# Machine learning model to project the impact of Ukraine crisis

Javad T. Firouzjaee  Department of Physics, K. N. Toosi University of
Technology, P. O. Box 15875-4416, Tehran, Iran  School of Physics, Institute
for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531, Tehran, Iran
<EMAIL_ADDRESS>Pouriya Khaliliyan  Department of Physics, K. N. Toosi
University of Technology, P. O. Box 15875-4416, Tehran, Iran  Qorpi AI
Workgroup, P. O. Box 15875-4416, Tehran, Iran<EMAIL_ADDRESS>
###### Abstract

Russia’s attack on Ukraine on Thursday 24 February 2022 hitched financial
markets and the increased geopolitical crisis. In this paper, we select some
main economic indexes, such as Gold, Oil (WTI), NDAQ, and known currency which
are involved in this crisis and try to find the quantitative effect of this
war on them. To quantify the war effect, we use the correlation feature and
the relationships between these economic indices, create datasets, and compare
the results of forecasts with real data. To study war effects, we use Machine
Learning Linear Regression. We carry on empirical experiments and perform on
these economic indices datasets to evaluate and predict this war tolls and its
effects on main economics indexes.

##  I Introduction

It is known that Russia’s economy is a mixed economy, with big natural
resources, especially oil and natural gas. Russia had 11th rank in nominal GDP
in 2021 and is the fifth-largest economy in Europe. The key feature of Russia
is vast geography which is important in its economic activity, and some
sources estimate that the nation contains over $30\%$ of the world’s natural
resources ru-natural . Having huge energy resources, Russia has the largest
natural gas reserves in the world, the second rank on largest coal reserves,
the eighth, oil reserves. Russia is the main natural gas exporter, especially
to Europe regions, the second-largest natural gas producer after the United
States.

In contrast, Ukraine had number 56 in the ranking of GDP of the 196 countries
in 2020. Ukraine has experienced critical political, security, and economic
situations since 2013. The World Bank reported that Ukraine’s economic growth
rate was $2.3\%$ in 2016, thus this was ending the recession uk-gdp . In spite
of this progress, the International Monetary Fund reported in 2018, that
Ukraine had the lowest GDP per capita of all the countries in Europe. In Fig.
(1) you can compare the GDP per capita for Russia and Ukraine in the last
decade.

Figure 1: In this picture, we compare the GDP per capita for Russia and
Ukraine in the last decade.

To study the Ukraine war economic side-effects, exploring some main economic
data indexes and analyzing them can lead us to have better quantitative
interpretation. Nowadays, it became common to use the Machine learning and
Deep Learning approach to analyze economic events. Machine learning refers to
the study of algorithms and statistical models which subdivision of artificial
intelligence that gives computers the ability to learn from data and perform
tasks without being explicitly given step-by-step instructions, only having
the data it uses to train. Applying different approaches in artificial
intelligence, there are different ways to approach stock price prediction;
some of them include technical Analysis, fundamental Analysis, time series
analysis. For time series analysis, the Recurrent Neural Network known as one
of the effective ways refers to attack the sequential problem or temporal
aspects of data as time series which is a powerful tool in stock price
prediction Cen ; Pouria ; Gupta . Here, our approach is to use the linear
regression method in Machine Learning to study the economic effect of the
Ukraine crisis.

The plan of the paper is as follows: Section II is dedicated to an analysis of
the correlation between different economic indexes due to the Ukraine war. In
Section III, we apply the machine learning approach to predict some main
economic indexes involved in this war. The paper ends in Section VI with a
brief summary.

##  II Involved economic indexes and their correlation

In statistics, the dependence of any statistical causal or non-causal ratio
between two accidents or data is described by the correlation index. This
correlation coefficient value is located between -1 and 1 which negative value
or inverse correlation (anti-correlation) expresses a relationship that one
value increases as the other decreases. The correlation coefficient is equal
to zero if there is no relationship between the two features. In this paper,
we select some main economics indexes, such as Gold, Oil (WTI), RUBCNY
(RUB/CNY or RUBCNY is the abbreviation for the Russia Ruble and Chinese Yuan
pair. It shows how much the RUB (base currency) is worth as measured against
the CNY), UAHCNY, and the US dollar index to find out the relationship between
features before the Ukraine crisis and after it. Fig. (2) and Fig. (3) use
Alpha Vantage API data to analyze these economic indexes.

Figure 2: Correlation between USD, WTI, Gold, RUBCNY, and UAHCNY before start
Russia and Ukraine crisis (from 2022/01/01 to 2022/02/01).  Figure 3:
Correlation between USD, WTI, Gold, RUBCNY, and UAHCNY after start Russia and
Ukraine crisis (from 2022/02/01 to 2022/03/01).

###  II.1 Data and Features

We use following features to predict each stock indexes as following table:

Table 1: Experiment Result For Royal Dutch Shell Shares | feature1 | feature2 | feature3 | feature4 | feature5 | feature6 | feature7 | Predict feature
---|---|---|---|---|---|---|---|---
US Dollar index | Open | High | Low | RUBCNY | UAHCNY | WTI | Gold | Close
NDAQ | Open | High | Low | Gold | US Dollar | WTI | - | Close
WTI | Open | High | Low | RUBCNY | UAHCNY | US Dollar | Gold | Close
Gold | Open | High | Low | RUBCNY | UAHCNY | WTI | US Dollar | Close

Our training data is from 2019/05/21 to 2021/06/14, and data from 2021/06/15
to 2021/12/31 is used for testing which extracted from Alpha Vantage API.
We use data from 2022/01/03 to 2022/01/31 to predict economics indexes from
2022/02/01 to 2022-03-01 in the case of no war crisis.

##  III War effect estimation from machine learning approach

###  III.1 Machine Learning

Machine learning is one of the subdivisions of artificial intelligence, in
which it examines how the machine learning process is based on mathematical
indicators and is known as the correction of implicit calculations. Tom
Mitchel defined machine learning michel :
”A computer program is said to learn from experience E with respect to some
class of tasks T and performance measure P, if its performance at tasks in T,
as measured by P, improves with experience E.”

###  III.2 Supervised Learning

Machine Learning can be classified to Supervised learning, Semi-supervised
learning, Unsupervised learning, and Reinforcement learning. In supervised
learning, we give the machine the correct answer for each input, to learn and
model based on input and output data which enable us to make our own
predictions.

In data science, regression is a statistical process for estimating the
relationships between features. This method includes numerous techniques for
modeling and analyzing specific variables, which focus on the relationship
between the dependent variable and one or more independent variables.
Regression is commonly used for prediction. Furthermore, people use Regression
analysis to identify the relationship between the independent and dependent
variables and the shape of these relationships. In certain circumstances, this
analysis can be used to infer excellent relationships between independent and
dependent variables.

###  III.3 Linear Regression

Linear regression is a kind of supervised learning algorithm which measures
the effect of an independent variable on a dependent variable and examines the
correlations between them.
The regression equation which is used to construct a probabilistic model
hypothesis can be defined using coefficients $w$ as a linear coefficient and
$x$ as an independent variable as follows:

$h_{i}=\sum_{0}^{N}w_{i}x_{i}+\epsilon,$ (1)

where the $\epsilon$ is the error value. The predicted values for the US
dollar, WTI, and Gold indexes were depicted in Fig. (4), Fig. (5) and Fig. (6)
in the case of no Ukraine conflict (We designed the machine experience based
on task which there is no war).

Figure 4: In this graph, we predict the US dollar index in the case of no
crisis and compare it with real happened data.  Figure 5: In this graph, we
predict the WTI index in the case of no crisis and compare it with real
happened data.  Figure 6: In this graph, we predict the Gold index in the case
of no crisis and compare it with real happened data.

###  III.4 NDAQ

NDAQ is an American financial holding company that owns a stock market network
and several US-based stock and options exchanges and operates three stock
exchanges in the US. NDAQ is headquartered in New York. In Fig. (7), we
predict the NDAQ index in the case that no crisis and compare it with real
happened data.

Figure 7: In this graph, we predict the NDAQ index in the case that no crisis
and compare it with real happened data.

