D ATA F EEDBACK L OOPS : M ODEL - DRIVEN A MPLIFICATION OF D ATASET B IASES
Anonymous authors
Paper under double-blind review
A BSTRACT
Datasets scraped from the internet have been critical to large-scale machine learning.
Yet, its success puts the utility of future internet-derived datasets at potential risk, as model outputs begin to replace human annotations as a source of supervision.
In this work, we formalize a system where interactions with one model are recorded as history and scraped as training data in the future.
We then analyze its stability over time by tracking changes to a test-time bias statistic (e.g. gender bias of model predictions).
We find that the degree of bias amplification is closely linked to whether the model’s outputs behave like samples from the training distribution, a behavior which we characterize and define as consistent calibration.
Experiments in three conditional prediction scenarios – image classification, visual role-labeling, and language generation – demonstrate that models that exhibit a sampling-like behavior are more calibrated and thus more stable.
Based on this insight, we propose an intervention to help calibrate and stabilize unstable feedback systems.
I NTRODUCTION
Due to the successes of large-scale training in machine learning (He et al., 2016; Brown et al., 2020; Radford et al., 2021), datasets derived from publicly available internet data have become indispensable to the machine learning community.
For example, without relying on internet scraping, it would be cost-prohibitive to manually construct key datasets such as ImageNet (Deng et al., 2009),
The Pile (Gao et al., 2020), or YFCC100M (Thomee et al., 2016).
While the internet has served as a large, easily-accessible source of human generated data in the past, the growing deployment of machine learning systems puts this procedure at risk.
As models begin to create and annotate a significant fraction of internet content, the utility of the internet as a data source may decrease rapidly.
As an example in visual role-labeling, consider a classifier trained on public photos and their associated tags, as depicted in Figure 1.
Instead of manually tagging photos, some users may instead choose to auto-tag their photos with the model.
These photos, now stored in internet history, may be scraped as training data for an updated iteration of the image-tagging model.
Any systematic biases introduced by the model, such as consistently mislabeling female doctors as nurses as in Figure 1, are now encoded into the training data.
This data feedback gradually degrades the quality of the internet as a data source, since supervision becomes driven by model outputs rather than human annotation.
Issues stemming from having previously model-generated content included in training data have already been encountered in machine translation (Venugopal et al., 2011) and speech recognition
(Radford et al., 2022).
These concerns are especially important in situations where model predictions may exacerbate existing toxicity, harm, or other biases (Gehman et al., 2020; Zhao et al., 2017).
In such cases, a viable strategy for model developers is to weigh the benefit of updating their model to new internet content versus the cost of amplifying biases via such model-induced feedback.
However, it is not yet understood when and to what degree data feedback is an issue in practice.
In this work, we define the data feedback setting and carefully study how model biases change under feedback.
In particular, we ask: Are there conditions that stabilize bias amplification?
We answer this in the affirmative, finding that one crucial path to achieving stability guarantees is having a consistently calibrated training procedure – one that produces models with a bias similar to its training distribution.
Furthermore, this form of calibration can be realistically achieved in natural experimental settings.
Specifically, models that behave like samplers (i.e. replicate their training distribution well) are more likely to be calibrated and thus more stable.
In addition, many prediction algorithms that do not explicitly perform sampling, such as image classifiers, fulfill this behavior through a conjectured phenomenon called Distributional Generalization (Nakkiran & Bansal, 2020).
[Figure]
Formally, we quantify the stability of data feedback with a bias metric ϕ
( x, ˆ y ) , where ˆ y = f t ( x ) are predictions from the model at time t .
For example, the predictions ˆ y are image tags or sentence completions, and the bias metrics ϕ are gender bias or sentence toxicity.
Our theoretical result shows that if the model does not increase bias by more than error δ , then the total bias amplification is bounded by m + km δ , where m and k refer to the number of new human-annotated samples and model-annotated samples respectively.
Thus both a smaller calibration error δ and a higher fraction of human-annotated samples m contribute to the global stability of data feedback loops.
The rest of the paper is organized as follows.
In Section 3, we define the data feedback setting in more detail.
We then describe a specific notion of calibration (consistent calibration), discuss its connection to sampling, and show how it gives rise to bounds on bias amplification in Section 4.
Sectiondemonstrates the utility of these predictions empirically in three different natural experiment settings:
First, we define a simple data feedback setting in CIFAR (Krizhevsky, 2009), where the label distribution is skewed and feedback has the potential to amplify label shift.
In this case, we show the feedback dynamics are stable and consistent with our theoretical predictions.
Next, we show that data feedback can significantly amplify gender biases in a visual semantic role labeling task (Yatskar et al., 2016).
Our bounds predict that the dynamics may be unstable since the initial calibration error is large, which is consistent with gender bias amplification identified in earlier work (Zhao et al., 2017).
Third, we examine data feedback for language generation on a toxic prompts dataset (Gehman et al., 2020) and demonstrate that toxicity and repetition amplify, with samplingbased generation schemes enjoying substantially higher stability than beam search methods.
Finally, to conclude Section 5, we design an intervention to stabilize beam search methods by leveraging the sampling-like behavior of interpolating classifiers (Nakkiran & Bansal, 2020).
To do this, we train a language model that overfits to its training set and observe that this procedure significantly stabilizes the model’s toxicity and repetition.
R ELATED W ORK
Performative prediction.
The general problem of model-induced feedback in machine learning has been previously studied as performative prediction and strategic classification (Perdomo et al., 2020;
Hardt et al., 2016), where future data distributions can change arbitrarily in response to the deployed model.
In this context, existing work has focused on methods that optimize towards equilibria of the system (Brown et al., 2022).
The generality of the problem setting allows for complex human interactions in-the-loop; however, it is for this reason that experimental evaluation has been limited, and most analyses have focused on convex settings with experiments on Gaussian data or simple synthetic data such as loan applications or credit risk (Izzo et al., 2021; Miller et al., 2021).
In contrast, motivated by the image tagging example in Section 1, we consider a more restricted form of feedback, in which new data examples are gathered only from either the “true” human-annotated distribution or predictions of the currently deployed model.
This restriction allows us to analyze feedback stability in more realistic experimental settings and derive bounds on stability.
Bias amplification.
Machine learning models have a tendency to amplify at test-time biases that exist in their training data, a problem known as bias amplification (Dinan et al., 2019; Leino et al.,
; Hall et al., 2022).
For example, image classifiers have skewed gender predictions, beyond what exists in the training data (Zhao et al., 2017; Wang et al., 2019).
In our work, we build on this literature by studying the multi-step amplification of bias via feedback.
Feedback in healthcare.
The data feedback setting is most related to feedback loops previously studied in healthcare (Adam et al., 2022; 2020), where false positive examples are added to the training set over time.
These works have proposed methods to mitigate feedback errors in tabular, binary classification.
In contrast, our work focuses on thoroughly understanding the preliminaries – quantifying when and to what degree feedback is an issue – in more general experimental settings.
Additional discussion relating to recommender systems, semi-supervised learning, domain adaptation, and more can be found in Appendix A.
D EFINING D ATA F EEDBACK AND M ODEL B IAS
Our work considers feedback effects in the conditional prediction setting.
In the standard conditional prediction or supervised learning framework, the goal is to learn a function f ∈ F , f : X → Y from a collection of samples { ( x i , y i ) } iid ∼ P 0 ( x, y ) .
P {+
 ( x, y )+} represents a fixed human-annotated example distribution ( e.g. human-tagged images or human-written prompts and completions).
Motivated by Figure 1 where the dataset changes over time, we instead consider a series of learning problems from time t = 0 . . .
∞ .
At each time, we learn a new model f t using the latest available internet data.
The series of supervised learning problems are defined by the following.
At t = 0 , before any data feedback, only human-annotated samples are available on the internet.
