# Detecting Label Errors by using Pre-Trained Language Models

Derek Chong111Equal contribution.
Stanford University
<EMAIL_ADDRESS>
Jenny Hong111Equal contribution.
Stanford University
<EMAIL_ADDRESS>

Christopher D. Manning
Stanford University
<EMAIL_ADDRESS>

###### Abstract

We show that large pre-trained language models are inherently highly capable
of identifying label errors in natural language datasets: simply examining
out-of-sample data points in descending order of fine-tuned task loss
significantly outperforms more complex error-detection mechanisms proposed in
previous work. To this end, we contribute a novel method for introducing
realistic, human-originated label noise into existing crowdsourced datasets
such as SNLI and TweetNLP. We show that this noise has similar properties to
real, hand-verified label errors, and is harder to detect than existing
synthetic noise, creating challenges for model robustness. We argue that
human-originated noise is a better standard for evaluation than synthetic
noise. Finally, we use crowdsourced verification to evaluate the detection of
real errors on IMDB, Amazon Reviews, and Recon, and confirm that pre-trained
models perform at a 9–36% higher absolute Area Under the Precision-Recall
Curve than existing models.

##  1 Introduction

Improving model performance in the presence of label errors comprises an area
of active research Song et al. (2022). However, existing methods focus on
label errors in training data. Although seldom acknowledged, evaluation label
errors are at least as pernicious as training label errors: pervasive errors
in commonly used NLP benchmarks have been found to destabilize model
performance Malik and Bhardwaj (2011); Northcutt et al. (2021b). Such findings
suggest that improving training methods does not preclude the need for
improving the underlying data. We propose a simple method for using large,
pre-trained language models (LLMs) to directly identify label errors for the
purposes of correcting or removing them.

$\displaystyle{0.0}$$\displaystyle{0.2}$$\displaystyle{0.4}$$\displaystyle{0.6}$$\displaystyle{0.8}$$\displaystyle{1.0}$Recall$\displaystyle{0.0}$$\displaystyle{0.2}$$\displaystyle{0.4}$$\displaystyle{0.6}$$\displaystyle{0.8}$$\displaystyle{1.0}$PrecisionBaselineFM LossFM EnsembleCL Overlays Figure 1: Precision-recall curves for label error detection: Large language models detect label errors with high precision, and far more effectively than a baseline word vector-based neural classifier. Overlaying a state-of-the-art model-agnostic error detection method, Confident Learning, results in little to no improvement (TweetNLP-5; §7).  Dataset |  Text | Label | Sentiment
---|---|---|---
IMDB |  It is really unfortunate that a movie so well produced turns out to be such a disappointment. I thought this was full of (silly) cliches. It had all sorts of differences that it tried to tie together (not a bad thing in itself) but the result is at best awkward, but in fact ridiculous–too many clashes that wouldn’t really happen. Then the end of the movie–the last 10 minutes–ruined all the rest. At first I thought Xavier was OK but with retrospect I think he was pretty bad. And that’s all really too bad, because technically it was really good, and the soundtrack was great too. So the form was good, but the content pretty horrible. | Positive | Negative
IMDB |  The ending made my heart jump up into my throat. I proceeded to leave the movie theater a little jittery. After all, it was nearly midnight. The movie was better than I expected. I don’t know why it didn’t last very long in the theaters or make as much money as anticipated.  Definitely would recommend. | Negative | Positive
Amazon |  The new design only has a thin layer of cellulose sponge material. It will not last as long. Already showing signs of wearing out. The picture does not represent the item received. | Neutral | Negative
Table 1: Organic label errors from sentiment datasets IMDB and Amazon, shown
with the original dataset label. Each example was hypothesized by our model to
be erroneous, and later verified by crowd workers.

The majority of work in identifying label errors, and in data-centric
artificial intelligence (DCAI) more broadly, focuses on image and healthcare
data DCAI Workshop (2021). However, the success of the foundation model (FM)
paradigm in applying pre-trained language models to a variety of NLP tasks
(Bommasani et al., 2021; Reiss et al., 2020) suggests that FMs may be a
powerful tool for detecting and correcting label errors in language datasets.
Pre-training has been shown to imbue models with properties such as resistance
to label errors, class imbalance Karthik et al. (2021), out-of-distribution
detection Hendrycks et al. (2018), and confidence calibration Desai and
Durrett (2020), while conferring robustness, generalization, and natural
language understanding capabilities Wang et al. (2018); Petroni et al. (2019).
Our primary contribution is to show that simply verifying items in order of
their out-of-sample loss on a foundation model improves precision by an
absolute 15–28% and Area Under the Precision-Recall Curve (AUPR) by an
absolute 9–36%.

Many methods for label error detection rely on artificially introduced label
errors as ground truth for evaluating their methods. Northcutt et al. (2021a)
develop a state-of-the-art model for identifying label errors, Confident
Learning (CL), and use the better approach of crowdsourced human evaluations
to determine the ground truth of label errors. We model our experiments on
real data after their verification protocol, replicating this on real errors
in IMDB Maas et al. (2011), Amazon Reviews McAuley et al. (2015), and Recon
Hong et al. (2021), with adaptations to mitigate annotator fraud Kennedy et
al. (2020).

In the process of assessing our results, we contribute a novel technique and
protocol for introducing realistic, human-originated label noise into existing
crowdsourced datasets, and apply it to two such datasets, TweetNLP Gimpel et
al. (2010) and SNLI Bowman et al. (2015). We demonstrate that our technique
better approximates organic (real, naturally occurring) label errors than
existing methods. We provide evidence that this realism is essential to
properly assessing model performance: even models that are robust to standard
synthetic noising approaches show limited robustness to human-originated
noise.111Data noising library and evaluation data available at
https://github.com/dcx/lnlfm.

##  2 Related Work

Learning with Noisy Labels (LNL) focuses on the model-training stage. Noise-
robust approaches examine model enhancements such as the design of loss
functions Joulin et al. (2016); Amid et al. (2019); Liu and Guo (2020); Ma et
al. (2020), regularization Azadi et al. (2015); Zhou and Chen (2021),
reweighting Bar et al. (2021); Kumar and Amid (2021), hard negative mining and
contrastive learning Zhang and Stratos (2021). Noise-cleansing approaches aim
to segregate clean data from noisy data in training, e.g. bagging and boosting
Wheway (2000); Sluban et al. (2014), $k$-nearest neighbors Delany et al.
(2012), outlier detection Gamberger et al. (2000); Thongkam et al. (2008),
bootstrapping Reed et al. (2014), and neural networks supervised directly on
detecting an error, when such data exist Jiang et al. (2018).

