Uncertainty propagation in auto-regressive random neural network models
We develop analytical and particle-based methods for uncertainty propagation in random neural network models, where both the inputs and network parameters are allowed to be random. Building on the piecewise-linear structure of the Leaky ReLU activation function, we derive a local approximation of the neural network output with respect to perturbations in both its inputs and parameters. This approximation is exact for perturbations that preserve the network activation pattern, and it allows us to compute analytical expressions for the probability density function and characteristic function of the network output, together with closed-form approximations for its mean and covariance. We exte...
| Authors | Janice Adams, Daniele Venturi |
|---|---|
| Primary category | stat.ML |
| Published | 20 August 2026 |
| Last updated at source | 20 August 2026 |
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