Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Exact marginal prior distributions of finite Bayesian neural networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase network depth at fixed finite widths | Finite linear and ReLU Bayesian neural networks · Single-input output-preactivation prior | sub-Weibull tail parameter: optimal tail parameter d/2 | Hurt |
| Increase hidden-layer widths while scaling κ_d to keep variance finite | Finite linear Bayesian neural networks · Single-input output-preactivation prior | distance from Gaussian prior | Helped |
| Approximate the finite-width prior with a finite-order Edgeworth expansion | Deep linear Bayesian neural networks · Single-input output-preactivation prior | tail behavior | Hurt |
| Use ReLU activations instead of linear activations with identical weight variances | Bayesian neural networks of the same width and depth · Single-input output-preactivation prior | output-preactivation variance: 2^{1-d} times | Hurt |
| Represent the ReLU prior as a mixture over active-unit counts and a point mass at zero | Finite ReLU Bayesian neural networks · Single-input output-preactivation prior | agreement with the exact prior | Helped |
| Introduce a narrow bottleneck between wide hidden layers | Deep linear Bayesian neural networks · Single-input output-preactivation prior | similarity to a uniformly narrow network prior | Helped |
Closest papers by meaning
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- Bayesian Neural Scaling Law Extrapolation with Prior-Data Fitted Networks (ICML 2025 · similarity 0.87)
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