Original: Li-ion Battery Material phase prediction through Hierarchical Curriculum Learning
Revised: Li-ion Battery Material phase prediction through Hierarchical Curriculum Learning

Original: Abstract
Revised: Abstract

Original: Li-ion Batteries (LIB), one of the most efficient energy storage devices, are widelyadopted in many industrial applications.
Revised: Li-ion Batteries (LIB), one of the most efficient energy storage devices, are widely adopted in many industrial applications.

Original: Imaging data of these battery electrodesobtained from X-ray tomography can explain the distribution of material constituents and allow reconstructions to study electron transport pathways.
Revised: Imaging data of these battery electrodes obtained from X-ray tomography can explain the distribution of material constituents and allow reconstructions to study electron transport pathways.

Original: Therefore,it can eventually help quantify various associated properties of electrodes (e.g.,volume-specific surface area, porosity) which determine the performance of batteries.
Revised: Therefore, it can eventually help quantify various associated properties of electrodes (e.g., volume-specific surface area, porosity) which determine the performance of batteries.

Original: However, these images often suffer from low image contrast between multiplematerial constituents , making it difficult for humans to distinguish and characterizethese constituents through visualization.
Revised: However, these images often suffer from low image contrast between multiple material constituents , making it difficult for humans to distinguish and characterize these constituents through visualization.

Original: A minor error in detecting distributionsamong the material constituents can lead to a high error in the calculated parameters of material properties.
Revised: A minor error in detecting distributions among the material constituents can lead to a high error in the calculated parameters of material properties.

Original: We present a novel hierarchical curriculum learningframework to address the complex task of estimating material constituent distribution in battery electrodes.
Revised: We present a novel hierarchical curriculum learning framework to address the complex task of estimating material constituent distribution in battery electrodes.

Original: To provide spatially smooth prediction, our frameworkcomprises three modules: (i) an uncertainty-aware model trained to yield inferencesconditioned upon global knowledge of material distribution, (ii) a technique tocapture relatively more fine-grained (local) distributional signals, (iii) an aggregator to appropriately fuse the local and global effects towards obtaining the finaldistribution. Code and data are available online.
Revised: To provide spatially smooth prediction, our framework comprises three modules: (i) an uncertainty-aware model trained to yield inferences conditioned upon global knowledge of material distribution, (ii) a technique to capture relatively more fine-grained (local) distributional signals, (iii) an aggregator to appropriately fuse the local and global effects towards obtaining the final distribution.

Original:  Introduction
Revised:  Introduction

Original: Lithium Ion batteries (LIB) are an advanced energy storage technology employed across many highlyimpactful mechanical and technological applications ranging from electric vehicles to smartphonesand laptops.
Revised: Lithium Ion batteries (LIB) are an advanced energy storage technology employed across many highly impactful mechanical and technological applications ranging from electric vehicles to smartphones and laptops.

Original: A critical facet of the functioning of LIB is the two electrodes (i e., anode and cathode)that enable the storage and flow of electricity.
Revised: A critical facet of the functioning of LIB is the two electrodes (i e., anode and cathode) that enable the storage and flow of electricity.

Original: These electrodes are typically composite materialsconsisting of electro-chemically active material particles (e.g., Li, Ni, Mn) and a polymeric binder(e.g., C) to bind the active material particles onto a substrate (typically a thin aluminum sheet).
Revised: These electrodes are typically composite materials consisting of electro-chemically active material particles (e g., Li, Ni, Mn) and a polymeric binder (e.g., C) to bind the active material particles onto a substrate (typically a thin aluminum sheet).

Original: Duringbattery manufacture, these ingredients (i e., active material particles and binder) are mixed in solventand finally coated onto the thin aluminum substrate.
Revised: During battery manufacture, these ingredients (i.e., active material particles and binder) are mixed in solvent and finally coated onto the thin aluminum substrate.

Original: The coating and the substrate together form theelectrode.
Revised: The coating and the substrate together form the electrode.

Original: Motivation: The microstructure of these composite electrode coatings significantly influences the
Revised: Motivation: The microstructure of these composite electrode coatings significantly influences the

Original: LIB performance.
Revised: LIB performance.

Original: Specifically, homogeneity of the coating thickness across the entire electrodeensures optimal electrical conductivity.
Revised: Specifically, homogeneity of the coating thickness across the entire electrode ensures optimal electrical conductivity.

Original: Since the primary purpose of the binder used in electrodes isto hold the active material in the electrodes, the distribution of the binder throughout the electrodecoating determines the thickness of the coating. The lack of homogeneous distribution of the binder to
Revised: Since the primary purpose of the binder used in electrodes is to hold the active material in the electrodes, the distribution of the binder throughout the electrode

Original: Many approaches have been proposed to account for the binder distribution but are all heuristicin nature.
Revised: Many approaches have been proposed to account for the binder distribution but are all heuristic in nature.

Original: Despite the advancements in imaging (e.g., X-ray microtomography), there has beennoticeable difficulty in resolving the location of all phases (i.e., active materials, binder, pores)within the microstructure Pietsch et al.
Revised: Despite the advancements in imaging (e.g., X-ray microtomography), there has been noticeable difficulty in resolving the location of all phases (i e., active materials, binder, pores) within the microstructure Pietsch et al.

Original: Since, existing imaging tools (at micro-scale) cannotdistinguish spatial distributions due to the complex microstructures and various compositionalmaterials of electrodes, identifying material constituents and phase transition in the microstructure ofelectrode coating from low contrast imaging (i.e., X-ray microtomography) becomes challenging.
Revised: Since, existing imaging tools (at micro-scale) cannot distinguish spatial distributions due to the complex microstructures and various compositional materials of electrodes, identifying material constituents and phase transition in the microstructure of electrode coating from low contrast imaging (i e., X-ray microtomography) becomes challenging.

Original: Fig.
Revised: Fig.

Original: 1(a) shows an example of a low contrast micro-scale image of an electrode.
Revised: 1(a) shows an example of a low contrast micro-scale image of an electrode.

Original: Every pixel of theimage either contains carbon binder (C) or active particles, e.g., nickel (Ni), or a pore.
Revised: Every pixel of the image either contains carbon binder (C) or active particles, e g., nickel (Ni), or a pore.

Original: Clearly, itis impossible to distinguish phase transitions between two material constituents by the human eye.
Revised: Clearly, it is impossible to distinguish phase transitions between two material constituents by the human eye.

Original: Thus, we leverage the power of machine learning techniques to address the problem of material phaseprediction from micro-scale images.
Revised: Thus, we leverage the power of machine learning techniques to address the problem of material phase prediction from micro-scale images.

Original: Specifically, we develop a framework to label each pixel inan image with its material phase (i.e., C, Ni, or Pore).
Revised: Specifically, we develop a framework to label each pixel in an image with its material phase (i.e., C, Ni, or Pore).

Original: We treat this problem of pixel-wise materialphase identification as an image segmentation task.
Revised: We treat this problem of pixel-wise material phase identification as an image segmentation task.

Original: Popular image segmentation architectures, (e.g.,
Revised: Popular image segmentation architectures, (e.g.,

Original: U-Net Ronneberger et al.
Revised: U-Net Ronneberger et al.

Original: [2015]), do not translate well to the current task.
Revised: [2015]), do not translate well to the current task.

Original: Fig. 1(b) shows thepredicted material constituents for each pixel obtained by U-Net .
Revised: Fig. 1(b) shows the predicted material constituents for each pixel obtained by U-Net .

Original: Although U-Net effectively capturesthe global properties of material constituents, it fails to predict the phase boundaries (i.e., transitionbetween two constituents) accurately.
Revised: Although U-Net effectively captures the global properties of material constituents, it fails to predict the phase boundaries (i.e., transition between two constituents) accurately.

Original: Additionally, the model predictions from U-Net also leadto artifacts (i.e., small regions of discontinuous predictions) especially at the phase boundary (see
Revised: Additionally, the model predictions from U-Net also lead to artifacts (i.e., small regions of discontinuous predictions) especially at the phase boundary (see

Original: Fig.
Revised: Fig.

Original: 1(b) - red rectangles are used to highlight artifacts).
Revised: 1(b) - red rectangles are used to highlight artifacts).