###  III.5 Evaluation Measures

There is some evaluation measures that people quantify the loss of the model
by Mean Square Error (MSE), Root means square error (RMSE), Mean Absolute
Error (MAE), and Mean Absolute Percentage Error (MAPE). MSE is defined as
below:

$MSE={{\sum\nolimits_{1}^{n}{{{(true-Prediction)}^{2}}}}\over n}.$

The average root of the squares of the errors quantified by RMSE which is
defined as:

$RMSE=\sqrt{{{\sum\nolimits_{1}^{n}{{{(true-Prediction)}^{2}}}}\over n}}.$

We measure the average of absolute error and use MAE to calculate errors
between pair observations which is defined as:

$MAE={{\sum\nolimits_{1}^{n}{|true-Prediction|}}\over n}.$

In last, to measure the size of the error in percentage terms people use MAPE
which is calculated for the mean of the absolute percentage errors of
prediction. It is defined as the following formula:

$MAPE={{{{\sum\nolimits_{1}^{n}{|true-Prediction|}}\over{true}}}\over n}\times
100.$ (2)

Now, one can apply these evaluation measures as error metrics in our
prediction as bellow table.

Table 2: Our Machine Learning model error measurement.  | MSE | RMSE | MAE | MAPE
---|---|---|---|---
US Dollar index | 1.0711 | 1.03494 | 0.04631 | 0.000723
NDAQ | 0.40524 | 0.03114 | 0.00023 | 0.63658
WTI | 0.39943 | 0.632008 | 0.48482 | 0.1454
Gold | 0.016860 | 0.12984 | 0.007183 | 0.00033

##  IV Discussion and Conclusion

Although Russia and Ukraine are responsible for up to $30\%$ of the world’s
wheat exports and $80\%$ of sunflower seed production in the world, according
to Capital Economics, this crisis can spark higher global inflation but it is
not probable to cause a recession. Russia has more than doubled its interest
rate to $20\%$ in a bid to stop a collapse in the value of its currency which
had about $30\%$ after one week from the war started. Although our prediction
showed that we could have the US dollar index growth in no conflict case but
analysts estimated each $\$20$ per barrel increase in oil (one week after
starting Russia’s attack) would raise core inflation excluding food and energy
by 0.035 percentage points and headline inflation by 0.2 percentage points but
exacts just a 0.1 percentage point hit to United States GDP cnbc . Our
correlation analysis shows an increase in the US dollar with RUBCNY which
shows non-significant US involvement in this crisis.

European markets break down at the open amid fears over financial stability,
but later decreased losses with London’s FTSE 100 closing down $0.4\%$, Paris
fell $1.3\%$, and Frankfurt $0.7\%$ bbc .

In contrast, analysts say that China could have profit from the diversion of
Russian exports if sanctions are imposed on Moscow in the long-term Aljazeera
. Since during the Ukraine crisis there was no significant change in Chinese
currency, we took it as an independent index and normalize the Russia and
Ukraine currency to it as RUBCNY and AUHCNY. We can summarise some results as
bellow items:

  * •

Before the crisis there was a weak correlation between UAHCNY and the gold
index, but after the war, this correlation changed to anti-correlation and its
value increased.

  * •

Similar to the Gold-UAHCNY case, before the crisis there was a weak
correlation between UAHCNY and WTI index, but after the war, this correlation
changed to anti-correlation and its value increased.

  * •

Before the crisis there was a significant anti-correlation between RUBCNY and
the gold index, but after the war, this value did not have a significant
change.

  * •

Before the crisis there was a significant anti-correlation between RUBCNY and
WTI index, but after the war, this value becomes greater.

  * •

Our Machine Learning model predicted that in the case of no crisis, US dollar
index and NDAQ will increase and WTI and Gold will get a small decrease.
Whereas, the Ukraine crisis causes that the WTI and Gold indexes increase and
the US dollar index and NDAQ decrease in their index price.

## References

  * (1) Kevin, M. Korabik. ”Russia’s Natural Resources and their Economic Effects.” Penn State College of Earth and Mineral Sciences (1997).
  * (2) ”Ukraine’s Economy is Recovering Modestly Despite Significant Headwinds”, World Bank (4 April 2017).
  * (3) Varun Gupta, & Ankit Pandey. (2018). Crude Oil Price Prediction Using LSTM Networks. International Journal of Information, Control and Computer Sciences, 11.0(3).
  * (4) Cen, Zhongpei, and Jun Wang. ”Crude oil price prediction model with long short term memory deep learning based on prior knowledge data transfer.” Energy 169 (2019): 160-171.
  * (5) ”Ukraine crisis: Asia braces for economic fallout”, Aljazeera, (22 February 2022).
  * (6) Firouzjaee, Javad T., and Pouriya Khaliliyan. ”LSTM Architecture for Oil Stocks Prices Prediction.” arXiv preprint arXiv:2201.00350 (2022).
  * (7) Michalski, Ryszard Stanislaw, Jaime Guillermo Carbonell, and Tom M. Mitchell, eds. Machine learning: An artificial intelligence approach. Springer Science & Business Media, 2013.
  * (8) ”Ukraine conflict: Russia doubles interest rate after rouble slumps”, BBC, (1 March 2022).
  * (9) Cox, Jeff, Inflation will go higher, but Ukraine conflict likely won’t halt economic growth in the U.S” CNBC, (25 February 2022).


mature | 1.45% | 1.06% | 0.59% | 0.48% | 1.07% | 0.14
teen | 0.26% | 1.07% | 0.72% | 0.38% | 1.07% | 0.05
elderly | 0.37% | 1.04% | 0.75% | 0.42% | 1.04% | 0.15
Table 22: Top 10 HolisticBias descriptors in the age axis, sorted by weighted
mean. Standard deviation in the last column. Many descriptors referring to
advanced age (“old”, “senior”, “older”) have disproportionately high
representation, but these words refer to much more than just people,
obfuscating direct comparison.

We present the top 10 HolisticBias descriptors found in the training corpora
discussed in Section 3.3, subselecting for the race/ethnicity (Table 20),
religion (Table 21), and age (Table 22) axes. Tables are sorted by weighted
mean, weighted by the number of documents in each dataset.

####  C.3.2 Relation of the term frequencies with model biases

We are interested in how the imbalance of demographic representations in
documents may contribute to biases. Using model bias measurements from the
HolisticBias paper (Smith et al., 2022), we compare these biases with the
standard deviations of the frequencies of the descriptors in each HolisticBias
axis (Table 23). We find that model biases do not necessarily correspond to a
larger standard deviation in the descriptor frequencies. It is important to
keep in mind, however, that the corpora that we measure HolisticBias
descriptor frequencies in do not align with those used to train these models,
meaning that a direct comparison is not possible in this case.

| DialoGPT | BlenderBot 2.0 3B | Std of frequencies (top 10) | Std of frequencies (all) | Mean
---|---|---|---|---|---
Gender and sex | 2.61 | 7.47 | 0.0122 | 0.0055 | 0.14%
Race and ethnicity | 3.09 | 5.78 | 0.0309 | 0.0214 | 0.94%
Religion | 2.20 | 5.40 | 0.0109 | 0.0073 | 0.34%
Age | 2.31 | 4.28 | 0.0474 | 0.0254 | 0.82%
Table 23: Model bias vs. frequency on four demographic axes. First two
columns: levels of model bias from the HolisticBias paper of Smith et al.
(2022), from models without bias tuning. Next two columns: standard deviations
of frequencies of HolisticBias descriptors in several popular training
datasets, as measured in this work, considering only the top 10 descriptors
per demographic axis by weighted mean (top 10), and considering all
descriptors in the axis (all). The higher the standard deviation, the more
variation there is for terms within each axis. We do not find a strong
relation between model bias and the standard deviations of these frequencies
for these four axes. Last column: we calculate for each term in the
HolisticBias axis what fraction of documents it appears in, and then we
compute the average over all terms in that axis. The corpora that we measure
HolisticBias descriptor frequencies in do not align with those used to train
these models, meaning that a direct comparison is not possible in this case.

####  C.3.3 Gender pronouns

In Table 24 we show the percentage of documents mentioning any gender pronoun,
for each group of gender pronouns and each dataset. We make the following
observations:

  1. 1.

The ratio of He pronouns to She pronouns is generally greater than 1, meaning
that in many existing popular public datasets, He pronouns are still typically
over-represented.

  2. 2.

They pronouns typically have the highest level of representation in the
datasets, except for Wikipedia (en). This may reflect Wikipedia typically
referencing specific people with specific (usually binary) gender pronouns.

Some variations in these percentages across datasets are as follows:

  1. 1.

HackerNews features a very high He:She pronoun ratio of 3.78, which may
reflect gender patterns in the specific domains represented by this news
aggregation service.

  2. 2.

Web crawl datasets and Wikipedia also have relatively high He:She ratios.

Our pronoun frequency numbers show directional similarity with the related
analysis in the PaLM paper Chowdhery et al. (2022), which reports 41% of data
points containing they/them pronouns, 30% containing he/him pronouns, and 14%
containing female pronouns.

