Fairness via In-Processing in the Over-parameterized Regime: A Cautionary Tale with MinDiff Loss
Authors: Akshaj Kumar Veldanda
Ivan Brugere
Jiahao Chen
Sanghamitra Dutta
Alan Mishler
Siddharth Garg
Venue: Accepted by TMLR ()

Abstract: Prior work has observed that the test error of state-of-the-art deep neural networks often continues to decrease with increasing over-parameterization, a phenomenon referred to as double descent. This allows deep learning engineers to instantiate large models without having to worry about over-fitting. Despite its benefits, however, prior work has shown that over-parameterization can exacerbate bias against minority subgroups. Several fairness-constrained DNN training methods have been proposed to address this concern. Here, we critically examine MinDiff, a fairness-constrained training procedure implemented within TensorFlow's Responsible AI Toolkit, that aims to achieve Equality of Opportunity. We show that although MinDiff improves fairness for under-parameterized models, it is likely to be ineffective in the over-parameterized regime. This is because an overfit model with zero training loss is trivially group-wise fair on training data, creating an “illusion of fairness,” thus turning off the MinDiff optimization (this will apply to any disparity-based measures which care about errors or accuracy; while it won’t apply to demographic parity). We find that within specified fairness constraints, under-parameterized MinDiff models can even have lower error compared to their over-parameterized counterparts (despite baseline over-parameterized models having lower error compared to their under-parameterized counterparts). We further show that MinDiff optimization is very sensitive to choice of batch size in the under-parameterized regime. Thus, fair model training using MinDiff requires time-consuming hyper-parameter searches. Finally, we suggest using previously proposed regularization techniques, viz. L2, early stopping and flooding in conjunction with MinDiff to train fair over-parameterized models. In our results, over-parameterized models trained using MinDiff+regularization with standard batch sizes are fairer than their under-parameterized counterparts, suggesting that at the very least, regularizers should be integrated into fair deep learning flows, like MinDiff.

Published in Transactions on Machine Learning Research (05/2023)
Fairness via In- In-Processing in the Over-parameterized Regime: A Cautionary Tale with MifDiff Loss
Akshaj Kumar Veldanda
alu dlm275mmmu.edd
Electrical and Computer Engineering Deportment
New York University
Ivan Brugere" JP Morgan Chase AI Research
ioan. brugere Wippecase.cchccccccccccooo
Jiahao Chen* Parily
cjinhao@@gmail com
Sanghamitra Dutta"
sanghamd@humd edu
Electrical and Computer Engineering Department University of Moryland College Park
Alan Mishler*
alan, alan.mishter mishher@@jpmchhse.comm
Morgan Chase Al Research
Siddharth Garg
sg1 75 750ty...cdd edu
Electrical and Computer Engineering Deportment
New York University
Reviewed on OpenReview: https: openreview. net/ pormm id= (A
Abstract
Prior work has observed that the test error of state-of-the-art deep neural networks often continues decrease with increasing prereearaettiiiition,, phenomenon referred to as double descent. This allows deep learning engineers to instantiate large models without having to worry about over-fitting Despite its benefits, however, prior work has shown that over- parameterization can exacerbate bias against minority subgroups. Several fairnss--cossrrinne DNN training methods have been proposed to address this concern. Here, we critically training procedure implemented within consorFlow'ss Responsible AT Toolkit, that aims achieve Equality of Opportunity. We show that although MinDiff improves fairness for under-pantt pator-paramttrized models, it likely to be ineffoctive in the wer-parameteeriee regime. This is because overfit model with zero training loss is trivially group- wise fair on training data, creating "illusion of fairness, " thus turning off the MinDiff optimization (this will apply to any disparity- basod measures which care about errors or accuracy: while it won't apply to demographic parity). We find that within specified fairness constraints, under-parameterizel MinDiff models can even have lower error compared to their over- parameterizee counterparts (despite baseline over- wer-paaameteriied models having lower error compared to their under-paree mndee-parameterizeed counterparts). We further show that MinDiff optimization is very sensitive to choice of batch size in the umder-parameterizer regime. Thus, fair model training using MinDiff requires timo-consuming hyper-paramcter searches. Finally, we suggest using previously proposed regularization techniques, viz. L2, early stopping and flooding in conjunction with MinDiff to train fair over- wee-paammtterieed models. In our results, worrpaaammtterized models trained using MinDiff togglfiirggulliizaattooo with standard batch sizes are fairer than their under-paranne paramterrraeeer counterparts, suggesting that at the very least, regularizers should be integrated into fair deep learning flows, like MinDiff.
examine MinDiff, a cairness-constraiie
"Equa Contribution

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Published in Transactions on Machine Learning Research (05/2023)
1 Introduction
Over the past few years, machine learning (ML) solutions have found wide applicability in a wide range of domains. However, recent work has shown that ML. methods can exhibit unintended biases towards
specific population groups, for instance in applications like hiring (Schumann et al. 2020 credit verification
[Khandani et al. 2010), facial recognition (Buolamwini & Gebru 2018 Grother et al. 2010 Ngan & Grother
2015], recidivism prediction [Chouldechova 2017) and recommendation systems (Biega et al.) [0188] Singh & Joachims 2018), resulting in negative societal consequences. To address this concern, there is a growing and influential body of work on mitigating algorithmic unfairness of ML models. These solutions are being integrated within widely used ML frameworks and are beginning to find practical deployment (Responsible-Ae AI Akihiko Fukuchi 2020). As ML fairness methods make the transition from theory to practice, their ability to achieve stated goals in real-world deployments merits closer examination.
Methods to train fair models can be broadly categorized based on the stage at which they are used: pre-training, in-training, or post-training, Of these, only in-training methods substantively modify the model training process. This paper examines the performance of MinDiff (Prost et al. 2019), the principal in-training method integrated within TensorFlow's 's Responsible AT Toolkit (Respousible- Alj. We are particularly interested in MinDiff for training fair deep learning models because, given TensorFlow's widespread adoption, there is good reason to believe that it will be picked as the default choice by practitioners working within this framework.
We evaluate MinDiff on three datasets, Waterbirds, CelebA, and HAM10000, that are commonly used in fairness literature; and we observe several notes of cantion. Because the success of deep learning can be attributed at least in part to the surprising ability of ever-pararetteizeed deep networks to generalize (Nakkiran et al. 2020), we begin by evaluating the relationship between model capacity and fairness with Min Diff. Over- wver-parameterized models have more parameters than required to memorize the training dataset; under- paramcterized models have fewer. The point at which a model is just large enough to memorize the training data is referred lo as the interpolation threshold. We observe that MinDiff does increase fairness for small, under-patee paleeer-arrmtteizeeed models, but is almost entirely ineffective on larger over pee-paarmeterizee networks. Thus, in some cases, mnder-parameteriaet MinDiff models can have lower fairness-constrainct error compared to their over- wver-parameterized counterparts even though over-parameterized models are always better on baseline error (i.e., error on models trained without MinDiff optimization). We caution that when using MinDiff for fairness, ML practitioners must carefully choose model capacity, something which is generally unnecessary when fairness is not concern and the goal is simply to minimize error.
We find the reason MinDiff is ineffective in the over- ver-parameterized regime is because when model's training loss goes to zero, any fairness metric that relies differences in the model's accuracy across different sub-groups will also go to zero, thus creating an "illusion of fairness' and turning off MinDiff optimization. For completeness, we note that this argument does not apply to demographic parity (Calders et al. 2009)
which cares about equal proportions of positive predictions in cach group. Thus, we explore whether strong regularization used along with MinDiff can alleviate its ineffectiveness. Specifically, we consider two classes of regularization techniques: implicit such as batch sizing (Smith et al. [201] Barrett & Dherin [021] | and early stopping (Morgan & Bourlard 1990), and explicit such as weight decay (Krogh & Hertz 1992) and
recently proposed "loss flooding" method (Ishida et al., 2020) regularizers. We find that: (1) batch sizing only helps for medium sized models around the interpolat ion threshold; (2) the remaining three methods all improve fairness in the over-parameterized regime; (3) early-stopping and flooding result in the fairest models for the Waterbirds, CclebA and HAM10000 datasets, respectively; and (4) with effective rogularization, over-parameterized models are fairer than their under- under-parammtterieed counterparts.
2 Related Work
There are several techniques in the literature to miligate algorithmic bias. These techniques can be broadly categorized as: pre-processing, in-processing and post- post-processing. Pre-processing techniques aim to de-identify
sensitive information and create more balanced training datasets (Quadrianto et al. 2019 Ryu et al. 2018
Feldman et al. 20155 Wang & Deng. 2019: Karkkainen & Joo 2021: Dixon et al. 2018). In-processing
techniques Prrstt. et al. 2019 Cherepanova et. al.] 2021
Sagawa et. al. 2020a b Padala & Gujar 2021
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Published in Transactions on Machine Learning Research (05/2023)
Agarwal et al. 2018 Zafar et al.
2019
Donini et al., 2018
Lahoti et al.
