Paper presented in ICML 2020 Workshop on Uncertainty & Robustness in Deep Learning Paper link: http://www.gatsby.ucl.ac.uk/~balaji/udl2020/accepted-papers/UDL2020-paper-134.pdf

1. Maximizing the Representation Gap
between In-domain & OOD Examples
Jay Nandy Wynne Hsu Mong Li Lee
National University of Singapore
{jaynandy,whsu,leeml}@comp.nus.edu.sg
ICML workshop on Uncertainty & Robustness in Deep Learning, 2020

2. Predictive Uncertainty of DNNs
 Data or Aleatoric uncertainty:
 Arises from the natural complexities of the
underlying distribution, such as class
overlap, label noise, homoscedastic and
heteroscedastic noise
 Distributional Uncertainty:
 Distributional mismatch between the
training and test examples during inference
 Model or Epistemic uncertainty
 Uncertainty to estimating the network parameters, given training data
 Reducible given enough training data
In-domain example with Data
or Aleatoric uncertainty
Out-of-distribution (OOD)
example, that leads to
distributional uncertainty
[Gal, 2016; Candela et al., 2009]

3. Contributions
 Motivation:
 In presence of high data uncertainty among multiple classes, the existing OOD
detectors, including DPN (Malinin & Gales, 2018), tend to produce similar
representation for both in-domain and OOD examples.
 Leads to compromise the performance for OOD detection
 Proposed solution:
 Maximize the representation gap between in-domain and OOD examples
 A different representation for distributional uncertainty of OOD examples
 Propose a novel loss function for DPN framework
 Experimental Results:
 Consistently outperforms existing OOD detectors by addressing this issue.

4. Existing Approaches: Non-Bayesian
• Representation of predictive uncertainty:
• Sharp categorical posterior for in-domain examples
• Flat categorical posterior for out-of-domain (OOD) examples
• Limitations:
• Cannot robustly determine the source of uncertainty
• In particular, high data uncertainty among multiple class leads to the same
representation for both in-domain and OOD examples.
In-Domain
Misclassification
Out-of-Domain (OOD)
Examples
In-Domain
Confident Prediction
[Hendrycks et al., 2019b, Lee et al., 2018]

5. Existing Approaches: Bayesian
• Bayesian neural networks assumes a prior distribution over the network parameters
• Approximation requires to estimate the true posterior of the model parameters
• Sample model parameters using MCMC or Deep Ensemble etc.
• Limitations:
• Computationally expensive to produce the ensemble
• Difficult to control this desired behavior
In-Domain Confident pred.
• Ensemble of prediction in one
corner of the simplex.
In-Domain Misclassification:
• Ensemble of prediction in the
middle of the simplex.
OOD Examples:
• Ensemble of prediction are
scattered over the simplex.
. . .
. . .
. . .
. . .
. . .
. . .
[Gal and Ghahramani, 2016; Lakshminarayanan et al., 2017]

6. Dirichlet Prior Network (Existing)
• Parameterize a prior Dirichlet distribution to the categorical posteriors over a
simplex
• Objective: Efficiently emulating the behavior of Bayesian (ensemble) approaches
Sharp Dirichlet in one corner
 Uni-modal categorical.
Sharp Dirichlet in the middle
 Multi-modal categorical
Flat Dirichlet
 Uniform categorical
over all class labels.
Confident prediction
(In-Domain Examples)
Misclassification
(In-Domain Examples)
OOD Examples
[Malinin & Gales, 2018; 2019]

7. Proposed Representation for OOD
• Limitation (high Data uncertainty)
• In-domain examples with high data-uncertainty, among multiple classes, leads to
producing flatter Dirichlet distribution
• Can be observed for classification task with large number of classes
• This often leads to indistinguishable representation from OOD examples.
• Compromise the OOD detection performance
Confident prediction
(In-Domain Examples)
Misclassification
(In-Domain Examples)
OOD Examples
Desired Actual
[see detailed analysis in our paper]

8. Proposed Representation for OOD
• Maximize the representation gap of OOD examples from In-domain examples
• Sharp multi-modal Dirichlet with densities uniformly distributed at each corner for
OOD examples, instead of flat Dirichlet
Confident prediction
(In-Domain Examples)
Misclassification
(In-Domain Examples)
OOD Examples
Desired Actual Existing Proposed

9. Proposed Loss function
Confident prediction
(In-Domain Examples)
Misclassification
(In-Domain Examples)
OOD Examples
Desired Actual Existing Proposed
We propose a novel loss function to separately model the mean and precision of the
output Dirichlet distribution:
• Mean: Cross entropy loss with soft-max activation
• Precision:A novel explicit precision regularization function
Provides a better control on the desired representation.
We show that the existing RKL loss cannot produce this representation
[see more detailed analysis in our paper]

10. Proposed Loss function
• A neural network with soft-max activation can be viewed as DPN.
• Concentration parameters of the Dirichlet is given by exponential of logits
Categorical posterior is given by the
mean of the output Dirichet:

11. Dirichlet distributions with different
concentration parameter values
Sharp uni-modal Dirichlet:
• Large precision value
• Large concentration value for the correct class.
Flat Dirichlet distribution:
• Small precision values.
• Equal concentration values > 1
Sharp multi-modal Dirichlet, uniform at all corners:
• Small precision value.
• Equal concentration values < 1

12. Proposed Loss function
In-Domain
Examples
• Objective: Model the mean position + Model the precision values
(Standard Cross-entropy loss) (Proposed regularizer)
(Bounded approximation
of the precision)
Maximum concentration
value for the correct class

13. Proposed Loss function
• Objective: Model the mean position + Model the precision values
(Standard Cross-entropy loss) (Proposed regularizer)
Standard CE loss w.r.t uniform dist.
 Equal prob. for all classes
OOD Examples
Proposed representation for OOD

14. Uncertainty Measures

15. Total Uncertainty Measure
High maxP score:
Confident Prediction
Low maxP score:
In-domain misclassification/ OOD?

16. Distributional Uncertainty Measure
Confident Pred.
First Term
Second Term
MI (Overall)
Low
Low
Low (~0)

17. Distributional Uncertainty Measure
Given prob. mass is
concentrated
High
Low
High
In-Domain Example OOD Example
Misclassification (Malinin & Gales) ProposedConfident Pred.
Maximizes the gap
First Term
Second Term
MI (Overall)
Low
Low
Low (~0)
High
High
Low (~0)
High
Average
Average

18. Synthetic Dataset
In-Domain Training Data

19. Synthetic Dataset
In-Domain Training Data
Larger uncertainty scores for both
in-domain examples with class
overlap (i.e data uncertainty ) and
OOD examples.

20. Synthetic Dataset
In-Domain Training Data

21. Synthetic Dataset
In-Domain Training Data
Precision as dist. uncertainty measure:
• High scores for in-domain examples
• Low scores for OOD examples

22. Benchmark Vision Datasets

23. Conclusion
 We show that: in presence of high data uncertainty, the existing OOD detection
models, including DPN, tend to produce similar representation for both in-domain
and OOD examples, leading to compromise OOD detection performance
 We propose to model the distributional uncertainty using multi-modal Dirichlet
distribution for DPN (Malinin & Gales, 2018) to maximize the representation gap
between in-domain and OOD examples
 Experimental results demonstrates that our proposed technique consistently
outperforms other OOD detection models by addressing this issue.
Thank You 