Dataset | Dataset type | Num. docs |  She pronouns |  He pronouns |  They pronouns |  He:She ratio
---|---|---|---|---|---|---
HackerNews | News | 816,171 | 7.23% | 27.33% | 59.87% | 3.7813
Common Crawl | Web crawl | 641,934,446 | 26.58% | 47.86% | 71.04% | 1.8004
OpenWebText2 | Web crawl | 16,636,626 | 23.63% | 52.53% | 65.19% | 2.2228
Wikipedia (en) | Wiki | 5,862,377 | 14.37% | 39.45% | 33.90% | 2.7462
Table 24: Percentage of documents mentioning gender pronouns. She pronouns
consist of "she", "her", "hers", "herself"; He pronouns consist of "he",
"him", "his", "himself"; and They pronouns consist of "they", "them", "their",
"theirs", "theirself", "themself", "themselves". These choices are consistent
with the PaLM paper Chowdhery et al. (2022).

####  C.3.4 Future directions

One expansion of the analysis of HolisticBias descriptors in pretraining
datasets could be to create a new version of the dataset that better clusters
descriptors together to represent specific demographic groups, perhaps with
the consultation of linguists and sociologists.

###  C.4 Bias measurements

In this section, we provide more details for our fairness analysis. In the
following tables we estimate $PrNeg(X^{b}_{s_{i}})$ for each subgroup $s_{i}$
and each benchmark dataset $b$ via bootstrapping and provide the confidence
intervals for $\max_{s_{i}\in S_{b}}{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in Table
25. Note that $\widehat{PrNeg}(X^{b}_{s_{i}})$ is the median of bootstrapping
estimation. In addition, we report the subgroups associated with
$\max_{s_{i}\in S_{b}}{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in Table 26. The
diversity of subgroups in Figure 5 across datasets illustrates that the
prompt-based datasets that we use for measuring social bias are able to
surface different types of harms. For example, the ToxiGen (v2) results in
Table 26 imply the presence of systematic bias against the Latino/Latina
subgroup in the LLMs we test. Moreover, the Regard dataset shows that all of
the LLMs perform the worst on its LGBTQ+ subgroup (i.e. “The gay person was
known for…”).

Moreover, for each prompt dataset, we select the top three subgroups with the
highest $PrNeg(.)$ given by the medians of the bootstrap sampling. The
distribution of these groups across all models and datasets is shown in Figure
5. This figure is a representation of which groups in general are most
marginalized by the LLMs studied in this work.

Figure 5: Distribution of the top three subgroups associated with the highest $\widehat{PrNeg}(X^{b}_{s_{i}})$, compiled over all benchmark datasets and models in Table 3. $PrNeg(X^{b}_{s_{i}})$ is the likelihood of negative LLM responses about a subgroup $s_{i}$, and $\widehat{PrNeg}(X^{b}_{s_{i}})$ is the median of the $PrNeg(X^{b}_{s_{i}})$ bootstrapping distribution. The subgroups are color-coded based on their demographics (red is race/ethnicity, blue is religion, orange is political, green is sexuality, pink is gender, and grey is other). Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | [0.9, 11.1] | [16.8, 24.2] | [23.4, 25.7] | [31.4, 38.1] | [50.0, 100.0]
GPT2-L (774M) | [0.9, 11.1] | [15.2, 22.4] | [21.9, 24.2] | [31.0, 37.7] | [50.0, 100.0]
GPT2-M (355M) | [1.2, 13.4] | [15.2, 22.4] | [0.0, 46.7] | [32.1, 38.9] | [40.0, 100.0]
GPT2-S (124M) | [0.9, 10.6] | [12.8, 19.5] | [16.5, 18.5] | [48.2, 55.3] | [40.0, 100.0]
OPT-175B | [4.1, 12.9] | [31.5, 40.2] | [38.0, 39.4] | [46.1, 53.1] | [37.5, 100.0]
OPT-30B | [2.4, 15.9] | [28.5, 36.9] | [38.1, 39.6] | [45.0, 52.0] | [50.0, 100.0]
OPT-1.3B | [3.7, 16.7] | [28.6, 37.4] | [37.1, 38.6] | [42.7, 49.7] | [30.0, 90.0]
BB3-175B | [2.9, 11.7] | [27.8, 36.2] | [36.2, 37.7] | [43.8, 51.0] | [60.0, 100.0]
BB3-30B | [0.0, 21.4] | [25.6, 34.0] | [33.3, 34.7] | [41.8, 48.8] | [70.0, 100.0]
BB3-3B | [2.9, 11.7] | [16.7, 24.1] | [23.5, 24.5] | [43.8, 51.0] | [40.0, 100.0]
BLOOM (7.1B) | [1.7, 13.0] | [14.3, 21.4] | [23.7, 25.0] | [39.8, 46.7] | [56.2, 68.1]
BLOOM (3.0B) | [0.0, 7.3] | [14.1, 21.0] | [22.7, 24.0] | [28.4, 34.9] | [30.0, 90.0]
BLOOM (1.7B) | [0.0, 14.3] | [14.1, 21.0] | [16.5, 26.1] | [32.0, 38.9] | [40.0, 100.0]
BLOOM (1.1B) | [0.0, 7.3] | [15.3, 22.4] | [16.8, 26.4] | [29.0, 35.5] | [40.0, 100.0]
BLOOM (559M) | [0.0, 10.2] | [15.2, 22.2] | [19.6, 20.8] | [35.8, 42.7] | [50.0, 100.0]
LLaMa (7B)* | [1.8, 8.8] | [23.2, 31.3] | [31.3, 32.7] | [26.0, 32.6] | [50.0, 100.0]
LLaMa (7B)${\dagger}$ | [1.8, 8.8] | [22.6, 30.6] | [26.4, 37.1] | [28.7, 35.2] | [30.0, 90.0]
Table 25: The confidence intervals for $arg\max_{s_{i}\in S_{b}}{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in each benchmark dataset, where $\widehat{PrNeg}(X^{b}_{s_{i}})$ is the median of bootstrapping estimation. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | islam | latino | jewish | The gay person |  an addict
GPT2-L (774M) | islam | mexican | jewish | The gay person |  a felon
GPT2-M (355M) | right-wing | mexican | other sexual orientation | The gay person |  a drug addict
GPT2-S (124M) | left-wing | mexican | jewish | The gay person |  a drug addict
OPT-175B | christianity | latino | muslim | The gay person |  an asylum seeker
OPT-30B | right-wing | mexican | muslim | The gay person |  a drug addict
OPT-1.3B | islam | mexican | muslim | The gay person |  a felon
BB3-175B | christianity | latino | muslim | The gay person |  a Jew
BB3-30B | atheism | mexican | muslim | The gay person |  a drug addict
BB3-3B | christianity | mental dis | white | The gay person |  a Satanist
BLOOM (7.1B) | fascism | mexican | muslim | The gay person |  with a criminal background
BLOOM (3.0B) | right-wing | latino | muslim | The gay person |  a drug addict
BLOOM (1.7B) | atheism | latino | other disability | The gay person |  a felon
BLOOM (1.1B) | right-wing | latino | other disability | The gay person |  a drug addict
BLOOM (559M) | populism | latino | muslim | The gay person |  an addict
LLaMa (7B)* | christianity | mexican | muslim | The gay person |  an asylum seeker
LLaMa (7B)${\dagger}$ | christianity | latino | other disability | The gay person |  an Ashkenazi Jew
Table 26: The most marginalized group in each prompt dataset. We selected
these groups based on the median value of bootstrapped negative
regard/toxicity rate.

Moreover, we leverage the demographic axes introduced in the HolisticBias
dataset and perform bias analysis per demographic axis. We report the
$BiasScore$ and confidence intervals of $arg\max_{s_{i}\in
S_{b}}{\widehat{PrNeg}(X^{b}_{s_{i}})}$, and the associated subgroups for Body
type (Table 29, 27, 28), None (Table 32, 30, 31), Culture (Table 35, 33, 34),
Religion (Table 38, 36, 37), Race/Ethnicity (Table 41, 39, 40),
Characteristics (Table 44, 42, 43), Ability (Table 47, 45, 46), Sexual
orientation (Table 50, 48, 49), Gender (Table 53, 51, 52), Political
ideologies (Table 56, 54, 55), Age (Table 59, 57, 58), Socioeconomic class
(Table 62, 60, 61), and Nationality (Table 65, 63, 64).

Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | [44.69, 57.19]
GPT2-L (774M) | - | - | - | - | [43.44, 55.94]
GPT2-M (355M) | - | - | - | - | [41.56, 54.06]
GPT2-S (124M) | - | - | - | - | [38.44, 50.94]
OPT-175B | - | - | - | - | [41.80, 55.86]
OPT-30B | - | - | - | - | [41.88, 54.37]
OPT-1.3B | - | - | - | - | [36.56, 49.06]
BB3-175B | - | - | - | - | [46.88, 59.38]
BB3-30B | - | - | - | - | [46.25, 58.44]
BB3-3B | - | - | - | - | [36.56, 49.06]
BLOOM (7.1B) | - | - | - | - | [41.25, 53.75]
BLOOM (3.0B) | - | - | - | - | [42.81, 55.31]
BLOOM (1.7B) | - | - | - | - | [41.88, 54.06]
BLOOM (1.1B) | - | - | - | - | [33.44, 45.94]
BLOOM (559M) | - | - | - | - | [35.62, 48.12]
LLaMa (7B)* | - | - | - | - | [38.12, 50.31]
LLaMa (7B)${\dagger}$ | - | - | - | - | [36.56, 48.75]
Table 27: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis body type. We only report this metric for the datasets that have subgroup labels associated with body type demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | hideous
GPT2-L (774M) | - | - | - | - | hideous
GPT2-M (355M) | - | - | - | - | hideous
GPT2-S (124M) | - | - | - | - | hideous
OPT-175B | - | - | - | - | hideous
OPT-30B | - | - | - | - | hideous
OPT-1.3B | - | - | - | - | obese
BB3-175B | - | - | - | - | acne-ridden
BB3-30B | - | - | - | - | hideous
BB3-3B | - | - | - | - | grungy
BLOOM (7.1B) | - | - | - | - | hideous
BLOOM (3.0B) | - | - | - | - | hideous
BLOOM (1.7B) | - | - | - | - | hideous
BLOOM (1.1B) | - | - | - | - | hideous
BLOOM (559M) | - | - | - | - | ugly
LLaMa (7B)* | - | - | - | - | hideous
LLaMa (7B)${\dagger}$ | - | - | - | - | hideous
Table 28: The most marginalized group in the demographic axis body type. We only report this metric for the datasets that have subgroup labels associated with body type demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | 64.47 | 64.47
GPT2-L (774M) | - | - | - | - | 59.87 | 59.87
GPT2-M (355M) | - | - | - | - | 59.87 | 59.87
GPT2-S (124M) | - | - | - | - | 52.63 | 52.63
OPT-175B | - | - | - | - | 75.00 | 75.00
OPT-30B | - | - | - | - | 75.00 | 75.00
OPT-1.3B | - | - | - | - | 76.97 | 76.97
BB3-175B | - | - | - | - | 66.45 | 66.45
BB3-30B | - | - | - | - | 74.34 | 74.34
BB3-3B | - | - | - | - | 53.95 | 53.95
BLOOM (7.1B) | - | - | - | - | 60.53 | 60.53
BLOOM (3.0B) | - | - | - | - | 53.29 | 53.29
BLOOM (1.7B) | - | - | - | - | 60.53 | 60.53
BLOOM (1.1B) | - | - | - | - | 61.84 | 61.84
BLOOM (559M) | - | - | - | - | 51.97 | 51.97
LLaMa (7B)* | - | - | - | - | 57.89 | 57.89
LLaMa (7B)${\dagger}$ | - | - | - | - | 70.39 | 70.39
Table 29: The percentage of body type subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with body type demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | [12.50, 21.88]
GPT2-L (774M) | - | - | - | - | [10.00, 18.44]
GPT2-M (355M) | - | - | - | - | [11.88, 21.25]
GPT2-S (124M) | - | - | - | - | [14.37, 24.06]
OPT-175B | - | - | - | - | [26.95, 40.23]
OPT-30B | - | - | - | - | [29.38, 41.56]
OPT-1.3B | - | - | - | - | [24.69, 35.94]
BB3-175B | - | - | - | - | [23.44, 34.69]
BB3-30B | - | - | - | - | [28.12, 40.01]
BB3-3B | - | - | - | - | [8.75, 17.19]
BLOOM (7.1B) | - | - | - | - | [12.19, 21.56]
BLOOM (3.0B) | - | - | - | - | [12.50, 21.88]
BLOOM (1.7B) | - | - | - | - | [9.38, 17.81]
BLOOM (1.1B) | - | - | - | - | [8.12, 15.94]
BLOOM (559M) | - | - | - | - | [9.06, 17.50]
LLaMa (7B)* | - | - | - | - | [8.12, 16.56]
LLaMa (7B)${\dagger}$ | - | - | - | - | [15.94, 26.25]
Table 30: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis nonce: terms in this axis are nonsensical by design (Smith et al., 2022), are not in common use in the varieties of English spoken by the authors, and are used here as a baseline. We only report this metric for the datasets that have subgroup labels associated with nonce demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | blicket
GPT2-L (774M) | - | - | - | - | fitch
GPT2-M (355M) | - | - | - | - | fitch
GPT2-S (124M) | - | - | - | - | fitch
OPT-175B | - | - | - | - | blicket
OPT-30B | - | - | - | - | fitch
OPT-1.3B | - | - | - | - | fitch
BB3-175B | - | - | - | - | fitch
BB3-30B | - | - | - | - | blicket
BB3-3B | - | - | - | - | blicket
BLOOM (7.1B) | - | - | - | - | doff
BLOOM (3.0B) | - | - | - | - | doff
BLOOM (1.7B) | - | - | - | - | tannin
BLOOM (1.1B) | - | - | - | - | fitch
BLOOM (559M) | - | - | - | - | coodle
LLaMa (7B)* | - | - | - | - | fitch
LLaMa (7B)${\dagger}$ | - | - | - | - | tannin
Table 31: The most marginalized group in the demographic axis nonce. We only report this metric for the datasets that have subgroup labels associated with nonce demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | 25.00 | 25.00
GPT2-L (774M) | - | - | - | - | 25.00 | 25.00
GPT2-M (355M) | - | - | - | - | 25.00 | 25.00
GPT2-S (124M) | - | - | - | - | 37.50 | 37.50
OPT-175B | - | - | - | - | 75.00 | 75.00
OPT-30B | - | - | - | - | 75.00 | 75.00
OPT-1.3B | - | - | - | - | 87.50 | 87.50
BB3-175B | - | - | - | - | 75.00 | 75.00
BB3-30B | - | - | - | - | 62.50 | 62.50
BB3-3B | - | - | - | - | 37.50 | 37.50
BLOOM (7.1B) | - | - | - | - | 50.00 | 50.00
BLOOM (3.0B) | - | - | - | - | 37.50 | 37.50
BLOOM (1.7B) | - | - | - | - | 25.00 | 25.00
BLOOM (1.1B) | - | - | - | - | 25.00 | 25.00
BLOOM (559M) | - | - | - | - | 37.50 | 37.50
LLaMa (7B)* | - | - | - | - | 0.00 | 0.00
LLaMa (7B)${\dagger}$ | - | - | - | - | 50.00 | 50.00
Table 32: The percentage of nonce subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with nonce demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | [36.25, 48.75]
GPT2-L (774M) | - | - | - | - | [20.00, 80.00]
GPT2-M (355M) | - | - | - | - | [40.00, 100.00]
GPT2-S (124M) | - | - | - | - | [29.75, 90.00]
OPT-175B | - | - | - | - | [37.50, 100.00]
OPT-30B | - | - | - | - | [41.25, 54.06]
OPT-1.3B | - | - | - | - | [20.00, 80.00]
BB3-175B | - | - | - | - | [20.00, 90.00]
BB3-30B | - | - | - | - | [30.00, 90.00]
BB3-3B | - | - | - | - | [10.00, 80.00]
BLOOM (7.1B) | - | - | - | - | [20.00, 80.00]
BLOOM (3.0B) | - | - | - | - | [39.69, 52.19]
BLOOM (1.7B) | - | - | - | - | [35.00, 46.88]
BLOOM (1.1B) | - | - | - | - | [35.31, 47.81]
BLOOM (559M) | - | - | - | - | [10.00, 70.00]
LLaMa (7B)* | - | - | - | - | [35.31, 47.51]
LLaMa (7B)${\dagger}$ | - | - | - | - | [20.00, 80.00]
Table 33: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis cultural. We only report this metric for the datasets that have subgroup labels associated with cultural demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | anti-vaccine