Original: Accurate prediction of these constituents atphase boundaries is crucial as this influences the quantification of various physical properties of theelectrode by domain experts.
Revised: Accurate prediction of these constituents at phase boundaries is crucial as this influences the quantification of various physical properties of the electrode by domain experts.

Original: Even a minor error in predicting these phase boundaries translates to ahigh error in calculating the physical properties of the material.
Revised: Even a minor error in predicting these phase boundaries translates to a high error in calculating the physical properties of the material.

Original: We posit that the failure of traditional segmentation models to represent the microstructure accuratelyis two-fold: (a) the inability of flat modeling architectures to learn at different granularity acrossdifferent regions of the microstructure.
Revised: We posit that the failure of traditional segmentation models to represent the microstructure accurately is two-fold: (a) the inability of flat modeling architectures to learn at different granularity across different regions of the microstructure.

Original: For example, predictions conditioned upon a coarse-grainedrepresentation might suffice in a homogeneous region of the microstructure.
Revised: For example, predictions conditioned upon a coarse-grained representation might suffice in a homogeneous region of the microstructure.

Original: In contrast, a lesshomogeneous region (i.e., a region concentrated with many constituents) requires a relatively morefine-grained representation learning ability (b) traditional segmentation models do not possess theability to accurately distinguish between tasks of differing degrees of difficulty (e.g., predicting pixelsat phase transitions vs. predicting pixels within a single phase).
Revised: In contrast, a less homogeneous region (i.e., a region concentrated with many constituents) requires a relatively more fine-grained representation learning ability (b) traditional segmentation models do not possess the ability to accurately distinguish between tasks of differing degrees of difficulty (e.g., predicting pixels at phase transitions vs. predicting pixels within a single phase).

Original: To address these failure modes, we propose a novel deep-learning framework, Material Phase
Revised: To address these failure modes, we propose a novel deep-learning framework, Material Phase

Original: Prediction ( MatPhase ), for LIB microstructure reconstruction.
Revised: Prediction ( MatPhase ), for LIB microstructure reconstruction.

Original: To address failure mode (a), weintroduce two architectures that are designed to learn representations at varying complexities (i.e.,a coarse-grained model and a fine-grained model).
Revised: To address failure mode (a), we introduce two architectures that are designed to learn representations at varying complexities (i.e., a coarse-grained model and a fine-grained model).

Original: To address the failure mode (b), we develop a hierarchical curriculum learning framework to automatically distinguish between regions with lowand high degrees of prediction difficulty.
Revised: To address the failure mode (b), we develop a hierarchical curriculum learning framework to automatically distinguish between regions with low and high degrees of prediction difficulty.

Original: Fig.
Revised: Fig.

Original: 1(c) shows our final predicted result after incorporatingcurriculum learning.
Revised: 1(c) shows our final predicted result after incorporating curriculum learning.

Original: Comparing with Fig. 1(b), see the pixels within corresponding red rectangleslike the leftmost red rectangle.
Revised: Comparing with Fig. 1(b), see the pixels within corresponding red rectangles like the leftmost red rectangle.

Original: The small black dot of pore is not seen in the corresponding rectanglein Fig.
Revised: The small black dot of pore is not seen in the corresponding rectangle in Fig.

Original: 1(c).
Revised: 1(c).

Original: Overall, our predictions are smoother around phase boundaries without the artifacts thatare apparent without using the curriculum.
Revised: Overall, our predictions are smoother around phase boundaries without the artifacts that are apparent without using the curriculum.

Original: Our Contribution: To the best of our knowledge, there is no existing technique to identify thecomplex phase boundaries from low contrast tomography images of electrodes, and MatPhase is thefirst attempt to address this challenge.
Revised: Our Contribution: To the best of our knowledge, there is no existing technique to identify the complex phase boundaries from low contrast tomography images of electrodes, and MatPhase is the first attempt to address this challenge.

Original: Our contributions are: (i)
Revised: Our contributions are: (i)

Original: We develop a novel uncertainty-aware
Revised: We develop a novel uncertainty-aware

Original: ML framework MatPhase to predict material phases of electrodes from low-contrast micro-scaleimage samples obtained through X-ray tomography.
Revised: ML framework MatPhase to predict material phases of electrodes from low-contrast micro-scale image samples obtained through X-ray tomography.

Original: (ii) First time in the literature, we introducea hierarchical curriculum learning technique to predict the fine-grained material phase boundariesfrom a low-contrast image.
Revised: (ii) First time in the literature, we introduce a hierarchical curriculum learning technique to predict the fine-grained material phase boundaries from a low-contrast image.

Original: (iii)
Revised: (iii)

Original: To aid smooth fine-grained phase boundary prediction, we build amulti-class classifier which can capture both local and global representations.
Revised: To aid smooth fine-grained phase boundary prediction, we build a multi-class classifier which can capture both local and global representations.

Original: (iv) Through rigorousexperiments, we show MatPhase yield better predictions than any non-trivial competitors.
Revised: (iv) Through rigorous experiments, we show MatPhase yield better predictions than any non-trivial competitors.

Original:  Background and Preliminaries
Revised:  Background and Preliminaries

Original: We consider each individual material constituent in a low contrast micro-scale image of an electrodeas a class and state our problem as a downstream task of material phase prediction.
Revised: We consider each individual material constituent in a low contrast micro-scale image of an electrode as a class and state our problem as a downstream task of material phase prediction.

Original: Problem 2.1 (Material Phase Prediction) .
Revised: Problem 2.1 (Material Phase Prediction) .

Original: Given , a set of labeled datasets D =
Revised: Given , a set of labeled datasets D =

Original: ( X , Y ) Ni
Revised: ( X , Y ) Ni

Original: =1 , and aset of classes C .
Revised: =1 , and a set of classes C .

Original: Each X i ∈
Revised: Each X i ∈

Original: X is an image of n × m pixels.
Revised: X is an image of n × m pixels.

Original: Y i ∈ Y consists of n × m instances 2for the corresponding pixels in X i , where each instance belongs to a class c ∈ C .
Revised: Y i ∈ Y consists of n × m instancesfor the corresponding pixels in X i , where each instance belongs to a class c ∈ C .

Original: Predict , ˆY for anunlabeled X .
Revised: Predict , ˆY for an unlabeled X .

Original: Hierarchical Curriculum Learning:
Revised: Hierarchical Curriculum Learning:

Original: A learning task often requires a set of multiple curricula S(i.e. , ordered learning strategies) to enable a model to learn effective representations.
Revised: A learning task often requires a set of multiple curricula S (i.e., ordered learning strategies) to enable a model to learn effective representations.

Original: It is possiblethat these multiple curricula could each govern a subset of the overall dataset D .
Revised: It is possible that these multiple curricula could each govern a subset of the overall dataset D .

Original: Additionally, the setof curricula { s 1 , .., s n } ∈ S themselves have (latent) dependencies .
Revised: Additionally, the set of curricula { s 1 , .., s n } ∈ S themselves have (latent) dependencies .

Original: In such a scenario, we introducethe paradigm of hierarchical curriculum learning (HCL) as a solution to address learning in theaforementioned context.
Revised: In such a scenario, we introduce the paradigm of hierarchical curriculum learning (HCL) as a solution to address learning in the aforementioned context.

Original: We define the goal of hierarchical curriculum learning (HCL) as being the implementation of multiplecomplementary curriculum strategies in a hierarchical fashion to order data by relative hardness (i.e.,from easy to hard).
Revised: We define the goal of hierarchical curriculum learning (HCL) as being the implementation of multiple complementary curriculum strategies in a hierarchical fashion to order data by relative hardness (i.e., from easy to hard).

Original: Specifically, assume S =
Revised: Specifically, assume S =

Original: { s 1 , s 2 } where |S| (i.e., number of curricula) may bederived by expert knowledge.
Revised: { s 1 , s 2 } where |S| (i.e., number of curricula) may be derived by expert knowledge.

Original: Further, let us assume h ( s 1 ) <
Revised: Further, let us assume h ( s 1 ) <

Original: h ( s 2 ) where h ( · ) is a hardness measurealso specified by a domain expert.
Revised: h ( s 2 ) where h ( · ) is a hardness measure also specified by a domain expert.