2020
Beutel al. 2019 Martinez
et al. 2020 Wadsworth et al.
2018 Goel et al.
2018
Wang & Deng
2019:
Hashimoto et al.) 2018) alter
the training mechanism by imposing fairness constraints to the training objective, or utilize adversarial
training [Beutel et al.) 2017 Zhang ct al.] 2018
Madras et al. 2018) to make predictions independent of
sensitive altributes. Post-processing techniques
Hardt et al.] 2016; Wang et al. 2020; Savani et al. 2020
Chzhen et al.) 2019 Jiang et al., 2020 Wei et al.
2020) alter the outputs of an existing model, for instance,
using threshold correction (Zhou & Liu 2006 Collell et al. 2016 Menon et al., 2021a) that applies different
classification thresholds to each sensitive group (Hardt et al. 2016 In this paper, we focus on MinDiff (Prost) et al. 2019). the primary in-processing procedure implemented within TensorFlow's Responsible AT toolkit. While our quantitative conclusions might differ, we believe that similar qualitative conclusions might hold for other in-processing methods because overfit models are trivially fair.
With the growing adoption of large over-parameterized deep networks, recent efforts have sought to investigate
their fairness propertics (Menon ct al.] 2021b Sagawa et al., 2020a Cherepanova et al. 2021 Sagawa et al., 2020b). Pham al.
2022 ; Dehghani et al. (2023) observed that seee-parameteriiee ERM models have better
grosp generalization compared to their under- parameterized counterparts. However, Maity et al. 2022 warn that bascline ERM models should not be considered state-of-thc-art to train fair over-parameterized
models. Sagawa et al. 2020b) proposed a pre-processing technique by investigating the role of training data characteristics (such as ratio of majority to minority groups and relative informativeness of spurious versus core features) on fairness and observed that sub-sampling improves fairness in the over-parameterized regime. Menon et al. (2021b) found that post-processing techniques including retraining with sub-sampled majority groups and threshold correction also enhance fairness in over-parameterizel models. Alabdulmohssin & Lucic [2021 proposed post-processing algorithm that can be effectively used to dcbias large models. Cherepanova et al. (2021) report that in-processing convex surrogates of fairness constraints like equal loss, equalized odds penalty, disparate impact penalty, etc., (Padala & Gujar, 2021) are ineffective on over pee-paarameterized models, but do not propose any techniques to increase the effectiveness of in-processing methods. [aldd et al. (2022) theoretically show that interpolating models cannot satisfy fairness constraints. However, it is not thoroughly investigated how fairness constraints can be effectively implemented in over-parameeterized models. Tt is possible that using methods such as MinDiff may improve the training of fair over- over-paranenn parameterizee models. Our work is the first to systematically compare under- vs. ovcr-parameterized deep lcarning models trained using in- in-processing fairness methods, using MinDiff as a representative technique.
Regularization techniques (Morgan & Bourlard 1990 Srivastava et al. 2014 Krogh & Hertz 1992 Ishida
ct al. 2020) are popularly used in dcep learning frameworks to avoid over-fitting. Lately, rescarchers have also exploited the benefits of regularizers to train fair models. For example, Sagawa et al. (2020a) proposed distributionally robust optimization (DRO) to improve worst-group generalization, but they observed that their approach fails if training loss converges to zero. Hence, they use L2 weight regularization and early stopping to improve fairness in the over perammaameter regime. Our paper systematically evaluates different regularizers, including batch sizing, early stopping, weight decay and the recently proposed flooding loss (Ishida ct al.) 2020) for MinDiff training across different model sizes, and makes several new obscrvations about the role of regularization in enhancing fairness.
3 Methodology
We now describe our evaluation methodology.
3.1 Formal Setup
In this paper, we consider binary classification problem on a training dataset D = (zi, ds. v. where xa is an input (an image for instance) a4 E {0,1} is a sensitive attribute of the input, and yı E {0, is the corresponding ground-truth label. The training data is sampled from a joint distribution Dx, over random variables X, A, and Y. Deep neural network (DNN) classifiers are represented as paraneterized function So X + [0, 1]. where 0 are trainable parameters, obtained in practice by minimizing the empirical binary
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cross-entropy primary loss function Lp:
N Lp
Iu log(fo(z;)) + +11 y:) log((1 (1 - fo (x4))
(1)
N
via stochastic gradiont descent (SGD).
We denote the classification threshold as T which can be used to make predictions fz(;;) as shown below
1, fo(e) fo(I;t)= = {1.
(2)
otherwise.
The goal is to attain low error at the population level, ie.. P(fo(X:T) * Y] (typically, r 0.5). As the data-generating distribution is unavailable, standard DNN training seeks to achieve low empirical error on a test sct, which we refer to as test error for short. However, performance conditioned on sensitive attributes can vary, leading to outcomes that are biased in favor of or against specific sub-groups. Several fairness metrics have been defined in prior work to account for this bias; in this paper, will use the widely adopted equality of opportunity metric (Hardt et al. 2016).
Equality of Opportunity (Hardt et al. 2016 is a widely adopted fairness notion that seeks to equalize false negative rates (FNR) across sensitive groups to achieve fairness in contexts where a higher FNR for a certain group can result in unfair outcomes, such as wrongful convictions or denial opportunities comparison to other groups. For binary sensitive attributes the FNRggp the population level is defined as:
(P]o(()))) = O|Y = 1, A 0] P(fo((X:) O|Y = -,AA
(3)
In practice, we measure the population-level FNR on test set, which we will refer to as just FNRgap for short. As we describe next, MinDiff (and several other methods) seek to minimize the FNR during training.
3.2 MinDiff Training
MinDiff (Prost et al. 2019) an in-processing optimization framework that seeks to achieve a balance between two objectives: low test error and low FNRgaap- For this, MinDiff proposes modified loss function CT = Lp XLM, where Lr is the total loss, that is a weighted sum of the primary cross-entropy loss, defined in Equation [ and LM, a differentiable proxy for the FNRgap- In the modified loss function, À E R4 is a user-defined parameter that controls the relative importance the fairness versus the empirical cross-entropy loss. The fairness term in the modified loss function, LM. uses the maximum mean discrepancy (MMD) distance between the neural network's outputs for the two sensitive groups when Y 1, i.e.,
LM MMD( Y fo 1, 1).
(4)
Intuitively, the MMD loss LM penalizes any statistical dependence between the predictions for the two subgroups which are made by the model on positive examples. We refer the reader to Appendix A for a formal mathematical definition of the MMD distance (Prost et al. 2019
3.3 Post-hoc Threshold Correction
Due to fairness requirements of the application, ML practitioners might seek to train models with population level FNRgap lower than a specified threshold AFNR This can be done using an additional post-processing step as proposed by Hardt et al. (2016). The idea is to use different classification thresholds for each sub-group,
TA=0 and TA=I, that are selected such that the population level FNR under these thresholds below the constraint:
[[( OJY 1,4= = 0] P((o(X:TAA)))= o/ 1, 1,4=10 AFNR
(5)
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We show the misel-wise double descent behaviour on baseline models trained using (a) Waterbirds and (b) CelebA datasets respectively. Interpolation threshold (shown in green dotted line) is the point where the model is large enough to fit the training data. The region beyond the interpolation threshold is called the over-parameterized regime.
Figure 1:
In practice, the two thresholds can be picked using grid search and empirically measuring population level 2a each grid point a validation dalaset. The resulting thresholds yield test error which we refer to as the
test error. Pareto front of fairness-conse constrained test error and AFNR is used to compare different model sizes and fairness methods. In particular, model or method is fairer if it has lower ceiness-constraingg test error compared to the alternative for a fixed APNR.
3.4 Regularization Techniques
We evaluate four regularization techniques to improve performance of MinDiff over-parameeeerized networks.
Due the stochastic nature of SGD, smaller batch sizes can as implicit regularizers during training (Smith et al.] 2021 Barrett & Dherin 2021 This is because smaller batch sizes provide a noisy estimate of the total loss Lr.
Reduced Batch Sizes:
explicitly penalizes the parameters @ of the DNN from growing too large. Weight decay adds a penalty, usually the L2 norm of the weights, to the loss function.
Weight Decay:
Weight decay (Krogh & Hertz
1992
1990) terminates DNN training earlier than the point at which training loss converges to a local minima, and has been shown to be particularly effective for over-parameterized deep networks (T.i et al., 2019). A common implementation of early stopping is to terminate training once the validation loss has not improved for a certain number gradient steps or epochs (Morgan Bourlard, 1990). For models trained with MinDiff, we explore two versions of early stopping in which we use either the primary loss, Lp, or total loss, Cr, as a stopping criterion.