GPT2-L (774M) | - | - | - | - | a conspiracy theorist
GPT2-M (355M) | - | - | - | - | a conspiracy theorist
GPT2-S (124M) | - | - | - | - | a conspiracy theorist
OPT-175B | - | - | - | - | a conspiracy theorist
OPT-30B | - | - | - | - | anti-vax
OPT-1.3B | - | - | - | - | an ally
BB3-175B | - | - | - | - | a conspiracy theorist
BB3-30B | - | - | - | - | a conspiracy theorist
BB3-3B | - | - | - | - | a conspiracy theorist
BLOOM (7.1B) | - | - | - | - | a conspiracy theorist
BLOOM (3.0B) | - | - | - | - | anti-vax
BLOOM (1.7B) | - | - | - | - | vaccine-hesitant
BLOOM (1.1B) | - | - | - | - | anti-vax
BLOOM (559M) | - | - | - | - | a conspiracy theorist
LLaMa (7B)* | - | - | - | - | anti-vaccine
LLaMa (7B)${\dagger}$ | - | - | - | - | a bystander
Table 34: The most marginalized group in the demographic axis cultural. We only report this metric for the datasets that have subgroup labels associated with cultural demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | 78.95 | 78.95
GPT2-L (774M) | - | - | - | - | 76.32 | 76.32
GPT2-M (355M) | - | - | - | - | 73.68 | 73.68
GPT2-S (124M) | - | - | - | - | 81.58 | 81.58
OPT-175B | - | - | - | - | 81.58 | 81.58
OPT-30B | - | - | - | - | 92.11 | 92.11
OPT-1.3B | - | - | - | - | 84.21 | 84.21
BB3-175B | - | - | - | - | 81.58 | 81.58
BB3-30B | - | - | - | - | 81.58 | 81.58
BB3-3B | - | - | - | - | 71.05 | 71.05
BLOOM (7.1B) | - | - | - | - | 71.05 | 71.05
BLOOM (3.0B) | - | - | - | - | 68.42 | 68.42
BLOOM (1.7B) | - | - | - | - | 63.16 | 63.16
BLOOM (1.1B) | - | - | - | - | 76.32 | 76.32
BLOOM (559M) | - | - | - | - | 73.68 | 73.68
LLaMa (7B)* | - | - | - | - | 71.05 | 71.05
LLaMa (7B)${\dagger}$ | - | - | - | - | 78.95 | 78.95
Table 35: The percentage of cultural subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with cultural demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | [0.93, 11.11] | [6.74, 12.23] | [23.45, 25.73] | - | [30.00, 90.00]
GPT2-L (774M) | [0.93, 11.11] | [6.74, 12.23] | [21.89, 24.16] | - | [30.00, 90.00]
GPT2-M (355M) | [0.00, 14.29] | [6.56, 11.88] | [19.69, 21.83] | - | [20.00, 80.00]
GPT2-S (124M) | [1.17, 7.60] | [6.03, 11.17] | [16.51, 18.50] | - | [20.00, 90.00]
OPT-175B | [4.09, 12.87] | [13.65, 20.74] | [37.96, 39.41] | - | [37.50, 100.00]
OPT-30B | [2.78, 14.81] | [15.96, 23.58] | [38.10, 39.55] | - | [40.00, 100.00]
OPT-1.3B | [3.70, 16.67] | [12.77, 19.68] | [37.11, 38.59] | - | [20.00, 80.00]
BB3-175B | [2.92, 11.70] | [12.23, 18.97] | [36.24, 37.70] | - | [60.00, 100.00]
BB3-30B | [0.00, 21.43] | [10.63, 17.02] | [33.30, 34.74] | - | [50.00, 100.00]
BB3-3B | [2.92, 11.70] | [6.03, 11.17] | [21.61, 22.89] | - | [40.00, 100.00]
BLOOM (7.1B) | [0.00, 8.33] | [6.03, 11.17] | [23.68, 24.99] | - | [45.00, 57.50]
BLOOM (3.0B) | [0.00, 5.56] | [7.98, 14.01] | [22.69, 23.99] | - | [39.38, 51.88]
BLOOM (1.7B) | [0.00, 14.29] | [6.21, 11.70] | [20.50, 21.72] | - | [20.00, 80.00]
BLOOM (1.1B) | [0.00, 6.48] | [6.21, 11.53] | [19.15, 20.35] | - | [20.00, 80.00]
BLOOM (559M) | [0.00, 6.48] | [7.62, 13.48] | [19.56, 20.76] | - | [30.00, 90.00]
LLaMa (7B)* | [1.75, 8.77] | [7.80, 13.65] | [31.26, 32.68] | - | [10.00, 90.00]
LLaMa (7B)${\dagger}$ | [1.75, 8.77] | [6.25, 11.63] | [29.35, 30.74] | - | [30.00, 90.00]
Table 36: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis religion. We only report this metric for the datasets that have subgroup labels associated with religion demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | islam | muslim | jewish | - | a Conservative Jew
GPT2-L (774M) | islam | muslim | jewish | - | a Cheondoist
GPT2-M (355M) | atheism | muslim | jewish | - | an Evangelical
GPT2-S (124M) | christianity | muslim | jewish | - | a Satanist
OPT-175B | christianity | muslim | muslim | - | a Shia Muslim
OPT-30B | islam | muslim | muslim | - | a Roman Catholic
OPT-1.3B | islam | muslim | muslim | - | an Ashkenazi Jew
BB3-175B | christianity | muslim | muslim | - | a Jew
BB3-30B | atheism | muslim | muslim | - | a Druze
BB3-3B | christianity | muslim | muslim | - | a Satanist
BLOOM (7.1B) | islam | muslim | muslim | - | Satanist
BLOOM (3.0B) | islam | muslim | muslim | - | Satanist
BLOOM (1.7B) | atheism | muslim | muslim | - | a Satanist
BLOOM (1.1B) | islam | muslim | muslim | - | an atheist
BLOOM (559M) | islam | muslim | muslim | - | an atheist
LLaMa (7B)* | christianity | muslim | muslim | - | a Protestant
LLaMa (7B)${\dagger}$ | christianity | jewish | muslim | - | an Ashkenazi Jew
Table 37: The most marginalized group in the demographic axis religion. We only report this metric for the datasets that have subgroup labels associated with religion demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | 57.14 | 50.00 | 85.71 | - | 66.32 | 66.67
GPT2-L (774M) | 57.14 | 50.00 | 71.43 | - | 76.84 | 74.77
GPT2-M (355M) | 57.14 | 50.00 | 71.43 | - | 68.42 | 67.57
GPT2-S (124M) | 57.14 | 50.00 | 71.43 | - | 81.05 | 78.38
OPT-175B | 85.71 | 50.00 | 42.86 | - | 91.58 | 87.39
OPT-30B | 71.43 | 50.00 | 71.43 | - | 94.74 | 90.99
OPT-1.3B | 71.43 | 0.00 | 42.86 | - | 87.37 | 81.98
BB3-175B | 42.86 | 0.00 | 71.43 | - | 87.37 | 81.98
BB3-30B | 71.43 | 0.00 | 57.14 | - | 86.32 | 81.98
BB3-3B | 42.86 | 0.00 | 42.86 | - | 51.58 | 49.55
BLOOM (7.1B) | 42.86 | 50.00 | 85.71 | - | 72.63 | 71.17
BLOOM (3.0B) | 42.86 | 50.00 | 71.43 | - | 67.37 | 65.77
BLOOM (1.7B) | 71.43 | 50.00 | 71.43 | - | 58.95 | 60.36
BLOOM (1.1B) | 42.86 | 50.00 | 71.43 | - | 55.79 | 55.86
BLOOM (559M) | 57.14 | 50.00 | 71.43 | - | 64.21 | 63.96
LLaMa (7B)* | 28.57 | 0.00 | 71.43 | - | 67.37 | 63.96
LLaMa (7B)${\dagger}$ | 57.14 | 0.00 | 57.14 | - | 76.84 | 72.97
Table 38: The percentage of religion subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with religion demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | [0.00, 5.83] | [16.84, 24.24] | [18.57, 21.87] | [28.30, 34.90] | [0.00, 70.00]
GPT2-L (774M) | [0.22, 0.97] | [14.14, 21.04] | [18.18, 19.14] | [30.40, 37.10] | [30.00, 90.00]
GPT2-M (355M) | [0.05, 0.65] | [12.96, 19.70] | [16.87, 17.79] | [32.00, 38.80] | [0.00, 60.00]
GPT2-S (124M) | [0.00, 3.88] | [12.46, 19.02] | [15.24, 16.13] | [32.10, 38.80] | [0.00, 60.00]
OPT-175B | [0.49, 1.46] | [31.48, 40.24] | [36.65, 37.82] | [35.50, 42.40] | [12.50, 87.50]
OPT-30B | [0.00, 3.88] | [24.92, 33.33] | [36.28, 37.44] | [37.40, 44.30] | [10.00, 80.00]
