Uncertainty-Aware Attention for Reliable Interpretation and PredictionPermalink

ContentsPermalink

1. Abstract
2. Introduction
3. Approach
   1. Stochastic Attention with input-adaptive Gaussian Noise
   2. Variational Inference

0. AbstractPermalink

Attention mechanism은 relevant feature에 집중할 수 있게끔 하는 엄청난 기능을 가지지만….

$\rightarrow$ may be UNRELIABLE

이를 극복하기 위해….Input-dependent uncertainty라는 개념을 소개함

( = generates attention for each feature with varying degrees of noise based on the given input )

$\rightarrow$ learn larger variance on instances, with high uncertainty

propse UA ( Uncertainty-aware Attention ) mechanism using VI

1. IntroductionPermalink

BackgroundPermalink

• high reliability를 얻는 것은 매우 중요해! 특히 safety 관련해서!

• Attention : find most relevant features for each input instance

  ( + allows easy interpretation )

• Attention의 한계점 : unreliable

  $\rightarrow$ need a model that knows its own limitation!

  ( = 예측/판단을 내려도 될 정도로 safe한지를 모델 지 스스로 잘 알아야! )

ProposalPermalink

allow attention to output uncertainty on each input

• 더 나아가서, leverage them when making final predictions

• 구체적으로, attention weight를 Gaussian으로 모델링 ( input dependent noise O )

ContributionPermalink

• 1) Variational Attention 모델을 제안함
• 2) UA알고리즘이 accurate calibration of model uncertainty를 만듬
• 3) 6개의 real world 데이터에 테스스

2. ApproachPermalink

STOCHASTIC attention ( 최초 제안은 X )

• $\mathbf{v}(\mathbf{x}) \in \mathbb{R}^{r \times i}$ : concatenation of $i$ intermediate features
  • each column of which $\mathbf{v}_{j}(\mathbf{x})$ is a length $r$ vector
  • 이 $\mathbf{v}(\mathbf{x})$ 로부터 random variables $\left\{\mathbf{a}_{j}\right\}_{j=1}^{i}$ 가 conditionally 생성된다
• $\mathbf{c}(\mathbf{x})=\sum_{j=1}^{i} \mathbf{a}_{j} \odot \mathbf{v}_{j}(\mathbf{x})$ : context vector ( $\mathbf{c} \in \mathbb{R}^{r}$ )
• $\hat{\mathbf{y}}=f(\mathbf{c}(\mathbf{x}))$ : final output

attention은 deterministic / stochastic 할 수 있다

• ex) stochastic attention : $\mathbf{a}_j$ 는 Bernoulli distribution에서 생성됨.

  $\rightarrow$ maximize ELBO

• stochastic attention > deterministic counterpart, on image annotation task.

2-1. Stochastic Attention with input-adaptive Gaussian NoisePermalink

위의 Stochastic attention의 2가지 한계점

( stochastic attention을 directly하게 Bernoulli/Multinomial에서 뽑는다는 점에서 )

• [ 한계점 1 ] Bernoulli의 variance는 allocation probability $\mu$와 DEPENDENT

  • $\mathbf{a} \sim \text{Bernoulli}(\mu)$.
  • allocation probability $\mu$ : attention 연결 할지/말지
  • Bernoulli의 variance : $\sigma^{2}=\mu(1-\mu)$
  • 따라서, $\mathbf{a}$의 variance는 낮기 어렵다 ( if $\mu$가 0.5 부근 )

• [ 해결책 1 ]

  disentangle the attention strength a from the attention uncertainty

  $\rightarrow$ so that the uncertainty could vary even with the same attention strength

• [ 한계점 2 ] Vanilla stochastic attention models the noise independently of the input

  • (구 방식) input과 무관하게 noise를 모델링함

• [ 해결책 2 ] 위의 두 한계점들을 극복하기 위해…

  “input과 관련있게 noise를 모델링함 ( $\sigma(x)$ )”

  • (구) $p(\boldsymbol{\omega})=\mathcal{N}\left(\mathbf{0}, \tau^{-1} \mathbf{I}\right), \quad p_{\theta}(\mathbf{z} \mid \mathbf{x}, \boldsymbol{\omega})=\mathcal{N}\left(\boldsymbol{\mu}(\mathbf{x}, \boldsymbol{\omega} ; \theta), \operatorname{diag}\left(\boldsymbol{\sigma}^{2}\right)\right)$

  • (신) $p(\boldsymbol{\omega})=\mathcal{N}\left(\mathbf{0}, \tau^{-1} \mathbf{I}\right), \quad p_{\theta}(\mathbf{z} \mid \mathbf{x}, \boldsymbol{\omega})=\mathcal{N}\left(\boldsymbol{\mu}(\mathbf{x}, \boldsymbol{\omega} ; \theta), \operatorname{diag}\left(\boldsymbol{\sigma}^{2}(\mathbf{x}, \boldsymbol{\omega} ; \theta)\right)\right)$

