Original: M ACHINE L EARNING FROM E XPLANATIONS
Revised: M ACHINE L EARNING FROM E XPLANATIONS

Original: Anonymous authors
Revised: Anonymous authors

Original: Paper under double-blind review
Revised: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: Machine learning needs a huge amount of (labeled) data, as otherwise it might not learn the right model for different sub-populations, or even worse, they might pick up spurious correlations in the training data leading to brittle models.
Revised: Machine learning needs a huge amount of (labeled) data, as otherwise it might not learn the right model for different sub-populations, or even worse, they might pick up spurious correlations in the training data leading to brittle models.

Original: Also, for small training datasets, there is a huge variability in the learned models on randomly sampled training datasets, which makes the whole process less reliable.
Revised: Also, for small training datasets, there is a huge variability in the learned models on randomly sampled training datasets, which makes the whole process less reliable.

Original: But, collection of large amount of useful representative data, and training on large datasets, are very costly.
Revised: But, collection of large amount of useful representative data, and training on large datasets, are very costly.

Original: In this paper, we present a technique to train reliable classification models on small datasets, assuming we have access to some simple explanations (e.g., subset of important input features) on labeled data.
Revised: In this paper, we present a technique to train reliable classification models on small datasets, assuming we have access to some simple explanations (e.g., subset of important input features) on labeled data.

Original: We also propose a two stage training pipeline that optimizes the model’s output and finetunes its attention in an interleaving manner, to help the model to discover the reason behind the provided explanation while learning from the data.
Revised: We also propose a two stage training pipeline that optimizes the model’s output and finetunes its attention in an interleaving manner, to help the model to discover the reason behind the provided explanation while learning from the data.

Original: We show that our training pipeline enables a faster convergence to better models, especially when there is a severe class imbalance or spurious features in the training data.
Revised: We show that our training pipeline enables a faster convergence to better models, especially when there is a severe class imbalance or spurious features in the training data.

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Machine learning has an excellent performance in many challenging tasks (Dosovitskiy et al., 2020;
Revised: Machine learning has an excellent performance in many challenging tasks (Dosovitskiy et al., 2020;

Original: Liu et al., 2021; Zhang et al., 2020), reaching or even outperforming humans (Silver et al., 2016;
Revised: Liu et al., 2021; Zhang et al., 2020), reaching or even outperforming humans (Silver et al., 2016;

Original: Li et al., 2022), in controlled experiments.
Revised: Li et al., 2022), in controlled experiments.

Original: However, their real-life performance is often drastically worse, especially when there are natural spurious correlations in training data (Arjovsky et al., 2019;
Revised: However, their real-life performance is often drastically worse, especially when there are natural spurious correlations in training data (Arjovsky et al., 2019;

Original: Ribeiro et al., 2016), and in so many cases where the training data set is small, heterogeneous, or unbalanced .
Revised: Ribeiro et al., 2016), and in so many cases where the training data set is small, heterogeneous, or unbalanced .

Original: All this makes it hard for the existing learning algorithms to learn the right set of robust rules that can generalize well from training data.
Revised: All this makes it hard for the existing learning algorithms to learn the right set of robust rules that can generalize well from training data.

Original: This is a serious issue in many critical applications where machine learning promises to assist humans.
Revised: This is a serious issue in many critical applications where machine learning promises to assist humans.

Original: For example, the training data used in training human-level medical AI models often contain spurious features, and models overly rely on spurious features to classify medical images, which results in untrustworthy diagnoses in practice (Rieger et al., 2020).
Revised: For example, the training data used in training human-level medical AI models often contain spurious features, and models overly rely on spurious features to classify medical images, which results in untrustworthy diagnoses in practice (Rieger et al., 2020).

Original: To make it worse, models tend to extract more spurious reasons from the smaller sets, making models more useless for minority groups (Sagawa et al., 2020).
Revised: To make it worse, models tend to extract more spurious reasons from the smaller sets, making models more useless for minority groups (Sagawa et al., 2020).

Original: If the model does not learn the true reason, it usually finds reasons to favor the majority in the training set because it is an empirical risk minimizer.
Revised: If the model does not learn the true reason, it usually finds reasons to favor the majority in the training set because it is an empirical risk minimizer.

Original: Even if the model up-weights the minority group to prevent them from being left out, which is a common practice in long-tailed classification, the model cannot classify minorities well on unseen data because the reasons extracted cannot be generalized.
Revised: Even if the model up-weights the minority group to prevent them from being left out, which is a common practice in long-tailed classification, the model cannot classify minorities well on unseen data because the reasons extracted cannot be generalized.

Original: This discrepancy in group performance is also the base of the algorithmic (un)fairness problem in machine learning.
Revised: This discrepancy in group performance is also the base of the algorithmic (un)fairness problem in machine learning.

Original: Getting more data seems to help to solve some obvious problems, with a significant cost (for obtaining a large amount of high-quality, accurately labeled data, and for training models on large datasets).
Revised: Getting more data seems to help to solve some obvious problems, with a significant cost (for obtaining a large amount of high-quality, accurately labeled data, and for training models on large datasets).

Original: However, it does not seem to necessarily help to learn stable and generalizable models.
Revised: However, it does not seem to necessarily help to learn stable and generalizable models.

Original: We observe that running the same training algorithms on the same datasets can yield models of similar accuracies that have learned drastically different decision functions and have low prediction agreements among themselves (Ross et al., 2017; D’Amour et al., 2020; Watson et al., 2022).
Revised: We observe that running the same training algorithms on the same datasets can yield models of similar accuracies that have learned drastically different decision functions and have low prediction agreements among themselves (Ross et al., 2017; D’Amour et al., 2020; Watson et al., 2022).

Original: This comes as no surprise, given the high-dimensionality of input space and parameter space, for (classification) tasks with so few labels.
Revised: This comes as no surprise, given the high-dimensionality of input space and parameter space, for (classification) tasks with so few labels.

Original: To fully eliminate the ambiguity in parameter space, we need datasets of astronomical sizes, which prohibitively increases the cost of using machine learning for most real-world problems. 
Revised: To fully eliminate the ambiguity in parameter space, we need datasets of huge sizes, which prohibitively increases the cost of using machine learning for most real-world problems. Collecting more data is also not always possible.

Revised: For example, for (rare) disease diagnoses, there are not many new patients every year to expand the datasets.

Revised: In manufacturing industries, defect detection systems for new products also do not have much data available.

Revised: This shows there is a need to develop better learning algorithms in small data regimes.

Original: In this paper, we show that guiding machine learning with simple explanations can significantly improve its performance, reduce its sample complexity, and increase its stability .
Revised: In this paper, we show that guiding machine learning with simple explanations can significantly improve its performance, reduce its sample complexity, and increase its stability .

Original: We assume that for some training data points, in addition to their label, we also have an expert explanation for the assigned labels.
Revised: We assume that for some training data points, in addition to their label, we also have an expert explanation for the assigned labels.

Original: The explanation can have different degrees of complexity.
Revised: The explanation can have different degrees of complexity.

Original: However, in its simplest form, we can assume that a small subset of input features is highlighted to contain the high-level reason for the assigned label.
Revised: However, in its simplest form, we can assume that a small subset of input features is highlighted to contain the high-level reason for the assigned label.