Early Stopping: Early stopping (Morgan & Bourlard
Flooding Regularizer: Finally, motivated by our goal to prevent the primary training loss from going zero (which then turns off MinDiff as well), we apply the flooding regularizer (Ishida et al. 2020 that encodes this goal explicitly. Flooding operates by performing gradient descent only if Lp > b, where b is the flood level. Otherwise, if Lp < b, then gradient ascent takes place shown in [Equation 6 This phenomenon ensures that Lp floats around the flood level and never approaches zero. We implement flooding by replacing the primary loss term in Lx with a new loss term:
C' -p -b -b+ bb
(6)
which, in turn, enables continued minimization of the MinDiff loss term, LMs over the training process.
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==0
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Figure 2: We show the (a) average test error, and (b) FN gap versus model width for MinDiff optimization with À = (0.0,0.5, 1.0, 1.5)'s 's on Waterbirds dataset. MinDiff optimization has negligible to no impact on fairness the werr-paramtterized models. However, for under- pader-parameterized models, we find that increasing \ substantially reduces the FgRgap-
4 Experimental Setup
We perform our experiments on the Waterbirds (Sagawa et al. 2020ap, CelebA (Liu et al., 2015) and HAM10000 [Tschand] 2018) datasets which have previously been used in fairness evaluations deep learning models. Here, we describe network architectures, training and evaluations for the two datasets.
4.1 Waterbirds Dataset
Waterbirds is a synthetically created dataset (Sagawa et al. 2020a) which contains water- and land-bird images overlaid on water and land backgrounds. A majority of waterbirds (landbirds) appear in water (land) backgrounds, but in minority of cases waterbirds (landbirds) also appear land (water) backgrounds. As in past work, we use the background as the sensitive feature. Further, we use waterbirds as the positive class and landbirds as the negative class. The dataset is split into training, validation and test sets with 4795, 1199 and 5794 images in each dataset respectively.
We follow the training methodology described in (Sagawa et al. 2020b) train a deep network for this dataset. First, a fixed pre-trained ResNet-18 model is used to extract d-dimensional feature vector μ.. This feature vector is then converted into an m-dimensional feature n' ReLU(UU) where U E R is random matrix with each row sampled uniformly from unit sphere 8d-1, A logistic regression classifier is trained on p'. Model width is controlled by varying m, the dimensionality of μ', from 10 to 10, 000.
4.2 CelebA Dataset
The CelebA dataset consists of 202,599 celebrity face images annotated with 40 binary attributes including gender, hair colour, hair style, eyeglasses, etc. In our experiments, we set the target label y to be hair color, which is either blond (Y = 1) or non-blond (Y = 0), and the sensitive attribute to be gender. Blond individuals constitute only 15% of this dataset, and only 6% of blond individuals are men. Consequently baseline models make disproportionately large errors on blond men versus blond women. The objective of MinDiff training is to minimize the FNRgap between blond men and blond womer The dataset is split into training, validation and test sets with 162770, 19867 and 19962 images, respectively.
We used the Resaeet-peacct11 model for this dataset, and vary model capacity by uniformly scaling the number of channels in all layers. We also train a LeNet-5 architecture on CelebA dataset and compare it with the ResNeet-preatte model.
1 Note that the MinDiff paper uses False Positive Rate, but this totally arbitrary here the class labels are arbitrary.

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Figure 3: We show the progress of primary loss and population level FNRgap: evaluated on training datasel and the validation dataset, versus SGD steps during MinDiff optimization (A 1.5) for muder-parameterien and panamaaaactrr models on CelebA datasct. We find that por-parraeteriieed models over-fits to the training data and achieve zero population level FaRg on the training dataset, thus turning off MinDiff optimization. Whereas, population level gg on the training dataset is positive in the ander-parameterized models, allowing for MinDiff optimization to be effective.
4.3 HAM10000 Dataset
HAM10000 dataset consists of 10,015 dermatoscopic images for automatic diagnosis of pigmented skin lesions. Each image in the datasct contains several annotations including sensitive attributes like age, gender and the diagnosis labels of the patient. Medical imaging is a problem with direct human impact and this dataset has been previously studied in the context of bias and fairness (Daneshjou et al. 2022). Following prior work (Zong et al. 2023 Maron et al.) 2019), we split the 7 diagnostic labels into benign: basal cell carcinoma (bec), benign keratosis-like like lesions (bkl), dermatofibroma (df), melanocytic nevi (nv), and vascular lesions (vasc), and malignant: actinic keratoses and intraepithelial carcinoma Bowen's disease (akiec), and melanoma. (mel). In our experiments, we set the target label Y to be the diagnostic label, which is cither malignant (Y=1) 1) beuign (Y 0), and the sensitive attribute to be age. We categorize all patients into two demographic groups based on their age: those under 40 (< 40) and those 40 years old or above (2 40). Malignant. individuals constitute only 15% of this dataset, and only 6% of malignant individuals are < 40. Consequently baseline models make disproportionately large errors on malignant (< 40) individuals versus malignant (2 40) individuals. The objective MinDiff training is to minimize the FNR between malignant (< 40) and malignant (2 40) individuals. We discard images whose sensitive attributes are not available and the dataset is split into training, validation and test sets with 7967, 989 and 1002 images, respectively. We used the pre-trained NesNett-1 as over-parameterized model and LeNel-5 as under-parannellriieel model for this dataset.
4.4 Hyper-parameters and Training Details
000 gradient steps using the Adam optimizer. For our baseline experiments, we set batch size to 128 and use a learning rate schedule with initial learning rate = 0.01 and decay factor of 10 for every 10, 000 gradient steps. We ran every experiment 10 times with random initializations and report the average of all the runs. We trained and evaluated all the models using the Waterbirds dataset
Waterbirds We train for a total of 30,000
Intel Xeon Platinum 8268 CPU (24 cores, 2.9 GHz).
CelebA We train for a lotal of 48, 000 gradient sleps using the Adam optimizer. We set the baseline batch size to 128 and adopt a learning rate scheduler with initial learning rate of 0.0001 and decay factor of for every 16, 000 gradient steps. In our experiments, we varied the number of channels in the first ResNNet-peaact18 block from to 64 (the number of channels is then scaled up by two each block). We trained all the models using the CelebA dataset on NVIDIA 4 V100 (32 GB) GPU cards.
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HAM10000 We train for total of 12, 600 and 7, 000 gradient steps using the Adam optimizer for LcNet-5 and ResNet-18 architectures, respectively. We set the baseline batch size to 128 and set the learning rate to 0.0001. We adopt a learning rate scheduler with a decay factor of 10 for every 1, 260 gradient steps for ResNet-18 models. We trained all the models using the HAM10000 dataset on NVIDIA V100 (32 GB) GPU cards.
For Waterbirds and CelebA datasets, we performed MinDiff training with values of X 0.50, 1.0, 1.5), where recall that À controls the importance of the fairness objective. À = 0.0 corresponds to training with the primary loss only, and we refer to the resulting model as the baseline model. To study the effect of batch sizing, we trained additional models with batch sizes {8, 38.3 We explored with three different weight docay strengths = {0.001, 0.1, 10.0} and two different flood levels, E {0.05, 0.1}. We report the average + 95% confidence interval in all figures and tables. For HAM10000 dataset, we performed MinDiff training with values of À (0.0, 0.5, 1.5). We explored with two different weight decay strengths {0.001, 0.1} and {0.001, 3.01) for LeNet-ō and ResNet-18 architoctures, respectively. Additionally, we tested the impact of two different flood levels, which
E {0.2, 0.33 for LeNet-5 and b (0.05.011) for ResNet-18.
5 Experimental Results
5.1 Identifying the Interpolation Threshold
To distinguish between under- and over- parameterized models, we begin by identifying the interpolation threshold; the point where the model sufficiently large to interpolate the training data (achieve population level zero error on training data). Figure I(a) and Figure I(b) show the population level error on training data and test error curves for baseline training versus model width for the Waterbirds and CelebA datasets, respectively, showing interpolation thresholds at model widths of 400 for Waterbirds and 11 for CelebA. On both the datasets, also observe the double descent phenomenon (Nakkiran et al., 2020 where the test error decreases with increasing model capacity beyond the interpolation threshold. T That is, for the original model (training without MinDiff), the largest models provide high accuracy.
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Figure 4: We plot the fairness constrained test error with APNR I 10% constraint on the MinDiff trained models with À = {0.0, 0.5, 1.0, 1.5] on (a) Waterbirds and (b) CelebA datasets respectively. On both these datasets, we find that MinDiff only effective for anderparaameterize models.
5.2 MinDiff Evaluation
We now re-train our models with MinDiff optimization with À = (0.0, 0.5, 1.0, 1.5). Figure 2 shows the test. error and FNRgap versus model width for the Waterbirds dataset. In the under-pant mnder-parameterizerr regime, we observe that, increasing the MinDiff weights significantly reduces the FNR with only small drop accuracy. However, in the overpaaraetterized regime, we find that MinDiff training has no impact on either test the FNRgap-
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Figure 5: We plot the fairness constrained test error with AFNR I 10% constraint on the MinDiff trained model with À 1.5 on (a) Waterbirds and (b) CelebA datasets respectively. We find that smaller batch sizes are only effective around the interpolation threshold.