LNL methods have in most cases been evaluated using artificially-generated
label noise. A typical evaluation of an LNL method uses a standard benchmark
dataset, and programmatically corrupts training labels via one of three main
noising schemes Frenay and Verleysen (2014); Algan and Ulusoy (2020). Uniform
noise is most commonly used but unrealistic; deep neural networks have been
found to perform well even when noised labels outnumber original labels at a
ratio of 100 to 1 Rolnick et al. (2017). Class-dependent noise randomly
permutes labels based on a confusion matrix. However, research on annotator
disagreement suggests that label errors tend to result from feature-based, not
class-based ambiguity Hendrycks et al. (2018). Training models to generate
realistic feature-based or instance-dependent noise has recently emerged as an
area of active research Chen et al. (2021b); Xu et al. (2021); Dawson and
Polikar (2021). However, Algan and Ulusoy (2020) report that feature-dependent
noise may bias benchmark performance toward similar models to the ones used to
generate this noise.

The noising schemes above each fail in some way to simulate organic, naturally
occurring label errors, which are estimated to occur in common benchmarks at
1–5% of labels Redman (1998); Müller and Markert (2019); Northcutt et al.
(2021b); Kreutzer et al. (2022) or even as much as 20% Hovy et al. (2014);
Abedjan et al. (2016). For organic errors, CL Northcutt et al. (2021a)
predicts errors in IMDB, Amazon Reviews, and other datasets by estimating a
joint distribution between noisy and uncorrupted labels; Reiss et al. (2020)
pioneers using BERT for error detection on ConLL-2003 via a classifier trained
over a frozen BERT embeddings layer.

##  3 Methods

#### Motivation.

Empirical evidence on image data suggests that models exhibit high loss on
label errors in training data relative to the underlying features Huang et al.
(2019); Kim et al. (2021); Hong et al. (2021); Chen et al. (2021a). Hendrycks
and Gimpel (2017) show that predicted probabilities of (non pre-trained)
neural networks can identify out-of-distribution examples. We consider the
framing that label errors are one type of out-of-distribution data. Indeed, CL
Northcutt et al. (2021a) uses normalized predicted probabilities, also from
non pre-trained models, to directly identify label errors. Foundation models
are highly performant; we hypothesize that a low likelihood label is likely to
be an error.

$\displaystyle{10^{0}}$$\displaystyle{10^{1}}$Average
Loss$\displaystyle{0.0}$$\displaystyle{0.2}$$\displaystyle{0.4}$$\displaystyle{0.6}$Error
Detection PrecisionBERTDeBERTaGPT-2RoBERTaOtherRandom Figure 2: Loss exhibits
a strong log-linear relationship with error detection precision at a fixed
threshold, across a broad range of models and hyperparameters ($r^{2}$: 0.94;
TweetNLP-5, §7).

#### Foundation models.

0%5%10%15%75%80%85%90%95%Task AccuracyUniform Noise0%5%10%15%Class-Based
Noise0%5%10%15%Dissenting Label0%5%10%15%Dissenting Worker0%5%10%15%% Dataset
NoisedCrowd MajorityMeasurable Performance (Noisy Test)True Performance (Clean
Test) Figure 3: Assessing model robustness against a range of noising methods
on TweetNLP, with methods ordered by hypothesized realism. Solid orange lines
report task performance on noisy test data, reflecting observations in
practice; dashed blue lines report task performance on underlying clean test
data, reflecting models’ actual performance. Models may be robust to uniform
and class-dependent noise, where the true performance remains high even with
increasing levels of noise. However, they are not necessarily robust to human-
originated noise, where the true test performance decreases with increasing
noise.

The success of Reiss et al. (2020)’s approach in using frozen BERT embeddings
motivates directly applying the foundation model paradigm: we use a large
language model that was first pre-trained on a task-agnostic dataset, then
fine-tune the model for a given task.

We address classification tasks: given a model’s score $f_{i,c}$ for each item
$i$ and class $c$, its predicted probability is the softmax-normalized score
$p(c\mid x_{i})$. Because each item belongs to exactly one class, the
contribution of item $i$ to the loss is the negative log probability of the
score for the assigned class $y_{i}$:

$L_{i}=\sum_{i}-\textrm{log }p(y_{i}\mid x_{i}).$

We fine-tune such a model for the training split of each data set. To identify
label errors on a validation or test set, we hypothesize items from the
dataset as a label error in order of the item’s loss on that out-of-
distribution set.

We propose two main methods. Foundation Model Loss (FML) uses a single
foundation model, fine-tuned on the corresponding task (e.g., sentiment
classification, POS tagging), to hypothesize items in order of the model-
predicted loss. We augment FML using task-adaptive pre-training (TAPT;
Gururangan et al., 2020), which is further pre-training on in-domain data,
using only text on the pre-training objective without using any labels for
fine-tuning on the cross-entropy objective.

Foundation Model Ensembling (FME) combines multiple foundation models on the
same task. We hypothesize that ensembling may be disproportionately effective
at detecting label errors, as training noise induces models to learn random
spurious correlations Watson et al. (2022). Rather than using a validation set
to choose the single model with the lowest loss on the task, FME uses the top
three models trained in a hyperparameter sweep, and differing in both
hyperparameters and random initialization, as fully described in Appendix D.
FME creates a synthetic probability distribution over the task outputs by
averaging the probabilities predicted using each individual model. FME then
hypothesizes items in order of loss over the synthetic distribution.

##  4 Generating Realistic Label Noise

To better evaluate label noise detection performance, we prepare a set of
benchmark datasets populated with controllable, highly realistic, human-
originated label noise.

#### Sources of human error.

We observe that datasets often undergo multiple annotation passes:
crowdsourced labels typically aggregate several annotators’ inputs Hovy et al.
(2014); Wei et al. (2022), and subsets of data may receive more extensive
validation Bowman et al. (2015), gold labels by trained experts Plank et al.
(2014), or correction passes Reiss et al. (2020). We hypothesize that
differences between such annotations may be usefully repurposed as a source of
realistic, human-originated label noise, as disagreements between annotators
is known to reflect systematic ambiguity and human error Plank et al. (2014);
Zhang et al. (2017), and differs from the type of noise studied using existing
synthetic methods.

We construct three noising methods which may be applied in many of the above
scenarios. For any dataset which includes two levels of label quality, the
dissenting label method replaces final labels with disagreeing labels at
random, simulating imperfect quality control. Datasets which provide
individual annotator identifiers may apply the dissenting worker approach:
select one annotator at random, apply all of their labels which disagree with
final labels, and repeat until reaching the target noise rate. This simulates
gaps in annotator training, which introduce systematic idiosyncrasies. Finally
the crowd majority method applies to any dataset in which individual
annotations can be aggregated to produce a label other than the final label:
the former label simulates challenging, systematic errors in the latter.