Original: We propose an effective algorithm for machine learning with explanations, where we guide the model to identify the correct latent features most consistent with the explanations while optimizing the model’s overall accuracy based on labels.
Revised: We propose an effective algorithm for machine learning with explanations, where we guide the model to identify the correct latent features most consistent with the explanations while optimizing the model’s overall accuracy based on labels.

Original: Our approach significantly outperforms the baselines in convergence rate, accuracy, robustness to spurious correlations, and stability (with influences generalizability), especially for heterogeneous data.
Revised: Our approach significantly outperforms the baselines in convergence rate, accuracy, robustness to spurious correlations, and stability (with influences generalizability), especially for heterogeneous data.

Original: Under these settings, we show that baselines not only struggle to learn complex tasks, but also fail at properly learning the right reasons for classifying data for extremely simple tasks (e.g., detecting geometric shapes).
Revised: Under these settings, we show that baselines not only struggle to learn complex tasks, but also fail at properly learning the right reasons for classifying data for extremely simple tasks (e.g., detecting geometric shapes).

Original: Thus, we argue that it is necessary to incorporate explanations in learning algorithms, if we aim at using machine learning in real-world scenarios.
Revised: Thus, we argue that it is necessary to incorporate explanations in learning algorithms if we aim at deploying trustworthy ML models that do not latch onto spurious or counter-intuitive signals.

Original: Some prior works have explored the idea of using prior knowledge to improve machine learning (Ross et al., 2017;
Revised: Some prior works have explored the idea of using prior knowledge to improve machine learning (Ross et al., 2017;

Original: Rieger et al., 2020;
Revised: Rieger et al., 2020;

Original: Schramowski et al., 2020; Shao et al., 2021).
Revised: Schramowski et al., 2020; Shao et al., 2021).

Original: Although their objective is to be “right for the right reasons”, these methods are actually penalizing models when they learn the wrong reasons.
Revised: Although their objective is to be “right for the right reasons”, these methods are actually penalizing models when they learn the wrong reasons.

Original: As we show in our analysis, this does not necessarily result in learning the right reasons, thus it has a limited advantage to learning only from labels.
Revised: As we show in our analysis, this does not necessarily result in learning the right reasons, thus it has a limited advantage to learning only from labels.

Original: This is also fundamentally different from our proposed approach.
Revised: This is also fundamentally different from our proposed approach.

Original: Conceptually, providing the explanation for right reasons is much easier than enumerating all possible ways that the models might make mistakes, and doing so during the data collection phase.
Revised: Conceptually, providing the explanation for right reasons is much easier than enumerating all possible ways that the models might make mistakes, and doing so during the data collection phase.

Original: If there are known spurious correlations, a more straightforward and more effective solution (compared to penalizing the model on learning the spurious correlations) would be to remove them and train models on clean data (Friedrich et al., 2022).
Revised: If there are known spurious correlations, a more straightforward and more effective solution (compared to penalizing the model on learning the spurious correlations) would be to remove them and train models on clean data (Friedrich et al., 2022).

Original:  L EARNING FROM E XPLANATIONS 2. P ROBLEM S TATEMENT
Revised:  L EARNING FROM E XPLANATIONS 2. P ROBLEM S TATEMENT

Original: Given a labeled dataset D = { ( x , y ) i } , we also have access to explanations e ( x ) ⊂ x , which are a subset of the input features, of the label for each input point x .
Revised: Given a labeled dataset D = { ( x , y ) i } , we also have access to explanations e ( x ) ⊂ x , which are a subset of the input features, of the label for each input point x .

Original: The explanations are informative enough that they can sufficiently explain the labels.
Revised: The explanations are informative enough that they can sufficiently explain the labels.

Original: We want to train a model to produce outputs similar to the given labels and base their decisions using reasons close to the given explanations.
Revised: We want to train a model to produce outputs similar to the given labels and base their decisions using reasons close to the given explanations.

Original: 2. W HY DO PREVIOUS METHODS NOT WORK WELL ?
Revised: 2. W HY DO PREVIOUS METHODS NOT WORK WELL ?

Original: In this work, we focus on the image domain, where a wide range of model explanation methods have been studied.
Revised: In this work, we focus on the image domain, where a wide range of model explanation methods have been studied.

Original: There are some prior works (Ross et al., 2017;
Revised: There are some prior works (Ross et al., 2017;

Original: Rieger et al., 2020;
Revised: Rieger et al., 2020;

Original: Schramowski et al., 2020; Shao et al., 2021) on a similar problem to ours.
Revised: Schramowski et al., 2020; Shao et al., 2021) on a similar problem to ours.

Original: Explanations in their settings are bounding boxes of either the main object or the spurious features, which differ from our definition of “informative and sufficient subsets of input features”.
Revised: Explanations in their settings are bounding boxes of either the main object or the spurious features, which differ from our definition of “informative and sufficient subsets of input features”.

Original: Technically, they all adopt a loss-based approach, adding an explanation misalignment loss to the label loss:
Revised: Technically, they all adopt a loss-based approach, adding an explanation misalignment loss to the label loss:

Original: [Equation]
Revised: [Equation]

Original: The additional loss is computed by taking the difference between the feature attributions attr ( x ) computed by certain model explanation methods and the given explanation e ( x ) :
Revised: The additional loss is computed by taking the difference between the feature attributions attr ( x ) computed by certain model explanation methods and the given explanation e ( x ) :

Original: [Equation]
Revised: [Equation]

Original: While it is tempting to reuse the existing algorithms for our problem, they do not lead to higher test accuracy than vanilla training in practice.
Revised: While it is tempting to reuse the existing algorithms for our problem, they do not lead to higher test accuracy than vanilla training in practice.

Original: The first reason is that using model explanation methods to generate models’ attributions is questionable.
Revised: The first reason is that using model explanation methods to generate models’ attributions is questionable.

Original: Adebayo et al.
Revised: Adebayo et al.

Original: (2018) have shown that most popular model explanations do not even pass the sanity check.
Revised: (2018) have shown that many popular saliency map based explanations do not even pass the sanity check.

Original: Using them as a proxy of models’ attention is thus unreliable.
Revised: Using them as a proxy of models’ attention is thus unreliable.

Original: The second reason is with training.
Revised: The second reason is with training.

Original: Optimization of the joint loss is often done via gradient descent.
Revised: Optimization of the joint loss is often done via gradient descent.

Original: However, gradients of the two loss terms may point to different directions, creating a race condition that pulls and pushes the model into a bad local optimum.
Revised: However, gradients of the two loss terms may point to different directions, creating a race condition that pulls and pushes the model into a bad local optimum.

Original: Imagine the two gradients counteract each other.
Revised: Imagine the two gradients counteract each other.

Original: The weights are then updated with negligible aggregated gradients.
Revised: The weights are then updated with negligible aggregated gradients.

Original: This leads to models converging more slowly or not even getting updated in the worst case.
Revised: This leads to models converging more slowly or not even getting updated in the worst case.

Original: Rieger et al.
Revised: Rieger et al.

Original: (2020) and Friedrich et al.
Revised: (2020) and Friedrich et al.

Original: (2022) have empirically verified that these methods often do not outperform the vanilla models trained with labels only, and sometimes they are strictly worse than vanilla models.
Revised: (2022) have empirically verified that these methods often do not outperform the vanilla models trained with labels only, and sometimes they are strictly worse than vanilla models.