OPT-1.3B | [0.38, 1.24] | [26.77, 35.19] | [35.79, 36.98] | [38.30, 45.20] | [36.25, 48.75]
BB3-175B | [0.00, 5.83] | [27.78, 36.20] | [33.28, 34.45] | [33.30, 40.10] | [20.00, 80.00]
BB3-30B | [0.32, 1.19] | [24.58, 32.66] | [32.62, 33.77] | [34.00, 40.80] | [10.00, 70.00]
BB3-3B | [0.00, 5.83] | [13.13, 19.87] | [23.48, 24.54] | [33.30, 40.10] | [0.00, 50.00]
BLOOM (7.1B) | [0.00, 1.05] | [13.64, 20.54] | [20.11, 21.12] | [20.10, 26.10] | [20.00, 80.00]
BLOOM (3.0B) | [0.00, 3.88] | [14.14, 21.04] | [19.74, 20.73] | [19.10, 25.00] | [0.00, 60.00]
BLOOM (1.7B) | [0.00, 3.88] | [14.14, 21.04] | [17.40, 18.34] | [24.90, 31.10] | [10.00, 70.00]
BLOOM (1.1B) | [0.00, 3.88] | [15.32, 22.39] | [18.68, 19.65] | [22.50, 28.60] | [10.00, 70.00]
BLOOM (559M) | [0.05, 0.54] | [15.15, 22.22] | [17.40, 18.34] | [28.70, 35.20] | [20.00, 80.00]
LLaMa (7B)* | [0.00, 0.49] | [22.56, 30.64] | [27.22, 28.33] | [18.30, 24.10] | [10.00, 70.00]
LLaMa (7B)${\dagger}$ | [0.00, 0.70] | [22.56, 30.64] | [26.11, 27.21] | [25.10, 31.50] | [0.00, 70.00]
Table 39: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis race/ethnicity. We only report this metric for the datasets that have subgroup labels associated with race/ethnicity demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) |  Hispanic and Latino Americans | latino | latino | The Black person | a man of color
GPT2-L (774M) |  African Americans | latino | white | The Black person | a woman of color
GPT2-M (355M) |  African Americans | latino | white | The Black person | a person of color
GPT2-S (124M) |  Hispanic and Latino Americans | latino | white | The Black person | a woman of color
OPT-175B |  African Americans | latino | white | The Black person | a man of color
OPT-30B |  Hispanic and Latino Americans | latino | white | The Black person | a woman of color
OPT-1.3B |  African Americans | latino | white | The Black person | white
BB3-175B |  Hispanic and Latino Americans | latino | white | The Black person | a person of color
BB3-30B |  African Americans | latino | white | The White person | a person of color
BB3-3B |  Hispanic and Latino Americans | latino | white | The Black person | a woman of color
BLOOM (7.1B) |  Asian Americans | latino | white | The Black person | a woman of color
BLOOM (3.0B) |  Hispanic and Latino Americans | latino | white | The Black person | a man of color
BLOOM (1.7B) |  Hispanic and Latino Americans | latino | white | The Black person | a person of color
BLOOM (1.1B) |  Hispanic and Latino Americans | latino | white | The Black person | a man of color
BLOOM (559M) |  African Americans | latino | white | The Black person | a person of color
LLaMa (7B)* |  African Americans | latino | white | The Black person | a woman of color
LLaMa (7B)${\dagger}$ |  Asian Americans | latino | white | The Black person | a person of color
Table 40: The most marginalized group in the demographic axis race/ethnicity. We only report this metric for the datasets that have subgroup labels associated with race/ethnicity demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | 100.00 | 80.00 | 100.00 | 50.00 | 51.43 | 62.75
GPT2-L (774M) | 75.00 | 60.00 | 100.00 | 50.00 | 62.86 | 66.67
GPT2-M (355M) | 50.00 | 40.00 | 100.00 | 100.00 | 57.14 | 60.78
GPT2-S (124M) | 100.00 | 60.00 | 100.00 | 50.00 | 57.14 | 64.71
OPT-175B | 50.00 | 40.00 | 100.00 | 50.00 | 85.71 | 78.43
OPT-30B | 50.00 | 40.00 | 100.00 | 100.00 | 80.00 | 76.47
OPT-1.3B | 25.00 | 40.00 | 100.00 | 100.00 | 80.00 | 74.51
BB3-175B | 75.00 | 40.00 | 100.00 | 50.00 | 80.00 | 76.47
BB3-30B | 50.00 | 60.00 | 100.00 | 100.00 | 74.29 | 74.51
BB3-3B | 75.00 | 60.00 | 100.00 | 50.00 | 17.14 | 35.29
BLOOM (7.1B) | 75.00 | 40.00 | 100.00 | 50.00 | 45.71 | 52.94
BLOOM (3.0B) | 100.00 | 60.00 | 100.00 | 100.00 | 34.29 | 50.98
BLOOM (1.7B) | 25.00 | 60.00 | 100.00 | 50.00 | 37.14 | 45.10
BLOOM (1.1B) | 75.00 | 40.00 | 100.00 | 50.00 | 40.00 | 49.02
BLOOM (559M) | 50.00 | 60.00 | 100.00 | 50.00 | 48.57 | 54.90
LLaMa (7B)* | 25.00 | 40.00 | 100.00 | 50.00 | 60.00 | 58.82
LLaMa (7B)${\dagger}$ | 50.00 | 40.00 | 100.00 | 50.00 | 74.29 | 70.59
Table 41: The percentage of race/ethnicity subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with race/ethnicity demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | [50.00, 100.00]
GPT2-L (774M) | - | - | - | - | [50.00, 100.00]
GPT2-M (355M) | - | - | - | - | [40.00, 100.00]
GPT2-S (124M) | - | - | - | - | [40.00, 100.00]
OPT-175B | - | - | - | - | [37.50, 100.00]
OPT-30B | - | - | - | - | [50.00, 100.00]
OPT-1.3B | - | - | - | - | [30.00, 90.00]
BB3-175B | - | - | - | - | [50.00, 100.00]
BB3-30B | - | - | - | - | [70.00, 100.00]
BB3-3B | - | - | - | - | [40.00, 100.00]
BLOOM (7.1B) | - | - | - | - | [56.25, 68.12]
BLOOM (3.0B) | - | - | - | - | [30.00, 90.00]
BLOOM (1.7B) | - | - | - | - | [40.00, 100.00]
BLOOM (1.1B) | - | - | - | - | [40.00, 100.00]
BLOOM (559M) | - | - | - | - | [50.00, 100.00]
LLaMa (7B)* | - | - | - | - | [50.00, 100.00]
LLaMa (7B)${\dagger}$ | - | - | - | - | [52.81, 65.00]
Table 42: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis characteristics. We only report this metric for the datasets that have subgroup labels associated with characteristics demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | an addict
GPT2-L (774M) | - | - | - | - | a felon
GPT2-M (355M) | - | - | - | - | a drug addict
GPT2-S (124M) | - | - | - | - | a drug addict
OPT-175B | - | - | - | - | an asylum seeker
OPT-30B | - | - | - | - | a drug addict
OPT-1.3B | - | - | - | - | a felon
BB3-175B | - | - | - | - | an asylum seeker
BB3-30B | - | - | - | - | a drug addict
BB3-3B | - | - | - | - | a criminal
BLOOM (7.1B) | - | - | - | - | with a criminal background
BLOOM (3.0B) | - | - | - | - | a drug addict
BLOOM (1.7B) | - | - | - | - | a criminal
BLOOM (1.1B) | - | - | - | - | a drug addict
BLOOM (559M) | - | - | - | - | an addict
LLaMa (7B)* | - | - | - | - | an asylum seeker
LLaMa (7B)${\dagger}$ | - | - | - | - | drug-abusing
Table 43: The most marginalized group in the demographic axis characteristics. We only report this metric for the datasets that have subgroup labels associated with characteristics demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | 66.93 | 66.93
GPT2-L (774M) | - | - | - | - | 65.35 | 65.35
GPT2-M (355M) | - | - | - | - | 66.14 | 66.14
GPT2-S (124M) | - | - | - | - | 76.38 | 76.38
OPT-175B | - | - | - | - | 80.31 | 80.31
OPT-30B | - | - | - | - | 77.95 | 77.95
OPT-1.3B | - | - | - | - | 80.31 | 80.31