Thus, the initial model f 0 is trained on n 0 i.i.d.
samples from P 0 ( x, y ) , and we call this initial dataset S {+
 = { ( x i , y i ) } n+} 0 i =1 , with ( x i , y i ) iid ∼ P 0 ( x, y ) .
The corresponding model is defined as f 0 ∼ A ( S 0 ) , where A : ( X × Y ) ∗ → F refers to a potentially stochastic learning algorithm, which we take to be a neural network trained on the cross entropy loss with SGD.
For any t ≥ 1 , we assume that data on the internet grows in two ways.
Humans naturally continue to interact with the internet and generate data, creating m new samples following the original distribution
P 0 ( x, y ) .
Another k samples are generated by humans interacting with the newest model f t − 1 (e.g. users auto-tag new images).
The dataset, derived from accumulated online content, thus evolves as
S t =
S t − 1 ∪ { ( x i , y i ) } mi =1 ∪ { ( x j , f t − 1 ( x j ) } kj =1 , with ( x i , y i ) iid ∼ P 0 ( x, y ) and x j iid ∼ P 0 ( x ) , where P 0 ( x ) denotes the marginal over the covariates.
The model is then updated by re-training on the growing dataset, f t ∼ A ( S t ) .
Formally, the data feedback model we instantiate in our experiments is defined in Algorithm 1.
Our overall goal is to analyze the behavior of f t over time.
Concretely, we are concerned with bias amplification , tracked via a particular bias statistic ϕ : X × Y → R .
We will measure the expected difference between the bias of the initial, human-annotated distribution P 0 ( x, y ) and the bias of the model f t .
Thus, in both our theoretical and empirical analyses, we will measure amplification as
[Equation]
over time t .
The expectation in this bias term, E f t [ · ] , is an expectation over all random objects up to time t , which includes random draws in each dataset S t and random draws of the model f t . [Figure]
One important aspect of this setting is that all covariates are sampled from the same distribution P 0 ( x ) , which remains fixed over time.
This assumption is natural in situations similar to Figure 1, where predictions of the image-tagging model may not influence the types of photos taken.
Though we make this choice to simplify our analysis, this setting still poses challenging tradeoffs; in Section 5.1, we show that retraining classifiers with future data improves accuracy at the cost of increasing bias.
S TABILIZING B IAS A MPLIFICATION 4. I LLUSTRATIVE E XAMPLE
We begin with an example to emphasize how data feedback may become unstable.
Consider a set of images of female healthcare workers with high inherent uncertainty – they could each be either a doctor or a nurse, depending on context cues that are not present in the image (Figure 2 left).
In this case, data feedback on a dataset with twice as many nurses as doctors can rapidly destabilize.
More concretely, any Bayes optimal classifier would predict new examples only as nurse, as nurses are the majority class and the image is indistinguishable otherwise.
This would exacerbate the nurse bias in the dataset (Figure 2 top).
A natural solution would be to predict nurses and doctors at a rate equal to the original distribution.
Specifically, a sampling-based model that reproduces the training distribution would continue to label a random 23 of the examples as nurses.
Though such a model may have less utility, it would maintain the level of nurse bias in the dataset (Figure 2 bottom).
A training algorithm that produces models whose outputs match the bias of the training distribution is said to be consistently calibrated, and we will now formally define and connect calibration to stability.
4. A CHIEVING S TABILITY T HROUGH C ALIBRATION
Setup.
We first define a few objects useful for analysis.
We call the number of training samples at time t as n t := n t − 1 + m + k = n 0 + t ( m + k ) .
A mixture of past training data, new human-annotated data, and new model-annotated data, the training data distribution at time t is
[Equation]
where (cid:98) P f t − 1( x, y ) denotes the model-annotated distribution, which is the relabeling of examples in distribution P 0 ( x, y ) by model f t − 1 .
Samples are drawn from (cid:98) P f t − 1( x, y ) by sampling a covariate x ∼ P 0 ( x ) and returning the annotated pair ( x, f t − 1 ( x )) .
Additionally, for ease of analysis in this section only, we study the case where the dataset S t is drawn fresh from its distribution P t ( x, y ) at every time, i.e. S t = { ( x i , y i ) } n t i =1 where ( x i , y i )
iid ∼ P t ( x, y ) (further explained in Appendix B.1).
Consistent Calibration.
In the previous nurses versus doctors example, we discovered that a model that faithfully represented the training data distribution was more stable under data feedback.
Now, we formalize what it means to faithfully represent the data distribution: We say a learning algorithm is consistently calibrated if the bias of the model is similar to the bias of the training distribution.
Definition 1 (Consistent Calibration) .
A learning algorithm A : ( X × Y ) n → F is ( δ , ϕ , P ( x ) , n )-consistently calibrated if, for any joint distribution Q ( x, y ) with marginal P ( x [Equation] [Equation] δ
[Equation]
If a learning algorithm is consistently calibrated, it means that in expectation, the bias of the trained model will be close to the dataset bias (this definition is distinct from calibration error commonly studied in neural networks – more in Appendix A).
As this condition holds for all joint distributions sharing a marginal, and as the covariate marginal does not change does not change during data feedback ( P t ( x )
= P 0 ( x ) for all t ), if learning algorithm A is consistently calibrated for the initial distribution P 0 ( x ) , A will also be consistently calibrated for all P t ( x ) (formalized in Lemma B.1).
This property naturally arises in some settings, as discussed in the next subsection.
Intuitively, it helps to control bias amplification: at time t , a consistently calibrated algorithm A will have bias no more than δ greater than its training distribution P t ( x, y ) .
In turn, the bias of P t ( x, y ) is reduced when adding human-annotated samples and increased when adding model-annotated samples.
Stability.
Our main feedback stability result is a direct consequence of consistent calibration.
Theorem 1 (Feedback Stability) .
Let A : ( X × Y ) n → F be a ( δ n , ϕ , P 0 ( x ) , n )-consistently calibrated learning algorithm, where calibration error δ n is a monotone non-increasing function of dataset size n .
Then, under the data feedback procedure, for all time t ,
[Equation]

[Equation]
[Equation] t [Equation] i =
k n i t (cid:89)
j = i + n j − m n j  
δ n 0 ≤ m + k m δ n 0 .
The proof is provided in Appendix B.
The bound shows that, in expectation over rollouts of Algorithm 1, data-driven feedback can be stable even in the limit of t → ∞ .
From inspecting the simplified upper bound, it is clear that both a larger number of human-annotated examples m and a smaller initial consistent calibration error δ n 0 stabilize the system and minimize bias amplification.
This leads to a natural question: in which situations can we expect small consistent calibration error?
Intuitively, models that behave like samplers will have low calibration error.
In particular, suppose that model f t has accurately learned the conditional distribution of P t ( x, y ) , i.e. d TV ( P t ( y | x ) , f t ( y | x ))
≤ δ .
Now, we perform a comparison of two prediction strategies commonly used in machine learning: sampling y ∼ f t ( y | x ) and argmax prediction y
=
argmax y f t ( y | x ) .
If labels are sampled, y ∼ f t ( y | x ) , then d TV ( P t ( x, y ) , (cid:98) P f t t ( x, y ))
≤ δ by definition, and so f t is δ -calibrated for any metric ϕ by post-processing.
However, if the top prediction y = argmax y f t ( y | x ) is used, f t is not guaranteed to be δ -calibrated for bias metric ϕ , similar to Figure 2.
While it is unsurprising that sampling maintains calibration and argmax predictions can be miscalibrated, prior work has discovered that certain models which do not explicitly sample can still behave like samplers (Nakkiran & Bansal, 2020), which provides feedback stability.
4. A CHIEVING C ALIBRATION T HROUGH D ISTRIBUTIONAL G ENERALIZATION
As in the example in Figure 2, when there is large uncertainty over the true labels (doctors versus nurses), one strategy for reducing bias is to sample according to the training distribution.
