Bayesian Hypernetworks David Krueger*, Chin-Wei Huang* Riahsat Islam, Ryan Turner, Aaron Courville MILA and McGill RLLAB

What’s a Bayesian Hypernet? Hypernet: a DNN that generates params of another DNN (the “primary net”)

Task: predict y from x

Y Z Think GAN / VAE / Real NVP

Hypernet

Primary Net

X

What is a Bayesian Neural Net? Bayes Rule: Predict using ensemble: Argmax

“Weight Uncertainty in Neural Networks” - Blundell et al 2015

What’s special about Bayesian Neural Nets? Bayes Rule:

“Knows what it knows” “That’s my best guess”

“I’m 99% sure!”

“Calibrated confidence”

“Weight Uncertainty in Neural Networks” - Blundell et al 2015

Example: self-driving cars Q: Is there a person in the road? Car: No, and…. “That’s my best guess”

“I’m 51% sure!” “I’m 99.999999% sure!”

__________ Humans want?

Existential risk

AI Safety “Is the default outcome doom?”

Concrete Problems in AI Safety

● Five “concrete problems”, calibrated confidence helps in 4/5

← Reward uncertainty

← I don’t know, ask Tom Everrit

← active learning

← safe exploration

← anomaly detection

Technique

Variational Inference for Bayesian DNNs ● ELBO:

constant

maximize

minimize

● Examples: Weight Uncertainty Variational Dropout / MC dropout

Encourages stochasticity!

Problem with Variational Inference: KL divergence Variational inference can underestimate uncertainty! P = true posterior (mixture of Gaussians)

Q = variational approx (Gaussian)

Are Bayesian Hypernets the solution? ● Previous work: approximate posterior is factorial: ● Use a DNN! ○ ⇒ can be dependent, multimodal Y Z

Hypernet

Primary Net

X

Note: h must be invertible! ...but the image of h can be a subset of R^|theta|, unlike with NICE (generative model)

Some Qualitative Results: Multimodality

Correlation

Background: Hypernetworks

“Dynamic Filter Networks” - Brabandere et al. 2016 “Learning feed-forward one-shot learners” Bertinetto et al. 2016 “HyperNetworks” Ha et al. 2016

Background: Weight Normalization

“Weight Normalization” Salimans and Kingma (slide from NIPS 2016 talk)

Background: Invertible Deep Generative Models

Key property: tractable likelihood (via change of variable):

(figure and equation: “Density Estimation via Real NVP” - Dinh et al. 2016)

Some results (5000 examples of MNIST):

QUESTIONS?

Kill all humans??

Krueger - Bayesian Hypernetworks.pdf

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