#### Noising and robustness.

We assess the effect of these noising methods using TweetNLP Gimpel et al.
(2010), a corpus of 26,435 tokens from 1,827 American English tweets collected
from Twitter used to train part-of-speech (POS) tagging. TweetNLP includes
gold labels annotated by 17 experts, but later received a separate
crowdsourced assessment, aggregated by majority vote Hovy et al. (2014). We
noise TweetNLP to eight levels from 0-20% separately for each method, fine-
tune `DeBERTA-v3-base` He et al. (2021) on each noising, and evaluate models
on both noisy and clean test sets. Results from noisy test sets represent
model performance as measurable in practice; real datasets contend with noise
in evaluation data. Clean test set results represent true model performance.
Fig. 3 reports the results of this evaluation.

$\displaystyle{0}$$\displaystyle{2}$$\displaystyle{4}$$\displaystyle{6}$$\displaystyle{8}$Losses
of Noised Test
Items$\displaystyle{0.0}$$\displaystyle{0.2}$$\displaystyle{0.4}$$\displaystyle{0.6}$DensityUniform
NoiseClass-Based NoiseDissenting LabelDissenting WorkerCrowd MajorityClean
Data Points Figure 4: Distributions of losses of label errors on TweetNLP at
5% noising. Uniform and class-based noise produce high and distinctive losses;
human-originated noise is widely distributed, and has greater overlap with the
distribution of clean data points; §6.

For uniform and class-dependent noise, true performance remains high even for
high noise levels (per Rolnick et al., 2017). But crucially, this robustness
does not extend to human-originated noise: human label errors are correlated
to input text, and so contain systematic erroneous features, which models may
learn in training. On more challenging noising methods, although measured
performance appears to increase, true performance actually linearly decreases
with noise. Fig. 4 explores this further via the distributions of model losses
for each noising method: loss induced by human-originated noise overlaps
significantly with clean items, whereas loss from uniform and class-based
noising is distinctively higher.

#### Noise detection benchmarks.

We standardize a set of benchmarks from existing datasets for use in our main
experiments. TweetNLP-5 and SNLI-5 aim to simulate typical data noise
conditions: we apply dissenting worker and dissenting label noising to a 5%
level (see Appendix A for details). SNLI is a corpus of 570,152 sentence
pairs, in which the task is to label each pair with entailment, contradiction,
or semantic independence; we use the 10% subset which includes five
crowdsourced annotations per item, as collected by Bowman et al. (2015) during
data validation.

We construct TweetNLP-M to investigate robustness to systematic error
introduced by the crowdsourcing process. We apply crowd majority noising,
comparing noisy majority-vote aggregated labels by Hovy et al. (2014) to clean
expert labels, which serve as a measure of true performance. Accordingly, we
retain all disagreements, or 20.46% of the dataset. We also report results on
Recon, a legal classification dataset of 1,279 documents in which Hong et al.
(2021) found label errors to destabilize model evaluation; as above, we
compare non-expert and expert annotator labels.

##  5 Validation on Real Label Errors

In addition to human-originated noise datasets, we evaluate error detection
performance on organic errors in two benchmark datasets, following Northcutt
et al. (2021a)’s protocol.

#### Datasets.

The IMDB Large Movie Review Dataset is a collection of movie reviews for
binary sentiment classification (Maas et al., 2011), and is split into train
and test sets of 25,000 items each. Amazon Reviews is a collection of reviews
and 5-point star ratings from Amazon customers (McAuley et al., 2015). We used
the version released by Northcutt et al. (2021a), which includes the following
modifications: It uses 1-star, 3-star, 5-star reviews with net positive
helpful upvotes as a ternary sentiment task, resulting in a dataset of
9,996,437 reviews. For tractability we use a train split of a random sample of
2.5 million items, and a test split of 25,000 items.

IMDB | New Protocol
---|---
Old Protocol | C | NA | NE | Total
Correctable | 105 | 44 | 24 | 173
Non-Agreement | 75 | 252 | 225 | 552
Non-Error | 3 | 62 | 520 | 585
Total | 183 | 358 | 769 | 1310
Amazon | New Protocol
Old Protocol | C | NA | NE | Total
Correctable | 142 | 43 | 117 | 302
Non-Agreement | 140 | 79 | 211 | 430
Non-Error | 75 | 31 | 162 | 268
Total | 357 | 153 | 490 | 1000
Table 2: Re-evaluation of baselines: The number of Correctable, Non-Agreement,
and Non-Error assessments produced by the CL Mechanical Turk evaluation
protocol and the new protocol, on the same set of items. The new protocol
substantially reduces annotator non-agreement; §5.

#### Baseline protocol.

Workers are presented with review text and asked to determine whether overall
sentiment is positive, negative, neutral, or off-topic. Each review is
independently presented to five workers. An example is considered a “Non-
Error” if at least three workers agree the original label is correct.
Otherwise, we consider the label to be correctly identified as an error. We
further categorize label errors as “Correctable” if at least three workers
agree on the same replacement label, or “Non-Agreement” if no majority exists.

#### New adaptations.

While conducting initial experiments, we found that the Northcutt et al.
(2021a) MTurk protocol resulted in a significant amount of annotator fraud.
Some workers spent unreasonably short amounts of time on the text, and
frequently disagreed with both expert and peer annotators, reflecting
increasingly common issues in crowdsourced annotations Kennedy et al. (2020).
Appendix C describes four extra conditions we added to improve the Northcutt
et al. (2021a) protocol.

In order to establish an accurate baseline, we re-evaluate the label errors
hypothesized by CL (Northcutt et al., 2021a). On the new protocol, Fleiss’
$\kappa$ inter-annotator agreement increases from 0.131 to 0.464 for IMDB, and
0.014 to 0.556 for Amazon, and Table 2 shows that Non-Agreement decreases by
35% in IMDB and 65% in Amazon. This suggests a substantial decrease in low-
quality annotations.

