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openai.com·13h ago
AI Research
arXiv CS.AI·Jun 9·5 min read
How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs
TL;DR
Deep Gaussian processes (GPs) have been studied primarily in the context of wide networks, but their behavior when each layer is a vector-valued GP is less understood. This research investigates the limiting behavior of compositional GPs, revealing a sharp threshold in their depth-dependent kernel.
✦ Why It Matters
Engineers can leverage insights on non-Gaussian limits to improve deep Bayesian model design and performance.
Key Takeaways
- Identify the critical bandwidth threshold for deep GPs.
- Utilize non-degenerate distributions for better modeling.
- Explore multimodal behaviors in limit distributions.
- Adjust model parameters based on depth to enhance performance.
How It Works
The study introduces a sharp threshold for bandwidth in deep GPs, where the behavior of the model changes significantly. Below the threshold, the model can represent complex distributions, while above it, the model's output becomes trivial, limiting its application.
This threshold is crucial for practitioners to understand when designing deep GP models.