Original: s 1 may for instance be considered the curriculum geared towardlearning global properties of the problem while s 2 may be the curriculum for learning (nuanced) localvariations (thus h ( s 1 ) <
Revised: s 1 may for instance be considered the curriculum geared toward learning global properties of the problem while s 2 may be the curriculum for learning (nuanced) local variations (thus h ( s 1 ) <

Original: h ( s 2 ) ).
Revised: h ( s 2 ) ).

Original: In this context, automatic-HCL comprises a learning framework which automatically learns toaddress the task of interest by first partitioning D into D
Revised: In this context, automatic-HCL comprises a learning framework which automatically learns to address the task of interest by first partitioning D into D

Original: =
Revised: =

Original: {D 1 , D 2 } such that D 1 ⊆ D , D 2 ⊆ D ,
Revised: {D 1 , D 2 } such that D 1 ⊆ D , D 2 ⊆ D ,

Original: D 1 ∩ D 2 = ∅ and h ( D 1 ) <
Revised: D 1 ∩ D 2 = ∅ and h ( D 1 ) <

Original: h ( D 2 ) .
Revised: h ( D 2 ) .

Original: The partitioning step may be viewed as a coarse-grainedcurriculum that initially restricts learning to the easier instances in the dataset.
Revised: The partitioning step may be viewed as a coarse-grained curriculum that initially restricts learning to the easier instances in the dataset.

Original: This partitioning step not only learns effective representations for D 1 but is also designed to yield fine-grained curricula for training models on the harder D 2 data.
Revised: This partitioning step not only learns effective representations for D 1 but is also designed to yield fine-grained curricula for training models on the harder D 2 data.

Original: Hence, the coarse and fine-grained curricula together comprise an automatic-HCL framework for effective learning of the task of interest.
Revised: Hence, the coarse and fine-grained curricula together comprise an automatic-HCL framework for effective learning of the task of interest.

Original:  Our Framework
Revised:  Our Framework

Original: This section describes our framework MatPhase , which predicts material phases from low-contrast images not easily perceived by humans.
Revised: This section describes our framework MatPhase , which predicts material phases from low-contrast images not easily perceived by humans.

Original: MatPhase first predicts the material phases through a global model (learning global data features).
Revised: MatPhase first predicts the material phases through a global model (learning global data features).

Original: This is followed by a data partitioning step governed by the performance of global model on D , which forms the coarse-grained curriculum.
Revised: This is followed by a data partitioning step governed by the performance of global model on D , which forms the coarse-grained curriculum.

Original: The partitioningstep concludes with the global model which learns the properties of easier data partition ( D 1 ), whileyieliding a measure of hardness for D 2 , which forms the fine-grained curriculum.
Revised: The partitioning step concludes with the global model which learns the properties of easier data partition ( D 1 ), while yieliding a measure of hardness for D 2 , which forms the fine-grained curriculum.

Original: We design a localmodel to be trained on D 2 , governed by the fine-grained curriculum to learn local data features. 
Revised: We design a local model to be trained on D 2 , governed by the fine-grained curriculum to learn local data features. the paper

Original: 3.1 Uncertainty-aware Global Segmentation Model ( UGSM )
Revised: 3.1 Uncertainty-aware Global Segmentation Model ( UGSM )

Original: We initially view Problem 2.1 as an image segmentation task using U-Net Ronneberger et al.
Revised: We initially view Problem 2.1 as an image segmentation task using U-Net Ronneberger et al.

Original: [2015]due to its precise object localization and adaptability to be trained with a few samples.
Revised: [2015] due to its precise object localization and adaptability to be trained with a few samples.

Original: However,to achieve smooth prediction (as mentioned in Sec.
Revised: However, to achieve smooth prediction (as mentioned in Sec.

Original: 1 Fig. 1), we pursue U-Net as a global modelinstead.
Revised: 1 Fig. 1), we pursue U-Net as a global model instead.

Original: Our idea is to leverage a course-grained curriculum which learns the global representationsof the model.
Revised: Our idea is to leverage a course-grained curriculum which learns the global representations of the model.

Original: Then, partition the incorrectly predicted instances (i.e., harder data D 2 ) from thecorrectly predicted instances ( D 1 ).
Revised: Then, partition the incorrectly predicted instances (i.e., harder data D 2 ) from the correctly predicted instances ( D 1 ).

Original: Hence, we aim for an uncertainty-aware global segmentationmodel ( UGSM ).
Revised: Hence, we aim for an uncertainty-aware global segmentation model ( UGSM ).

Original: Our assumption A1 is: high uncertainty tends to incorrect predictions.
Revised: Our assumption A1 is: high uncertainty tends to incorrect predictions.

Original: We pursue
Revised: We pursue

Original: Monte-Carlo Dropout (MCD) based uncertainty estimation Gal and Ghahramani [2016] due to itseasy adaptability by any deep-learning model.
Revised: Monte-Carlo Dropout (MCD) based uncertainty estimation Gal and Ghahramani [2016] due to its easy adaptability by any deep-learning model.

Original: For UGSM , we incorporate a dropout layer (dropoutprobability 0 . 5 ) after each convolution block of U-Net proposed by DeVries et al.
Revised: For UGSM , we incorporate a dropout layer (dropout probability 0 . 5 ) after each convolution block of U-Net proposed by DeVries et al.

Original: DeVries and Taylor[2018].
Revised: DeVries and Taylor [2018].

Original: During inference, UGSM samples T predictions.
Revised: During inference, UGSM samples T predictions.

Original: For each input X , the final output of
Revised: For each input X , the final output of

Original: UGSM consists of two pairs: (i) predicted class per pixel, i.e, ˆY G ∈ R n × m , (ii) an uncertainty map
Revised: UGSM consists of two pairs: (i) predicted class per pixel, i.e, ˆY G ∈ R n × m , (ii) an uncertainty map

Original: U G ∈ R n × m .
Revised: U G ∈ R n × m .

Original: Suppose, UGSM samples a set of logits P = { P i } Ti =1 , where P i ∈ R | C |× n × m .
Revised: Suppose, UGSM samples a set of logits P = { P i } Ti =1 , where P i ∈ R | C |× n × m .

Original: Nowif F = 1 T (cid:80) P i ∈P P i .
Revised: Now if F = 1 T (cid:80) P i ∈P P i .

Original: ˆY G = arg max softmax ( F ) .
Revised: ˆY G = arg max softmax ( F ) .

Original: For uncertainty map U G , we compute the entropy each instance.
Revised: For uncertainty map U G , we compute the entropy each instance.

Original: Suppose, p ic is the probability that
Revised: Suppose, p ic is the probability that

Original: UGSM labels instance i as class c .
Revised: UGSM labels instance i as class c .

Original: We calculate u i = − (cid:80)
Revised: We calculate u i = − (cid:80)

Original: c
Revised: c

Original: ∈ C p c log ( p c ) .
Revised: ∈ C p c log ( p c ) .

Original: 3.2 Automatic Hierarchical Curriculum Learning (HCL)
Revised: 3.2 Automatic Hierarchical Curriculum Learning (HCL)

Original:  uncertainties 
Revised: (black as pore, white as C, and grey as Ni). The density of red instances in Fig. (b) is higher than pixels with high uncertainty value in Fig. (a), indicating that UGSM also assigns low uncertainties to a significant portion of incorrect predictions invalidating assumption A1.

Original: As mentioned in Sec. 2, our automatic HCL consists of coarse-grained curriculum s 1 and a finegrained curriculum s 2 .
Revised: As mentioned in Sec. 2, our automatic HCL consists of coarse-grained curriculum s 1 and a finegrained curriculum s 2 .

Original: We view the incorrectly predicted instances of UGSM as harder data D 2 .
Revised: We view the incorrectly predicted instances of UGSM as harder data D 2 .

Original: In this context, our curriculum s 1 is the process of automatically partitioning D into D 1 and D 2 ,where D 1 is the set of correctly predicted instances of UGSM .
Revised: In this context, our curriculum s 1 is the process of automatically partitioning D into D 1 and D 2 , where D 1 is the set of correctly predicted instances of UGSM .

Original: If assumption A1 was to hold, s 1could be a simple rule-based classifier with a pre-set uncertainty threshold that identifies D 2 usingthe uncertainty map U G obtained by UGSM .
Revised: If assumption A1 was to hold, scould be a simple rule-based classifier with a pre-set uncertainty threshold that identifies D 2 using the uncertainty map U G obtained by UGSM .