##  6 Experiments

| Area Under Precision-Recall Curve | Precision, Recall @ Error%333Precision and recall are equal when evaluating a number of items equal to the total error count. | Recall @ 2 $\cdot$ Error%
---|---|---|---
| I | Am. | R | T-5 | T-M | S-5 | I | Am. | R | T-5 | T-M | S-5 | R | T-5 | T-M | S-5
H&G | - | - | - | 0.30 | 0.41 | 0.20 | - | - | - | 0.31 | 0.44 | 0.22 | - | 0.54 | 0.63 | 0.34
CL | 0.24 | 0.31 | 0.25 | 0.30 | 0.41 | 0.17 | 0.41 | 0.51 | 0.31 | 0.36 | 0.44 | 0.18 | 0.46 | 0.47 | 0.63 | 0.32
FML | 0.58 | 0.39 | 0.37 | 0.66 | 0.48 | 0.54 | 0.68 | 0.64 | 0.46 | 0.65 | 0.47 | 0.45 | 0.62 | 0.88 | 0.64 | 0.66
FME | 0.60 | 0.40 | 0.38 | 0.68 | 0.48 | 0.61 | 0.69 | 0.66 | 0.38 | 0.66 | 0.48 | 0.46 | 0.69 | 0.88 | 0.65 | 0.68
FME+CL | 0.20 | 0.17 | 0.37 | 0.68 | 0.48 | 0.62 | - | - | 0.38 | 0.69 | 0.48 | 0.47 | 0.69 | 0.89 | 0.66 | 0.68
Table 3: Main experiment: Evaluating label error detection methods using
datasets containing highly-realistic label errors (IMDB, Amazon Reviews,
Recon, TweetNLP-5, TweetNLP-M, SNLI-5). Foundation model-based methods
significantly outperform baselines on every dataset, as shown by an overall
performance metric (AUPR). In practice, estimating the number of dataset
errors and checking this many items quickly catches up to 69% of errors, at
the same accuracy (P,R@Err%).333Precision and recall are equal when evaluating
a number of items equal to the total error count. For improved coverage,
checking twice this number of items catches up to 89% of errors
(R@2$\cdot$Err%).
$\displaystyle{0}$$\displaystyle{2}$$\displaystyle{4}$$\displaystyle{6}$$\displaystyle{8}$Losses
of Noised Test
Items$\displaystyle{0.0}$$\displaystyle{0.2}$$\displaystyle{0.4}$$\displaystyle{0.6}$DensityUniform
NoiseClass-Based NoiseReal Label ErrorsClean Data Points Figure 5:
Distributions of losses of hypothesized label errors that MTurk workers
verified for IMDB. As with Fig. 4, uniform and class-based methods do not
approximate real, worker-identified errors, and losses of real label errors
have greater overlap with the distribution of clean data; §6.

#### Label noise realism.

Section 4 defined the human-originated noising protocol used to generate
TweetNLP-5, TweetNLP-M, and SNLI-5. Section 5 specified a protocol for
identifying organic label errors present in IMDB and Amazon. We assess the
realism of synthetic noise methods by comparing loss distributions against
models trained with organic noise (for real label errors, we refer to items
verified as Correctable via MTurk). We quantify the degree to which noising
induces erroneous learning by measuring the Wasserstein distances between
noisy and clean loss distributions.

#### Overall LLM performance.

We assess broad error detection capabilities by evaluating 13 commonly-used
LLMs on TweetNLP-5. We measure performance against loss, model size, and GLUE
score (a proxy for general model capability; Wang et al., 2018). Appendix D
provides implementation details. This experiment’s results inform model
selection: we use `DeBERTA-v3-base` for all further experiments.222We also use
RoBERTa-BigBird for Recon in order to handle its long input passages Hong et
al. (2021).

#### Main experiment.

Using our realistic noising benchmarks, and the MTurk baselines and
verification protocol, we can now assess the performance of each label error
detection method. We evaluate Foundation Model Loss (FML) and Foundation Model
Ensembling (FME).

As a baseline, we evaluate Confident Learning (CL; Northcutt et al., 2021a).
CL is not a standalone method; it augments existing models. Given an
underlying model’s predicted scores for each class and the true proportion of
each class, CL forms a reweighting matrix, called the confident joint. To form
a label error prediction score, CL reweights the model’s scores by the
confident joint. CL hypothesizes items in order of this resulting score.

CL uses FastText Joulin et al. (2017) for IMDB and Amazon, but includes no
implementations for POS tagging or NLI. As a result, for TweetNLP and SNLI, we
apply CL to the H&G baseline Hendrycks and Gimpel (2017), a two-layer neural
classifier over word vectors pre-trained on a corpus of 56 million tweets
Owoputi et al. (2013). For all datasets, we also assess applying CL to
foundation models (FME+CL).

For each dataset, we run 25 hyperparameter sweeps which each fine-tune a model
for the given task (e.g., POS tagging) using noisy data, and select the model
with the best validation set task performance. We report label error detection
performance (not task performance). Area Under the Precsion-Recall Curve
(AUPR) provides an overall performance score Saito and Rehmsmeier (2015);
Hendrycks and Gimpel (2017). We also report metrics representing performance
on competing data cleaning priorities: efficiency requires high precision on a
small number of items, whereas coverage requires high recall on a larger
number of items. Appendix E.1 describes the Truncated AUPR used for IMDB and
Amazon, which are too costly to fully crowd verify.

#### End-to-end noising.

We finally isolate the effects of noise and label error correction for
validation and test splits. For each dataset, we prepare three versions of the
validation and test splits, respectively: a clean version assumed to contain
zero errors,444For TweetNLP, we justify our assumption in §4: expert labels by
Hovy et al. (2014) are considered noise free compared to crowd labels. For
IMDB and Amazon, we follow Northcutt et al. (2021a), which adds several
percentage points more noise than naturally occurs. a noisy version, with
label noise deliberately introduced, and a corrected version generated from
noisy splits using our main error detection method (ranking errors with FME
and correcting the top Err% data points). We train 40 hyperparameter sweeps,
with performance cross-evaluated on all prepared data splits.

We report three different metrics. We report each model’s accuracy on the
clean test split as the true accuracy. Following the norms of Fig. 3, we
report the measurable accuracy as the accuracy of the model selected using
performance on the noisy or corrected validation split on the corresponding
test split. Finally, we report the rank of the model as the rank of the
model’s performance on clean test data. The best performing model among all
sweeps has rank 1, and the worst has rank 40. This metric emphasizes that
different validation sets select different models.

We perform this exercise using IMDB and Amazon noised to 5% (I-5, A-5), and
TweetNLP-5 and TweetNLP-M.

##  7 Results

$\displaystyle{0.0}$$\displaystyle{0.2}$$\displaystyle{0.4}$$\displaystyle{0.6}$Error
Detection Recall
(Estimated)$\displaystyle{0.5}$$\displaystyle{0.6}$$\displaystyle{0.7}$$\displaystyle{0.8}$$\displaystyle{0.9}$$\displaystyle{1.0}$Error
Detection PrecisionBaselineFM LossFM EnsembleCL Overlays Figure 6: Precision-
recall curves for label error detection on Amazon by method. FML+CL and FME+CL
produce fewer items and do not extend to a recall past 0.21. Applying CL to FM
changes little compared to using FM alone.