Table 1:
We pick three under-parameteriied and four werrparameterized model widths and report the average test error and FN for baseline training and several values of À on CelebA dataset. We find that, in the under-parameterized models, the drop in FNRgap for MinDiff training vs baseline training is more compared to that in the over- parameterized models. We report each data point by averaging over 10 runs.
Width
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Error
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Error
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Error
FNR Gap
Error
FNR Gap
5 (Under-)
4.74 0.07
48.77 + 1.44
5.55 1 0.39
39.85 + 3,82
5.46 + 0.36
40.45 + 5.58
5.47 + 0.34
37 - 5.88
7 (Under-)
5.07 + 0.07
47.35 + 1.53
5.76
+ 0.5
40.27 + 2.45
5.64 + 0.52
42.7 + 3.12
5.48 + 0.4
43.05 + 4.2
9 (Under-)
5.31 + 0.07
44.78 + 1.72
5.72 172+00. 0.4
42.37 + 1.75
5.77 + 0.53
40.91 + 3.28
5.52 0.42
42.43 + 3.74
13 (Over-)
5.52 0.07
42.79 + 2.03
5.57 0.1
42.16
2.33
5.66 + 0.17
42.53 0.98
5.67 0.32
43.07 + 2.12
19 (Over-)
5.36++0.08
43.98 + 1.81
5.33 0.05
42.52 + 1.25
5.42 + 0.07
42.63 1.01
0.11
41.34 + 1.41
55 (Over-)
4.98 +
44.14 + 1.55
5.05 + 0.07
42.46 + 1.28
5.24 + 0.06
42.65 + 1.85
5.47 0.15
41.93 + 1.88
64 (Over-)
4.99
42.54
2.01
5.11 + 0.06
43.12
+ 2.04
5.28 + 0.12
41.8 + 2.32
5.40
41.56 2.7
Table shows the test error and FNRgap for selected under- and over- pee--parametrizee models on the CelebA dataset trained with MinDiff. Our conclusions are qualitatively the same as for Waterbirds. We find that, MinDiff training significantly reduces the FNRgap compared to the baseline model in the under-parameterizzed regime, for example, from a 48% FNR gap without MinDiff to 37% FNR gap with A = 1.5 for model width of 5. On the other hand, MinDiff training compared with the baseline model has negligible effect on both test error and FNRgap in the par-paaameterized regime, sometimes even resulting in (small) increase in both.
Table 2: We tabulate the fairness constrained Lest error (with a AFNR S 10% constraint) of early stopped MinDiff models (trained with À (0.5, 1.0, 1.5)) for different widths. We compare two methods for early stopping (es) based on the stopping criterion: primary validation loss (es(Cr)) and total validation loss (es(CT)). We find that, for CelebA dataset, MinDiff + es(Cp) is better than MinDiff + es(CT).
A= 0.5
A= 1.0
A= 1.5
Width
Width 19
Width 64
Width
Width 19
Width 64
Width
Width
Width 64
es
6.36 0.51
6.54
3.88
6.25 0.43
6.43 0.41::.12
6.06
6.36 + 0.35
6.54 0.18
6.07 0.2
es( es(Cp)
6.17 0.34
5.91 +
5.45
6.32 + 0.28
5.82 + 01.2
4.79+ 0.17
6.37
5.63 + 0.3
4.70 0.07
es(Cr) 7.76 0.56
6.47 + 0.31
5.76 0.61
7.79 +79 0.47
7.18 0.58
6.05 + 0.53
8.65 +: 0.65
7.38 0.77
6.80 - 0.64
We observe that MinDiff performs poorly for over-parameterizee models: Figure shows how the population level primary loss and FNRgap's 's change, evaluated on training and validation datasets, during SGD steps for madd-pparamtterized and over-parameterizet models on the CelebA dataset. We note that at the beginning of training, the population level FNRgap on training dataset is small because randomly initialized models make random predictions. These random predictions are fair w.r.t. the error rates but not necessarily fair according
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to other criteria like Demographic Parity. As training progresses, the over-parameterized model eventually over-fits the training data at around 20,000 steps, achieving zero primary loss. This model also appears to be trivially fair from the standpoint of the training data- observe that at the same point, the population level gap gap on the training dataset also goes to zero, and no further optimization takes place. On the other hand, the population level FNRgap during training remains posilive for the under-parameterieed model.
Figure 4 plots the fairness constrained test error with a ΔNNR S 10% constraint using post-training threshold correction on the MinDiff trained models. We can again observe that MinDiff is only effective for under- parameterized models. We include results for larger À e {8.0, 16.0, 32.0} values in Appendix B and observe that the findings do not change. For CcicbA, the lowest fairness constrained test error is actually achieved by an muder-parameterizee model. In other words, achieving fairness via MinDiff oplimization requires careful selection of model width, including exploring the under- palder-arameterizee regime.
Table 3: We tabulate the fairness constrained test error (with ΔNNR S 10% constraint) for different regularization schemes used in conjunction with MinDiff optimization (A 1.5) on LeNet-5 and ResNet- preact-18 (with three model widths E {5, 19, 64}) models trained using CelebA dataset. The performance of best regularizer is highlighted in bold for each model width. Notation: we is weight decay, es(Cp) is early stopping w.r.t primary loss and fl is flooding.
Method
LeNet-5
Width = 5
Width = 19
Width = 64
Under-
Under-
Over-
Over-
== 0
9.73 0.26
5.92 + 0.19
6.51 0.11
5.76 0.1
A 1.5
9.53 + 0.17
6.36 + 0.35
6.54
6.07 = 0.2
A= 1.5 + wd 0.001
9.87 + 0.28
5.82 0.2
6.53 0.16
5.08 0.15
A = wd 0.1
12.68 + 0.03
6.15 0.15
0.16
6.57 =
A= 1.5 + (C))
9.44 0.14
6.37 +: 0.25
5.63
4.70
A= 1.5 + fl 0.05
9.53 0.17
6.28 + 0.25
6.30
5.49 0.11
A 1.5 ft 0.1
9.52
6.30 +: 0.3
5.25 0.225
4.67 0.112
5.3 Impact of Regularization in ever-parameterized Regime
We now examine additional regularization can help improve the fairness of MinDiff-regularieee models the over-parane weerpparamtterieed regime. Unless otherwise stated, in all subsequent evaluations we perform post-training threshold correction with APNR 10% constraint and compare fairness constrained test error.
Batch sizing only helps around the interpolation threshold. Small batch sizes cause primary training loss curves converge more slowly, potentially providing more opportunity for MinDiff optimizations. In Figure 5(a] and Figure 5(b) we plot fairness constrained test error curves versus model widths for different. batch sizes on the Waterbirds and CelebA datasets, respectively. We find that smaller batch sizes improve fairness constrained test error only around the interpolation threshold for both the datasets, but do not noticeably benefit. smaller and larger models. On further examination, we note the benefits around the interpolation threshold are because smaller batch sizes induce stronger rogularization effects and push the interpolation threshold to the right (see Appendix Figure 13). As a result, MinDiff is effective on a slightly increased range of model widths. However, other than this behaviour, we see no other benefits of using batch sizing as regularizer and do not explore it further.
Early stopping criterion. We evaluate two methods for early stopping. The first uses the primary validation loss (MinDifffes((p)) (P)) as a stopping criterion, while the second uses total validation loss for stopping (MinDiff+es(Cr)) Figure 6 plots fairness constrained test error versus model width for these two schemes and different values of À on Waterbirds, and Table 2 shows the same data for CelebA. We find that both schemes improve fairness for wer-paramettrized models, but have limited impact in the under- parameterized regime. For Waterbirds, the differences between the two are small, although using primary validation loss as the stopping criterion (MinDiff+es(CP)) is marginally better than using total validation However, for CelebA, we find that primary loss stopping criterion (MinDiff+os(Cp)) is substantially better than total loss stopping criterion (MinDiff+es(Cr) )), especially for large models. Thus, we use the former for the remainder of our experiments.
loss (MinDiff+
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Comparing regularization methods Waterbirds. In Figure
we plot the fairness constrained test error versus model width for different regularization schemes including early stopping (A+es), weight decay with two different values (A+wd=0.001, A+wd=0.1) and flooding (A+fl) on Waterbirds. We find that the early stopping and weight decay regularizes substantially improve fairness for models just below the interpolation threshold and over-parameteriveel models. In contrast, flooding shows only small improvements in fairness. For = 0.5, we find that early stopping is the best across the board. For 1.5, either early stopping and weight decay are the best depending on model width, although the differences are small.
20
20
20
À es(Cp)
À + es(CT)
Test Error (%)
15
15
15
Test Error
Test Error
10
10
10
5
Over- parameterized
5
Over- parameterized
5
Over- parameterized zed
0
0
0
1
2
1
2
4
1
2
4
Model Width (log scale)
Model Width (log scale)
Model Width (log scale)
(a) A 0.5
(b) A= 1.0
(c) A = 1.5
Figure 6: We plot the fairness constrained test error (with AFNR S 10% constraint) of carly stopped MinDiff models (trained with À {0.5, 1.0, 1.5]) for several model widths. We compare two methods for early stopping (es) based on the stopping criterion: primary validation loss (es(C)) and total validation loss (es(Cr)). We find that, for Waterbirds dataset, using either stopping criterion will significantly improve fairness constrained error, especially in the over-parametterized regime.