Original: 2. T UNING MODELS ’ ATTENTION ON LATENT FEATURES TO LEARN FROM THE EXPLANATION
Revised: 2. T UNING MODELS ’ ATTENTION ON LATENT FEATURES TO LEARN FROM THE EXPLANATION

Original: To design a working algorithm that teaches the reason to models, the first step is to teach models to identify the predictive features highlighted by explanations.
Revised: To design a working algorithm that teaches the reason to models, the first step is to teach models to identify the predictive features highlighted by explanations.

Original: However, as input pixels are less semantically meaningful for image data, we need to guide the model to recognize important features in the latent space.
Revised: However, as input pixels are less semantically meaningful for image data, we need to guide the model to recognize important features in the latent space.

Original: Since explanations are sufficient, the latent representations of the given explanations should also be distinctive enough for the classifier.
Revised: Since explanations are sufficient, the latent representations of the given explanations should also be distinctive enough for the classifier.

Original: Hence, the core idea is to make the latent features extracted by our models more similar to the latent representations of the explanations.
Revised: Hence, our core idea is to make the latent features extracted by our models more similar to the those of the explanations.

Original: We minimize the  difference between  latent features x′ feat and x ′ feat by optimizing the feature misalignment loss, which is the KL divergence between two normalized feature maps:
Revised: We minimize the distributional difference between normalized latent features x feat and x ′ feat by optimizing the feature misalignment loss, which is the KL divergence between two normalized feature maps using softmax:

Original: [Equation]
Revised: [Equation]

Original: where N is the size of the latent features.
Revised: where N is the size of the latent features.

Revised: There are two important design choices in this loss function.

Revised: The first one is using normalized feature maps.

Revised: Without normalization, latent features can be very large or very small, potentially resulting in exploding or vanishing gradients.

Revised: Secondly, we use KL divergence as the loss criterion.

Revised: The main reason is that we want the distributions to be more similar, which can imply that the model’s focus is primarily on the reasons region.

Original:  Since we also need to make models accurate, weneed to minimize the label loss, which is the cross entropy loss between the prediction y ′ and true label y :
Revised: Other loss functions may work empirically, but do not provide similar distributional intuition. Since we also need to make models accurate, we minimize the label loss, which is the cross entropy loss between the prediction y ′ and true label y :

Original: [Equation]
Revised: [Equation]

Original: To avoid creating the same race condition in prior work, we propose to optimize them sequentially.
Revised: To avoid creating the same race condition in prior work, we propose to optimize them sequentially.

Original: Our training algorithm alternatives between minimizing the label loss and the feature misalignment loss.
Revised: Our training algorithm alternates between minimizing the label loss and the feature misalignment loss.

Original: Algorithm 1 describes our two-stage optimization.Algorithm
Revised: Algorithm 1 describes our two-stage optimization.

Original: Require:
Revised: Require:

Original: Input data x , model h  consists of feature extractor f  and fully connected layers c ,mapping layer m , target y , explanation e ( x ) , learning rates λ 1 and λ 2 for cross entropy loss and feature map loss
Revised: Input data x , model h = c ◦ m ◦ f consists of feature extractor f , mapping layer m , and fully connected layers c , target y , explanation e ( x ) , learning rates η 1 and η 2 for cross entropy loss and feature map loss

Original: 1: L CE ← − y log( h ( x )) − (1 − y )
Revised: 1: L CE ← − y log( h ( x )) − (1 − y )

Original: log(1 − h ( x )) 2: θ h ← θ h + λ 1 ∇ θ h L CE 3: x ′ ← x ⊗ e ( x ) 4: x ′ feat ←  f ( x ′ ) 5: x feat ←  m ( f ( x )) 6: Normalize the two feature maps
Revised: log(1 − h ( x )) 2: θ h ← θ h − η 1 ∇ θ h L CE 3: x ′ ← x ⊗ e ( x ) 4: x ′ feat ← softmax ( f ( x ′ )) 5: x feat ← softmax ( m ( f ( x ))) 6: L feat ← KL ( x ′ feat ∥ x feat )

Original: [Figure]
Revised: [Table]

Revised: : θ m ←

Original: [Equation]
Revised: [Table]

Original: [Figure] [Equation] [Figure]
Revised: m

Original: [Equation] [Figure] 
Revised: [Table] [Figure] [Table]

Original: [Equation] [Figure] 
Revised: [Figure] [Table] feat

Original: Fig 1 illustrates our two-stage training process.
Revised: Fig 1 illustrates our two-stage training process.

Original: Given a convolutional neural network (CNN) h , we first decompose it into two parts: (i) the feature extractor f , which contains all the convolutional layers, and (ii) the classifier c , which contains all the fully connected (FC) layers.
Revised: Given a convolutional neural network (CNN) h , we first decompose it into two parts: (i) the feature extractor f , which contains all the convolutional layers, and (ii) the classifier c , which contains all the fully connected (FC) layers.

Original: In the first stage, we do a normal forward pass and then backpropagate the label loss to update the entire model.

Original: Note that we insert a mapping layer  between the feature extractor and the classifier in the model.
Revised: We insert a mapping layer m in between f and c .

Original: This mapping layer is a linear layer that maps features extract by f back to the same feature space.
Revised: The mapping layer is a linear layer that maps features extracted by f back to the same feature space.

Original: It will be trained to filter out irrelevant information and amplify signals from the reasons region.
Revised: It will be trained to filter out irrelevant information and amplify signals from the reasons region.

Original: This addition is introduced because we do not want to update the weights of the feature extractor in the second stage.
Revised: This addition is introduced because we do not want to update the weights of the feature extractor in the second stage.

Original: Otherwise, it would cause similar problems in prior work where two gradients counteract each other.
Revised: Otherwise, it would cause similar problems in prior work where two gradients counteract each other.

Revised: In the first stage, we do a normal forward pass and then backpropagate the label loss to update the entire model.

Original: Inthis case, in the second stage, we use the explanation e ( x ) as a binary mask over the input image x to obtain the masked input x ′ .
Revised: In the second stage, we use the explanation e ( x ) as a binary mask over the input image x to obtain the masked input x ′ .

Original: We can then pass the masked input to the feature extractor to obtain its feature map x ′ feat =  f ( x ′ ) .
Revised: We can then pass the masked input to the feature extractor to obtain its feature map x ′ feat = softmax ( f ( x ′ )) .

Original: We then compute the feature map x feat =  m ( f ( x )) and minimize its difference with the reasons’ feature map x ′ feat using Equation 3.
Revised: We then compute the feature map x feat = softmax ( m ( f ( x ))) and minimize its difference with the reasons’ feature map x ′ feat using Equation 3.

Original: We subsequently update the weights of the mapping layer m by backpropagating the feature misalignment loss. 
Revised: We subsequently update the weights of the mapping layer m by backpropagating the feature misalignment loss. [Figure] MappingLayer [Figure]

Revised: Fully-connected

Revised: Layers c

Original:   E MPIRICAL A NALYSIS
Revised: Output [Figure]  E MPIRICAL A NALYSIS

Original: We focus on binary classification with three datasets in our empirical analysis.
Revised: We focus on binary classification with three datasets in our empirical analysis.