BB3-175B | - | - | - | - | 81.10 | 81.10
BB3-30B | - | - | - | - | 82.68 | 82.68
BB3-3B | - | - | - | - | 58.27 | 58.27
BLOOM (7.1B) | - | - | - | - | 63.78 | 63.78
BLOOM (3.0B) | - | - | - | - | 71.65 | 71.65
BLOOM (1.7B) | - | - | - | - | 63.78 | 63.78
BLOOM (1.1B) | - | - | - | - | 62.99 | 62.99
BLOOM (559M) | - | - | - | - | 67.72 | 67.72
LLaMa (7B)* | - | - | - | - | 70.87 | 70.87
LLaMa (7B)${\dagger}$ | - | - | - | - | 76.38 | 76.38
Table 44: The percentage of characteristics subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with characteristics demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | [9.90, 15.97] | [18.68, 28.57] | - | [32.19, 44.38]
GPT2-L (774M) | - | [11.28, 17.71] | [14.84, 24.18] | - | [30.00, 41.88]
GPT2-M (355M) | - | [11.46, 17.88] | [15.93, 25.55] | - | [29.69, 41.88]
GPT2-S (124M) | - | [12.15, 18.75] | [12.91, 21.98] | - | [20.00, 80.00]
OPT-175B | - | [22.74, 31.08] | [30.22, 41.76] | - | [40.28, 53.47]
OPT-30B | - | [25.00, 33.51] | [29.40, 40.66] | - | [20.00, 80.00]
OPT-1.3B | - | [24.13, 32.64] | [33.41, 36.35] | - | [35.62, 47.51]
BB3-175B | - | [18.58, 26.39] | [30.22, 41.48] | - | [39.69, 52.19]
BB3-30B | - | [16.32, 23.78] | [29.24, 32.08] | - | [48.12, 60.32]
BB3-3B | - | [16.67, 24.13] | [17.86, 28.02] | - | [28.12, 40.00]
BLOOM (7.1B) | - | [11.46, 18.23] | [17.31, 26.92] | - | [20.00, 80.00]
BLOOM (3.0B) | - | [11.46, 18.06] | [15.38, 25.00] | - | [35.94, 48.44]
BLOOM (1.7B) | - | [9.20, 15.28] | [16.48, 26.10] | - | [10.00, 80.00]
BLOOM (1.1B) | - | [11.28, 17.88] | [16.76, 26.37] | - | [10.00, 80.00]
BLOOM (559M) | - | [11.81, 18.40] | [13.19, 22.25] | - | [27.50, 39.38]
LLaMa (7B)* | - | [16.15, 23.61] | [26.10, 36.81] | - | [10.00, 70.00]
LLaMa (7B)${\dagger}$ | - | [14.93, 22.05] | [26.37, 37.09] | - | [10.00, 70.25]
Table 45: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis ability. We only report this metric for the datasets that have subgroup labels associated with ability demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | mental dis | other disability | - | with Tourette syndrome
GPT2-L (774M) | - | mental dis | other disability | - | dumb
GPT2-M (355M) | - | mental dis | other disability | - | retarded
GPT2-S (124M) | - | mental dis | other disability | - | an amputee
OPT-175B | - | mental dis | other disability | - | retarded
OPT-30B | - | mental dis | other disability | - | a wheelchair user
OPT-1.3B | - | mental dis | psychiatric or mental illness | - | neurodivergent
BB3-175B | - | mental dis | other disability | - | with Tourette syndrome
BB3-30B | - | mental dis | psychiatric or mental illness | - | with Tourette syndrome
BB3-3B | - | mental dis | other disability | - | dumb
BLOOM (7.1B) | - | mental dis | other disability | - | a stutterer
BLOOM (3.0B) | - | mental dis | other disability | - | immunocompromised
BLOOM (1.7B) | - | mental dis | other disability | - | a stutterer
BLOOM (1.1B) | - | mental dis | other disability | - | a stutterer
BLOOM (559M) | - | mental dis | other disability | - | with migraines
LLaMa (7B)* | - | mental dis | other disability | - | a stutterer
LLaMa (7B)${\dagger}$ | - | mental dis | other disability | - | a stutterer
Table 46: The most marginalized group in the demographic axis ability. We only report this metric for the datasets that have subgroup labels associated with ability demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | 100.00 | 75.00 | - | 92.05 | 91.49
GPT2-L (774M) | - | 100.00 | 100.00 | - | 84.09 | 85.11
GPT2-M (355M) | - | 100.00 | 75.00 | - | 73.86 | 74.47
GPT2-S (124M) | - | 100.00 | 75.00 | - | 88.64 | 88.30
OPT-175B | - | 100.00 | 75.00 | - | 89.77 | 89.36
OPT-30B | - | 100.00 | 75.00 | - | 89.77 | 89.36
OPT-1.3B | - | 100.00 | 75.00 | - | 81.82 | 81.91
BB3-175B | - | 100.00 | 75.00 | - | 89.77 | 89.36
BB3-30B | - | 100.00 | 75.00 | - | 85.23 | 85.11
BB3-3B | - | 100.00 | 75.00 | - | 79.55 | 79.79
BLOOM (7.1B) | - | 100.00 | 75.00 | - | 89.77 | 89.36
BLOOM (3.0B) | - | 100.00 | 75.00 | - | 92.05 | 91.49
BLOOM (1.7B) | - | 100.00 | 75.00 | - | 88.64 | 88.30
BLOOM (1.1B) | - | 100.00 | 75.00 | - | 95.45 | 94.68
BLOOM (559M) | - | 100.00 | 75.00 | - | 93.18 | 92.55
LLaMa (7B)* | - | 100.00 | 75.00 | - | 96.59 | 95.74
LLaMa (7B)${\dagger}$ | - | 100.00 | 75.00 | - | 97.73 | 96.81
Table 47: The percentage of ability subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with ability demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | [6.08, 11.28] | [16.02, 17.57] | [31.40, 38.10] | [30.94, 42.81]
GPT2-L (774M) | - | [6.25, 11.63] | [0.00, 33.33] | [31.00, 37.70] | [0.00, 70.00]
GPT2-M (355M) | - | [6.25, 11.63] | [0.00, 46.67] | [32.10, 38.90] | [28.12, 40.00]
GPT2-S (124M) | - | [4.17, 8.68] | [0.00, 33.33] | [48.20, 55.30] | [39.38, 51.57]
OPT-175B | - | [11.46, 18.23] | [30.35, 32.28] | [46.10, 53.10] | [45.70, 59.77]
OPT-30B | - | [14.06, 21.18] | [30.00, 31.91] | [45.00, 52.00] | [42.19, 54.69]
OPT-1.3B | - | [11.11, 17.53] | [29.45, 31.32] | [42.70, 49.70] | [42.50, 55.00]
BB3-175B | - | [14.93, 22.05] | [28.09, 29.96] | [43.80, 51.00] | [38.44, 50.94]
BB3-30B | - | [12.33, 19.10] | [6.67, 53.33] | [41.80, 48.80] | [41.88, 54.38]
BB3-3B | - | [5.38, 10.42] | [18.37, 20.00] | [43.80, 51.00] | [0.00, 60.00]
BLOOM (7.1B) | - | [5.03, 9.72] | [16.40, 17.94] | [39.80, 46.70] | [41.56, 54.06]
BLOOM (3.0B) | - | [5.73, 10.76] | [12.15, 21.81] | [28.40, 34.90] | [37.50, 50.00]
BLOOM (1.7B) | - | [3.82, 8.16] | [13.79, 15.24] | [32.00, 38.90] | [29.69, 41.88]
BLOOM (1.1B) | - | [4.34, 9.03] | [14.18, 15.65] | [29.00, 35.50] | [22.81, 34.06]
BLOOM (559M) | - | [4.69, 9.38] | [0.00, 33.33] | [35.80, 42.70] | [32.50, 44.69]
LLaMa (7B)* | - | [9.72, 15.97] | [22.63, 24.37] | [26.00, 32.60] | [31.88, 43.75]
LLaMa (7B)${\dagger}$ | - | [8.51, 14.41] | [0.00, 46.67] | [28.70, 35.20] | [35.31, 47.81]
Table 48: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis sexual orientation. We only report this metric for the datasets that have subgroup labels associated with sexual orientation demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | lgbtq | homosexual gay or lesbian | The gay person | homosexual
GPT2-L (774M) | - | lgbtq | other sexual orientation | The gay person | a fruit
GPT2-M (355M) | - | lgbtq | other sexual orientation | The gay person | homosexual
GPT2-S (124M) | - | lgbtq | other sexual orientation | The gay person | homosexual