Test Error (9%)
15
Test Error (%)
15
5
Over- parameterized
5
Over- param earameterized
0
Model Width (log scale)
Model Width (log scale)
(a) À 0.5
(b) A = 1.5
-=
wd = 0.001
es(Cp) fl = 0.1
À
A + wd = 0.1
Figure 7: We plot fairness constrained test error (with AFNR < 10% constraint) versus model widths for different regularization schemes used in conjunction with MinDiff optimization on Waterbirds dataset. We find that early stopping and weight decay are preferred choice of regularizers for Waterbirds dataset. Notation: wd is weight decay, es cL)rr carly stopping w.r.t primary loss and fl is flooding.
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Table 4: We tabulate the fairness constrained test error (with a ΔrNN I 10% constraint) for different. regularization schemes used in conjunction with MinDiff optimization (A 0.5, A 1.0 and = 1.5) on HAM10000 dataset. The performance of best regularizer highlighted in bold for each model. Notation: wd is weight decay, es(Cp) is early stopping w.r.t primary loss, es(Cr) is early stopping w... total loss and fl is
flooding.
A 0.5
A 1.0
A 1.5
LeNet-5
ResNet-18
LeNet-5
ResNet-18
LeNet-5
ResNet-18
== A
14.64 0.40
10.85 + 0.22
14.61 0.40
10.85 = 0.22
14.64 0.40
10.85 + 0.22
14.60=0...
11.91 0.12
14.34 0.74
10.86 0.45
14.61 0.53
11.47 + 0.19
A + wd = 0.001
13.97
12.77 = 1.02
14.60 = 0.47
12.34 0.46
15.01 + 0.64
10.75 0.08
A + wd = 0.01
10.91 = 1.29
12.74 1.23
12.35 + 0.66
À + wd 0.1
0.10
14.11 0.08
14.1
es(Cp)
14.30
13.41 1.32
1.14
12.04 1.09
14.73
13.12 1.31
+ es(C.)
14.20+0.00
12.54 + 0.77
14.14
12.51 + 0.86
14.15 0.16
12.95 1.4
À + Al = 0.05
12.11 + 0.37
10.68 + 0.59
11.02 + 0.79
À + fl 0.1
11.78 + 1.07
12.64 + 1.13
12.82 + 0.51
À + 0.2
14.47 0.22
14.27 0.65
14.53 0.56
+ = 0.3
14.77 + 0.72
14.50 + 0.64
15.13 + 0.89
Comparing regularization methods on CelebA. Table 3 compares different regularization schemes for x = 1.5 on LeNet-5 architecture and three RosNet-preact-18 model widths, each trained on CelebA dataset. For LeNet-5, we observe that early stopping results in lowest fairness constrained test error. For ResNett-preact188 with smallest. width, we find that weight decay schemes result. in the lowest fairness constrained test error, while for the large over- peeapaarmeeer model, flooding works best. Comparing across all models, we find that, the largest model with flooding provides the overall lowest fairness constrained test error. Recalling that flooding was ineffective on Waterbirds, we conclude that one regularizer works best across datasets and model widths, but additional regularization in general can restore the benefits of ree-pparameterization with MinDiff training.
Comparing regularization methods on HAM10000. From Appendix Figure 9 observe that for ResNet-18 (A = 1.5) the primary loss orer-fits to the training dataset and achieves zero training loss thus turning off MinDiff optimization on the wver-parameterized model. In contrast, for the under-parameterixet model, MinDiff optimization is active and aids in improving fairness since training loss is non-zero. Table 4 compares different regularization schemes on the HAM10000 dataset for À = 0.5, A = 1.0 and = 1.5. We can observe that the fairness caistr lest error of MinDiff model is lower for LeNet-5 architect compared to bascline model, whereas, for over-parameterizer ResNet-18 model, the fairness constrained test error of baseline model is lower compared to MinDiff model. However, for both the models, regularization improves the fairness constrained test error for all values of X except for ResNet-18, where smaller value of X = 0.5 seems to be having no effect on fairness.
6 Conclusion
In this paper, we have critically examined the performance of MinDiff, an in in-training fairness regularization technique implemented within TensorFlow's Responsible AT toolkit, with respect to DNN model complexity, with particular eye towards over-parameterized models. We find that although MinDiff improves the fairness of under-paraameeriiee models relative baseline, it is ineffective in improving fairness for over-parameterized models. As result, find that for one of our datasets, under-parametee parameterized MinDiff models have lower fairness constrained test error than their wer-ppaaaeterized counterparts, suggesting that time-consuming searches for best model size might be necessary when MinDiff is used with the goal of training fair model.
To address these concerns, we explore traditional batch sizing, weight decay and early stopping regularizers to improve MinDiff training, addition to flooding, a recently proposed method that is evaluated for the first time in the context of fair training. We find that batch sizing is ineffective in improving fairness except for model widths near the interpolation threshold. The other regularizers do improve fairness for
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wver-parameterized models, but the best regularizer depends on the dataset and model size. In particular, flooding results in the fairest models on the CelebA dataset, suggesting its utility for MinDiff optimization. Finally, we show that with appropriate choice of regularizer, peer-parametriized MinDiff models regain their benefits over under-parameterized counterparts even from a fairness lens.
Availability
Code with README.1xL file available al: http///...o//maaaaaaaaaaarr////a
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A Maximum Mean Discrepancy
Maximum Mean Discrepancy (MMD) is statistic to test the statistical dependency between two sample distributions. It's mathematical formulation consists of taking the mean between two samples Zo (consisting of m elements) and Zi (consisting of n elements) mapped into a Reproducing Kernel Hilbert Subspace, and is computed as follows Prost et al.
2019):
m
MMD(ZZ. 21)
k 20.1)
k=0051 21.)
m
mn 1
n2 1,==1
(-=1
where & is either Gaussian or Laplace kernel, (20,))i=1, and (21,))i1,,n are elements from Zu and Zi, respectively.
B MinDiff Evaluation
To study the sensitivity analysis on A, we plot the fairness constrained test error (with AFNR & 10% constraint) on Waterbirds dataset for different values of = {0, 1.5, 8.0, 16.0, 32.0) in Figure g We observe that MinDiff is only effective for nuder-pparameterized models even for larger values of X, but provides no significant gains compared to smaller values of A. We also observe that when set to high values, like X 8.0 16.0 32.0, the optimization prioritizes minimizing FNRgap rather than accurately classifying the data, leading to poor classification performance in the over-parameterized regime. Therefore, it is crucial to choose lambda carefully in order to strike balance between classification accuracy and fairness for different. model widths.
80
À
70
A 1.5
Test Error (%)
60
A 8.0
50
A = 16.0
A 32.0
40
30
20
10
1
3
4
Model Width (log scale)
Figure 8: We plot the fairness constrained test crror with APNR I 10% constraint on the MinDiff trained models with A = (0.0, 1.5, 8.0, 32.0) on Waterbirds dataset.
On HAM10000 dataset, observe that for Resnet-18 the primary loss over-fits to the training dataset and achieves zero training loss thus turning off MinDiff optimization on the over-parameterized model. Tn contrast, for the suder-parameterizer model, MinDiff optimization is active and aids in improving fairness since training loss is non-zero.
C Impact of Regularization in Over-parameterized Regime
C.1 Batch Size
C.1.1 Waterbirds
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0.42
Train Validation
0.40
Classification Loss
Classification Lass
0.3
0.36
Train Validation
0.34
0.2
0.30
0.28
0.0
0.0
0.5
1.0
1.5
2.0
0.0
0.2
0.4
0.6 Fpochs
0.8
1.0
Fpochs
162
162
(a) LeNet-5
(b) ResNet-18
Figure 9: We show the progress of primary loss, evaluated training dataset and the validation dataset, versus epochs during MinDiff optimization (A 1.5) for under-parameterized (LeNet-5) and over- parameterized (ResNet-18) models on HAM10000 dataset. We find that over-parameterized ResNet-18 model over-fits to the training data, thus turning off MinDiff optimization.