Original: Two of the datasets are synthetic geometric datasets that are easy for humans but challenging for machines, and one is a real dataset that is difficult even for normal humans:[Figure] ConvolutionalLayers MappingLayer
Revised: Two of the datasets are synthetic geometric datasets that are easy for humans but challenging for machines, and one is a real dataset that is difficult even for normal humans:

Original: Fully

Original: [Figure] Output [Figure] • Triangle Orientation Dataset: If a triangle is pointing upwards, it is assigned to be Class 1.
Revised: • Triangle Orientation Dataset: If a triangle is pointing upwards, it is assigned to be Class 1.

Original: Otherwise, it is Class 0.
Revised: Otherwise, it is Class 0.

Original: The explanation is a rectangular area highlighting the spatial arrangement of the vertex and the bottom.
Revised: The explanation is a rectangular area highlighting the spatial arrangement of the vertex and the bottom.

Original: (Details in Appendix A.1) • Fox vs Cat Dataset: Foxes (Class 1) have triangular heads and cats (Class 0) have round heads.
Revised: (Details in Appendix A.1) • Fox vs Cat Dataset: Foxes (Class 1) have triangular heads and cats (Class 0) have round heads.

Original: The explanation is a square highlighting either the vertex or the arc.
Revised: The explanation is a square highlighting either the vertex or the arc.

Original: (Details in Appendix A.2) • Bird Dataset: We select Indigo Buntings and Blue Grosbeaks from the CUB-200dataset (Wah et al., 2011) to form our binary Bird dataset.
Revised: (Details in Appendix A.2) • Bird Dataset: We select Indigo Buntings and Blue Grosbeaks from the CUB-200dataset (Wah et al., 2011) to form our binary Bird dataset.

Original: The two species are visually identical except for the sizes of their beaks.
Revised: The two species are visually identical except for the sizes of their beaks.

Original: The explanation is then a small square highlighting the beaks.
Revised: The explanation is then a small square highlighting the beaks.

Original: (Details in Appendix A.3)
Revised: (Details in Appendix A.3)

Original: We start our empirical analysis from simple geometric datasets where a human can apply a very simple rule to perfectly classify all images.
Revised: We start our empirical analysis from simple geometric datasets where a human can apply a very simple rule to perfectly classify all images.

Original: However, such simple datasets are surprisingly challenging for machine learning models if they are trained with labels only.
Revised: However, such simple datasets are surprisingly challenging for machine learning models if they are trained with labels only.

Original: Not only do models fail to learn the simple rule from more than enough data, but they also often pick up wrong rules that do not generalize well.
Revised: Not only do models fail to learn the simple rule from more than enough data, but they also often pick up wrong rules that do not generalize well.

Original: We have presented the intuition of our algorithm in the previous section, so we want to empirically verify that models trained with reasons using our training pipeline are better.
Revised: We have presented the intuition of our algorithm in the previous section, so we want to empirically verify that models trained with reasons using our training pipeline are better.

Original: After observing how conventional ML training algorithms fail on the easy geometric synthetic dataset, we naturally extend our analysis to the harder Bird dataset where domain knowledge or expert advice is needed to explain the decision labels.We want to explore the following problems in our empirical analysis: Do models benefit from learning with explanations? (Sec 3.1) 2.
Revised: After observing how conventional ML training algorithms fail on the easy geometric synthetic dataset, we naturally extend our analysis to the harder Bird dataset where domain knowledge or expert advice is needed to explain the decision labels.

Original: Do models learn the reasons suggested by the provided explanations?

Original: (Sec 3.2) 3.

Original: Does training become more consistent if we present explanations to models?

Original: (Sec 3.3)

Original: [Figure]
Revised: [Figure]

Original: Epoch

Original: T e s t
Revised: e s t

Original: A cc u r ac y 10 Samples
Revised: A cc u r ac y 10 Samples

Original: Classes are balanced[-
-]
Revised: Classes are balanced[-
-]

Original: [Figure]
Revised: [Figure]

Revised: [Figure]

Original: Epoch 50 Samples
Revised: Epoch 50 Samples

Original: Classes are balanced 100 0 .0 .0 .0 .0 .
Revised: Classes are balanced [Figure] [Figure]

Original: Epoch 100 Samples
Revised: Epoch 100 Samples

Original: Classes are balanced
Revised: Triangle

Original: [Figure]
Revised: [Figure]

Original: Epoch

Original: T e s t
Revised: T e s t

Original: A cc u r ac y 10 Samples
Revised: A cc u r ac y 10 Samples

Original: Class ratio 9 :
Revised: [Figure] [Figure] [Figure]

Original: [Figure]
Revised: [Figure]

Original: Epoch 50 Samples
Revised: Epoch 50 Samples

Original: Class ratio 9 : 100 0 .0 .0 .0 .
Revised: Class ratio 9 : [Figure]

Original: Epoch 100 Samples
Revised: Epoch 100 Samples

Original: Class ratio 9 :
Revised: Class ratio 9 :

Original: No Expl
Revised: No Expl

Original: Grad Reg
Revised: Grad Reg

Original: Focal Loss
Revised: Focal Loss

Original: Ours
Revised: Ours

Original: Ours(Sparse)
Revised: Ours(Sparse)

Revised: We want to explore the following problems in our empirical analysis:

Revised: Do models benefit from learning with explanations?

Revised: (Sec 3.1) 2.

Revised: Do models learn the reasons suggested by the provided explanations?

Revised: (Sec 3.2) 3.

Original:  Can models still learn the suggested reason when there are multiple or spurious reasons for the same decision?
Revised: Does training become more consistent if we present explanations to models? (Sec 3.3) 4. Can models still learn the suggested reason when there are multiple or spurious reasons for the same decision?

Original: (Sec 3.4)
Revised: (Sec 3.4)

Original: 3. D O MODELS BENEFIT FROM LEARNING WITH EXPLANATIONS ?
Revised: 3. D O MODELS BENEFIT FROM LEARNING WITH EXPLANATIONS ?

Original: We train 30 models with early stopping for all datasets and sample sizes under each training setup.
Revised: We train 30 models with early stopping for all datasets and sample sizes under each training setup.

Original: For balanced datasets, we use the vanilla training algorithm that trains with labels only.
Revised: For balanced datasets, we use the vanilla training algorithm that trains with labels only.

Original: We also use the gradient regularization (Grad Reg) method proposed by Ross et al.
Revised: We also use the gradient regularization (Grad Reg) method proposed by Ross et al.

Original: (2017) as a baseline.
Revised: (2017) as a baseline.

Original: For imbalanced datasets, we add two more settings.
Revised: For imbalanced datasets, we add two more settings.

Original: Firstly, we replace the cross entropy loss with focal loss (Lin et al., 2017), a popular loss function for imbalanced datasets, to train models with labels only.
Revised: Firstly, we replace the cross entropy loss with focal loss (Lin et al., 2017), a popular loss function for imbalanced datasets, to train models with labels only.

Original: Then we consider a sparse explanation setting where we only have explanations on the minority class.
Revised: Then we consider a sparse explanation setting where we only have explanations on the minority class.

Original: We train models with the normal cross entropy loss and tune their feature maps on points with explanations.
Revised: We train models with the normal cross entropy loss and tune their feature maps on points with explanations.

Original: The implementation details  can be found in Appendix B.
Revised: The implementation details and hyper-parameters choices can be found in Appendix B.