Original: Fig.
Revised: Fig.

Original: 2 (a) shows example of an uncertainty map of
Revised: 2 (a) shows example of an uncertainty map of

Original: UGSM for an image X .
Revised: UGSM for an image X .

Original: The high values (white colored pixels) denote high uncertainty.
Revised: The high values (white colored pixels) denote high uncertainty.

Original: We observethat majority of the instances with high uncertainty lie at the phase boundaries .
Revised: We observe that majority of the instances with high uncertainty lie at the phase boundaries .

Original: Fig.
Revised: Fig.

Original: 2(b) shows theheatmap of the ground-truth label (material phases) for the same input X .
Revised: 2(b) shows the heatmap of the ground-truth label (material phases) for the same input X .

Original: The red pixels represent incorrect predictions of UGSM .
Revised: The red pixels represent incorrect predictions of UGSM .

Original: We notice that the number of incorrect classifications (Fig. 2(b) redpixels) is much higher than the number of instances with high uncertainty (Fig. 2(a)).
Revised: We notice that the number of incorrect classifications (Fig. 2(b) red pixels) is much higher than the number of instances with high uncertainty (Fig. 2(a)).

Original: This implies that
Revised: This implies that

Original: UGSM assigns low uncertainties to a significant portion of instances that it predicts incorrectly.
Revised: UGSM assigns low uncertainties to a significant portion of instances that it predicts incorrectly.

Original: Thisimplies that our simplistic assumption A1 is a necessary but not a sufficient condition for identifyingincorrect predictions in the context of the current model pipeline.
Revised: This implies that our simplistic assumption A1 is a necessary but not a sufficient condition for identifying incorrect predictions in the context of the current model pipeline.

Original: Our goal through curriculum s 1 is brieflydescribe
Revised: Our goal through curriculum s 1 is hence to segregate (i.e., coarse-grained curriculum)

Revised: all these red instances as D 2 .Next, we briefly describe the coarse-grained and fine-grained curriculum.

Original: Coarse-grained curriculum ( HCL-IDK ): We intend s 1 to automatically learn the representations of
Revised: Coarse-grained curriculum ( HCL-IDK ): We intend s 1 to automatically learn the representations of

Original: Fig of the UGSM logits, F of each class c ∈ C (pore, carbon and nickel) for the input X
Revised: D 1 and D 2 by UGSM for partitioning.

Original: Fig.
Revised: Fig.

Revised: 3 shows the heatmaps of the UGSM logits, F of each class c ∈ C (pore, carbon, and nickel) for the input X in Fig.

Original: For e.g. consider Fig. 3(b) which is the  the The for all the that contains
Revised: For e.g., consider Fig. 3(b) which is the heatmap of the logits of class carbon.

Original:  C 
Revised: The logits for all the pixels that contains class carbon (C) bear values within range (2 , 6) . Also, the logits of the pixels across the C boundaries bear similar values, i.e., all values within range (0 . 5 , 1) , (pixels colored in white).

Original: Also
Revised: Comparing with Fig. 2(b) , we see these white pixels or pixels of carbon boundaries (at Fig. 3(b)) match with the incorrectly predicted red pixels around carbon (Fig. 2(b)). We observe similar behavior for the heatmaps of logits

Original: We leverage a binary Feed-forward classifier for s 1 to identify the IDK instances.
Revised: We leverage a binary Feed-forward classifier for s 1 to identify the IDK instances.

Original: The goal of theclassifier is to learn an effective latent representations for IDK through UGSM features, i e. F and
Revised: The goal of the classifier is to learn an effective latent representations for IDK through UGSM features, i.e. F and

Original: U G .
Revised: U G .

Original: For each instance j , the input of the classifier is a vector idk j ∈ R 4 which consists of thefeatures, i.e., F j ∈ R 3 and u j .
Revised: For each instance j , the input of the classifier is a vector idk j ∈ R 4 which consists of the features, i.e., F j ∈ R 3 and u j .

Original: Let, Y IDK be the set of all instances that classifier identifies as IDKand Y ′ IDK be the complement of Y IDK .
Revised: Let, Y IDK be the set of all instances that classifier identifies as IDK and Y ′ IDK be the complement of Y IDK .

Original: Hence, our easy data D 1 comprises of the instances presentin Y ′ IDK , and hard data D 2 comprises of the instances in Y IDK .
Revised: Hence, our easy data D 1 comprises of the instances present in Y ′ IDK , and hard data D 2 comprises of the instances in Y IDK .

Original: Fine grained curriculum ( HCL-USI ): For learning the set of hard instances in D 2 , we adoptcurriculum s 2 .
Revised: Fine grained curriculum ( HCL-USI ): For learning the set of hard instances in D 2 , we adopt curriculum s 2 .

Original: Here, s 2 is a fine-grained curriculum that quantifies the hardness of every instancein D 2 .
Revised: Here, s 2 is a fine-grained curriculum that quantifies the hardness of every instance in D 2 .

Original: We employ the uncertainty map U G of UGSM as the hardness function.
Revised: We employ the uncertainty map U G of UGSM as the hardness function.

Original: Hence, our s 2curriculum progresses by training with increasingly hard instances governed by the instance-wiseuncertainty of UGSM ( HCL-USI ).
Revised: Hence, our scurriculum progresses by training with increasingly hard instances governed by the instance-wise uncertainty of UGSM ( HCL-USI ).

Original: 3.3 Local Classification Model with Global Annotated Region ( LCGAR )
Revised: 3.3 Local Classification Model with Global Annotated Region ( LCGAR )

Original: The main goal of LCGAR is to provide smooth predictions for the IDK instances in D 2 .
Revised: The main goal of LCGAR is to provide smooth predictions for the IDK instances in D 2 .

Original: We aimto capture both the local and global features of the target instance for this task.
Revised: We aim to capture both the local and global features of the target instance for this task.

Original: We motivate fora classifier that accepts multiple features, i.e., (i) a local image of X surrounding the target IDKinstance, (ii) predicted class labels of UGSM , i.e., ˆY G , (iii) UGSM logits, i.e., F j for the targetinstance j .
Revised: We motivate for a classifier that accepts multiple features, i.e., (i) a local image of X surrounding the target IDK instance, (ii) predicted class labels of UGSM , i.e., ˆY G , (iii) UGSM logits, i.e., F j for the target instance j .

Original: By training our model with global features from UGSM , we intend to learn latent localrepresentations of target instances, hence yield smooth predictions.
Revised: By training our model with global features from UGSM , we intend to learn latent local representations of target instances, hence yield smooth predictions.

Original: We denote L j ∈ R h × h as bounded local region of the original input image X centered aroundthe candidate pixel of interest j (target IDK instance).
Revised: We denote L j ∈ R h × h as bounded local region of the original input image X centered around the candidate pixel of interest j (target IDK instance).

Original: Here h is the width/height of the boundedregion from the center of the pixel of interest.
Revised: Here h is the width/height of the bounded region from the center of the pixel of interest.

Original: For the corresponding pixels in L j , we incorporatethe predicted class of UGSM in the form of one hot encoder channel, i.e., a 3d input tensor ( I ji ∈
Revised: For the corresponding pixels in L j , we incorporate the predicted class of UGSM in the form of one hot encoder channel, i.e., a 3d input tensor ( I ji ∈

Original: R | C |× h × h ).
Revised: R | C |× h × h ).

Original: If a predicted class of L ji is IDK by HCL-IDK , we interpolate I ji with zero masking.
Revised: If a predicted class of L ji is IDK by HCL-IDK , we interpolate I ji with zero masking.

Original: We adopt a CNN architecture of LCGAR .
Revised: We adopt a CNN architecture of LCGAR .

Original: To capture rich information about the arrangement of thesurrounding for the target pixel of interest, we concatenate UGSM logits ( F j ) with the flatteninglayer of CNN.
Revised: To capture rich information about the arrangement of the surrounding for the target pixel of interest, we concatenate UGSM logits ( F j ) with the flattening layer of CNN.

Original: The overall CNN architecture is shown in the appendix.
Revised: The overall CNN architecture is shown in the appendix.

Original: 3.4 MatPhase Framework
Revised: 3.4 MatPhase Framework

Original: [Figure]

Original: Fig.
Revised: Fig.