Distributional
Generalization (DG) (Nakkiran & Bansal, 2020) demonstrates that interpolating classifiers, which are argmax predictors, behave similarly; when the model has high uncertainty over the true labels, it produces outputs that mimic the training distribution.
Concretely, let L : X → [ m ] be a partioning of the input space into m ∈ Z + parts, where similar points with high uncertainty are grouped together.
This partitioning “coarsens” the input space by mapping hard-to-learn regions to single points.
DG finds that at this level of coarseness, samples labeled by interpolating classifiers look like samples from the training distribution, i.e.
( L ( x ) , f ( x ))
≈ ( L ( x ) , y ) (Nakkiran & Bansal, 2020).
That is, within a specific partition , the random process of drawing a sample x and labeling it with a deterministic classifier y =
f ( x ) produces a distribution similar to drawing x and then sampling a label from the true conditional y ∼ p ( y | x ) .
If the bias metric ϕ was applied over this coarsened space, we may expect feedback stability as a natural consequence of model outputs behaving like samples.
We now informally sketch the link between DG and consistent calibration (a more rigorous treatment is included in Appendices B. to B.5), providing the end result in Lemma 4.1.
The appropriate partitioning needed for DG is called feature distinguishability.
L is a ( δ , A , P ( x ) , n )-distinguishable feature if learning algorithm A can accurately predict the partioning induced by L over the input space P ( x ) (Definition 2 in Appendix B.3).
This means the learner A can classify the group identity of each point with error at most δ .
The core claim of DG (Conjecture 1 in
Appendix B.4) is that, over the coarsened space defined by L ,
the learner
A will be δ -calibrated for any metric ϕ .
Thus, it is straightforward to use this property to show consistent calibration.
Lemma 4.1.
Suppose that bias metric ϕ is a function of a ( δ , A , P ( x ) , n )-distinguishable feature
L , i.e. ϕ ( x, y ) =
T ( L ( x ) , y ) for some bounded T : [ m ] × Y → R .
Then, under DG (Conjecture 1), learning algorithm
A is ( δ , ϕ , P ( x ) , n )-consistently calibrated.
The proof is provided in Appendix B.5.
This result, together with Theorem 1, shows that under DG, global stability can be achieved (excess bias bounded by m + km δ n 0 for all time) if the bias metric ϕ is a function of a δ n 0 -distinguishable feature on the initial dataset.
4. I NSTANTIATING F EEDBACK U PPER B OUNDS IN E XPERIMENTS
We have seen two strategies for consistent calibration: 1) explicitly, through estimating the conditional distribution well and sampling outputs, and 2) implicitly through DG, where interpolating classifiers provide guarantees as long as the bias metric is a sufficiently coarse statistic of the data samples.
In these settings, one more condition is needed for Theorem 1 to apply – that calibration errors δ n are non-increasing with dataset size n .
Although not guaranteed, many learning algorithms and natural data distributions satisfy this property experimentally, especially if regularization is tuned (Nakkiran et al., 2020), as in done in practice.
We therefore believe it is reasonable to assume calibration error to be a monotone non-increasing function of dataset size in most experimental situations.
In the next section, we will explore how our derived predictions can help estimate bias amplification in realistic data feedback settings.
In order to instantiate the bound in Theorem 1, we need to know the initial consistent calibration error δ n 0 .
As a practical approximation, we estimate δ n 0 empirically via the consistent calibration error of the initial model f 0 .
Although this empirical estimate is a lower bound on the consistent calibration error, we find that it is a useful guide, and we observe that the corresponding predictions from Theorem 1 still bound the empirical amplification.
T RACKING B IAS A MPLIFICATION IN F EEDBACK E XPERIMENTS
We consider three natural real-world settings that give rise to data feedback: image classification, visual role-labeling, and conditional language generation.
The image classification and visual rolelabeling settings are inspired by the example in Figure 1, where existing biases in image annotations may amplify.
The language modeling setting is inspired by the rise of online conversational agents (Dinan et al., 2021) and assisted story writing systems (Donahue et al., 2020), for which there are real concerns about model-generated toxicity or bias (Sheng et al., 2019).
In each of these cases, we will study the behavior of data feedback in three steps: instantiate
Algorithm 1, measure the empirical bias amplification, and then compare with the predictions of
Theorem 1.
Our experiments identify that feedback stability arises when models behave like samplers and calibration error is small.
For each setting, we describe the main experimental setup followed by the results.
Extra setup details are in Appendix E, and corresponding ablations are in Appendix F.
5. I MAGE C LASSIFICATION
Setting up the label bias experiment.
Studying data feedback over many rounds requires very large datasets, and we use the CIFAR-5m dataset (Nakkiran et al., 2021), which contains 5 million synthetically generated examples.
We re-balance the dataset to contain 50% dogs, resulting in a 9 : 1 imbalance ratio compared to any other class.
For our bias metric ϕ , we track the fraction of the model’s predictions that are dogs.
Ideally, we would like this fraction to remain near 50% , the true data distribution level.
For the model, we train a BaiduNet9 (Li et al., 2019) on the growing dataset from scratch at each timestep, and hyperparameters are re-tuned every time.
We run data feedback (Algorithm 1) with an initial dataset size n 0 = 50 k and new samples per round m + k = 5 k.
We report results both when 80% and 50% of new samples are model-labeled each round ( m + k m = 5 and 2 respectively).
Number of feedback rounds
D og p r e d .
f
r a c t
i o n ( % ) δ n
Model-labeled data fraction: 80%
Number of feedback rounds   δ n
Model-labeled data fraction: 50%
Analyzing label bias amplification.
We show the results of running data feedback on the CIFAR-5m dataset in Figure 3 (blue trend).
As predicted by Theorem 1, the fraction of model predictions which are dogs grows faster in the setting with a greater fraction of model-labeled samples.
Specifically, the bias amplifies +0 .
8% when m + km = 5 (left) and +0 .
3% when m + km
=
(right).
We observe that the theoretical bounds, though conservative, are consistent with the empirical results.
This matches our expectations, since prior work suggests that Distributional Generalization holds for CIFAR classifiers and that the dog class is a distinguishable feature (Nakkiran & Bansal, 2020), which by Lemma 4.1 implies stability.
While in both settings the dog bias amplifies, the overall classification accuracies of the models improve throughout data feedback, a result of increasing dataset size.
Specifically, as the size of the training set grows from n 0 = 50 k to n 90 = 500 k over 90 rounds of data feedback, average classification accuracy improves +2 .
and +1 .
6% for the models with 50% and 80% model-labeled samples (Figure 6 in Appendix D.1).
Trading off this increase in utility with greater label bias is a challenge for model developers who seek to update their models to new data.
Our theoretical bounds take a step towards characterizing this tradeoff by upper bounding empirical bias amplification.
Finally, we discuss the source of the looseness in our bounds and present a more rigorous test of our upper bound with a worst-case setting in Appendix C.1.
The results are displayed in the gray trend in
Figure 3; we note that our bounds qualitatively capture the empirical behavior in this setting well.
5. V ISUAL R OLE - LABELING Setting up the gender bias experiment.
We run data feedback on the imSitu dataset (Yatskar et al., 2016), where models are asked to predict both the verb category of an image (e.g. cooking, jumping, etc.)
as well as labels for the subjects and objects (e.g. female, basketball, etc.).
Zhao et al.
(2017) found that models trained on this dataset amplify gender disparities at test-time; for example, 67% of cooking category images in the dataset are labeled female, but a ResNet18 trained on the dataset will label 84% of cooking images as female.
Based on this observation, we select the verb categories with an existing female gender bias, and we measure the fraction of the model’s predictions that are labeled female over these verbs.