    ( 위 두 식에서, $\mathbf{z}$는 attention score before squashing… 즉 $\mathrm{a}=\pi(\mathrm{z})$ )

  • empirically shown that the quality of uncertainty improves

2-2. Variational InferencePermalink

( 위 2-1.에서 세운 방법을, VI를 통해 푼다 )

$\mathbf{Z}$ : set of latent variables $\left\{\mathbf{z}^{(n)}\right\}_{n=1}^{N}$ that stands for attention weight before squashing.

Posterior $p(\mathbf{Z}, \boldsymbol{\omega} \mid \mathcal{D})$ is usually computationally intractable !

$\rightarrow$ use VI ( Variational Inference )

Variational Distribution :

• $q(\mathbf{Z}, \boldsymbol{\omega} \mid \mathcal{D})=q_{\mathbf{M}}(\boldsymbol{\omega} \mid \mathbf{X}, \mathbf{Y}) q(\mathbf{Z} \mid \mathbf{X}, \mathbf{Y}, \boldsymbol{\omega})$.

• 1번째 term) MC Dropout 사용 ( variational parameter $\mathbf{M}$ )
• 2번째 term) 그냥 set $q(\mathbf{Z} \mid \mathbf{X}, \mathbf{Y}, \boldsymbol{\omega})=p_{\theta}(\mathbf{Z} \mid \mathbf{X}, \boldsymbol{\omega})$

이를 정리하면, 아래의 ELBO를 maximize하는 것과 동일하다.

• $\begin{aligned} \log p(\mathbf{Y} \mid \mathbf{X}) \geq & \mathbb{E}_{\boldsymbol{\omega} \sim q_{\mathbf{M}}(\boldsymbol{\omega} \mid \mathbf{X}, \mathbf{Y}), \mathbf{Z} \sim p_{\theta}(\mathbf{Z} \mid \mathbf{X}, \boldsymbol{\omega})}[\log p(\mathbf{Y} \mid \mathbf{X}, \mathbf{Z}, \boldsymbol{\omega})] \\ &-\mathrm{KL}\left[q_{\mathbf{M}}(\boldsymbol{\omega} \mid \mathbf{X}, \mathbf{Y}) \| p(\boldsymbol{\omega})\right]-\operatorname{KL}\left[q(\mathbf{Z} \mid \mathbf{X}, \mathbf{Y}, \boldsymbol{\omega}) \| p_{\theta}(\mathbf{Z} \mid \mathbf{X}, \boldsymbol{\omega})\right] \end{aligned}$.

최종 maximize할 대상 : $\mathcal{L}(\theta, \mathbf{M} ; \mathbf{X}, \mathbf{Y})=\sum \log p_{\theta}\left(\mathbf{y}^{(n)} \mid \tilde{\mathbf{z}}^{(n)}, \mathbf{x}^{(n)}\right)-\lambda\|\mathbf{M}\|^{2}$.

• step 1) sample random weights with dropout masks $\widetilde{\omega} \sim q_{\mathrm{M}}(\boldsymbol{\omega} \mid \mathbf{X}, \mathbf{Y})$
• step 2) sample $\mathbf{z}$ such that $\tilde{\mathbf{z}}=q(\mathbf{x}, \tilde{\varepsilon}, \widetilde{\omega}), \tilde{\varepsilon} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$

Testing new input $\mathbf{x}^{*}$ : MC-sampling 사용해서..

• $p\left(\mathbf{y}^{*} \mid \mathbf{x}^{*}\right)=\iint p\left(\mathbf{y}^{*} \mid \mathbf{x}^{*}, \mathbf{z}\right) p\left(\mathbf{z} \mid \mathbf{x}^{*}, \boldsymbol{\omega}\right) p(\boldsymbol{\omega} \mid \mathbf{X}, \mathbf{Y}) \mathrm{d} \boldsymbol{\omega} \mathrm{d} \mathbf{z} \approx \frac{1}{S} \sum_{s=1}^{S} p\left(\mathbf{y}^{*} \mid \mathbf{x}^{*}, \tilde{\mathbf{z}}^{(s)}\right)$/

Uncertainty CalibrationPermalink

ECE (Expected Calibration Error)가 보다 나음을 확인!

( = expected gap w.r.t the distribution of model confidence )

$\mathrm{ECE}=\mathbb{E}_{\text {confidence }}[\mid p($ correct $\mid$ confidence $)-$ confidence $\mid]$