Original: 4 provides an overview of MatPhase .
Revised: 4 provides an overview of MatPhase .

Original: We first train the uncertainty-aware global segmentationmodel ( UGSM ).
Revised: We first train the uncertainty-aware global segmentation model ( UGSM ).

Original: For each image, X ∈ X , UGSM provides a pixel-wise prediction map ( ˆY G ) and anuncertainty map ( U G ) associated with the prediction.
Revised: For each image, X ∈ X , UGSM provides a pixel-wise prediction map ( ˆY G ) and an uncertainty map ( U G ) associated with the prediction.

Original: Our coarse-grained curriculum HCL-IDK istrained to partition all the instances in ˆY G into two sets, Y IDK and Y ′ IDK .
Revised: Our coarse-grained curriculum HCL-IDK is trained to partition all the instances in ˆY G into two sets, Y IDK and Y ′ IDK .

Original: Next, the fine-grainedcurriculum HCL-USI orders Y IDK by increasing prediction uncertainty obtained from the UGSMmodel.
Revised: Next, the fine-grained curriculum HCL-USI orders Y IDK by increasing prediction uncertainty obtained from the UGSM model.

Original: Next, our local model LCGAR is trained on both the global and local features to learn localcontext of Y IDK to yield corresponding predictions ˆY L .
Revised: Next, our local model LCGAR is trained on both the global and local features to learn local context of Y IDK to yield corresponding predictions ˆY L .

Original: Finally, an ensemble model aggregates ˆY Gand ˆY L to provide spatially smoother predictions, i.e., ˆY .
Revised: Finally, an ensemble model aggregates ˆY G and ˆY L to provide spatially smoother predictions, i.e., ˆY .

Original: ˆY = ˆY jG , if j ∈ Y IDK , else ˆY = ˆY jL .
Revised: ˆY = ˆY jG , if j ∈ Y IDK , else ˆY = ˆY jL .

Original:  Experiments
Revised:  Experiments

Original: [Figure]

Original: Our framework is implemented in PyTorch.
Revised: Our framework is implemented in PyTorch.

Original: All models are trained using 3 V100 Tesla GPUs.
Revised: All models are trained using 3 V100 Tesla GPUs.

Original: Forevery X-Ray Computed Tomography (XCT) imaging of electrode cross-sections, we obtain theground-truth labels by utilizing cross-sectioning with Focused-Ion beam (FIB/SEM) experiments
Revised: For every X-Ray Computed Tomography (XCT) imaging of electrode cross-sections, we obtain the ground-truth labels by utilizing cross-sectioning with Focused-Ion beam (FIB/SEM) experiments

Original: Vierrath et al.
Revised: Vierrath et al.

Original: The detail of the data collection process and pre-processing is in the appendix.
Revised: The detail of the data collection process and pre-processing is in the appendix.

Original: We will release the code and datasets in public for research purposes.
Revised: Code and datasets are available for research purposes 2 .

Original: Research Questions: Our goal is to demonstrate that MatPhase can capture better predictions thanany other state-of-the-art (SOTA) image segmentation models.
Revised: Research Questions: Our goal is to demonstrate that MatPhase can capture better predictions than any other state-of-the-art (SOTA) image segmentation models.

Original: We are interested to analyze whetherour automatic HCL framework is useful for modeling smooth phase predictions.
Revised: We are interested to analyze whether our automatic HCL framework is useful for modeling smooth phase predictions.

Original: Specifically we wantto address: Q1.
Revised: Specifically we want to address: Q1.

Original: Is our automatic curriculum learning (HCL) effective for modeling phase boundaries?
Revised: Is our automatic curriculum learning (HCL) effective for modeling phase boundaries?

Original: Q2.
Revised: Q2.

Original: Does incorporating global information aid local modeling?
Revised: Does incorporating global information aid local modeling?

Original: Q3.
Revised: Q3.

Original: How does MatPhase predictover SOTA?
Revised: How does MatPhase predict over SOTA?

Original: Q1 and Q2 are aligned with justifying the effectiveness of MatPhase .
Revised: Q1 and Q2 are aligned with justifying the effectiveness of MatPhase .

Original: With Q3 , weplan to showcase MatPhase performance comparing with multiple non-trivial competitors.
Revised: With Q3 , we plan to showcase MatPhase performance comparing with multiple non-trivial competitors.

Original: Measure of success: We evaluate the quality of MatPhase predictions on a downstream task of
Revised: Measure of success: We evaluate the quality of MatPhase predictions on a downstream task of

Original: Problem 2.1 for low contrast image data.
Revised: Problem 2.1 for low contrast image data.

Original: We choose four evaluation metrics: (i) F1-score.
Revised: We choose four evaluation metrics: (i) F1-score.

Original: (ii) Pixelaccuracy (ACC) for k best performing and worst performing predictions to evaluate smoothness ofmaterial phase predictions.
Revised: (ii) Pixel accuracy (ACC) for k best performing and worst performing predictions to evaluate smoothness of material phase predictions.

Original: (iii) Mean intersection over union (mIU) from the standard practice ofimage segmentation models Long et al.
Revised: (iii) Mean intersection over union (mIU) from the standard practice of image segmentation models Long et al.

Original: [2015], Badrinarayanan et al.
Revised: [2015], Badrinarayanan et al.

Original: (iv) Frequency weightedintersection over union (fIU) to evaluate in presence of class imbalance from the standard practice forimage segmentation models Long et al.
Revised: (iv) Frequency weighted intersection over union (fIU) to evaluate in presence of class imbalance from the standard practice for image segmentation models Long et al.

Original: We describe each metric in the appendix.
Revised: We describe each metric in the appendix.

Original: Baselines: We compare MatPhase with SOTA image segmentation models.
Revised: Baselines: We compare MatPhase with SOTA image segmentation models.

Original: Specifically, to providepixel to pixel predictions and to compare with different variants of UGSM , we use (1) DeepLabV3 Florian and Adam [2017] (2)
Revised: Specifically, to provide pixel to pixel predictions and to compare with different variants of UGSM , we use (1) DeepLabV3 Florian and Adam [2017] (2)

Original: MANet Fan et al.
Revised: MANet Fan et al.

Original: FCN Long et al.
Revised: FCN Long et al.

Original: [2015], (4) SegNet Badri- narayanan et al.
Revised: [2015], (4) SegNet Badrinarayanan et al.

Original: [2017], (5) U-Net Ronneberger et al.
Revised: [2017], (5) U-Net Ronneberger et al.

Original: [2015], (6) U-Net++ Zhou et al.
Revised: [2015], (6) U-Net++ Zhou et al.

Original: MCD-U-Net DeVries and Taylor [2018]: Monte-Carlo dropout based U-Net, similar to our globalmodel UGSM .
Revised: MCD-U-Net DeVries and Taylor [2018]: Monte-Carlo dropout based U-Net, similar to our global model UGSM .

Original: (8) Local-U-Net : Replace our local model LCGAR with a U-Net model Ronnebergeret al.
Revised: (8) Local-U-Net : Replace our local model LCGAR with a U-Net model Ronneberger et al.

Original: For training, we mask the cross-entropy loss values (with zeros) for the instances thatare not classified by HCL-IDK .
Revised: For training, we mask the cross-entropy loss values (with zeros) for the instances that are not classified by HCL-IDK .

Original: ResNet-18 He et al.
Revised: ResNet-18 He et al.

Original: [2016]: Our aim is to check with a pixel bypixel classifier model using same the input representation of LCGAR architecture.
Revised: [2016]: Our aim is to check with a pixel by pixel classifier model using same the input representation of LCGAR architecture.

Original: We leverage a
Revised: We leverage a

Original: ResNet-18 model, setting the bounded local region h
Revised: ResNet-18 model, setting the bounded local region h

Original: = 11 for every instance in the image.
Revised: = 11 for every instance in the image.

Original: Note that,we also try with ResNet-34, ResNet-50 and only show the record which yield the best result.
Revised: Note that, we also try with ResNet-34, ResNet-50 and only show the record which yield the best result.

Original: Adapted-LCGAR : Predict every instances of image with pre-trained LCGAR .
Revised: Adapted-LCGAR : Predict every instances of image with pre-trained LCGAR .

