Self-Expanding Neural Networks (2307.04526v3)

Abstract: The results of training a neural network are heavily dependent on the architecture chosen; and even a modification of only its size, however small, typically involves restarting the training process. In contrast to this, we begin training with a small architecture, only increase its capacity as necessary for the problem, and avoid interfering with previous optimization while doing so. We thereby introduce a natural gradient based approach which intuitively expands both the width and depth of a neural network when this is likely to substantially reduce the hypothetical converged training loss. We prove an upper bound on the ``rate'' at which neurons are added, and a computationally cheap lower bound on the expansion score. We illustrate the benefits of such Self-Expanding Neural Networks with full connectivity and convolutions in both classification and regression problems, including those where the appropriate architecture size is substantially uncertain a priori.

• The paper presents a novel mechanism where neural networks start small and expand on-the-fly based on natural gradient scores to add capacity only when needed.
• It outlines a clear methodology for determining when, where, and what to add in the network, ensuring expansions do not disrupt prior optimizations.
• Experimental results across regression, classification, and image tasks show that SENNs adapt dynamically, maintain efficiency, and improve overall performance.

Self-Expanding Neural Networks: Expanding Capacity On-the-Fly

Overview

Choosing the right neural network architecture can be challenging, especially when the problem at hand isn't well understood. The research discussed here dives into an intriguing concept: Self-Expanding Neural Networks (SENN). These networks start small and expand dynamically during training, adding neurons and layers only when needed. This method ensures that the network maintains an appropriate size and complexity without restarting the training process.

The SENN Mechanism

SENN introduces new rules for expanding neural networks based on natural gradients. Here’s a breakdown:

1. Starting Small: The training begins with a minimal architecture.
2. Measuring Need for Expansion: An expansion score (termed as the natural expansion score, $\eta$) determines when the current capacity of the network is insufficient.
3. Expanding Capacity: When the score indicates a need, the network adds neurons or layers where they would be most effective.
4. Maintaining Optimization: The method ensures that adding new components doesn't interfere with the previously optimized parts.

Addressing Expansion Questions

When to Expand?

The network expands its capacity when the increase in the natural expansion score, $\Delta \eta$, surpasses both a relative threshold $\tau$ and an absolute criterion $\alpha$. Essentially, if adding neurons or layers significantly boosts the score, expansion happens.

Where to Expand?

Neurons or layers are added where they will most improve the score. The method identifies the exact placement within the network (either in width, adding neurons, or in depth, adding layers) that maximizes the score $\eta$.

What to Add?

The initialization of new neurons or layers is chosen to maximize the improvement in $\eta$. This ensures that new additions are as effective as possible right from the start.

Experimental Insights

Regression and Classification

In a series of experiments:

• Regression Tasks: SENNs effectively allocate new neurons in regions where existing neurons struggle, ensuring better fits without restarting training. This was visualized by adding neurons in high-error regions in a one-layer model.
• Binary Classification: For classification tasks, SENNs add depth when necessary. For instance, in a 2D binary classification with the half-moons dataset, SENNs dynamically adjusted the model's depth to improve decision boundaries.

Image Classification

• MNIST Dataset: SENNs start with small networks, and as training progresses, they add layers and neurons, stabilizing at a reasonable size and maintaining high performance.
• CIFAR-10 Dataset: SENNs not only expand but also effectively prune neurons, adapting to changing learning rates during training and maintaining performance.

Practical Advantages

SENN offers notable practical benefits:

• Avoiding Over-parameterization: SENNs only add capacity when necessary, steering clear of excessively large models.
• Adaptive and Efficient: This approach can scale dynamically with the problem, maintaining computational efficiency.
• Stability and Adaptability: SENNs can stabilize after perturbations and adapt to new tasks, making them useful for transfer learning and continual learning scenarios.

Future Prospects

The paper's authors highlight potential applications beyond traditional neural networks. The SENN framework could extend to models like transformers and normalizing flows, given its reliance on parameterized models. This opens new doors for more adaptive and efficient AI systems in various domains such as natural language processing and image generation.

Conclusion

Self-Expanding Neural Networks represent a step towards more intelligent and adaptable AI models that grow as needed. By innovatively addressing when, where, and what to expand in a neural network, SENNs ensure efficient learning and optimal architecture, paving the way for smarter allocation of computational resources and more robust AI systems.