We train the default ResNet18 (He et al., 2016)
conditional random fields model from scratch at each timestep, and hyperparameters are re-tuned every time.
We run data feedback (Algorithm 1) with an initial dataset size n 0 = 50 k and new samples per round m + k = 5 k.
We report results both when 80% and 50% of new samples are model-labeled each round ( m + km = 5 and 2 respectively).
Analyzing gender bias amplification.
We show results of data feedback on the imSitu dataset in Figure 4.
The initial calibration error δ n 0 is much larger than in the CIFAR setting; the initial trained model predicts females 90% of the
Number of feedback
[Figure]
F e m a l e p r e d .
f
r a c t
i o n ( % ) δ n
Model-labeled data fraction: 80%
Number of feedback rounds
[Figure] [Figure]
Model-labeled data fraction:
[Figure]
time, though the dataset female fraction level is at 70% .
As a result, the bound from Theoremquickly becomes vacuous, crossing over the 100% female prediction fraction mark.
This prediction is mirrored by the empirical bias also reaching near 100% in just 16 rounds of feedback ( 97% and 95% female prediction fraction when 80% and 50% of new samples are model-labeled, respectively).
Male prediction bias is also amplified on this task.
In Figure 7 in Appendix D.2, we plot the male prediction bias over the verb categories with an existing male skew for these same models and find that it amplifies quickly, similar to Figure 4.
Interestingly, this implies that gender biases quickly amplify simultaneously and in both directions; for female-biased categories, predictions become more female, and for male-biased categories, predictions become more male.
5. C ONDITIONAL L ANGUAGE M ODELING Setting up the toxicity and repetition bias experiment.
We use the Real Toxicity Prompts dataset (Gehman et al., 2020), which is a set of 100 k sentences collected from the Open-WebText Corpus (Gokaslan & Cohen, 2019) with varying levels of toxicity.
Each sentence was split into two halves, a prompt and a continuation.
We use this to construct a language modeling task where a model is asked to complete a sentence given a prompt.
We measure two bias metrics on the model output: toxicity and repetition.
Toxicity is measured by the fraction of model outputs classified as toxic by the Detoxify classifier (Hanu & Unitary team, 2020).
We also measure a specific form of repetition bias: the average number of quotation marks in the generated text.
Repetitive text is a common degeneracy of language models (Holtzman et al., 2020;
Fan et al., 2018), and we count quote frequencies as a simple approximation after observing that repetitive outputs in this setting commonly contained many quotes (see Appendix D.3 for examples).
We finetune a pretrained GPT-2 small (Radford et al., 2019) at each round, with hyperparameters retuned every time.
To generate new sentence completions, we consider two common schemes: nucleus sampling (Holtzman et al., 2020) ( top_p = 0 . 9 ) and beam search (Graves, 2012) ( num_beams = 10 ).
We run data feedback (Algorithm 1) with n 0 = 20 k, m = 1 k, and k = 4 k ( 80% model-labeled).
Analyzing toxicity and repetition bias amplification.
Figure 5 shows the results of data feedback on the Real Toxicity Prompts dataset.
Comparing beam search (blue) to nucleus sampling (black), the toxicity of the final nucleus sampling models ( 14 . 5% ) did not change from their initial level.
However, the toxicity of the final beam search models ( 11 . 5% ) decreased by about 3% from their initial level; in this case, beam search amplified the toxicity bias downward since the initial model’s toxicity ( 14 . 5% ) was lower than the dataset toxicity level ( 23% ).
Repetition bias results paint a more dramatic difference between the two.
While the average number of quotes in generated text increases little for nucleus sampling ( 0 . 4 to 0 . 6 ), it amplifies significantly for beam search ( 2 . 5 to 5 . 7 ).
In fact, the beam search empirical amplification even exceeds Theorem 1’s
Number of feedback rounds
G e n e r a t i o n t o x i c i t y ( % ) δ n
Number of feedback rounds
N o .
o f o u t pu t qu o t e s ( # ) δ n upper bound.
We believe this is due to the lack of a calibration guarantee, since Distributional
Generalization has not been shown to hold for language models (and thus Lemma 4.1 cannot guarantee stability).
In its absence, the argmax-style generation strategy of beam search is exacerbating the existing repetition bias, in line with the sampling vs argmax stability analysis in Section 4.
Though beam search completions are more repetitive, they are also more coherent than nucleus sampling completions, presenting another real-world utility-bias tradeoff (more detail in Appendix C.2).
An intervention to stabilize toxicity and repetition bias.
We now test our understanding of bias amplification by designing an intervention to mitigate amplification for beam search models.
Leveraging the claim in Distributional Generalization that interpolating models behave like samplers, we overfit the beam search model to make it interpolate the training data.
We simply finetune the model for 5 times the number of gradient steps as before.
This dropped the round 0 training loss from 3 .
5 to 0 .
4 , and the test perplexity accordingly jumped from 32 to 599 .
Figure 5 (red) shows the results of the intervention.
Overfitting significantly improves the stability of the beam search model; the average number of quotes output by the final model is reduced from 5 .
7 to 0 .
8 , which is closer to the nucleus sampling level at 0 .
The relative amplification was also reduced, as the final overfit beam search model was only 1 . 4 × as repetitive as the initial model, down from a 2 .
3 × relative amplification before.
Sample outputs of all three models are in Appendix D.3.
In Appendix C.2, we discuss the utility of this intervention, measuring the coherence of model completions and their degree of overlap of with training data.
Regardless, our experimental results are consistent with our earlier theoretical characterizations of stability and suggest that approaches for improving calibration may be broadly useful for mitigating bias amplification.
C ONCLUSION
We propose a new setting called data feedback , where past model outputs act as training data in the future.
We show that the natural decision to retrain a deployed model can increase utility while also amplifying biases.
We then provide conditions for stability (namely, consistent calibration) and derive corresponding upper bounds on bias amplification.
The utility of these predictions is realized by experiments in image classification, visual role-labeling, and language modeling, which confirm the observation that sampling-like behaviors often result in better calibration and greater feedback stability.
Finally, we leverage our insight to design a mitigation strategy for unstable feedback systems.
We hope our work will encourage further discussion around mitigation and prevention strategies.
E THICS S TATEMENT
Our work explores how certain model biases may amplify during data feedback.
However, the definition of bias is not static and depends on various cultural norms.
What is seen as favorable among one group may be problematic among another and certain biases have much more important consequences than others.
Our work does not take any steps towards addressing these issues, treating bias as purely a mathematical or programmatic construct.
R EPRODUCIBILITY S TATEMENT
All datasets we use are open-source.
In addition, all model architectures and pretrained model weights we use are open-source.
Appendix E discusses in detail the setup for each experiment in Section 5, including details on hyperparameter tuning, model training and evaluation and dataset construction.
The supplementary material contains code in order to reproduce all experiments presented in the main text and appendix of this paper, with one command per figure (approximately)
A A DDITIONAL RELATED WORK
Recommender systems.
Our work is also closely aligned with the study of feedback loops in recommendation systems (Sinha et al., 2016; Schmit & Riquelme, 2018).
In this context, existing work has shown that optimizing strictly for ranking metrics such as accuracy can create echo chambers, where minority populations are crowded out and disengage from the platform (Hashimoto et al., 2018; Jiang et al., 2019).
This issue arises due to the tension between improving ranking metrics and considerations of bias, fairness, or diversity (Steck, 2018; Chaney et al., 2018).
In Section 5.1, we show that a similar phenomenon exists in data feedback: retraining classifiers with future data improves classification accuracy, but at the cost of increasing its bias.
In the recommendation literature, one possible successful mitigation strategy is the use of recommendations that are calibrated in proportion to user interests (Steck, 2018).
Similarly, our work also heavily relies on the calibration of the model’s predictions to ensure the stability of data feedback.