22
22
22
Batch Size 8
20
Batch Size 32
20
20
Batch Size 128
Error (%)
18
18
18
16
Over parameterized
Error
16
Error
16
14
14
parameterized
14
parameterized
12
12
12
10
10
10
8
8
8
1
2
1
1
Model Width (log scale)
Model Width (log scale)
Model Width (log scale)
(a) MinDiff (A = 0.5)
(b) MinDiff (A -A=30 1.0)
(c) MinDiff (2 1.5)
Figure 10: Batch size - THR with fairness constraint < 10%
C.2
All Other Regularizers
C.2.1
Waterbirds
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22
Batch Size 8
22
22
20
Batch Size 32
20
20
Batch Size 128
Test Error (%)
18
18
18
16
Over- parameterized
Test Error
16
Over- parameterized
Test Error
16
Over-
14
14
14
parameter zed
12
12
12
10
10
10
8
8
8
Model Width (log scale)
Model Width (log scale)
Model Width (log scale)
(a) MinDiff (A= 0.5)
(b) MinDiff 1.0)
(c) MinDiff 1.5)
Figure 11: Batch size
THR with fairness constraint
5%
22
Batch Size 8
22
22
Batch Size
20
Batch Size 128
20
20
Test Error (%6
18
Error (96
18
18
Test Error
16
16
16
Over- parameterized
Over- parameterized
Over- parameterized
14
14
14
12
12
12
10
10
10
8
8
8
Model Width (log scale)
Model Width (log scale)
Model Width (log scale)
(a) MinDiff 0.5)
(b) MinDiff 1.0)
(c) MinDiff 1.5)
Figure 12: Batch size THR with fairness constraint 1%
C.2.2 CelebA
Table 5: We labulate the fairness constrained lest, error (with AFNR S 10% constraint) for different
regularization schemes used in conjunction with MinDiff optimization (A = 0.5) on CelebA dataset. The performance of best regularizer highlighted in bold for cach model width. Notation: wd is weight decay, es(Cp) early stopping w.r.t primary loss and fl is flooding
Method
Width = 5
Width 19
Width 64
Under-
Over-
Over-
A =
5.92 + 0.27
6.51 = 0.16
5.76 0.14
À 0.5
6.36 + 0.72
6.54 = 0.17
5.88 0.19
À 0.5 wd 0.001
5.89 + 0.32
6.94 - 0.18
6.25 0.48
X 0.5 + wd 0.1
5.66 + 0.18
5.27
6.40
X = 0.5 es(Cp)
6.17
5.91 0.37
5.43
A = 0.5 + fl 0.05
6.53 0.21
0.09
A = 0.5+ fl = 0.1
6.34 + 0.63
5.75 + 0.35
4.80 + 0.28
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Batch Size 8
Batch Size 8
Batch Size = 8
20
Batch Size 32
20
Batch Size
20
Batch Size
Batch Size 128
Batch Size 128
Batch Size 128
15
Error (%)
Error (%)
15
Error (%)
15
10
10
10
5
5
5
0
0
0
1
2
1
1
Model Width (log scale)
Model Width (log scale)
Model Width (log scale)
(a) MinDiff (A= 0.5)
(b) MinDiff (A (A= 1.0)
(c) MinDiff (A = 1.5)
Figure 13: Training loss vs model widths for different batch sizes
20
20
20
Test Error (%)
15
Test Error (%)
15
Test Error (%)
15
10
10
10
5
Over-
5
Over-
5
Over- parameterized
parameterized
parameterized
0
0
0
1
2
1
1
Model Width (log scale)
Model Width (log scale)
Model Width (log scale)
(a) MinDiff (A = 0.5)
(b) MinDiff (A = 1.0)
(c) MinDiff (2 1.5)
A=
+ wd 0.001
+ es(Cp)
+ wd 0.1
A + fl = 0.1
Figure 14: Regularization THR with fairness constraint 10%
Table 6: We tabulate the fairness constrained test error (with a AFNR I 10% constraint) for different
regularization schemes used in conjunction with MinDiff optimization (A 1.0) on CelebA dataset. The performance of best regularizer highlighted in bold for each model width. Notation: wd is weight decay, es(Cp) is early stopping w.r.t primary loss and fl is flooding
Method
Width = 5
Width 19
Width 64
Under-
Over-
Over-
==
5.92 + 0.27
6.51 + 0.16
5.76 + 0.14
X = 1.0
6.25 + 0.61
6.43 = 0.17
6.06 + 0.09
A = 1.0 + wd = 0.001
5.94 +: 0.39
6.75 = 0.35
5.90 - 0.24
À = 1.0 + wd = 0.1
5.80 = 0.17 0.17
5.55 0.19
6.42
X 1.0 cs(Cr)
6.32 + 0.40
5.82 = 0.46
4.79 0.24
A 1.0
0.05
0.68
6.43 0.17
5.87 0.11
A 1.0 + fl 0.1
6.33 + 0.52
5.4 + 0.35
4.77 + 0.13
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Published in Transactions on Machine Learning Research (05/2023)
20
20
20
Test Error (%)
15
Test Error (%)
15
15
Test Error
10
10
10
5
Over- parameterized
5
Over- parameterized
Over parameterized
0
0
0
1
2
1
4
1
4
Model Width (log scale)
Model Width (log scale)
Model Width (log scale)
(a) MinDiff 0.5)
(b) MinDiff 1.0)
(c) MinDiff (A 1.5)
A=0
+ 0.001
+ es(Cp)
+ wd 0.1
fl 0.1
Figure 15: Regularization THR with fairness constraint < 5%
20
20
20
Test Error (9)
Test Error (%)
Test Error (%)
15
15
15
10
10
5
Over-
5
Over-
5
Over-
parameterized
parameterized
parameterized
0
0
0
1
2
1
2
1
2
Model Width (log scale)
Model Width (log scale)
Model Width (log scale)
(a) MinDiff (A = 0.5)
(b) MinDiff (A (A= 1.0)
(c) MinDiff (A = 1.5)
A=
+ wd 0.001
es(Cp) A + fl = 0.1
+ wd = 0.1
Figure 16: Regularization
THR with fairness constraint 1%
Table 7: CelobA (MinDiff: 0.5, FNR Gap < 5%, Batch Size: 128)
Method
Width
Width = 19
Width 64
Under-
Over-
Over-
Original Model MinDiff MinDiff + wd 0.001
6.22 + 0.31
6.81 t 0.21
6.10 + 0.14
6.72 = 0.70
6.78
+ 0.16
6.18 t 0.25
6.20 + 0.35
7.29 0.21
6.51 0.55
MinDiff + wd 0.1
5.84 + 0.13
5.51 1 0.15
6.70 0.14
MinDiff + es
6.48 + 0.48
6.14 0.38
5.61 + 0.30
MinDiff + fl = 0.05
6.73 - 0.70
6.80 + 0.21
6.47 + 0.11
MinDiff + 0.1
6.65 + 0.67
5.99 + 0.37
5.03 t 0.29
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Published in Transactions on Machine Learning Research (05/2023)
Table 8: CelebA (MinDiff: 1.0, FNR Gap 2 5%. Batch Size: 128)
Method
Width
Width 19
Width 64
Under-
Over-
Over-
Original Model MinDiff MinDiff + wd 0.001
6.22 + 0.31
6.81
+ 0.21
6.10 + 0,14
6.57 = 0.56
6.74
+ 0.20
6.35 t 0.07
6.26 + 0.45
7.11 0.34
6.21 0.23
MinDiff + wd 0.1
6.15 = 0.18
5.82 - 0.14
6.70 0.14
MinDiff + es
6.60 + 0.40
6.15
+ 0.50
5.05 + 0.18
MinDiff + fl 0.05
6.57 = 0.70
6.74
0.14
- 0.14
6.15 + 0.15
MinDiff + 0.1
6.58 + 0.43
5.67 0.38
4.92 0.06
Table 9: CelebA (MinDiff: 1.5, FNR Gap S 5%, Batch Size: 128)
Method
Width =
Width 19
Width 64
Under-
Over-
Over-
Original Model MinDiff
6.22 + 0.31
6.81 + 0.21
6.10 t 0.14
6.65 + 0.46
6.90 + 0.30
6.40
0.26
MinDiff + wd = 0.001
6.15 + 0.41
6.85 + 0.30
5.33
+ 0.21
MinDifT + wd 0.1
6.45 + 0.18
6.11:..15 0.13
6.81 + 0.10
MinDiff
6.73 = 0.43
5.89 + 0.45
4.88
+ 0.05
MinDiff + 0.05
6.58 = 0.39
6.64 0.40
5.77 0.18
MinDiff + 0.1
6.68 + 0.44
5.56 + 0.41
4.86 0.14
Table 10: CelebA (MinDiff: 0.5, FNR Gap < 1%, Batch Size: 128)
Method
Width
Width
Width
Over-
Over-
Original Model Min
6.57 0.32
7.13 + 0.22
6.31
0.12
6.96 0.72
7.07 - 0.14
6.50
MinDiff +
0.001
6.52 0.35
7.57 0.24
6.86
0.55
MinDiff wd 0.1
6.12 0.13
5.82 2 0.18
6.94 144400 0.20
MinDiff +
6.71 = .048
6.41 + 0.42
0.42
5.85 + 0.29
MinDiff + fl = 0.05
7.04 = 0.70
7.09 + 0.24 0.24
6.78 + 0.10
MinDiff fl 0.1
6.94 0.67
6.20
- 0.42
5.17 0.28
Table 11: CelebA (MinDiff: 1.0, FNR Gap & 1%, Batch Size: 128)
Method
Width = 5
Width = 19
Width 64
Under-
Over-
Over-
Original Model MinDiff MinDiff + wd 0.001
6.57 0.32
7.13 + 0.22
6.31
6.76 0.54
7.00
- 0.18
6.55 + 0.14
6.54 = 0.46
7.43 + 0.41
6.46
+ 0.20
MinDiff + wd 0.1
6.43 = 0.22
6.11 11100.10 0.12
6.97
+ 0.17
MinDiff + es
6.86 0.42
6.40
+ 0.53
5.24 0.21
MinDiff +
= 7.04
MinDiff fl 0.1
6.90 0.41
5.94 - 0.33
5.09
0.08
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Published in Transactions on Machine Learning Research (05/2023)
Table 12: CelebA (MinDiff: 1.5, FNR Gap < 1%, Batch Size: 128)
Method
Width
Width
Width
Over-
Over-
Original Model Min
6.57 0.32
7.13 + 0.22
6.31
0.12
0.49
7.24 - 0.31
6.64
0.26
MinDiff + 0.001
6.42 0.45
7.13
0.30
5.68
0.25
MinDiff + wd 0.1
6.75 0.22
0.177
7.05 + 0.14
MinDiff +
6.97 0.38
6.12 + 0.49
5.07 + 0.06
MinDiff + fl = 0.05
6.85 = 0.39
6.92 0.42
0.42
5.93 + 0.24
MinDiff fl 0.1
6.89 0.45
5.84 0.442
5.04
25


Reviews:
[{"review_id": "5Go3t7A4A7", "reviewer": "Reviewer_VRnw", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Advantages:\n1. This paper addresses an important issue regarding fairness, exploring how the performance of mitigation algorithms changes in relation to the number of parameters in DNN models. Specifically, it investigates whether fairness algorithms are effective for over-parameterized models.\n2. The study presents interesting experimental findings, including the discovery that under-parameterized MinDiff models can have lower error rates compared to their over-parameterized counterparts.\n\n\n\nMy concerns:\n1. When considering fairness, it is crucial to keep in mind that datasets typically involve people. Waterbirds is a dataset typically used for domain generalization/worst group robustness. There are no people in this dataset. If the research topic is for domain generalization/worst group robustness, both Waterbirds and CelebA can be used as the testing datasets. However, it is not feasible the other way around. It is strongly recommended to use other datasets to replace Waterbirds.