Original: 4.1 Effectiveness (Q1-Q2)
Revised: 4.1 Effectiveness (Q1-Q2)

Original: Next, we aim to demonstrate the effectiveness of MatPhase , by analyzing the importance of (i)coarse-grained ( HCL-IDK ) and fine-grained ( HCL-USI ) curriculum of HCL, (ii) input representationsof LCGAR , which incorporates global data features of to aid local modeling.
Revised: Next, we aim to demonstrate the effectiveness of MatPhase , by analyzing the importance of (i) coarse-grained ( HCL-IDK ) and fine-grained ( HCL-USI ) curriculum of HCL, (ii) input representations of LCGAR , which incorporates global data features of to aid local modeling.

Original: [Table]
Revised: [Table]

Original: Effectiveness of HCL: For Q1 , we want to evaluate the importance of curriculum learning.
Revised: Effectiveness of HCL: For Q1 , we want to evaluate the importance of curriculum learning.

Original: Hence,we describe the models varying the implementation of HCL learning strategies: (i) UGSM :
Revised: Hence, we describe the models varying the implementation of HCL learning strategies: (i) UGSM :

Original: We obtainthe predictions from our pre-trained UGSM without any partitioning steps governed by curriculum
Revised: We obtain the predictions from our pre-trained UGSM without any partitioning steps governed by curriculum

Original: HCL-IDK .
Revised: HCL-IDK .

Original: (ii) MatPhase w/o HCL-USI : The model is trained directly using the hard data partitionedby HCL-IDK , which further is not learnt by HCL-USI .
Revised: (ii) MatPhase w/o HCL-USI : The model is trained directly using the hard data partitioned by HCL-IDK , which further is not learnt by HCL-USI .

Original: For testing, we replace our local model with
Revised: For testing, we replace our local model with

Original: MatPhase w/o HCL-USI and use the same framework MatPhase .
Revised: MatPhase w/o HCL-USI and use the same framework MatPhase .

Original: We compare the performance of
Revised: We compare the performance of

Original: MatPhase , which is governed by both the curriculum HCL-IDK and HCL-USI against the modelsmentioned above in Table 1.
Revised: MatPhase , which is governed by both the curriculum HCL-IDK and HCL-USI against the models mentioned above in Table 1.

Original: We evaluate multiple metrics, mean F1-score per class across all the testdatasets, average pixel accuracy rate of best 5 and worst 5 predictions, and mean IoU. For accuracy,the values ( ± ) denote the percentage of deviation among the 5 predictions.
Revised: We evaluate multiple metrics, mean F1-score per class across all the test datasets, average pixel accuracy rate of best 5 and worst 5 predictions, and mean IoU. For accuracy, the values ( ± ) denote the percentage of deviation among the 5 predictions.

Original: We observe, MatPhaseoutperforms UGSM across all the metrics.
Revised: We observe, MatPhase outperforms UGSM across all the metrics.

Original: Effectiveness of UGSM features for LCGAR : For Q2 , our goal is to capture how incorporatingglobal features of UGSM to LCGAR aid modeling predictions.
Revised: Effectiveness of UGSM features for LCGAR : For Q2 , our goal is to capture how incorporating global features of UGSM to LCGAR aid modeling predictions.

Original: We use different variants of LCGARvarying the input representations.
Revised: We use different variants of LCGAR varying the input representations.

Original: We train each model based on the same target instances used in
Revised: We train each model based on the same target instances used in

Original: MatPhase , only changing the input representation.
Revised: MatPhase , only changing the input representation.

Original: (i) Only-Image : Consider LCGAR input as thelocal input image surrounding the target instances as mentioned in Sec. 3.3.
Revised: (i) Only-Image : Consider LCGAR input as the local input image surrounding the target instances as mentioned in Sec. 3.3.

Original: We do not consider
Revised: We do not consider

Original: UGSM logits F j in the flattening layer.
Revised: UGSM logits F j in the flattening layer.

Original: (ii) Image+ UGSM -Y : LCGAR input consists of the inputimages and the UGSM predictions ˆY G surrounding the target instances as mentioned in Sec. 3.3.
Revised: (ii) Image+ UGSM -Y : LCGAR input consists of the input images and the UGSM predictions ˆY G surrounding the target instances as mentioned in Sec. 3.3.

Original: We do not consider UGSM logits F j . (iii) Image+ UGSM -Emb : Consider LCGAR input as the localinput image surrounding the target instances.
Revised: We do not consider UGSM logits F j . (iii) Image+ UGSM -Emb : Consider LCGAR input as the local input image surrounding the target instances.

Original: Also include logits F j of the target instance j .
Revised: Also include logits F j of the target instance j .

Original:  Table 2 shows the performance of LCGAR for different input representations.
Revised: [Table] Table 2 shows the performance of LCGAR for different input representations.

Original: MatPhase uses all theglobal features as mentioned in Sec. 3.3.
Revised: MatPhase uses all the global features as mentioned in Sec. 3.3.

Original: MatPhase clearly outperforms all the models.
Revised: MatPhase clearly outperforms all the models.

Original: On averageusing global features, F1- score of MatPhase increase to 0 .
Revised: On average using global features, F1- score of MatPhase increase to 0 .

Original: 17 for pore, 0 .
Revised: 17 for pore, 0 .

Original: 15 for C, and 0 .
Revised: 15 for C, and 0 .

Original: 03 for
Revised: 03 for

Original: Ni) comparing with Only-Image which uses no global features.
Revised: Ni) comparing with Only-Image which uses no global features.

Original: Comparing with Image+ UGSM -Y ,the low mIU and fIU indicates that MatPhase predicts better phase boundaries, hence lead to smoothprediction.
Revised: Comparing with Image+ UGSM -Y , the low mIU and fIU indicates that MatPhase predicts better phase boundaries, hence lead to smooth prediction.

Original: Note that, all the models in Table 2 follow the exact same architecture of MatPhase , withthe only difference being the change of input to LCGAR (i.e., the local component of the MatPhase ).
Revised: Note that, all the models in Table 2 follow the exact same architecture of MatPhase , with the only difference being the change of input to LCGAR (i.e., the local component of the MatPhase ).

Original: Details about each variant are described in Sec. 4.1.
Revised: Details about each variant are described in Sec. 4.1.

Original: [Table]

Original: 4.2 Comparison with baselines (Q3)
Revised: 4.2 Comparison with baselines (Q3)

Original: We show the performance of MatPhase against SOTA image segmentation models and some nontrivial competitors.
Revised: We show the performance of MatPhase against SOTA image segmentation models and some nontrivial competitors.

Original: Our goal is to demonstrate that achieving smooth predictions for material phasesfrom low-contrast images is challenging and cannot be easily captured by a SOTA.
Revised: Our goal is to demonstrate that achieving smooth predictions for material phases from low-contrast images is challenging and cannot be easily captured by a SOTA.

Original: [Table]
Revised: [Table]

Original: Table 3 shows the performance MatPhase comparing with all the baselines described in Sec. 4.
Revised: Table 3 shows the performance MatPhase comparing with all the baselines described in Sec. 4.

Original: Weobserve MatPhase outperforms all the baselines.
Revised: We observe MatPhase outperforms all the baselines.

Original: On average, our F1-score improves 0 .
Revised: On average, our F1-score improves 0 .

Original: 5 for pore,0 .
Revised: 5 for pore, 0 .

Original: 14 for C, and 0 .
Revised: 14 for C, and 0 .

Original: 2 for Ni.
Revised: 2 for Ni.

Original: w.r.t.
Revised: w.r.t.

Original: mIU and fIU , on average MatPhase performance improves 8 .
Revised: mIU and fIU , on average MatPhase performance improves 8 .

Original: 5%and 6% than the baselines.
Revised: 5% and 6% than the baselines.

Original: It indicates that leveraging automated curriculum learning (HCL) andincorporating global information to capture local and global features for predicting target instancescan provide quality predictions (smooth and free of artifacts ).
Revised: It indicates that leveraging automated curriculum learning (HCL) and incorporating global information to capture local and global features for predicting target instances can provide quality predictions (smooth and free of artifacts ).