Original: We observe from the top rows in Fig 2 and 3, and Fig 4 that our training pipeline can accelerate the learning process and make final models generalize better on unseen data across all datasets when classes are balanced in the training set.
Revised: We observe from the top rows in Fig 2 and 3, and Fig 4 that our training pipeline can accelerate the learning process and make final models generalize better on unseen data across all datasets when classes are balanced in the training set.

Original: Even when there is a severe class imbalance , where theclass ratio in the training set is 9 : 1 , the bottom rows in Fig 2 and 3 show our models can reach higher test accuracy on a balanced test set. To save the annotation cost, sometimes it makes sense to only query explanations on data points from the under-represented groups . We simulate this realistic scenario by only training with explanations when the data are from the minority class (Class 1). The cyan lines in Fig 2 and 3 demonstrate that our training strategy still outperforms others, even with sparse explanations.
Revised: Even when there is a severe class imbalance , where the

Original: This is very significant

Original: [Figure]
Revised: [Figure]

Original:  ac
Revised: A cc u r ac

Original: [Figure]
Revised: [Figure]

Original: 50 Samples Classesare balanced
Revised: Classes

Original: [Figure]
Revised: [Figure]

Revised: balanced

Original: [Figure]
Revised: [Figure]

Original: Epoch 100 Samples Classes are balanced  100 0 .0 .0 .0 .0 . Epoch 500 Samples
Revised: Samples

Original: Classes are balanced
Revised: Classes are balanced

Original: [Figure]
Revised: [Figure]

Original: T
Revised: Epoch 500 Samples

Original: [Figure] s
Revised: Classes are

Original: [Figure]
Revised: [Figure]

Original:  A cc u r ac y50 Samples
Revised: T e s t A cc u r ac y

Original: Class ratio 9 :

Original: [Figure]

Original: [Figure]
Revised: [Figure]

Original: Epoch 100 Samples

Original: Class ratio 9 :

Original: [Figure]
Revised: [Figure]

Original: Epoch 500 Samples

Original: Class ratio 9 :

Original: No Expl

Original: Grad Reg
Revised: Grad Reg

Original: Focal Loss
Revised: Focal Loss

Original: Ours
Revised: Ours

Original: Ours(Sparse) 
Revised: Ours(Sparse) class ratio in the training set is 9 : 1 , the bottom rows in Fig 2 and 3 show our models can reach higher test accuracy on a balanced test set. We report the standard deviations over 30 trials in Table 5 in the appendix, and we observe our models are more consistent with standard deviations of one magnitude smaller. [Figure] Expl

Original: [Figure]
Revised: [Figure]

Original: Grad Reg 
Revised: Reg Ours

Revised: To save annotation costs, sometimes it makes sense to only query explanations on data points from the under-represented groups .

Revised: We simulate this realistic scenario by only training with explanations when the data are from the minority class (Class 1).

Revised: The cyan lines in Fig 2 and 3 demonstrate that our training strategy still outperforms others, even with sparse explanations.

Original: Ours given the small sample sizes in our experiments.
Revised: This is very significant given the small sample sizes in our experiments.

Original: For example, when we use a sample size of 50, the additional information only explains five images.
Revised: For example, when we use a sample size of 50, the additional information only explains five images.

Original: Nevertheless, our algorithm can significantly improve the generalization performance and convergence speed.
Revised: Nevertheless, our algorithm can significantly improve the generalization performance and convergence speed.

Revised: The reason for our method’s usefulness in imbalanced settings without using popular re-weighting (citation needed) or sampling-based solutions shows that our models extract very useful features for minority groups under the guidance of explanations, so useful that the classification layers can easily distinguish the two classes in the latent space.

Original: More notably, Fig 2, 3 and 4 reveal that the existing algorithm from Ross et al.
Revised: In addition, Fig 2, 3 and 4 reveal that the existing algorithm from Ross et al.

Original: (2017) rarely outperforms the baseline, as the orange lines are often below the blue lines.
Revised: (2017) rarely outperforms the baseline, as the orange lines are often below the blue lines.

Original: This is aligned with our claim that existing methods do not work well in practice.
Revised: This is aligned with our claim that existing methods do not work well in practice.

Original: 3. D O MODELS LEARN THE REASONS SUGGESTED BY THE PROVIDED EXPLANATIONS ?
Revised: 3. D O MODELS LEARN THE REASONS SUGGESTED BY THE PROVIDED EXPLANATIONS ?

Original: While we have empirically observed that presenting explanations to models helps (Section 3.1), we want to know if the superiority stems from the fact that our models learn the suggested reasons better.
Revised: While we have empirically observed that presenting explanations to models helps (Section 3.1), we want to know if the superiority stems from the fact that our models learn the suggested reasons better.

Original: To analyze the alignment between the suggested reasons and the reasons models learned, previous work (Ross et al., 2017; Rieger et al., 2020; Shao et al., 2021; Schramowski et al., 2020) relies mainly on model explanation methods to visualize saliency maps and inspecting the input features with high attribution values.
Revised: To analyze the alignment between the suggested reasons and the reasons models learned, previous work (Ross et al., 2017; Rieger et al., 2020; Shao et al., 2021; Schramowski et al., 2020) relies mainly on model explanation methods to visualize saliency maps and inspecting the input features with high attribution values.

Original: However, as many researchers in the community have found out, many popular model explanation methods are bad proxies of models’ behavior (Adebayo et al., 2018; Shah et al., 2021).
Revised: However, as many researchers in the community have found out, many popular model explanation methods are bad proxies of models’ behavior (Adebayo et al., 2018; Shah et al., 2021).

Original: Hence, to make our analysis more convincing, we construct additional test datasets that share the same classification rules as the synthetic datasets:
Revised: Hence, to make our analysis more convincing, we construct additional test datasets that share the same classification rules as the synthetic datasets:

Original: • Pentagon Orientation Dataset: We construct this dataset by taking a vertical slice from the middle of each triangle in the test set of the Triangle Orientation dataset.
Revised: • Pentagon Orientation Dataset: We construct this dataset by taking a vertical slice from the middle of each triangle in the test set of the Triangle Orientation dataset.

Original: The vertical slice will be a pentagon.
Revised: The vertical slice will be a pentagon.

Original: If the triangle points upwards, the pentagon should also point upwards.
Revised: If the triangle points upwards, the pentagon should also point upwards.

Original: • Triangle vs Circle Dataset: We construct this dataset by removing the rectangles in the test set of the Fox vs Cat dataset. 
Revised: • Triangle vs Circle Dataset: We construct this dataset by removing the rectangles in the test set of the Fox vs Cat dataset. [Table]

Original: If models have learned the suggested reasons from the training datasets, they should be able to apply the same reasons to the additional datasets and reach high accuracy.
Revised: If models have learned the suggested reasons from the training datasets, they should be able to apply the same reasons to the additional datasets and reach high accuracy.

Original: From the results listed in Table 1, we observe that our models almost always perform the best on these datasets, suggesting our models have learned the most from the suggested reasons.
Revised: From the results listed in Table 1, we observe that our models almost always perform the best on these datasets, suggesting our models have learned the most from the suggested reasons.

Original: Moreover, our approach outperforms the other training methods even in the sparse explanation setting.
Revised: Moreover, our approach outperforms the other training methods even in the sparse explanation setting.

Original: Hence, we safely claim that our models generalize better and faster because they grasp the suggested reasons better.
Revised: Hence, we safely claim that our models generalize better and faster because they grasp the suggested reasons better.

