efficiency. Additionally, ensure that the training process takes place on a GPU, as this significantly speeds up the training.

Step 3: Train the Larger Network

The larger network would be trained to output the smaller network. This involves fine-tuning the larger network’s parameters to map specific inputs to the corresponding smaller networks. The process requires a combination of careful design and extensive experimentation.

Challenges and Considerations

Several challenges arise when attempting to implement this approach:

Output Layer Alignment

The output layer of the larger network should ideally be linear to avoid scaling and distortion issues. If non-linear outputs are used, the training becomes more complex due to the need for additional scaling and distortion corrections. This can significantly complicate the training process.

Weight Sensitivity

Neural networks are highly sensitive to weight changes, especially those closer to the input layer. If the output of the larger network is not precisely aligned, the generated smaller network might be inaccurate. This can lead to overfitting, where the neural network performs well on the training data but poorly on unseen data.

Regularization Techniques

To mitigate the risk of overfitting, regularization techniques such as Dropout can be employed. Dropout randomly drops units (along with their connections) from the network during training, which prevents the network from relying too much on any single neuron.

Training Overhead

The entire process is computationally intensive and can take a very long time to train, especially for complex datasets. It requires careful optimization of both the larger and smaller networks.

Boosting for Precision

Despite the challenges, boosting can be a promising technique to improve the precision of generated smaller networks. Boosting involves iteratively training smaller models to focus on difficult cases, gradually improving overall accuracy.

Alternative Approach: Contrastive Restricted Boltzmann Machines (CRBMs)

For a more promising solution, Contrastive Restricted Boltzmann Machines (CRBMs) by Graham Taylor offer a different approach. CRBMs can model complex relationships between variables and are known for their robustness and ability to generalize well.

Training CRBMs

CRBMs are typically trained using a combination of CD (Contrastive Divergence) and backpropagation, although Taylor did not provide the backpropagation code. If you have a large dataset, it is advisable to fine-tune the CRBMs using backpropagation to ensure optimal performance.

Conclusion

In conclusion, training a neural network to output a smaller network is a challenging but potentially rewarding endeavor. While the approach via backpropagation faces significant challenges, techniques like regularization and boosting can help improve its reliability. For more robust results, exploring methods like CRBMs may provide a more effective solution.

Keywords

Neural network Backpropagation CRBM