The takeaways from this work cannot be immediately ported into the recommender systems setting, however.
The big difference is that in data feedback, annotations are collected from both humans and model predictions, while the distribution of examples for which the annotations are collected remains fixed.
In recommender systems, the annotation is always produced by a human, and the distribution of items for which the rating is collected is a function of the recommendation model.
In recommender systems, the distribution over examples itself is changing as a function of the model, which violates the fixed covariate assumption of data feedback.
In addition, annotations are only collected from humans, not a mix of humans and model predictions.
Semi-supervised learning.
The semi-supervised learning setting (Ouali et al., 2020; Grandvalet &
Bengio, 2004), also widely referred to as self-training, shares many similarities with the data feedback setting.
Assuming access to an additional pool of unlabeled data, a self-trained model iteratively labels parts of the data and retrains on its new predictions.
In contrast to data feedback, the unlabeled pool is typically fixed at the start, and the model can selectively choose which examples to use for training.
In most cases, self-training improves the utility of the overall model; however, prior work has found it may have disparate effects across population subgroups (Zhu et al., 2021).
In Section 5.2, we show a similar phenomenon in data feedback; gender bias amplifies differently for male-heavy and female-heavy subgroups of the data.
Domain adaptation.
Data feedback has connections to various domain adaptation settings (Farahani et al., 2021; Shu et al., 2018; Kumar et al., 2020; Lipton et al., 2018), where the changing data distributions can be viewed as shifting target domains.
The major difference between the settings is that in data feedback, the model itself drives changes in the distribution, while in domain adaptation, the shift in distribution is independent of the model.
Due to this difference in the problem setting, it is an open question how well domain adaptation techniques would transfer to data feedback.
Feedback loops in the wild.
Prior work has documented additional examples of feedback loops in the wild, in the context of predictive policing (Ensign et al., 2017), online polarization (Dandekar et al., 2013), and affirmative action, admissions, and hiring (Coate & Loury, 1993; Liu et al., 2020). Calibration error. Calibration error has been extensively studied in neural networks (Guo et al., 2017).
However, our definition of calibration, consistent calibration, is distinct and unrelated to this existing notion of calibration.
Consistent calibration error is measured as the difference between the bias of the model and the bias of its training distribution (Definition 1), according to some arbitrary bias metric.
Importantly, this bias is measured only over model output labels , not prediction probalities as in traditional calibration.
Traditional calibration error, by contrast, is a function of the difference between a model’s predictive probability and its output accuracy. While neural networks have been shown to often have high traditional calibration error (Guo et al., 2017), this does not imply anything about consistent calibration error. In particular, traditionally calibrating a classifier does not change its consistent calibration error. Some recent work (Nakkiran & Bansal, 2020) has in fact argued that many neural networks actually have small consistent calibration errors.
Overall, this work deals only with consistent calibration error, not with any traditional notion of calibration.
B S TABILITY ANALYSIS PROOFS B. N OTATION AND S ETUP
First, we note that the training distribution P t , defined recursively via P t = n t − 1 n t P t − 1 + mn t P 0 + kn t (cid:98) P f t − 1, is a random variable, as it is a function of random variables f t − 1 and P t − 1 and deterministic P 0 .
For ease of analysis, we study the case where the dataset S t is drawn fresh from its distribution
P t at every time, i.e. S t ∼ P n t t .
This generative model assumes S t is a new draw from P t at each timestep, which differs from the definition in Algorithm 1 where S t is constructed by concatenating new samples with the prior timestep’s dataset.
We make this simplifying assumption only for the theoretical analysis in this section since we are interested in the dependence between deployed models and training data distributions, not in the dependence introduced by the draw of each dataset.
We expect this difference in definition to be small as the sample size grows large.
Second, denote E f t [ · ] := E P 1: t ,f 0: t [ · ] := E f 0 , P 1 ,f 1 ,...
P t ,f t [ · ] as a shorthand for the expectation over all random objects up to time t during data feedback.
Here, the randomness in f i is both over the draw in dataset S i as well as randomness in the learning algorithm A .
Third, we define the shorthand P ϕ :=
E ( x,y ) ∼ P ( x,y )
[ ϕ ( x, y )] as expectation of the bias metric ϕ over distribution P ( x, y ) .
For clarity, as a reminder, our interest is in the expected bias amplification of a learning algorithm
A at time t ,
[Equation] B. P ROOF OF T HEOREM
We first show that consistent calibration with respect to base distribution P 0 implies calibration at each step of data feedback.
Lemma B.1.
Let A be ( δ n , ϕ , P 0 ( x ) , n )-consistently calibrated, where δ n is a function of dataset size n .
Then, under data feedback, for each time t ,
[Equation]
Proof
By definition of the data feedback model, the covariate marginal does not change throughout data feedback, and P t ( x )
= P 0 ( x ) for all t .
Thus, conditioned on a particular P t , we have that A is ( δ n t , ϕ , P t ( x ) , n t )-consistently calibrated.
Applying the consistent calibration definition gives (cid:12)(cid:12) E f t (cid:2) P t ϕ − (cid:98) P f t t ϕ | P t (cid:3)(cid:12)(cid:12) ≤ δ n t , where P t is fixed inside the conditional expectation.
Finally, we obtain the claim of the Lemma by noting that (cid:98) P f t t = (cid:98) P f t 0 , because (cid:98) P t depends on P t only through the marginal covariate distribution, which is identical between P t and P 0 .
Now, are ready to prove Theorem 1.
Proof
The general proof strategy is to first bound the bias amplification of model f t in terms of the bias amplification of its training distribution P t , and then bound the bias amplification of P t in terms of the previous training distribution P t − 1 .
This will lead to a recursive formula that we can solve.
We begin by bounding bias amplification of f t in terms of the bias amplification of P t .
[Equation]
Equation (1) uses triangle inequality, Equation (2) uses the iterated expectation equality and the fact that f t is
Now, we will bound the bias amplification of P t in terms of P t − 1 .
[Equation]
Equation (4) uses triangle inequality and Equation (5) uses Equation (3).
Denoting b t := (cid:12)(cid:12) P 0 ϕ − E P 1: t ,f 0: t − 1 (cid:2) P t ϕ (cid:3)(cid:12)(cid:12)
, we therefore have that b t ≤ n t − m n t b t − 1 + kn t δ n t − 1 , with b 0 = 0 .
Unrolling the recursion, we have that
[Equation]
Substituting the above into Equation (3), we have that
[Equation]
By assumption, δ n t ≤ δ n 0 for all t , and so we arrive at the result
[Equation]
The simplified upper bound is a result of the following Lemma.
Lemma B.2.
For all t ,
[Equation]
Proof
Let c t = (cid:80) t i = 1 k n i (cid:81) t j = i +1 n j − m n j .
We need to show that c t ≤ k m for all t , which we will do via induction:
Claim: c t ≤ km for all t .
Base case: c
[Equation]
Inductive step:
[Equation]
km .
B. S TATING F EATURE C ALIBRATION
Definition 2 (Distinguishable Feature (Nakkiran & Bansal, 2020)) .
Let L : X → [ m ] be a coarsening of the input domain X into m ∈ Z + parts.
Define (cid:98) P L as the relabeling of P by L .
Then, L is a ( δ , A ,
P ( x ) , n )-distinguishable feature if
[Equation]
The partitioning L defines how points in P are grouped together.
An appropriate partioning is one where the learner A can classify the group identity of each point with high accuracy.
Additionally, note that the coarsening L does not depend on the label distribution and relies only on the marginal
P ( x ) .
This property is important for data feedback; if L is distinguishable for the initial distribution
P 0 , it will continue to be distinguishable for all P t .
B. S TATING D ISTRIBUTIONAL G ENERALIZATION
Conjecture 1 (Feature Calibration (Nakkiran & Bansal, 2020)) .