\n2. Another significant concern is whether the study's findings can be generalized to other research studies and more practical real-world settings. The authors used a fixed pre-trained ResNet-18 model to extract a d-dimensional feature vector µ, then transformed it using a linear transformation and one RELU activation to a new feature space. The dimension of this space, along with the logistic regression classifier, determined whether the model was under-parameterized or over-parameterized. This setting is not commonly used in other research studies or real-world applications. A more practical approach would be to use a range of ResNet models, such as ResNet-18, ResNet-34, ResNet-50, ResNet-101, ResNet-110, ResNet-152, ResNet-164, and ResNet-1202. ResNet-18 could be treated as an under-parameterized model, while a shallower model like Alexnet could also be used. In contrast, deeper models like ResNet-110 and ResNet-152 would be considered over-parameterized models. It would be interesting to see whether the findings of this study hold true in this more practical real-world setting of under-parameterization and over-parameterization.\n3. It is unclear whether the findings are only applicable to \"MinDiff optimization\" or whether they can be generalized to other fairness mitigation algorithms.\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "As the deep neural networks are increasingly being used in real-world applications, the fairness issue has also received increasing attention from the community. This work studies one widely used fairness algorithm, i.e,.MinDiff, and has some interesting findings. First, under-parameterized MinDiff models can even have lower error compared to their over-parameterized counterparts within specified fairness constraints. In addition, MinDiff optimization is also sensitive to choice of batch size in the under-parameterized regime, requiring time-consuming hyper-parameter searches. It is suggested to use regularization techniques such as L2, early stopping, and flooding in conjunction with MinDiff to train fair over-parameterized models. Over-parameterized models trained using MinDiff+regularization with standard batch sizes are fairer than their under-parameterized counterparts, suggesting that regularizers should be integrated into fair deep learning flows. \n", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please refer to the Strengths And Weaknesses section.", "broader_impact_concerns": "No ethical concerns found.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "tRpolTRr2u", "reviewer": "Reviewer_vZV8", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "\nStrengths:\n\n- The problem setting is interesting and of current relevance in potentially many applications.\n- The experimental results are presented with sufficient detail to be reproduced (I think) and with discussions.\n- It is believable that the paper's claims are supported by the experimental evaluations results.\n\nWeaknesses:\n\n- The paper has major (in my opinion) clarity/readability problems that may affect the ability of readers to understand it.\n- The mathematical notations are unclear in some cases and the precise mathematical meaning of some things is missing.\n- Most notably, there \"test error\" has two meanings that are conflated in this work, which can lead to confusions and may spread some misconceptions among the readership if this work is published as is.\n- Many editorial changes need to be carried out before this paper is acceptable for publication (details below).\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "\nAs far as I understand, this paper targets the problem of learning a classification model such as to meet fairness conditions. Presumably for the sake of simplicity the problems (datasets) considered in this work are binary with respect to class labels (two classes) and the special attribute values (two possible attribute values). The classification models are neural network models with many layers, hence deep learning. The paper proposes a training objective for the said kinds of problems, and empirical evaluations, with claims of improvements (or some better properties) with respect to the MinDiff method, the latter being a fairness-constrained training procedure made available by the TensorFlow Responsible AI Toolkit.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Abstract:\n\nAppears to be endorsing debatable claims such as \"ability to generalize\" (which has to be measured according to a suitable notion of generalization which the abstract has not specified) and the connections between things are not very clear. The written in the first parenthetical is strange because it is split by a period, could be avoided. Try without parenthesis: \"This will apply to any disparity-based measures which care about errors or accuracy; while it won’t apply to demographic parity.\"\n\nSec. 1 Introduction\n\nLine 1: \" in a wide range\" (insert \"a\")\n\nA bit further down: \" there is a growing\" (replace \"an\" with \"a\")\n\nNext para, first sentence: \"Methods to ensure fairness can be broadly categorized according to the stage at which they are used:\npre-training, in-training, or post-training.\"\n\nNext page, top line: Replace \"Framework\" with \"Toolkit\". It is not at all apparent that \"(AI)\" is a citation and hyperlink, try changing to \"(Google AI)\" to fix this. Then the corresponding reference item (when clicking the hyperlink) should read something like \"Google AI. TensorFlow Responsible AI Toolkit. URL https://www.tensorflow.org/responsible_ai. (Accessed DD.MM.YYY)\" -- Important to record the date because the content of web pages is subject to changes overtime.\n\nNext paragraph: \"We evaluate MinDiff on two datasets, Waterbirds and CelebA, that are commonly used in fairness literature;\nand we observe several notes of caution.\" (comma after \"CelebA\" and \"we observe\")\n\nNext sentence: The message of this paragraph is unclear, and there are incorrect descriptions such as the given description of \"over-parametrized\" while there is no description of the meaning of \"under-parameterized\" which is then being assumed to be known by the readers, or delegated for readers to figure out elsewhere. This needs to be improved. Trying to suggest how to reformulate:\n\n\"Because the success of deep learning can be attributed at least in part to the surprising ability of over-parameterized deep networks to generalize (Nakkiran et al., 2020), we begin by evaluating the relationship between model capacity and fairness with MinDiff. Recall that over-parameterized networks are those with more trainable parameters than training data, which therefore have sufficient capacity to\nmemorize the training dataset; while under-parameterized networks are those with less parameters than training data. The setting where the number of trainable parameters matches the amount of training data is usually referred to as the interpolation threshold. We observe that MinDiff does increase fairness for small, under-parameterized models, but is almost entirely ineffective on larger over-parameterized networks. Thus, in some cases, under-parameterized MinDiff models can have lower fairness-constrained error compared to their over-parameterized counterparts even though over-parameterized models are always better on baseline error (i.e., error on models trained without MinDiff optimization). We caution that when using MinDiff for fairness, ML practitioners must carefully choose model capacity, something which is generally unnecessary when fairness is not a concern and the goal is simply to minimize error.\"\n\nNext paragraph: Suggesting to succinctly discuss the meaning of \"disparity-based\" for the sake of the unfamiliar readers. Same comment for the meaning of \"demographic parity\" which needs to be made explicit for the unfamiliar readers. Or point to suitable references.\n\nNoting that the period inside a parenthetical is strange. Try to avoid. Suggesting how to reformulate:\n\n\"[..] thus turning off the MinDiff optimization. This will apply to any disparity-based measures which care about errors or accuracy, whereas It won’t apply to demographic parity which cares about [..]. Thus, we explore [..]\"\n\nNext: The parenthesis within parenthesis are an obstacle to clarity. Try to avoid. Try:\n\n\"Specifically, we consider two classes of regularization techniques: implicit such as batch sizing (Smith et al., 2021;\nBarrett & Dherin, 2021) and early stopping (Morgan & Bourlard, 1990), and explicit such as weight decay (Krogh &\nHertz, 1992) and a recently proposed “loss flooding\" method (Ishida et al., 2020). We find [..]\"\n\nSec. 2 Related Work\n\nFirst line: \"in the literature\" (insert \"the\")\n\n\"In-processing techniques (Prost et al. [..]) alter the training mechanism [..]\"\n\nBottom of the paragraph: \" similar qualitative conclusions might hold for other\" (replace \"will\" with \"might\")?\n\nBottom of the page (last line): remove space before \"Sagawa\"\n\nNext page, top paragraph, last sentence: \"deep learning models trained using\" (insert \"learning\")\n\nSec. 3 Methodology\n\nSubsec.3.1: augment the title \"Setup\" to \"Formal Setup\" ?