#### Label noise realism.

Human-originated noise appears to closely approximate real label noise. Figs.
4 and 5 show that the losses of both real and human-originated label errors
are lower and more widely-distributed than existing noising methods. Their
Wasserstein distances to the distribution of clean data are significantly
lower than existing noising methods, suggesting comparable erroneous learning
(Appendix B).

#### Overall LLM performance.

We discover a strong log-linear relationship between error detection
performance and loss, which holds across many model families and
configurations ($r^{2}$: 0.94, Fig. 2). We also find relationships between
error detection performance and general model capability, in terms of GLUE
score ($r^{2}$: 0.79) and model size (Fig. 10). Fig. 7 illustrates key
findings using models’ receiver operating characteristic (ROC) curves.
Ensembling confers signficantly more gains in error detection performance
higher than gains on underlying task performance, across a broad range of
models and hyperparameters; Appendix E.3 explores ensembling in greater
detail.

#### Main experiment.

Table 3 shows that Foundation Model Ensembling significantly improves AUPR
from the CL and H&G baselines on all datasets, with an absolute difference of
0.36 on IMDB, 0.09 on Amazon, and a difference of 0.07–0.44 on synthetic data.

Fig. 1 shows that applying CL to FME has minimal effect on performance at
every level of recall; most numbers are identical across the FME and FME+CL
rows of Table 3. In fact, CL does not necessarily improve upon the H&G
baseline across datasets, with CL performance sometimes dipping below H&G by
0.01–0.03.

While loss naturally ranks all data points, CL only hypothesizes a fixed
number of potential errors: Appendix E.2 shows the raw counts of items at
fixed thresholds, per the original CL study. At the CL threshold, we
outperform CL by an absolute 15–28%. At the CL+FME threshold, predicted items
are almost exactly the same, with Jaccard similarities of 0.59–0.99. By
contrast, ensembling improves performance over FML by a greater amount on
almost every measure, and introduces no such constraint.

$\displaystyle{0.0}$$\displaystyle{0.1}$$\displaystyle{0.2}$$\displaystyle{0.3}$$\displaystyle{0.4}$False
Positive
Rate$\displaystyle{0.6}$$\displaystyle{0.7}$$\displaystyle{0.8}$$\displaystyle{0.9}$$\displaystyle{1.0}$True
Positive Rate77%: bert-small84%: bert-base-uncased86%: bert-large-uncased87%:
roberta-base88%: deberta-v3-small90%: roberta-large90%: deberta-v3-base91%:
deberta-v3-large91%: deberta-v2-xlarge Figure 7: ROC curves for error
detection performance on TweetNLP-5: LLM loss is highly effective for
detecting label errors, and performance is highly correlated with general
language understanding (GLUE, $r^{2}$: 0.79).

#### End-to-end noising.

Cleaning validation data selects better models. Noise in validation splits
reduces performance by encouraging the selection of models with lower true
performance. Noise in test splits significantly reduces measureable (noisy
test) performance, as expressed by the difference between measureable and true
performance. In general, correcting label errors improves task performance:
even when the reported task performance worsens, the reported performance is
closer to the true performance of the model, measured using clean training and
validation data.

Eval. | Test Perf. | I-5 | A-5 | T-5 | T-M
---|---|---|---|---|---
Noisy | Measurable | 90.1 | 88.3 | 89.3 | 89.3
True | 94.2 | 91.0 | 92.8 | 82.0
Rank | 10 | 1 | 3 | 10
Corr. | Measurable | 95.1 | 90.7 | 92.9 | 88.5
True | 95.1 | 90.8 | 93.0 | 82.0
Rank | 4 | 5 | 2 | 8
Clean | True | 95.8 | 91.0 | 93.8 | 82.1
Table 4: End-to-end effects of label noise on task performance, as evaluated
on noisy, corrected, and clean validation and test data splits. True accuracy
is measured on clean test sets, and measurable accuracy on noisy or corrected
test sets. Rank is a relative measure of true accuracy; lower numerical ranks
have higher accuracy. Corrections which improve or reduce performance metrics
are highlighted in green or red, respectively. Metrics are evaluated on models
trained on noisy data.

##  8 Discussion

#### Rapid data “health check”.

Sorting evaluation data by each item’s loss is an easy way to quickly
highlight label errors. Using this simple technique with a foundation model
appears to generally identify over half of all label errors through human re-
evaluation of a single-digit percentage of all data (Table 3). We expect this
technique to work across deep learning domains, due to its simplicity and the
extensive use of training loss in LNL research Song et al. (2022). Given
estimates for typical rates of label errors and the gain observed in the end-
to-end experiment, our technique may enable a 1–2% increase in reportable test
accuracy across many datasets, in addition to the gains from improving model
selection.

#### Pre-training and robustness.

We demonstrate that despite established findings on artificial noising
Hendrycks et al. (2018), pre-training confers limited robustness to realistic
human noise. The majority of label errors are systematic in nature Snow et al.
(2008); Plank et al. (2014); Samuel et al. (2022), and crowdsourced labels
form, to an extent, a different distribution from reality, as approximated by
expert labels Hendrycks et al. (2020). When trained on crowdsourced or other
data containing systematic errors, FMs quickly drift towards this incorrect
distribution.

#### Applying AI to data-centric AI.

Data-centric AI aims to improve AI through labeling, curating, and augmenting
the underlying data. We find that AI itself can be applied towards improving
data quality, as part of a human-in-the-loop (HITL) iteration, which
contributes an additional positive feedback loop between data quality and AI
performance.

#### New challenges in LNL.

Standard noising methods are unrealistic and no longer challenging for state-
of-the-art language models Algan and Ulusoy (2020); recent LNL analyses study
conditions where up to 80% of labels are noised Song et al. (2022). Our
findings reinforce the need to reassess LNL methods in the context of more
realistic noise Zhu et al. (2022).

Our human-originated noising method produces realistic label errors, and can
be applied to any crowdsourced dataset which includes raw annotation data. As
such datasets emerge across deep learning domains Wei et al. (2022), we hope
this method may inspire challenging and realistic new LNL performance
benchmarks. Our method also enables detailed exploration of the properties of
human noise, which may support work on open LNL problems such as improving
feature-based noising techniques, and estimating dataset noise Bäuerle et al.
(2022); Northcutt et al. (2021b).