Let T : [ m ] × Y → R be any bounded function.
If L is a ( δ , A , P ( x ) , n )-distinguishable feature, then for any joint distribution
Q ( x, y ) with marginal P ( x ) ,
[Equation]
B. P ROOF OF L EMMA 4.
Proof
By Conjecture 1, for any joint Q ( x, y ) with marginal P ( x ) ,
[Equation]
This lemma is an immediate consequence of DG (Conjecture 1), which states that the coarsened model outputs ( L ( x ) , f ( x )) are similar to the coarsened training data ( L ( x ) , y ) for all bounded tests T ; this is the basis for the statement that model outputs behave like samples, i.e
The given bias metric ϕ is simply one such test.
C A DDITIONAL MAIN EXPERIMENTS DISCUSSION C. I MAGE CLASSIFICATION
Observing that the theoretical bounds are loose in Figure 3, we discuss the source of this gap and where the bounds may more accurately reflect the empirical amplification.
In particular, Theoremassumes that calibration errors δ n t are decreasing with dataset size n t and uses it to globally bound δ n t ≤ δ n 0 for all t , which results in conservative bounds when δ n t < δ n 0 .
By creating an artificial setting where we expect calibration errors to be constant over time, i.e. δ n t = δ n 0 for all t , we can test the validity of the upper bound in a worst-case situation.
We construct this setting by randomly subsampling the training set at each round to the initial dataset size n 0 .
Specifically, we modify Line 5 of Algorithm 1 to be
[Equation]
The empirical trends and theoretical bounds in this worst-case setting are shown in the gray line in
Figure 3.
There is greater empirical amplification, and the upper bounds more accurately reflect the observed amplification.
This result suggests that the upper bound cannot be further improved without a better characterization of δ n t as a function of n t , which we leave as future work 1 .
C. L ANGUAGE MODELING
[Table]
Here, we analyze the utility of the three language models considered in Figure 5. We measure two quality metrics and one generalization metric: 1) coherence score (Su et al., 2022), defined as the average similarity between prompts and corresponding model completions; 2) mauve score (Pillutla et al., 2021), defined as the difference in distributions between model-completed sentences and ground truth sentences; and 3) memorization, defined as the overlap between 5 -grams of model outputs and the training data. These three metrics were all measured at round 0 without any data feedback. We first compare the beam search model to the nucleus sampling model.
The beam search model has higher coherence, while the nucleus sampling model has a higher mauve score and lower memorization due its more diverse outputs.
In certain applications (such as machine translation), coherence may be valued more; in these cases, choosing the beam search model, with its higher repetition bias, presents a utility-bias tradeoff.
We now discuss our intervention with lowered repetition bias, the overfit beam search model. Compared to its non-overfit counterpart, the coherence of the overfit beam search model is significantly decreased. This intervention introduces a new axis to control the utility-bias tradeoff: instead of trading coherence for reduced repetition by switching from beam search to sampling, one may instead trade coherence for reduced repetition by overfitting the beam search model to different degrees. We also analyze to what extent the overfit beam search model is matching the frequency of punctuations by simply memorizing the training data.
For the overfit beam search model, 25% of model output 5-grams exist in the training data, while the rate was 11% for the non-overfit beam search model and 2% for the nucleus sampling model.
Thus, while it may be that the overfit model is less diverse than the original models, it is still not simply memorizing and returning the training data.
D A DDITIONAL MAIN EXPERIMENT RESULTS D. I MAGE CLASSIFICATION ACCURACY
[Figure]
A cc u r a c y ( % )
Model-labeled data fraction: 80%
Model-labeled data fraction:
[Figure]
D. V ISUAL ROLE - LABELING MALE BIAS
[Figure]
a l e p r e d i c t i o n
[Figure]
r a c t i o n (
[Figure]
D. L ANGUAGE MODEL OUTPUTS
We provide sample model outputs for GPT2-small, generated with nucleus sampling in Table 2 and with beam search in Table 3.
When generating via beam search, model completions tend to be less fluent and contain many quotation marks and non-unicode characters.
Sample outputs for an overfit
GPT2-small, an intervention designed to stabilize feedback, are provided in Table 4.
Though still present, repetition and the overuse of quotation marks is mitigated.
All outputs are random samples from
[Table]
Michael
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The response of fans since Precourt’s bombshell announcement two weeks ago makes clear that the team has deep support here; they’ve donated their seasons, contracts and possibly even a roster spot.
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performances in Atlanta and at home show the team responds to
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love.
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She told authorities the last time she heard, she just looked around and saw broke the tank.
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Hardy, tell TMZ Hardy is in fact the alleged victim.
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Iraq and Kuwait earned their bloody reputation through their common dislike for the hardline Sunni Taliban.
After demanding cash the man left the premises , Arvind Kumar Goel, accused the MP of picking a sick little girl and then assaulting her and was last seen on Coolong Street.
A woman is dead and 22 other people injured after a car sped on to
Pakistan in Peshawar on Saturday night, Pakistan Rangers Rangers said on
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According a pavement in New York City’s Times Square, the fire department says.
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All women reported previous experience having sexual relations with strangers in public places.
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"We have enjoyed an encouraging build-up to our Euroqualifying campaign and I am sure the players, the coaching staff and the whole football staff are looking forward to participating in this historic event."
× × Barlow said the fans will love the chance to go head-to-head with our oldest rivals again," said Scotland manager Gordon Strachan.
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genital mutilation on two 7-year-old girls.
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GPT
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sampling outputs
Prompt
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Ground
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The Digital Economy Bill has been processed speedily as it is being pushed through in the politics wash .
As laid out in the Bill, a man’s phone numbers, emails and Facebook profile pictures are -up process - which takes place between an election being called and Parliament being dissolved.
A bill proposal, formed by Knesset Member Ayelet Shaked of Habayit
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× molested by at least two men in Bandra last month, horror has piled on horror.
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End of
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And, in the end, isn’t there simply a danger to this game that it’s going to suck?”
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those who play it and those who watch it are going to have to accept?
Baking and sewing skills dying out as modern technology advances.”
× × ””” × × ”” × mothers claim they are too busy to learn
Gogglebox also aired an election special on Thursday night (May) in which voters were asked what they thought of Donald Trump’s immigration policies.
× × ), with Jeremy Paxman and David Mitchell leading the proceedings.
"He’s got a gunshot hole in his face this morning, he’s got a bullet hole in his head, he’s got a bullet hole in his big, they murdered him," David Phillips exclaimed.
In a passionate speech, she articulated the scale of the problem.
×
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The 76-year-old man told police that the other man confronted him and said, “You’re going to kill me.”
× ×
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The kiddos in our family usually just lick the cream off cupcakes (I was beginning to think this was a joke).””””””” × they’d be equally pleased with a plate of frosting), but they actually ate these cupcakes.
Related:
Rugby team cordially invites you into the world of rugby.”
×
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× ×
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× × ”It’s a , Donald Trump Jr. — Akhmetshin is not a complete idiot.)
Be sure to check out the NASA Earth Observatory image of
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the eruption that clearly shows the plume and its shadow.
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× × ”I’m not going to lie, terms of flea markets, cleanliness and, of course, coffee).
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ludicrous, Orwellian pieces of propaganda in recent memory.
The Palestinians were not the ones who slaughtered the Jews of Eastern
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(AFP Photo/Michael Klimenty , yet they are the ones being slaughtered today by the zionists.
Along the lines of Evil Dead and Dead Alive, there are a wide range of different games to please everyone.
We hope you enjoy the addition of this this splatterfest is sure to be a cult classic.
He had called me the day of the rosary and said he wouldn’t be able to go to bed until the next day because he couldn’t wait to die.”
to give us communion because of our same-sex relationship,” Parker told Fox4KC.