\n\nFirst para, third line: Delete the coma after $P_{X,A,Y}$\n\nEq. (1): Could use \"\\log\" in math mode LaTeX to produce a nice looking \"log\" function. Also, on the left-hand side, the notation $\\mathcal{L}_P$ is confusing because the expression on the right hand side is the empirical loss which is a function of the data but not the data-generating distribution. The notation $\\mathcal{L}_D$ would then be preferable (and replace throughout the paper).\n\nNext line: \"via stochastic gradient descent (SGD).\"\n\nLine after Eq. (2): \"seek to achieve low error\" (delete \"test\"). Note that \"test error\" could be interpreted as \"error on the test set\" while the expression following this phrase defines the error of $\\hat{f}_\\theta$ at population level.\n\nAfter Eq. (3): Insert some comment about why/when it make sense to minimise $\\mathrm{FNR}_\\mathrm{gap}$ to achieve fairness.\n\nSubsec.3.2, first para, fourth line: \"Equation (1)\" (eq. number enclosed in parentheses, same as in the displayed eq's)\n\n\"and $\\mathcal{L}_M$ is  a differentiable proxy for the $\\mathrm{FNR}_\\mathrm{gap}$\"\n\nNext line: \"importance of the fairness versus the empirical cross-entropy loss\" (not \"test error\")\n\nEq. (4): Provide the mathematical definition of the right-hand side. Perhaps discuss its meaning and why it is used as the proxy in this setting.\n\nSubsec.3.3, first para, third line: \"as proposed by Hardt et al. (2016)\" (use \\citet{} instead of \\citep{} in this case)\n\nTwo lines further down: \"constraint is met and the error is minimized:\" (remove \"test\" replace with \"the\" and delete period)\n\nEq (5): Remove the comma at the end of the eq.\n\nNext paragraph mentions \"test error\" a few times. Perhaps this suggests that earlier in the paper you should clearly define what you mean by \"test error\" (mathematical definition) and discuss differences with \"error on the test set\"\n\nSubsec.3.4, no comments here.\n\nSec. 4 Experimental Setup\n\nSubsec.4.1, first para, first line: \"Waterbirds is a synthetically created dataset\" (insert \"a\")\n\nNext para: Specify details about the random matrix $U$, e.g. independent Gaussian entries? What parameters for the Gaussian distribution? Assuming that all entries are Gaussian with the same parameters, but this needs to be specified as well.\n\nSubsec.4.2, first para: remove the space between \"women\" and the footnote number.\n\nSec. 5 Experimental Results\n\nSubsec.5.1: This section and related Figure 1 discuss the \"test error\" but in this case \"test error\" really actually means the empirical error rate evaluated on a test set (i.e. what I called \"error on the test set\" before) and once again the distinction needs to be made clear between the error notion at population level (which is distribution-dependent) and the empirical counterpart evaluated on a finite amount of data points (which is data-dependent). \n\nSubsec.5.2 and 5.3: Similar comment.\n\nNote that the figures necessarily show the test set error rates, while the target quantity of interest I think must be the distribution-dependent error at population level, what has been presented before as $\\mathbb{P}[\\hat{f}_\\theta(X;\\tau) \\neq Y]$ and the attribute conditioned probabilities $\\mathbb{P}[\\hat{f}_\\theta(X;\\tau) = 0 \\vert Y=1, A=0]$ and $\\mathbb{P}[\\hat{f}_\\theta(X;\\tau) = 0 \\vert Y=1, A=1]$. These things need to be discussed to improve the clarity.\n\n\nReferences:\n\nHardt et al. (2016) \"Equality of opportunity in supervised learning\" appears duplicate. Need to remove the duplicate.\n\nThe bibliographic information for Prost et al. (2019) is incomplete (how published?). Needs to be updated.\n\nSame for Grother ert al. (2010), Madras et al. (2018), Martinez et al. (2020), Ngan and Grother (2015), Ryu et al. (2018), Savani et al. (2020), Wadsworth et al. (2018), Wang and Deng (2019), Wang et al. (2020), Zhang et al. (2018); there are others like these.\n\nCheck all the reference items to make sure complete details are provided. Make venue names consistent. \n\nSome titles need capital-protecting (e.g. \"Pareto\")\n", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "0MPKPYYIaz", "reviewer": "Reviewer_ziUC", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "*Strengths*: \n- The paper is well-written and easy to read. The authors present an important message about the pitfalls of using in-processing techniques for mitigating error disparities in overparameterized models.\n- The authors consider several regularization techniques in their analysis and show (in the appendix) that their conclusions are insensitive to the choice of the post-hoc threshold level (which is always 10% in the main paper, but is varied in Appendix A).\n\n*Weaknesses*:\n- The main message is somehow known to practitioners already and does not only hold for in-processing methods but also in other techniques such as reweighting [1]. Since overparamterized models will drive the training error to zero, such techniques can be ineffective. As the authors cite in the paper, this has also been demonstrated in published works, such as [2] who also looked into regularization techniques including weight decay and early stopping.\n- The authors only demonstrate their claims using equality of opportunity. While I think the conclusions should also hold for other error-based metrics, such as equalized odds, it would be good to demonstrate them as well.\n- Throughout the experiments, the authors vary $\\lambda$ only in the set $\\{0, 0.5, 1, 1.5\\}$. I think the authors should use an exponential spacing. It's likely that MinDiff would perform better if a very large value of $\\lambda$ is used (because the loss now focuses on the proxy for error parity rather than on the cross entropy so the model wouldn't interpolate the training data). \n\n[1] Byrd, Jonathon, and Zachary Lipton. \"What is the effect of importance weighting in deep learning?\" ICML, 2019.\n\n[2] Sagawa, et al. \"Distributionally robust neural networks.\" ICLR, 2020\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors study the effectiveness of MinDiff for mitigating error disparity across subgroups in overparameterized models. Using experiments on CelebA and Waterbitrds in ResNet18 with varying widths, they argue that MinDiff alone is ineffective when the model is overparameterized but its effectiveness can be enhanced with regularization techniques, such as weight decay and flooding. The authors focus on equality of opportunity as a metric but the conclusions should also hold for any metrics based on error disparities, such as equalized odds, but not (for example) demographic parity.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- Typo in Page 4: \"once the validation loss has increased\"  --> \"once the validation loss has not increased\".\n- The authors should include experiments with $\\lambda\\in{4, 8, 16\\}$. If this is a challenge timewise, please report results with $\\lambda=16$.\n- Can you please clarify why the setups used in the two datasets are different? It seems that the authors only have access to GPUs for CelebA but not for Waterbirds. Is this the reason?\n- In Figure 3, can you also add within the same figure the loss and FNR gap for test data? This might help understand the effect of early stopping.\n- What does $\\lambda$ in the legend of Figure 6 mean? I think this is a typo.\n- The line space in Page 10 is different from the rest of the paper.\n- In Page 2, it is mentioned that Pham et al. (2021) observed that overparameterized models improve the worst case loss. This has also been recently demonstrated in ViT-22B [3]. It is also observed in [3] and [4] that overparamterization offers a more favorable tradeoff between bias and accuracy. Perhaps the paper would benefit from including this discussion in the related works since it touches upon the relationship between overparameterization and bias.\n\n[3] Dehghani, Mostafa, et al. \"Scaling Vision Transformers to 22 Billion Parameters.\" arXiv preprint arXiv:2302.05442 (2023).\n\n[4] Alabdulmohsin, Ibrahim M., and Mario Lucic. \"A near-optimal algorithm for debiasing trained machine learning models.\" NeurIPS, 2021.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The reviewers appreciate the paper's interesting findings and agree that reinforcing this understanding within the research community is important. The paper addresses various concerns effectively, and the reviewers believe it will be a valuable addition to TMLR. However, a major concern is the limited generalizability of the paper's finding, as the study only focuses on one particular in-processing algorithm. The authors are advised to either evaluate additional algorithms or reposition the title and paper structure to emphasize that this is a case study with MinDiff. This revision would better align the paper's claims and generalizability.
Decision: Accept (poster)