#### End-to-end noising.

The study of model performance on noise in validation and test data is
essential: noise in other splits can affect reported model performance as much
as noise in training data. Clean and noisy performance on evaluation data
provide useful insight into models’ overall performance.

##  9 Conclusions and Future Work

Pre-trained models effectively identify label errors on real NLP datasets,
definitively outperforming existing methods on the same benchmarks by an
absolute 9–36% in AUPR.

Human-originated noising techniques may present a solution to the clear
limitations of current LNL noising schemes: they are highly realistic and yet
controllable for experimental purposes. We invite further exploration of this
family of label noising techniques. We believe human-originated noising
enables future advancements across multiple areas of LNL, supporting new tasks
and metrics in areas such as the cost of human reannotation, estimation of
dataset error, and mitigation of bias.

Finally, we advocate for LNL to move towards an end-to-end approach of
evaluating with label noise, which takes into account noise within validation
and test splits, and more accurately models the conditions of data in
practice.

## Limitations

#### Partial metrics.

Determining the true recall of a label error detection method on a real
datasets is generally infeasible due to its high cost; this requires a
complete re-evaluation so as to identify every label error within the dataset.
While some datasets exist in which this has been undertaken, such as Hovy et
al. (2014) for TweetNLP, for most datasets containing organic label errors, we
can only assess precision directly.

To mitigate this, we can estimate recall by estimating total dataset error
counts using sampling techniques. As a result of this limitation, we prefer
AUPR over AUROC (Area Under the Receiving Operating Curve) as our overall
assessment metric: estimates of AUPR are scaled by a fixed ratio, and
therefore comparable between models on the same dataset, whereas AUROC is
nonlinear with respect to the estimate.

#### Requires multiple annotations per label.

Human-originated noising methods are only applicable to datasets which include
at least two human annotations per label. While it is becoming increasingly
common to release individual-level annotator data, this is not an ubiquitous
practice.

#### Cleaning benchmark data.

In our analysis of model performance gains derived from applying our methods
to cleaning evaluation data, we find that cleaning validation splits enables
the selection of models with better test performance. Such a method may be
useful in a large number of applications.

However, we caution against using this method to clean data intended for use
in comparing performance across model families and variants: the cleaning
process may bias any such benchmarks toward the models most similar to the
model used to clean the data. While our method improves the performance of a
given model on a task, and correcting label errors always improves the
validity of test data, these improvements is unlikely to improve the
performance of all models by the same amount.

This limitation is shared with other existing model-based scoring methods such
as BERTScore Zhang* et al. (2020).

## Acknowledgements

We would like to thank Google.org for credits for use of the Google Cloud
Platform. We are also grateful to our anonymous reviewers, members of the
Stanford NLP Group, and Bryan H. Chong for their constructive feedback, as
well as the many researchers who made data publicly available to enable our
present work.

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##  Appendix A Noising Benchmarks

This section specifies how noising protocols were applied to create each fixed
crowdsourced dataset. Crowd labels for each dataset are available to download
from the respective GitHub projects.

###  A.1 TweetNLP-5

TweetNLP-5(%) is a fixed noising of TweetNLP to a 5% noise level in each
split. Of the label errors, 80% (i.e. 4% of each split) are assigned using the
dissenting worker method. The remaining 20% (i.e. 1% of each split) are
assigned using the dissenting label method. Fig. 4 shows that both methods
provide similar distributions of label errors. Although the dissenting worker
method more realistically captures individual worker idiosyncrasies, the
dissenting label method is actually slightly lower loss during training (i.e.
harder for a model to distinguish from correct labels).

###  A.2 TweetNLP-M

TweetNLP-M(ajority) directly uses the majority class labels collected by Hovy
et al. (2014) on the Crowdflower platform, which have a 79.54% agreement with
the high-quality expert gold labels collected by Gimpel et al. (2010). Per the
Hovy et al. (2014) protocol, in the rare case of ties, the tie is broken in
favor of the label that matches the gold label, if applicable. Otherwise, a
label is selected at random. The “-M” suffix distinguishes the Hovy et al.
(2014) labels from the gold labels.

###  A.3 SNLI-5

The Stanford Natural Language Inference dataset (SNLI) annotations do not
include a worker identifier, meaning each item is attached to five
crowdsourced labels, but there is no indication of which labels came from the
same annotator across the dataset. As a result, we cannot apply the dissenting
worker noising method.

SNLI-5 has exactly 5% of its data noised in each split. Of the label errors,
80% (i.e. 4% of each split) are assigned using a method that represents
systematic errors, to simulate of dissenting worker method: We use the
minority label when there is a 3-2 split between the five labels. The
remaining 20% (i.e. 1% of each split) are assigned using the dissenting label
method, as in TweetNLP-5.

$\displaystyle{0}$$\displaystyle{1}$$\displaystyle{2}$$\displaystyle{3}$$\displaystyle{4}$$\displaystyle{5}$$\displaystyle{6}$Losses
of Noised Test
Items$\displaystyle{0.0}$$\displaystyle{0.5}$$\displaystyle{1.0}$$\displaystyle{1.5}$DensityUniform
NoiseClass-Based NoiseMalicious WorkerDissenting LabelCrowd MajorityClean Data
Points Figure 8: Distributions of losses of label errors on SNLI at 5%
noising, which demonstrates similar performance characteristics to TweetNLP,
as shown in Fig. 4.
$\displaystyle{0}$$\displaystyle{2}$$\displaystyle{4}$$\displaystyle{6}$$\displaystyle{8}$Losses
of All Test
Items$\displaystyle{0.00}$$\displaystyle{0.02}$$\displaystyle{0.04}$$\displaystyle{0.06}$$\displaystyle{0.08}$$\displaystyle{0.10}$DensityUniform
NoiseClass-Based NoiseDissenting LabelDissenting WorkerCrowd Majority Figure
9: Combined distributions of losses of both noisy and clean data points, for
TweetNLP with 5% noising.

##  Appendix B Loss Distributions

Section 4 examines dataset noisings primarily in terms of loss distributions
on noised labels. To provide additional context, Fig. 8 provides an equivalent
view for SNLI, and Fig. 9 shows combined distributions of both clean and noisy
data points on TweetNLP.

Table 5 reports the Wasserstein distances (or earth mover’s distances)
measured between the loss distributions of noisy and clean data points for
models trained on TweetNLP and IMDB, as described in Section 7. Human-
originated label noise more closely resembles both clean data points and real
label noise as its hypothesized realism increases.