Original: in the table, we report the test dataset we use, the training dataset, the size of the training dataset, the class ratio in the training dataset

Original: [Table]

Original: and the test accuracy of different models obtained under different training schemes.

Original: [Table]

Original: 3. D OES TRAINING BECOME MORE CONSISTENT IF WE PRESENT EXPLANATIONS TO MODELS ?
Revised: 3. D OES TRAINING BECOME MORE CONSISTENT IF WE PRESENT EXPLANATIONS TO MODELS ?

Original: Without guidance from the reasons, models have too much freedom in choosing their decision functions.
Revised: Without guidance from the reasons, models have too much freedom in choosing their decision functions.

Original: This often results in huge variances and discrepancies in models trained even with the same data.
Revised: This often results in huge variances and discrepancies in models trained even with the same data.

Original: Since we have shown our models learn the given reasons better, it is important to see if they are more consistent with each other.
Revised: Since we have shown our models learn the given reasons better, it is important to see if they are more consistent with each other.

Original: We measure the pairwise agreement of final models by computing the percentage of identical predictions on test data.
Revised: We measure the pairwise agreement of final models by computing the percentage of identical predictions on test data.

Original: We then report the results in Table 2.
Revised: We then report the results in Table 2.

Original: Our models are always very consistent, implying they most probably use the same reasons for predictions.
Revised: Our models are always very consistent, implying they most probably use the same reasons for predictions.

Original: Models trained with labels only become more consistent when dataset size increases, supporting our hypothesis that these models can slowly infer the true reasons if the dataset is large enough.
Revised: Models trained with labels only become more consistent when dataset size increases, supporting our hypothesis that these models can slowly infer the true reasons if the dataset is large enough.

Original: [Table]
Revised: [Table]

Original: 3. C AN MODELS STILL LEARN THE SUGGESTED REASON WHEN THERE ARE MULTIPLE OR SPURIOUS REASONS FOR THE SAME DECISION ?
Revised: 3. C AN MODELS STILL LEARN THE SUGGESTED REASON WHEN THERE ARE MULTIPLE OR SPURIOUS REASONS FOR THE SAME DECISION ?

Original: To further demonstrate the usefulness of our method, we inject spurious features into training data.
Revised: To further demonstrate the usefulness of our method, we inject spurious features into training data.

Original: Appendix A.4 details how we introduce the spurious features.
Revised: A.4 details how we introduce the spurious features.

Original: If models can learn the right reasons to make decisions, training on spurious features should minimally affect the test performance on clean test sets.
Revised: If models can learn the right reasons to make decisions, training on spurious features should minimally affect the test performance on clean test sets.

Original: On the other hand, if models learn the spurious reasons in the training set, they will fail to generalize on the clean test set.
Revised: On the other hand, if models learn the spurious reasons in the training set, they will fail to generalize on the clean test set.

Original: Fig 5 shows our models are consistently the best-performing ones across all datasets and sample sizes on the clean test set, suggesting our models have learned the most out of the true reasons even when there are strong spurious signals.
Revised: Fig 5 shows our models are consistently the best-performing ones across all datasets and sample sizes on the clean test set, suggesting our models have learned the most out of the true reasons even when there are strong spurious signals.

Original: More results are provided in Fig 9 and Table 3 in the appendix.[Figure] No Expl Grad Reg
Revised: More results are provided in Fig 9 and Table 6 in the appendix.

Original: Ours

Original:  R ELATED W ORK
Revised:  R ELATED W ORK

Original: Previous work on making machine learning models learn desired reasons is mostly done via regularization with a given explanation.
Revised: Previous work on making machine learning models learn desired reasons is mostly done via regularization with a given explanation.

Original: Most papers are from natural language processing (NLP), where the attention vector is a natural source of feature attribution.
Revised: Most papers are from natural language processing (NLP), where the attention vector is a natural source of feature attribution.

Original: Pruthi et al.
Revised: Pruthi et al.

Original: (2022) trained a student model to simulate the teacher model better using attention scores.
Revised: (2022) trained a student model to simulate the teacher model better using attention scores.

Original: Bao et al.
Revised: Bao et al.

Original: (2018) utilized human attention on textual data to guide machine attention.
Revised: (2018) utilized human attention on textual data to guide machine attention.

Original: Liu & Avci (2019) treated feature attribution scores as priors to force the language models to produce similar feature attributions. 
Revised: Liu & Avci (2019) treated feature attribution scores as priors to force the language models to produce similar feature attributions. Besides attention, Chefer et al. (2022) regularized relevancy scores to shift transformers’ focus to the foreground. However, some

Revised: [Figure]

Original: However, some methods may only be useful in NLP due to the distinct characteristic of attention-based language models.
Revised: A cc u r ac y No Expl Grad Reg Ours methods may only be useful in NLP due to the distinct characteristic of attention-based language models.

Original: Input pixels of images are also less semantically meaningful than words in language data.
Revised: Input pixels of images are also less semantically meaningful than words in language data.

Original: To our best knowledge, Ross et al.
Revised: To our best knowledge, Ross et al.

Original: (2017) firstly explored the possibility of regularizing model explanation in training.
Revised: (2017) firstly explored the possibility of regularizing model explanation in training.

Original: However, their main point is that their algorithm can train diverse models focusing on different features with similar test accuracy.
Revised: However, their main point is that their algorithm can train diverse models focusing on different features with similar test accuracy.

Original: Du et al.
Revised: Du et al.

Original: (2019) focused on the alignment between model explanations and given attribution scores by optimizing the difference and enforcing sparsity, but the resulting test accuracy did not improve.
Revised: (2019) focused on the alignment between model explanations and given attribution scores by optimizing the difference and enforcing sparsity, but the resulting test accuracy did not improve.

Original: Rieger et al.
Revised: Rieger et al.

Original: (2020) considered another form of explanation and focused on avoiding learning spurious correlations.
Revised: (2020) considered another form of explanation and focused on avoiding learning spurious correlations.

Original: Similarly, Shao et al.
Revised: Similarly, Shao et al.

Original: (2021) considered second-order derivatives as explanations and Schramowski et al.
Revised: (2021) considered second-order derivatives as explanations and Schramowski et al.

Original: (2020) used
Revised: (2020) used

Original: GradCAMs.
Revised: GradCAMs.

Original: However, these methods use the knowledge of “wrong reasons” as explanations, which is fundamentally different from our approach.
Revised: However, these methods use the knowledge of “wrong reasons” as explanations, which is fundamentally different from our approach.

Original:  D ISCUSSION
Revised:  D ISCUSSION

Original: We have shown that we can improve the convergence rate and generalization performance of machine learning models by inserting an intermediate linear layer and performing a quick additional backpropagation in each training iteration if we can query an expert for explanations of the labels.
Revised: We have shown that we can improve the convergence rate and generalization performance of machine learning models by inserting an intermediate linear layer and performing an additional backpropagation in each training iteration if we can query an expert for explanations.

Original: Our approach is efficient and effective, especially in a small data regime where models trained under conventional pipelines struggle to extract useful information and learn correct patterns.
Revised: Our approach is efficient and effective, especially in a small data regime where models trained with conventional pipelines struggle to extract useful information and learn correct patterns.

Original: We also consider the usability of our approach in the long-tailed scenario where there exists a minority class.
Revised: We also consider the usability of our approach with imbalanced data.