Original:  Conclusion
Revised:  Conclusion

Original: With the collaboration between computer scientists and battery researchers, for the first time, wepresent MatPhase , a novel framework to predict material phases, especially phase boundaries, fromlow contrast images of an electrode.
Revised: With the collaboration between computer scientists and battery researchers, for the first time, we present MatPhase , a novel framework to predict material phases, especially phase boundaries, from low contrast images of an electrode.

Original: Our extensive study against multiple non-trivial competitors(deep-learning-based models) and SOTA show that, on average, MatPhase increases the performanceby 8 . 
Revised: Our extensive study against multiple non-trivial competitors (deep-learning-based models) and SOTA show that, on average, MatPhase increases the performance by 8 . 5% .

Original: We also show that incorporating HCL and the local model together on average increases ourperformance up to 7% 3 .
Revised: We also show that incorporating HCL and the local model together on average increases our performance up to 7% 3 .

Original: Our framework is practically useful to battery researchers for understandingof the distribution of material phases of the electrode from high noise data.
Revised: Our framework is practically useful to battery researchers for understanding of the distribution of material phases of the electrode from high noise data.

Original: We envision usingthe framework to study the cross-sections of cycled electrodes and understand various degradationmechanisms that impact the loss of capacities.
Revised: We envision using the framework to study the cross-sections of cycled electrodes and understand various degradation mechanisms that impact the loss of capacities.

Original: Appendix
Revised: Acknowledgments and Disclosure of Funding

Revised: This work is partially supported by the U.S. Department of Energy, the DOE Office of Electricity Dr, Imre Gyuk, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program, under the "RAPIDS Institute".

Revised: This research used resources of the Compute and Data Environment for Science (CADES) at the Oak Ridge

Revised: National Laboratory (ORNL), which is supported by the Office of Science of the U.S. Department of

Revised: Energy under Contract No. DE-AC05-00OR22725.

Original:   6.1 Relevant Work
Revised:  Appendix 6.1 Relevant Work

Original: Recently, multiple deep-learning based image segmentation models have been proposed for objector boundary detection in computer vision applications He et al.
Revised: Recently, multiple deep-learning based image segmentation models have been proposed for object or boundary detection in computer vision applications He et al.

Original: [2017], Ronneberger et al.
Revised: [2017], Ronneberger et al.

Original: Badrinarayanan et al.
Revised: Badrinarayanan et al.

Original: [2017], Long et al.
Revised: [2017], Long et al.

Original: Howard et al.
Revised: Howard et al.

Original: proposed a boundary detectionmodel by addressing the spatially varying intensities in velocity shock wave image data Howardet al.
Revised: proposed a boundary detection model by addressing the spatially varying intensities in velocity shock wave image data Howard et al.

Original: Researchers viewed the problem of identifying material constituents from electrodesamples as object detection Daemi et al.
Revised: Researchers viewed the problem of identifying material constituents from electrode samples as object detection Daemi et al.

Original: Errors induced during data binarization and how thatwould translate into uncertainties in the calculated parameters, such as porosity, tortuosity, or specificsurface area was demonstrated by Pietsch et al.
Revised: Errors induced during data binarization and how that would translate into uncertainties in the calculated parameters, such as porosity, tortuosity, or specific surface area was demonstrated by Pietsch et al.

Original: Pietsch et al.
Revised: Pietsch et al.

Original: Also, Jiang et al. developed amachine learning workflow that automatically identifies multiple fragments that broke away from thesame particle and quantifies every single NMC particle in electrode Jiang et al.
Revised: Also, Jiang et al. developed a machine learning workflow that automatically identifies multiple fragments that broke away from the same particle and quantifies every single NMC particle in electrode Jiang et al.

Original: Using thisapproach, they have also observed several regions of the NMC particles’ that are detached from thepolymeric binder domain in the severely damaged local region.
Revised: Using this approach, they have also observed several regions of the NMC particles’ that are detached from the polymeric binder domain in the severely damaged local region.

Original: Muller et al.
Revised: Muller et al.

Original: adopted a 3D U-Netarchitecture to achieve segmentation across electrode samples Ronneberger et al.
Revised: adopted a 3D U-Net architecture to achieve segmentation across electrode samples Ronneberger et al.

Original: However,none of these works adopt any non-trivial technique to achieve smooth predictions.
Revised: However, none of these works adopt any non-trivial technique to achieve smooth predictions.

Original: Labonte et al.proposed a binary segmentation for LIB electrode material, which can quantify uncertainty to thesegmentation LaBonte et al.
Revised: Labonte et al. proposed a binary segmentation for LIB electrode material, which can quantify uncertainty to the segmentation LaBonte et al.

Original: Multiple curriculum learning strategies have been proposed tosolve different tasks Wang et al.
Revised: Multiple curriculum learning strategies have been proposed to solve different tasks Wang et al.

Original: [2021], Sinha et al.
Revised: [2021], Sinha et al.

Original: Goyal et al. proposed a hierarchicalclass-based curriculum loss function to perform multi-class classification Goyal and Ghosh [2021].
Revised: Goyal et al. proposed a hierarchical class-based curriculum loss function to perform multi-class classification Goyal and Ghosh [2021].

Original: Toaccelerate inference along with prediction accuracy, Wang et al.
Revised: To accelerate inference along with prediction accuracy, Wang et al.

Original: proposed a framework ‘I don’t know’(IDK) that systematically selects a subset of instances of a pre-trained deep learning model Wanget al.
Revised: proposed a framework ‘I don’t know’ (IDK) that systematically selects a subset of instances of a pre-trained deep learning model Wang et al.

Original: Their proposed IDK framework is a rule-based function that selects instances if theentropy loss of the pre-trained model is within a user-defined threshold.
Revised: Their proposed IDK framework is a rule-based function that selects instances if the entropy loss of the pre-trained model is within a user-defined threshold.

Original: Liu et al. Liu et al.
Revised: Liu et al. Liu et al.

Original: [2021] employs an external style transfer module for image segmentation whichis used to govern the curriculum.
Revised: [2021] employs an external style transfer module for image segmentation which is used to govern the curriculum.

Original: However, for our method no external module is employed andcurriculum is learnt implicitly as part of the framework MatPhase .
Revised: However, for our method no external module is employed and curriculum is learnt implicitly as part of the framework MatPhase .

Original: To the best of our knowledge,our proposed hierarchical curriculum learning framework has not been adopted in any application forthe task of material phase prediction.
Revised: To the best of our knowledge, our proposed hierarchical curriculum learning framework has not been adopted in any application for the task of material phase prediction.

Original: 6.2 Extension to Sec3
Revised: 6.2 Extension to Sec

Original: LCGAR Architecture : Table 4 shows the architecture of LCGAR – a CNN.
Revised: LCGAR Architecture : Table 4 shows the architecture of LCGAR – a CNN.

Original: After each convolutionand fully connected layer, we implement activation LeakyRelu.
Revised: After each convolution and fully connected layer, we implement activation LeakyRelu.

Original: To capture rich information about thearrangement of the surrounding for the target pixel of interest, we concatenate UGSM logits ( F j )after flattening. 
Revised: To capture rich information about the arrangement of the surrounding for the target pixel of interest, we concatenate UGSM logits ( F j ) after flattening. [Table]

Original: 6.3 Extension to Sec4
Revised: 6.3 Extension to Sec

Original: Data Collection Process: X-Ray Computed Tomography (XCT) and similar techniques do notprovide information on carbon binder distribution as it is “transparent” for the X-Ray.
Revised: Data Collection Process: X-Ray Computed Tomography (XCT) and similar techniques do not provide information on carbon binder distribution as it is “transparent” for the X-Ray.

Original: It thusbecomes indistinguishable from the pores in the electrodes.
Revised: It thus becomes indistinguishable from the pores in the electrodes.

Original: For collecting the ground-truth labels, toidentify all the material constituents, we utilized cross-sectioning with Focused-Ion beam (FIB/SEM)experiments for imaging and Energy Dispersive X-Ray Spectroscopy (EDS) for chemical mappingof electrode cross-sections Vierrath et al.
Revised: For collecting the ground-truth labels, to identify all the material constituents, we utilized cross-sectioning with Focused-Ion beam (FIB/SEM) experiments for imaging and Energy Dispersive X-Ray Spectroscopy (EDS) for chemical mapping of electrode cross-sections Vierrath et al.

Original: The slicing was performed using Hitachi NB500dual-beam FIB/SEM.
Revised: The slicing was performed using Hitachi NB dual-beam FIB/SEM.