Noising Method | TweetNLP | IMDB
---|---|---
Uniform Noise | 5.62 | 5.04
Class-Based Noise | 5.23 | 4.91
Dissenting Label | 4.02 | -
Dissenting Worker | 3.44 | -
Crowd Majority | 2.33 | -
Real Label Errors | - | 2.67
Table 5: Wasserstein distances between loss distributions of noisy and clean
data points: Human-originated noising exhibits comparable levels of erroneous
learning to organic label errors.

##  Appendix C Mechanical Turk Protocol

| IMDB | Amazon
---|---|---
Original Protocol | 0.1314 | 0.0141
New Protocol | 0.4643 | 0.5561
Table 6: A comparison of inter-annotator agreement between the original and
new MTurk protocol results using Fleiss’ $\kappa$. A score of 1.0 represents
perfect agreement between workers, and 0.0 represents guessing at random.
Annotations from the original protocol are substantially closer to random
chance.

###  C.1 Change Specifications

We use Amazon Mechanical Turk to validate real label errors from IMDB Maas et
al. (2011) and Amazon Reviews McAuley et al. (2015). We begin with the
Northcutt et al. (2021a) protocol, and add four additional conditions, so as
to mitigate annotator fraud.

First, we pre-qualify workers by requiring them to correctly answer a
qualification test of four unambiguous questions Hovy et al. (2014); Agley et
al. (2021).

Second, after the initial qualification, we continue to monitor worker quality
by introducing sentinel questions with known answers into the workers’ regular
tasks. We periodically remove workers who fail the tasks.

Third, we set filter criteria to limit workers to the following Anglosphere
countries: United States, Canada, United Kingdom, Ireland, Australia, and New
Zealand Moss and Litman (2018), to improve the chances of finding annotators
with sufficient cultural context to correctly interpret review text.555Despite
these precautions, we recognize that every precaution is subject to fraud,
e.g., location is subject to VPN and bot attacks. Dennis et al. (2020); Mellis
and Bickel (2020); Kennedy et al. (2020) Our filter criteria include the
standard recommendations of requiring a $\geq$ 99% positive task approval rate
with $\geq$ 500 tasks approved.

Finally, we set a baseline target rate of US$10 per hour, calculated using
word counts and average reading speed (primarily for ethical reasons; the
effect of compensation and annotation quality is an area of active research;
Saravanos et al., 2021).

The new protocol’s labels are produced using a final set of approximately 70
workers. Workers averaged at least 12 seconds on each task; half the time
needed to read prompts at an average reading speed. The average time spent by
a worker in the Northcutt et al. (2021a) protocol was 5 seconds.666The
reported time is an upper bound on the average time a worker spends on a task.

###  C.2 Protocol Validation

We hypothesize that the Non-Agreements in the original protocol represent not
only ambiguous data points, but also noise in the original protocol resulting
from low quality work. Tables 2 and 6 show that the new protocol improves the
level of agreement between workers. As such, we confirm that the increased
agreement between workers in the new protocol results from higher quality
labels.

Following the Northcutt et al. (2021a) protocol for expert review, we
additionally select a total of 50 items from each of IMDB and Amazon for
expert review. The experts are blinded to both the original labels and MTurk
results and asked to label each item from scratch. They then reconciled
results and came to a consensus for each item. The results are compared at the
aggregate level of “Correctable,” “Non-Agreement,” and “Non-Error,” as opposed
to the individual sentiment level (Positive, Negative, Neutral, or Off-Topic).
The expert agreement with one another was 79%, so in 21% of the items, the
expert label was considered to be Non-Agreement and matched the MTurk workers
only if the workers also produced Non-Agreement. Table 7 provides the result
of this assessment.

For the original protocol, 52% of the items agreed with expert annotators, 31%
of the items were incorrectly labeled as Non-Agreement, 12% of the items were
incorrectly labeled as Correctables, and 5% of the items were incorrectly
labeled as Non-Errors. 8% of items were disagreements between experts and
crowd workers where neither side had a Non-Agreement. In other words, 8% of
all items were disagreements between Correctable and Non-Error.

For the new protocol, 72% of the items agreed with expert annotators, 4% of
the items were incorrectly labeled as Non-Agreement, 7% of the items were
incorrectly labeled as Correctable, and 17% were incorrectly labeled as Non-
Errors. 5% of items were disagreements between experts and crowd workers where
neither side had a Non-Agreement.

| IMDB | Amazon | Total
---|---|---|---
Original Correct | 33 | 19 | 52
New Correct | 41 | 31 | 72
Both Correct | 28 | 14 | 42
Table 7: A comparison of original and new MTurk protocol results against 100 expert-labeled data points. Dataset |  Num. Errors Hypothesized | Correctable | Non-Agreement | Non-Error
---|---|---|---|---
CL | FML | FME | CL | FML | FME | CL | FML | FME
IMDB | 1310 | 183 | 323 | 328 | 358 | 573 | 581 | 769 | 414 | 401
Amazon | 1000 | 357 | 508 | 517 | 148 | 131 | 143 | 495 | 361 | 340
TweetNLP-M | 250 | 121 | 158 | 165 | - | - | - | 129 | 92 | 85
Table 8: The number of each type of error accurately identified for each dataset by each noise detection method, keeping the number of errors hypothesized fixed for ease of comparison. (TweetNLP is expert reviewed and by construction does not have any Non-Agreement types.) Dataset |  Num. Errors Hypothesized | Correctable | Non-Agreement | Non-Error |  Jaccard Similarity
---|---|---|---|---|---
FME | FME+CL | FME | FME+CL | FME | FME+CL
IMDB | 316 | 168 | 168 | 108 | 108 | 40 | 40 | 0.99
Amazon | 381 | 226 | 204 | 65 | 56 | 90 | 121 | 0.60
TweetNLP-M | 129 | 93 | 98 | - | - | 36 | 31 | 0.59
Table 9: Examining the performance of overlaying Confident Learning on FME,
comparing the number of errors hypothesized by FME+CL. We also report the
Jaccard similarity between the two models.

##  Appendix D Overall LLM Performance Experiments

Due to the high costs associated with expert and crowdsourced validation, we
use TweetNLP-5 as a development dataset for model selection.

We selected the following models for exploration: XLNet (`base`, `large`),
RoBERTa (`base`, `large`), BERT (`small`, `base`, `large`), DeBERTa (V3:
`xsmall`, `small`, `base`, `large`, and V2: `xlarge`, `xxlarge`), GPT
(assorted). We performed 25 hyperparameter sweeps with each model, selecting
the top three runs for further analysis. In order to avoid model family-level
bias in the choice of hyperparameters, we set a broad shared range for three
hyperparameters: learning rate varying from $10^{-6}$ to $10^{-3}$, the number
of epochs from 2 to 8, and the batch size between 8, 16, 64, and 128. Training
time and the final hyperparameters varied based on the model.