Original: While standard training methods require more data, particularly from the minority class, to learn the under-represented class, our method substantially improves the classification performance for the minority class when explanations are available.
Revised: While standard training methods require more data, particularly from the minority class, to learn the under-represented class, our method substantially improves the classification performance for the minority class when explanations are available.

Original: To make it more realistic and reduce the annotation cost, we consider the situation where only data from the minority class has explanations.
Revised: To make it more realistic and reduce the annotation cost, we consider the situation where only data from the minority class has explanations.

Original: We demonstrate that models trained with our algorithm can still learn faster and better, even if the additional information is only the explanation of one or five data points.
Revised: We demonstrate that models trained with our algorithm can still learn faster and better, even if the additional information is only the explanation of one or five data points.

Original: Although neural networks are not intrinsically rule-based models, we show our training algorithm can guide the models to focus more on the given reasons region when compared with the vanilla training algorithm and existing method that claims to make models “right for the right reasons”.

Original: Admittedly, our method cannot make models base their decision-making mechanisms entirely on the reasons region or prevent models from looking at other regions in the data.

Original: However, our method is still helpful and inspiring for how much it can achieve with one additional layer and one gradient descent step.

Original: It will be interesting to see if we can fine-tune some hyper-parameters to achieve better results.

Original:  C ONCLUSION
Revised:  C ONCLUSION

Original: In this paper, we study a very important and useful machine learning setting: learning from explanations.
Revised: In this paper, we study a very important and useful machine learning setting: learning from explanations.

Original: We explain why previous papers fail to solve this problem and why previous loss-based methods do not bring substantial improvement.
Revised: We explain why previous papers fail to solve this problem and why previous loss-based methods do not bring substantial improvement.

Original: We propose a novel two-stage optimization pipeline that teaches the model to extract features according to the given explanation.
Revised: We propose a novel two-stage optimization pipeline that teaches the model to extract features according to the given explanation.

Original: We demonstrate that our algorithm significantly outperforms the current training pipeline and previous loss-based methods in both synthetic and real datasets.
Revised: We demonstrate that our algorithm significantly outperforms the current training pipeline and previous loss-based methods in both synthetic and real datasets.

Original: We also show that our models can learn the suggested reasons better and apply the reasons to applicable alternative datasets.
Revised: We also show that our models can learn the suggested reasons better and apply the reasons to applicable alternative datasets.

Original: We think our method can naturally extend to multi-class classification, and we leave it as future work.
Revised: We think our method can naturally extend to multi-class classification, and we leave it as future work.

Revised: We hope that our work can inspire more researchers to adopt this training pipeline such that more real world datasets with explanations can be curated.

Original:  E THICS S TATEMENT
Revised:  E THICS S TATEMENT

Original: Our work does not have direct ethical concerns.
Revised: Our work does not have direct ethical concerns.

Original: Instead, it can benefit the under-represented groups.
Revised: Instead, it can benefit the under-represented groups.

Original:  R EPRODUCIBILITY S TATEMENT
Revised:  R EPRODUCIBILITY S TATEMENT

Original: We provide the source code our of algorithms in the submission.
Revised: We provide the source code our of algorithms in the submission.

Original: It comes with the default parameter values and random seeds that we use to run experiments.
Revised: It comes with the default parameter values and random seeds that we use to run experiments.

Original: We also provide some details about implementation in Appendix B
Revised: We also provide some details about implementation in Appendix B

Original: A D ATASETS
Revised: A D ATASETS

Original: We use two synthetic geometric datasets and one real datasets that involves expert domain knowledge in our paper.
Revised: We use two synthetic geometric datasets and one real datasets that involves expert domain knowledge in our paper.

Original: A. T RIANGLE O RIENTATION
Revised: A. T RIANGLE O RIENTATION

Original: The first synthetic dataset is a binary classification dataset on the orientation of an triangle.
Revised: The first synthetic dataset is a binary classification dataset on the orientation of an triangle.

Original: A triangle is classified into class 1 if it is pointing upwards, otherwise 0.
Revised: A triangle is classified into class 1 if it is pointing upwards, otherwise 0.

Original: The explanation is the spatial arrangement of the vertex and the bottom line: if the vertex is above the bottom line, it is pointing upwards.
Revised: The explanation is the spatial arrangement of the vertex and the bottom line: if the vertex is above the bottom line, it is pointing upwards.

Original: The explanation is then represented as a mask highlighting the vertex and a portion of the bottom line.
Revised: The explanation is then represented as a mask highlighting the vertex and a portion of the bottom line.

Original: Each image is of grayscale with a size of 64 .
Revised: Each image is of grayscale with a size of 64 .

Original: A. F OX VS C AT
Revised: A. F OX VS C AT

Original: The second synthetic dataset is a minimalistic fox vs cat dataset.
Revised: The second synthetic dataset is a minimalistic fox vs cat dataset.

Original: A fox has a triangular head and a rectangular body, while a cat has a circular head and a rectangular body.
Revised: A fox has a triangular head and a rectangular body, while a cat has a circular head and a rectangular body.

Original: The explanation should then focus on their heads.
Revised: The explanation should then focus on their heads.

Original: However, an explanation does not have to highlight the entire head region.
Revised: However, an explanation does not have to highlight the entire head region.

Original: It only needs to highlight a distinctive feature of the heads that sufficiently distinguishes a fox from a cat.
Revised: It only needs to highlight a distinctive feature of the heads that sufficiently distinguishes a fox from a cat.

Original: Hence, the explanation for a fox is a mask highlighting the vertex of the triangular head, and the explanation for a cat is a mask highlighting the arc of the circular head (See Fig 6).
Revised: Hence, the explanation for a fox is a mask highlighting the vertex of the triangular head, and the explanation for a cat is a mask highlighting the arc of the circular head (See Fig 6).

Original: Each image is of grayscale with a size of 64 .
Revised: Each image is of grayscale with a size of 64 .

Original: [Figure]
Revised: [Figure]

Original: A. B IRD
Revised: A. B IRD

Original: We also extend our experiments to real datasets.
Revised: We also extend our experiments to real datasets.

Original: We use a subset of the CUB-200-2011 (We will refer to it as the Bird dataset in the rest of the paper) dataset (Wah et al., 2011), a fine-grained classification dataset with photos of 200 species of birds.
Revised: We use a subset of the CUB-200-2011 (We will refer to it as the Bird dataset in the rest of the paper) dataset (Wah et al., 2011), a fine-grained classification dataset with photos of 200 species of birds.

Original: From the ground truth distribution of attributes for each individual class, we identify two species that are most similar to each other: the Indigo Bunting and the Blue Grosbeak (See Fig 7a and 7c).
Revised: From the ground truth distribution of attributes for each individual class, we identify two species that are most similar to each other: the Indigo Bunting and the Blue Grosbeak (See Fig 7a and 7c).

Original: If we refer to their most likely attributes from the ground truth distribution, they are indistinguishable as they share the identical set of attributes.
Revised: If we refer to their most likely attributes from the ground truth distribution, they are indistinguishable as they share the identical set of attributes.

Original: However, according to a bird watcher website 1 , Blue Grosbeaks have bigger and heavier beaks.
Revised: However, according to a bird watcher website 1 , Blue Grosbeaks have bigger and heavier beaks.