Original: The cross-sections were at a distance of every 200 nm resulting in a total depthof 26 µm resulting in 133 images.
Revised: The cross-sections were at a distance of every 200 nm resulting in a total depth of 26 µm resulting in 133 images.

Original: Pre-processing: In this paper, we construct our data-set D using the corpus of 133 images collectedthrough cross-sections of an electrode.
Revised: Pre-processing: In this paper, we construct our data-set D using the corpus of 133 images collected through cross-sections of an electrode.

Original: Each low-contrast image X in the corpus consists of 224 × 256pixels.
Revised: Each low-contrast image X in the corpus consists of 224 ×pixels.

Original: The corresponding ground-truth (GT)
Revised: The corresponding ground-truth (GT)

Original: Y contains 224 × 256 material constituents consistingof pores, carbon binder (C), and Nickel (Ni).
Revised: Y contains 224 × 256 material constituents consisting of pores, carbon binder (C), and Nickel (Ni).

Original: We leverage a data augmentation technique for efficienttraining with few data samples.
Revised: We leverage a data augmentation technique for efficient training with few data samples.

Original: Our technique is: First, for every image X and the corresponding GT,we obtain k different images, removing a row of pixels from the top.
Revised: Our technique is: First, for every image X and the corresponding GT, we obtain k different images, removing a row of pixels from the top.

Original: Next, we resize each k images[Table] into original size, i.e., 224 × 256 .
Revised: Next, we resize each k images into original size, i.e., 224 × 256 .

Original: We choose k = 10 , as this is sufficient for training data.
Revised: We choose k = 10 , as this is sufficient for training data.

Original: Finally,to smooth the resized GT for the corresponding k images, we use existing knowledge provided bydomain experts: A pixel with Carbon (C) can not exist surrounding Ni pixels and vice-versa for apixel with Ni.
Revised: Finally, to smooth the resized GT for the corresponding k images, we use existing knowledge provided by domain experts: A pixel with Carbon (C) can not exist surrounding Ni pixels and vice-versa for a pixel with Ni.

Original: Using k nearest-neighbor rule, we remove noise from GT, i.e., if most surroundingpixels (nearest neighbors) around a C pixel are Ni, the GT label is changed to Ni.
Revised: Using k nearest-neighbor rule, we remove noise from GT, i.e., if most surrounding pixels (nearest neighbors) around a C pixel are Ni, the GT label is changed to Ni.

Original: Thus, our labeleddataset D consists of N = 1330 images and corresponding GT.
Revised: Thus, our labeled dataset D consists of N = 1330 images and corresponding GT.

Original: For the test, we split D , whichconsists of 50 image-GT pairs.
Revised: For the test, we split D , which consists of 50 image-GT pairs.

Original: 40 pairs among the test-set are completely unseen samples, i.e., theoriginal image of the electrode before the augmentation is not present in the training data.
Revised: 40 pairs among the test-set are completely unseen samples, i.e., the original image of the electrode before the augmentation is not present in the training data.

Original: Model Training: Both UGSM and LCGAR are trained with weighted cross-entropy loss due toheavy class imbalance in the ground-truth (on average C: 26% , Ni: 60% , Pore: 14% ).
Revised: Model Training: Both UGSM and LCGAR are trained with weighted cross-entropy loss due to heavy class imbalance in the ground-truth (on average C: 26% , Ni: 60% , Pore: 14% ).

Original: In all theexperiments, for LCGAR , we normalize input image between 1, 1] and use activation LeakyReLU [-,which yields the best results.
Revised: In all the experiments, for LCGAR , we normalize input image between , which yields the best results.

Original: Our UGSM model is trained on 100 epochs with batch size 20, while
Revised: Our UGSM model is trained on 100 epochs with batch size 20, while

Original: HCL-IDK and LCGAR were trained for 15 epochs with batch size 1024 .
Revised: HCL-IDK and LCGAR were trained for 15 epochs with batch size 1024 .

Original: Measure of Success:
Revised: Measure of Success:

Original: (i) F1-score : Our goal is to measure the overall prediction for each class c ,
Revised: (i) F1-score : Our goal is to measure the overall prediction for each class c ,

Original: i
Revised: i

Original: e., pore, carbon(C), and nickel (Ni) for the unseen datasets.(ii)
Revised: e., pore, carbon (C), and nickel (Ni) for the unseen datasets.

Original:  Pixel accuracy (ACC) :
Revised: (ii) Pixel accuracy (ACC) :

Original: Fraction of the number of pixels that are predicted correctly among total pixels (in % ).To measure smooth predictions Sinha et al.
Revised: Fraction of the number of pixels that are predicted correctly among total pixels (in % ).To measure smooth predictions Sinha et al.

Original: [2020], We aim to evaluate pixelaccuracy for k best performing and worst performing predictions to evaluate smoothness ofmaterial phase predictions.
Revised: [2020], We aim to evaluate pixel accuracy for k best performing and worst performing predictions to evaluate smoothness of material phase predictions.

Original: (iii) Mean intersection over union (mIU) :
Revised: (iii) Mean intersection over union (mIU) :

Original: We intend to quantify predictions from standard practice of image segmentation models Long et al.
Revised: We intend to quantify predictions from standard practice of image segmentation models Long et al.

Original: [2015], Badrinarayanan et al.
Revised: [2015], Badrinarayanan et al.

Original: Suppose,t c be the total number of pixels labeled as class c , n jc be the number of pixels of class c predicted as class j , and | C | are the total number of classes.
Revised: Suppose, t c be the total number of pixels labeled as class c , n jc be the number of pixels of class c predicted as class j , and | C | are the total number of classes.

Original: mIU = 1 | C | (cid:80) cn
Revised: mIU = 1 | C | (cid:80) c

Original: [Table]
Revised: [Table]

Original: n jc (iv) Frequency weighted intersection over union (fIU) :
Revised: jc (iv) Frequency weighted intersection over union (fIU) :

Original: To quantify predictions in presence ofclass imbalance, we incorporate fIU from the standard practice for image segmentationmodels Long et al.
Revised: To quantify predictions in presence of class imbalance, we incorporate fIU from the standard practice for image segmentation models Long et al.

Original: If t be the total number of pixels, fIU = 1 t (cid:80) c
Revised: If t be the total number of pixels, fIU = 1 t (cid:80) c

Original: [Table]

Original: 6.3.1 Additional Experiments on Sensitivity of LCGAR

Original: To check the effect of choosing different bounded local regions surrounding the target instancefor LCGAR , we plan to vary the local bounded region of input ( h ).

Original: We use the same architectureof LCGAR , varying h

Original: = x , where x denotes the height and width of the local input region.

Original: Weanalyze x =

Original: [11 , 17 , 25] which yield the best results.

Original: Table 5 shows the prediction performance ontest datasets varying the size of the input region and complexity of the local model.

Original: We observe

Original: LCGAR- h 11 which is built following the same architecture as our original LCGAR , outperforms all

Original: [Table]

Original: other models across all the evaluation metrics ( 0 .

Original: 005 on average w

Original: [Table]

Original: r

Original: [Table]

Original: t mean IoU and .

Original: 003 on averagew.r.t.

Original: fIU

Original: [Table]

Original: 6.4 Real-world Impact

Original: The ultimate goal of this work is to develop a deep learning model that can identify and distinguishmultiple heterogeneous material phases in a 2D slice of battery electrodes from the experiments withfeature sizes ranging in micrometers and having low contrast between different phases.

Original: The modelwould help quantify the confidence in phase transitions and contact areas between the phases from highnoise data sets.

Original: It is known that binder phase morphologies significantly impact effective electricalconductivity and subsequently define the electro-chemically active area, pore phase tortuosity

Original: [Table]
Revised: [Table]

Original: andeffective electrical conductivity.

Original: This knowledge would help advance the current understandingof binder distribution within the microstructure, which dictates the transport properties and helpoptimize the performance of the batteries.

Original: It is of paramount interest to understand the loss of contactbetween the binder phase and active material particles and the fracture of these particles after repeatedcycling, which causes degradation and aging of batteries.

Original: We envision using MatPhase to study thecross-sections of cycled electrodes and understand various degradation mechanisms that impact theloss of capacities.