We ultimately selected `DeBERTA-v3-base` as a compromise between performance
and training speed. We used Google Cloud Platform for training infrastructure.
Experiments were run using NVIDIA A100 GPUs, and runtime per training run was
approximately 20 minutes for IMDB, Recon, and SNLI, 3 minutes for TweetNLP,
and 4 hours for Amazon, when configured with a 2.5 million data point training
split.

$\displaystyle{10^{8}}$$\displaystyle{10^{9}}$Model Size (#
Parameters)$\displaystyle{0.5}$$\displaystyle{0.6}$$\displaystyle{0.7}$Error
Detection F1BERTDeBERTaGPTRoBERTa Figure 10: Label noise detection performance
by model size and family, evaluated on TweetNLP-5. GPT-based models exhibit
similar scaling trends, despite intrinsic disadvantages on classification
tasks (due to pure autoregressive pre-training).

##  Appendix E Main Experiment

###  E.1 Metrics

We calculate the Area Under the Precsion-Recall Curve (AUPR) using the
trapezoidal rule, given individual measurements of precision and recall at
every possible threshold.

We report the Truncated AUPR on IMDB and Amazon. Because IMDB and Amazon are
too expensive to fully crowd verify, we cannot calculate precision and recall
at the 25,000th item for each method, for each dataset, as it would require
every data point to be relabeled on MTurk. Instead, we use the CL framework of
predicting a fixed number of items. For example, for IMDB, CL hypothesizes
1,310 out of the 25,000 items to be label errors. We can calculate the
precision and recall for every threshold, up to the number hypothesized by
Confident Learning. We can calculate the precision and recall of the 1st, 2nd,
3rd, …, and 1,310th items.

We know the exact recall for all synthetic datasets. For IMDB and Amazon, we
use the estimate that 5% of the data is erroneous, which is consistent with
common understanding of the prevalence of label errors Redman (1998); Müller
and Markert (2019); Northcutt et al. (2021b); Kreutzer et al. (2022).

All results reported on synthetic datasets reflect the average of individual
scores from the three top-performing models from 25 hyperparameter sweeps.
However, for cost-efficiency, results which require crowdsourced evaluation
(such as IMDB and Amazon) are based on one run selected at random from a top
three.

###  E.2 Confident Learning

Northcutt et al. (2021b) reports results using raw counts, not the accuracy,
precision, recall, or any other metric. For ease of comparability, Table 8
reports the number of correctable, non-agreement, and non-error items
identified by each method on each dataset. CL hypothesizes a fixed number of
items, which is reported in the last column, and we assess a matching number
of items from each method.

When hypothesizing a fixed number of items, the foundation model approaches
far outperform CL baselines. On IMDB, FME correctly identifies 909 label
errors, a 28% absolute improvement in accuracy. On Amazon, the FME approach
correctly identifies 660 label errors, compared to the 505 identified by CL, a
15.5% absolute improvement.

Applying CL to FME results in a different model that hypothesizes a different
number of items (fewer, in all cases). Table 9 shows the raw counts of
correctable, non-agreement, and non-error items when each of our models
hypothesizes items at this reduced threshold.

Method | Task Accuracy | FM Error Detection Performance | Effects of CL Overlay
---|---|---|---
Noisy | Clean | Precision | Recall | F1 | Precision | Recall | F1
Averaged | $0.88\pm 0.03$ | $0.91\pm 0.03$ | $0.50\pm 0.11$ | $0.65\pm 0.03$ | $0.56\pm 0.08$ | $0.51\pm 0.11$ | $0.67\pm 0.03$ | $0.57\pm 0.07$
Ensembled | $0.89\pm 0.02$ | $0.92\pm 0.03$ | $0.56\pm 0.12$ | $0.62\pm 0.03$ | $0.58\pm 0.08$ | $0.58\pm 0.11$ | $0.65\pm 0.03$ | $0.61\pm 0.07$
Difference | $+1.14\%$ | $+1.24\%$ | $+12.52\%$ | $-4.31\%$ | $+4.66\%$ | $+13.89\%$ | $-2.98\%$ | $+6.03\%$
Table 10: Ensembling confers gains in error detection performance
disproportionate to gains in underlying task performance, across a broad range
of models and hyperparameters (on TweetNLP-5, results from top three models
per sweep, as measured at the fixed threshold set by CL).

Overlaying CL on foundation model loss appears to have little marginal
utility. Table 9 also shows a high Jaccard similarity across all datasets,
suggesting that applying CL on top of an FM changes little about the items
hypothesized. On many datasets, FME and FME+CL perform almost identically in
the number of items correctly hypothesized, slightly harming performance on
Amazon Reviews, and slightly improving it on TweetNLP-5 (Table 10). FME+CL
decreases the total number of hypothesized items compared to FME because of
the threshold set by CL. We compare the FME and FME+CL approaches at the
reduced number of hypothesized items in order to assess the impact of CL in
the presence of pre-training.

Not only is aggregate performance nearly identical, we see in Figs. 1 and 6
that FME and FME+CL perform similarly for the entire range of items
hypothesized along the Precision-Recall curve. The primary difference is that
FME can continue hypothesizing items even past FME+CL’s threshold.

###  E.3 Ensembling

Results from Tables 3 and 10 show that ensembling (FME) improves error
detection performance over using a single model (FML) in almost every scenario
tested, at a rate several times higher than gains to underlying task
performance.

We also observe a phenomenon of disproportionately high variance in model
error detection performance: Table 10 quantifies the standard deviation of the
former at three times the standard deviation of performance on the underlying
task, and Fig. 2 shows this to be the case even when comparing models with a
fixed loss. This finding persisted even when holding all hyperparameters and
data constant, with only the random seed being changed.

We hypothesize that label noise in training data induces models to learn
spurious correlations, which cause models to make errors in a structured
manner Watson et al. (2022); Jiang et al. (2022); this results in greater
levels of model disagreement, with minimal impact on top-line performance.
Ensembling may be disproportionately effective because it serves an added
function of reducing variance caused by these low-quality features.

###  E.4 TAPT

We perform Task-Assisted Pretraining (TAPT; Gururangan et al., 2020) using the
original hyperparameters everywhere except for the optimizer, in which we use
AdamW instead of Adam for DeBERTa. We run TAPT on the all splits of the
corresponding data for all datasets except Amazon Reviews, where because of
its size, we use TAPT on only 50,000 data points, or 0.5% of the full dataset.
After running TAPT, we then run 25 fine-tune sweeps.