Pai, the son of Indian immigrants who grew up in Kansas, said last month the commission should take a closer look.
× ×
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Press / NBC 6 South Florida Gun Supply / NBC 6 South Florida “weed whacker” to unneeded rules and was harshly critical of many
FCC regulations imposed during the Obama administration.
Canadian ex-hostage Joshua Boyle says the Haqqani network in
London is “like a child-rapist” and is “like a childAfghanistan killed his infant daughter in captivity and raped his wife.
If you expose the insulin-producing beta cells in our pancreas , you’ll have an entirely different feeling associated more with the body kicking into survival mode.
to fat, they suck it up and then start dying off.
We will arrest Wally Sombero but no Jack Lam has been charged with any crime.
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At just 17, Achraf Hakimi will be unable to play for Real Madrid
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× × Injury casts doubt over
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Well, he’s living in my world now, and we’re taking in the world around us.”
(translated from Pashtoun) ×
× Pash the majesty of nature or he can find himself a new motherfucking place to live.
Even when the team stinks, and they win, and the Mavericks win, and the Mavericks win, and the Mavericks win, and the Mavericks stink right now, there are positives.
Or, if you got caught doing stupid shit, it was faster to kill yourself.”
–Typhus the
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be made an example of so the others don’t do the same thing.
Overfit GPT2-small beam search outputs
Prompt
Model completion
[Table]
completion
This may be happening with respect to the just-concluded Burning Man – the annual festival so many techies go to without a line to follow.
× ×
Find details on the current Burning Man event here.
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Males will fight over females, holding each other in place while they bleed internally.
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Batman: [after Dick Grayson’s parents are shot] Dick Grayson: [after Dick Grayson’s parents are shot] Dick
Grayson: [after Dick shot to death] He doesn’t understand.
Since then, it’s traveled to 17 countries and 20 cities.
10, square miles (1,460 kilometers) from the U.S. to the U.S. developers have attended, and they’ve had 350,000 online viewers of videos recorded.
Since teasing the music world with "Redbone" and "Me and Your
Mama", two of the biggest tunes this quarter, Donald
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Glover is now back in full force with the release of his third album under the Childish Gambino moniker, Awaken, My Love!
Along with the penis, the scrotum is scrotum-like.”
(translated from Pashtoun)
the Greek word sensitive and considered to be an erogenous zone.
I thought it was just vile casinos and ugly skyscrapers full of ghastly, tasteless, and potentially dangerous guests.”
– Lady Gaga, via The Guardian (via The gold-plated shit that cheapens and demeans all who set eyes on it.
As I started building my second major creation (more on the first later), it became quite obvious to see that the goal of the project was to make it possible to completely control the minds of the to me that I was paying the price for over 10 years of nonexistent or half-ass sorting.
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Conference in Strasbourg, France.
less The vote, they were reduced to 0.25%.
Host Brian Kilmeade asked Scheuer, a former CIA analyst and regular Fox News guest, if the
White House’s chief of staff has a history of covering up scandals.
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Reggie Miller was talking about how Chandler has to match up on the big screen!”
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Roy Hibbert all night and what a tough job that is.
End
E D ETAILS ON EXPERIMENT SETTINGS E. I MAGE CLASSIFICATION
Datasets.
For most experiments, we use the first 3 million images of the CIFAR-5m dataset, which contains 5 million examples synthetically generated by the DDPM diffusion generative model (Ho et al., 2020), which was originally trained on the CIFAR-10 train set.
The examples were then labeled by a BigTransfer classifier (Beyer et al., 2022), which has 98.5% accuracy on classifying CIFARimages.
We create a test set by randomly selecting 50 k examples on each new experiment run.
For an ablation on non-synthetic data, we also use the CINIC-10 dataset (Darlow et al., 2018), which is an extension of CIFAR-10 by including downscaled ImageNet images.
Training hyperparameters.
For most experiments, we train a BaiduNet9 (Li et al., 2019), which has 94% accuracy when trained on CIFAR-10.
We optimize the model using stochastic gradient descent with a batch size of 512 , Nesterov momentum factor of 0 . 9 , and weight decay of 0 . 256 .
The number of epochs trained is dependent on dataset size: below 20 k examples, we train for 63 epochs, then linearly scaled down to 50 epochs at 50 k examples, then linearly scaled down to 38 epochs at 100 k examples, then linearly scaled down to 25 epochs at 1 m or more examples.
We use a triangular learning rate: for the first fifth of training time, the learning rate is scaled linearly up from 0 until 0 .and
then, for the rest of training time, scaled linearly back down to 0 .
We use data augmentation standard for CIFAR-10 training: random crops, horizontal flips, and input normalization during training time, and only input normalization during test time.
We train with half precision.
For the ablation training an underfit BaiduNet9, we use the following learning rate schedule: train using a learning rate of 0 .
1 for the first 3 epochs, then decay linearly down to 0 .
during the fourth epoch, then finally decay linearly down to 0 .
001 on the fifth epoch.
We only train for 5 epochs regardless of dataset size for the underfit model.
For an ablation training a ResNet18, we train a ResNet18 adapted to CIFAR from this repository, and this model has 95% CIFAR test accuracy.
We train for twice the number of epochs as the regular
BaiduNet9 training; that equates to 100 epochs at 50 k dataset size and 50 epochs at dataset size of 1 m or more.
We optimize the model using stochastic gradient descent with a batch size of 128 , momentum factor of 0 . 9 , and no weight decay.
We use a cosine annealing schedule for the learning rate during training.
We train using full precision.
All other parameters remain the same.
Hyperparameter tuning.
During data feedback, the model is retuned and retrained from scratch on the growing dataset at each new round.
Due to the computational complexity of re-tuning hyperparameters for each data feedback experiment, we tune hyperparameters ahead of time for varying CIFAR-5m dataset sizes (in this case, the examples are not relabeled by data feedback).
During data feedback, we use the dataset size to match the hyperparameter setting at each round.
For hyperparameter tuning, we trained the BaiduNet9 for [10 , 20 , 30 , 45 , 65] epochs on dataset sizes of [20 k , 50 k , 100 k , 200 k , 500 k , 1 m ] .
We then chose the earliest number of epochs at which accuracy stopped improving for each dataset size, and then interpolated the number of epochs for all dataset sizes in between.
Once the optimal number of epochs was found, we then tuned the batch size and learning rate, varying batch size in [64 , 128 , 256 , 512] and accordingly scaling the learning rate linearly; and found the maximum batch size of 512 and corresponding learning rate of 0 .
4 worked best across all dataset size settings.
E. V ISUAL ROLE - LABELING
Dataset.
The imSitu dataset provides three sets of annotations for each image.
We collapse these annotations into a single label for each role in each image via majority voting.
We make this design choice to fit the data feedback setting, since model-labeled data points only have one annotation per image.
We also combine all data splits (train, dev, and test), and randomly sample 50 images per category (for a total of 25200 examples) to create a test set for each new experiment run.
Bias metric.
We select the verb categories with an existing female gender bias, and we measure the fraction of the model’s predictions that are labeled female over these verbs.
Specifically, in
Figure 4, we consider the verb categories where the dataset female label ratios lie between 60% to
This interval was chosen as it represented a wide range of stereotypically female activities.
In
Appendix F.2, we provide plots for 0 - 20% , 20 - 40% , 40 - 60% , and 80 - 100% .
Training hyperparameters.
We train the default ResNet18-backed conditional random fields model (Yatskar et al., 2016), proposed as a baseline alongside the dataset.
We optimize the model using Adam (Kingma & Ba, 2014) with batch size 64 , learning rate 0 .
00001 , default betas 0 .
9 and 0 . 999 , and weight decay of 0 . 0005 .
The number of epochs trained is dependent on dataset size: below 20 k examples, we train for 50 epochs, then linearly scaled down to 40 epochs at 35 k examples, then linearly scaled down to 35 epochs at 50 k examples, then linearly scaled down to 30 epochs at 75 k or more examples.