Original: Hence, the explanations for our Indigo Bunting vs Blue Grosbeak classification are masks highlighting the beaks if they are visible (See Fig 7b and 7d).
Revised: Hence, the explanations for our Indigo Bunting vs Blue Grosbeak classification are masks highlighting the beaks if they are visible (See Fig 7b and 7d).

Original: We use the ground truth bounding box of birds to crop all images, before resizing them to the same size for training.
Revised: We use the ground truth bounding box of birds to crop all images, before resizing them to the same size for training.

Original: [Figure]
Revised: [Figure]

Revised: with an explanation mask on its beak

Original: A. I NJECTING SPURIOUS FEATURES
Revised: A. I NJECTING SPURIOUS FEATURES

Original: For the Fox vs Cat dataset, we add spurious features at fixed locations.
Revised: For the Fox vs Cat dataset, we add spurious features at fixed locations.

Original: For foxes, we add a square to the top left corner; for cats, we add a square to the top right corner.
Revised: For foxes, we add a square to the top left corner; for cats, we add a square to the top right corner.

Original: For the Triangle Orientation dataset, we add a square to a random location on the leftmost column for positive data.
Revised: For the Triangle Orientation dataset, we add a square to a random location on the leftmost column for positive data.

Original: We add the square to a random location on the rightmost column for negative 
Revised: We add the square to a random location on the rightmost column for negative data. For the CUB bird dataset, we add a green square to a random place to the negative class, and add a red square to a random place to the positive class. We make sure that these spurious features do not block the reasons masks. However, they can be arbitrarily close to the reasons.

Original: [Figure]
Revised: [Figure]

Original: B I MPLEMENTATION B. S YNTHETIC D ATASETS
Revised: B I MPLEMENTATION B. S YNTHETIC D ATASETS

Original: For the two synthetic datasets, we use a CNN with 3 convolutional layers and 1 FC layer.
Revised: For the two synthetic datasets, we use a CNN with 3 convolutional layers and 1 FC layer.

Original: We use
Revised: We use

Original: Adam with a learning rate of 0.01 when we train with no explanations.
Revised: Adam with a learning rate of 0 . 01 when we train with no explanations.

Original: When we add the gradient misalignment loss to the joint loss function, we optimize the joint loss with Adam with the same learning rate mentioned above.
Revised: When we add the gradient misalignment loss to the joint loss function, we optimize the joint loss with Adam with the same learning rate mentioned above.

Original: We set the balancing coefficient λ of the gradient misalignment loss to be 0 .
Revised: We set the balancing coefficient λ of the gradient misalignment loss to be 0 .

Original: 001 , which keeps the two loss terms of similar magnitude to ensure maximum performance.
Revised: 001 in equation 1, which keeps the two loss terms of similar magnitude to ensure maximum performance.

Original: This choice of hyper-parameter is mentioned by Ross et al.
Revised: This choice of hyper-parameter is mentioned by Ross et al.

Original: and also observed by us in hyperparameter tuning.
Revised: and also observed by us in hyper-parameter tuning.

Original: When using our method,  both optimizers are Adam with learning rates of 0 . 001 .
Revised: When using our method, we empirically evaluated the model with three learning rates for both η 1 and η 2 : { 0 . 1 , 0 . 01 , 0 . 001 } . We then pick the best combination. Note that we did not tune these hyper-parameters to a great depth, so it is very likely our model can perform even better with more tuning. In summary, both optimizers are Adam with learning rates of 0 .when

Revised: the class ratio is balanced with no spurious correlations.

Original: When there is a class imbalance, we change the learning rate  of the feature loss optimizer to 0 .
Revised: When there is a class imbalance or spurious correlation in data, we increase the learning rate η 2 of the feature loss optimizer to 0 .

Revised: The empirical evidence that η 2 needs to be increased in these two scenarios is intuitive, because models need to update their focus more to generalize well to class balanced test set.

Original: B. B IRD D ATASET
Revised: B. B IRD D ATASET

Original: For the bird dataset, we use a simple CNN with 2 convolutional layers and 1 FC layer.
Revised: For the bird dataset, we use a simple CNN with 2 convolutional layers and 1 FC layer.

Original: This is simpler than the model used in synthetic datasets because the size of training set is smaller for this dataset.
Revised: This is simpler than the model used in synthetic datasets because the size of training set is smaller for this dataset.

Original: To reduce the chance of overfit, we make the model simpler.
Revised: To reduce the chance of overfitting, we make the model simpler.

Original: We use SGD as the optimizer for this dataset.
Revised: We use SGD as the optimizer for this dataset.

Revised: For the baseline method without explanations, the learning rate is 0 .

Revised: For GradReg, the balancing coefficient is computed to make the two loss terms of similar magnitudes to ensure best performance.

Revised: Similar to the hyper-parameter selection procedure explained above, we pick the best combination of η 1 and η 2 from empirical results.

Revised: Across all settings, η 1 is always set to be 0 .

Original:  C A DDITIONAL R ESULTS
Revised: When the class ratio is balanced with no spurious correlations, we set η 2 to be 0 . On the other hand, when there is a class imbalance or spurious correlation in data, we increase the learning rate ηof the feature loss optimizer to 0 . C A BLATION S TUDIES There are two novel designs in our algorithm:

Revised: The mapping layer 2.

Revised: Two-stage optimization

Revised: We conduct ablation studies to see if any new designs bring significant improvement.

Revised: Tableshows that the combination of the two new designs yields the best final performance and fastest convergence rate, especially on the Bird dataset.

Revised: With the mapping layer, the feature difference loss is only backpropagated to the mapping layer; otherwise it will be backpropagated to all convolutional layers.

Revised: As argued before, updating the convolutional layers twice with different gradients may be less effective, and the two gradients might counteract each other.

Revised: On the other hand, doing joint training is conceptually inferior to our two-stage training.

Revised: The only difference would be that the feature difference loss in the joint optimization scheme will be computed before the feature extractor is updated by the label loss.

Revised: This is less ideal because the gradient of feature difference loss might be outdated compared to the gradient in the two-stage training scheme, so the mapping layer will be less tuned.

Revised: This inefficiency results in the slower convergence rate displayed in Table 3..

Revised: D C OST A NALYSIS

Revised: In this section, we analyze the benefit of training with explanations from the cost perspective.

Revised: First of all, Table 4 shows that our method leads to lower sample complexity as the dataset size needed to reach a certain performance threshold is much smaller than that if using labels only.

Revised: The table also shows that our method can achieve at least a 3x reduction in sample sizes, sometimes as much as 10x if the sample size is very small.

Revised: It takes an Amazon Turk worker 1.2 cents 2 to label an image, and 3.6 cents to provide bounding boxes.

Revised: The explanation used in our method is similar to bounding boxes where an annotator is only required to highlight an important region in the image.

Revised: Hence the cost to obtain explanations for each image would be approximately 3.6 cents, three times the cost of labels.

Revised: However, considering how much reduction in dataset sizes our methods can achieve, we believe it is more cost-efficient to query for both labels and explanations than simply collecting more data to train models if model creators start from a set of unlabeled data.

Revised: E A DDITIONAL R ESULTS

Original: We present some additional empirical results in this section.
Revised: We present some additional empirical results in this section.

Original: [Figure]
Revised: [Table]

Original: cc
Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original:  ac 
Revised: t A cc u r ac y No Expl Grad Reg

Original: [Figure] [Table]
Revised: Ours [Table] [Table]