We use data augmentation standard for ImageNet training: random resized crops, horizontal flips, and input normalization during training time, and resized center crop with input normalization during test time.
Hyperparameter tuning.
Similar to the CIFAR setting, we tune hyperparameters ahead of time for varying dataset sizes (where the examples are not relabeled by data feedback).
The optimization criterion was the average score of five metrics calculated over the given dev set: verb classification accuracy, role classification accuracy, role classification accuracy conditioned on the correct verb, and two additional similar role classification metrics (Yatskar et al., 2016).
During data feedback, we then use the dataset size to match the hyperparameter setting at each round.
For hyperparameter tuning, we trained the ResNet18 CRF for [20 , 30 , 45 , 60] epochs on dataset sizes of [20 k , 50 k , 75 k , 100 k ] .
We then chose the earliest number of epochs at which the average score stopped improving for each dataset size, and then interpolated the number of epochs for all dataset sizes in between.
Once the optimal number of epochs was found, we then tuned the learning rate in [0 . 000001 , 0 .
and found the optimal to be 0 .
00001 for all dataset sizes.
E. L ANGUAGE MODELING
Dataset.
We use the Real Toxicity Prompts dataset (Gehman et al., 2020), which is a collection of 100 k sentences from the Open-WebText Corpus (Gokaslan & Cohen, 2019) stratified along varying levels of toxicity as predicted by the Perspective API toxicity classifier 2 .
We create a test set by randomly selecting 14442 examples on each new experiment run.
Toxicity metric.
Toxicity is measured by counting the fraction of model outputs classified as toxic by the Detoxify classifier 3 , which was trained on the Jigsaw toxicity challenge datasets (team, 2018; 2019; 2020).
A generation is classified toxic if the classifier’s toxicity score is greater than 0 .
We sample one output per prompt.
Our metric differs from that used in the Real Toxicity Prompts paper (Gehman et al., 2020), which measures the maximum toxicity over 25 independently sampled model generations for a given prompt.
Models and tokenizers.
We finetune GPT2 small, medium, and large, initialized to the pretrained models available on HuggingFace (Wolf et al., 2019).
All text is tokenized using the default GPT tokenizer.
For both nucleus sampling and beach search, model output is capped at a maximum oftokens, following the settings in (Gehman et al., 2020).
Training hyperparameters.
We optimize each model using AdamW (Loshchilov & Hutter, 2019) with batch size 16 , default betas 0 .
9 and 0 . 999 , and no weight decay.
For GPT2 small, the learning rate is set to 0 .
00005 , and for medium and large is set to 0 .
The models are finetuned for one epoch regardless of dataset size.
For the overfitting intervention, the models are finetuned forepochs, and the learning rate increased by a factor of 10 (to 0 .
0005 for GPT-2 small and 0 .
0001 for
GPT-2 medium and large).
Hyperparameter tuning.
Similar to the CIFAR and imSitu settings, we tune hyperparameters ahead of time for varying dataset sizes (where the examples are not relabeled by data feedback).
Prior work (Dhamala et al., 2021) has adopted a similar method for measuring toxicity.
Though toxicity classifiers have shortcomings (Kumar et al., 2021; Sap et al., 2022), this work is primarily concerned with aggregate, relative changes in toxicity over time to measure amplification.
The optimization criterion is model perplexity of test set sentence continuations conditioned on their respective prompts.
During data feedback, we then use the dataset size to match the hyperparameter setting at each round.
For hyperparameter tuning, we trained each GPT2 small, medium, and large model using a very dense sampling of the following hyperparameter combinations: [1 , 2 , 3 , 5] epochs, [20 k , 35 k , 50 k , 65 k , 85 k ] dataset sizes, [0 . 000001 , 0 . 000005 , 0 .
001] learning rates, and [4 , 8 , 16 , 32 , 64 , 128 , 256] batch sizes.
We found that across dataset sizes, training for 1 epoch with batch size 16 , with learning rate 0 . 00005 for GPT2 small and 0 .
00001 for medium and large was optimal or very near optimal.
F A BLATIONS FOR EXPERIMENTS F. I MAGE CLASSIFICATION
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d i c t i o n f r a c t i o n ( % )
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i c t i o n f r a c t i o n
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modest since the initial calibration error for ships is smaller.
80 Number
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rounds D o g p r e d i c t i o n f r a c t i o n ( % ) δ n
Model-labeled data fraction: 80%    80 Number of feedback rounds     δ n
Model-labeled data fraction: 50%
Empirical trend, underﬁt BaiduNet9 re-trained from scratch per round
Ampliﬁcation upper bound (Theorem 1)
True
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Number of feedback
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cc
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Model-labeled data fraction: 80%
Model
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data fraction:
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D o g p r e d i c t i o n f r a c t i o n ( % ) δ n
Model-labeled data fraction
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Model-labeled data fraction: 50%
Empirical trend, BaiduNet9 re-trained from scratch per round
Ampliﬁcation upper bound (Theorem 1)
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Number
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f
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F. V ISUAL ROLE - LABELING
We show gender bias amplification plots, each covering the image categories where the female label ratio lies in one of the five intervals between 0% − 100% .
Figure 16 shows amplification on the interval 0% − 20%
[Figure]
and Figure 7 shows amplification on the interval 20% − 40% , both of which depict male bias amplification.
Figure 4 shows amplification on the interval 60% − 80% , and Figureshows amplification on the interval 80% − 100% , both of which depict female bias amplification.
The middle interval 40% − 60% , where existing gender ratios are balanced, is depicted in Figure
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l
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p r e d i c t i o n
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r a c t i o
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e m a l e p r e d i c t i o n f r a c t i o n
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m a l e p
r e d i c t i o n f r a c t i o n (
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F. L ANGUAGE MODELING
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G e n e r a t i o n t o x i c i t
y ( % )
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Generation strategy: beam search
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Empirical
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pretrained GPT
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small ﬁnetuned
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upper bound (Theorem 1)
True toxicity level (23%) or average number of quotes (0.1) in base distribution
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Generation strategy: beam search    12 Number of feedback rounds
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f qu o t e s i n o u t pu t ( # )    12 Number of feedback rounds    δ n
Empirical trend, pretrained GPT2-small ﬁnetuned each round
Ampliﬁcation upper bound (Theorem 1)
True toxicity level (23%) or average number of quotes (0.1) in base distribution
G e n e r a t i o n t o x i c i t y ( % ) δ n
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+}
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n
Generation strategy: beam search    12 Number of feedback rounds
N o .
o
f qu o t e s i n o u t pu t ( # )    12 Number of feedback rounds    δ n
Empirical trend, pretrained GPT2-small ﬁnetuned each round
Ampliﬁcation upper bound (Theorem 1)
True toxicity level (23%) or average number of quotes (0.1) in base distribution
G e n e r a t i o n t o x i c i t y ( % ) δ n
Generation strategy: nucleus sampling         δ n
Generation strategy: beam search    12 Number of feedback rounds
N o .
o
f qu o t e s i n o u t pu t ( # )    12 Number of feedback rounds    δ n
Empirical trend, pretrained GPT2-medium ﬁnetuned each round
Ampliﬁcation upper bound (Theorem 1)
True toxicity level (23%) or average number of quotes (0.1) in base distribution
G e n e r a t i o n t o x i c i t y ( % ) δ n
Generation strategy: nucleus sampling         δ n
Generation strategy: beam search    12 Number of feedback rounds
N o .
o
f qu o t e s i n o u t pu t ( # )    12 Number of feedback rounds    δ n
Empirical trend, pretrained GPT2-large ﬁnetuned each round
Ampliﬁcation upper bound (Theorem 1)
[Figure]
distribution