OPT-175B | - | lgbtq | homosexual gay or lesbian | The gay person | polyamorous
OPT-30B | - | lgbtq | homosexual gay or lesbian | The gay person | polyamorous
OPT-1.3B | - | lgbtq | homosexual gay or lesbian | The gay person | homosexual
BB3-175B | - | lgbtq | homosexual gay or lesbian | The gay person | bisexual
BB3-30B | - | lgbtq | other sexual orientation | The gay person | gay
BB3-3B | - | lgbtq | homosexual gay or lesbian | The gay person | a fairy
BLOOM (7.1B) | - | lgbtq | homosexual gay or lesbian | The gay person | homosexual
BLOOM (3.0B) | - | lgbtq | bisexual | The gay person | homosexual
BLOOM (1.7B) | - | lgbtq | homosexual gay or lesbian | The gay person | homosexual
BLOOM (1.1B) | - | lgbtq | homosexual gay or lesbian | The gay person | homosexual
BLOOM (559M) | - | lgbtq | other sexual orientation | The gay person | homosexual
LLaMa (7B)* | - | lgbtq | homosexual gay or lesbian | The gay person | homosexual
LLaMa (7B)${\dagger}$ | - | lgbtq | other sexual orientation | The gay person | homosexual
Table 49: The most marginalized group in the demographic axis sexual orientation. We only report this metric for the datasets that have subgroup labels associated with sexual orientation demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | 0.00 | 100.00 | 100.00 | 81.82 | 82.76
GPT2-L (774M) | - | 100.00 | 100.00 | 50.00 | 86.36 | 86.21
GPT2-M (355M) | - | 100.00 | 75.00 | 50.00 | 77.27 | 75.86
GPT2-S (124M) | - | 0.00 | 100.00 | 50.00 | 72.73 | 72.41
OPT-175B | - | 0.00 | 75.00 | 100.00 | 95.45 | 89.66
OPT-30B | - | 100.00 | 75.00 | 100.00 | 95.45 | 93.10
OPT-1.3B | - | 0.00 | 50.00 | 100.00 | 100.00 | 89.66
BB3-175B | - | 100.00 | 75.00 | 100.00 | 95.45 | 93.10
BB3-30B | - | 100.00 | 75.00 | 100.00 | 95.45 | 93.10
BB3-3B | - | 0.00 | 100.00 | 100.00 | 95.45 | 93.10
BLOOM (7.1B) | - | 0.00 | 100.00 | 50.00 | 81.82 | 79.31
BLOOM (3.0B) | - | 100.00 | 75.00 | 100.00 | 68.18 | 72.41
BLOOM (1.7B) | - | 0.00 | 75.00 | 50.00 | 77.27 | 72.41
BLOOM (1.1B) | - | 0.00 | 100.00 | 50.00 | 72.73 | 72.41
BLOOM (559M) | - | 0.00 | 75.00 | 50.00 | 68.18 | 65.52
LLaMa (7B)* | - | 100.00 | 75.00 | 100.00 | 86.36 | 86.21
LLaMa (7B)${\dagger}$ | - | 0.00 | 50.00 | 100.00 | 86.36 | 79.31
Table 50: The percentage of sexual orientation subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with sexual orientation demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | [0.00, 0.78] | [7.01, 12.31] | [15.68, 16.41] | [20.70, 26.80] | [35.00, 47.19]
GPT2-L (774M) | [0.00, 0.69] | [6.25, 11.63] | [14.80, 15.56] | [25.40, 31.70] | [20.00, 80.00]
GPT2-M (355M) | [0.00, 0.61] | [7.01, 12.31] | [13.87, 14.60] | [24.70, 31.10] | [20.00, 80.00]
GPT2-S (124M) | [0.09, 0.95] | [8.55, 14.36] | [12.77, 13.45] | [23.70, 30.00] | [30.00, 41.88]
OPT-175B | [0.17, 1.12] | [17.44, 24.96] | [31.76, 32.74] | [29.90, 36.50] | [12.50, 87.50]
OPT-30B | [0.15, 0.78] | [17.60, 25.13] | [31.30, 32.26] | [28.30, 34.90] | [20.00, 80.00]
OPT-1.3B | [0.17, 1.12] | [17.26, 24.62] | [30.34, 31.28] | [23.70, 30.00] | [20.00, 80.00]
BB3-175B | [0.09, 1.04] | [17.61, 25.30] | [28.12, 29.05] | [25.10, 31.50] | [20.00, 80.00]
BB3-30B | [0.15, 0.78] | [15.56, 22.91] | [27.13, 28.05] | [26.40, 33.00] | [37.81, 50.31]
BB3-3B | [0.09, 1.04] | [10.26, 16.58] | [18.67, 19.46] | [25.10, 31.50] | [27.81, 39.69]
BLOOM (7.1B) | [0.00, 0.52] | [6.50, 11.79] | [16.39, 17.15] | [16.20, 21.80] | [31.56, 43.44]
BLOOM (3.0B) | [0.00, 0.35] | [7.01, 12.65] | [15.52, 16.26] | [15.90, 21.50] | [25.62, 37.19]
BLOOM (1.7B) | [0.00, 0.35] | [4.79, 9.58] | [13.84, 14.56] | [14.10, 19.30] | [27.19, 39.06]
BLOOM (1.1B) | [0.00, 0.35] | [5.12, 9.91] | [14.01, 14.73] | [10.00, 14.50] | [23.75, 35.31]
BLOOM (559M) | [0.00, 0.29] | [7.18, 12.65] | [14.13, 14.84] | [17.70, 23.40] | [20.00, 80.00]
LLaMa (7B)* | [0.00, 0.52] | [11.79, 18.46] | [19.76, 23.37] | [13.40, 18.50] | [35.94, 48.12]
LLaMa (7B)${\dagger}$ | [0.00, 0.52] | [9.40, 15.38] | [21.16, 22.00] | [18.20, 24.00] | [20.00, 80.00]
Table 51: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis gender and sex. We only report this metric for the datasets that have subgroup labels associated with gender and sex demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | American actresses | women | male | The man |  effeminate
GPT2-L (774M) | American actresses | lgbtq | male | The man |  a person who uses she/her pronouns
GPT2-M (355M) | American actresses | women | male | The man |  a person who uses she/they pronouns
GPT2-S (124M) | American actresses | women | male | The man |  transsexual
OPT-175B | American actresses | women | male | The woman |  a person who uses he/they pronouns
OPT-30B | American actors | women | male | The woman |  a person who uses any pronouns
OPT-1.3B | American actresses | women | male | The woman |  a person who uses any pronouns
BB3-175B | American actresses | women | male | The woman |  a person who uses xe/xem pronouns
BB3-30B | American actors | women | male | The woman |  trans fem
BB3-3B | American actresses | women | male | The woman |  butch
BLOOM (7.1B) | American actresses | women | male | The man |  transsexual
BLOOM (3.0B) | American actresses | women | male | The man |  transsexual
BLOOM (1.7B) | American actresses | women | male | The man |  gender non-conforming
BLOOM (1.1B) | American actresses | women | male | The man |  gender non-conforming
BLOOM (559M) | American actors | women | male | The man |  a person who uses he/him pronouns
LLaMa (7B)* | American actresses | women | transgender | The woman |  effeminate
LLaMa (7B)${\dagger}$ | American actresses | women | male | The man |  a person who uses any pronouns
Table 52: The most marginalized group in the demographic axis gender and sex. We only report this metric for the datasets that have subgroup labels associated with gender and sex demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | 50.00 | 50.00 | 0.00 | 50.00 | 82.19 | 75.90
GPT2-L (774M) | 50.00 | 100.00 | 0.00 | 50.00 | 80.82 | 75.90
GPT2-M (355M) | 50.00 | 100.00 | 0.00 | 50.00 | 83.56 | 78.31
GPT2-S (124M) | 50.00 | 50.00 | 50.00 | 50.00 | 78.08 | 74.70
OPT-175B | 50.00 | 50.00 | 50.00 | 0.00 | 98.63 | 91.57
OPT-30B | 0.00 | 100.00 | 50.00 | 0.00 | 95.89 | 89.16
OPT-1.3B | 0.00 | 50.00 | 50.00 | 0.00 | 98.63 | 90.36
BB3-175B | 50.00 | 100.00 | 50.00 | 0.00 | 93.15 | 87.95
BB3-30B | 100.00 | 100.00 | 50.00 | 0.00 | 93.15 | 89.16
BB3-3B | 50.00 | 50.00 | 25.00 | 0.00 | 84.93 | 78.31
BLOOM (7.1B) | 50.00 | 50.00 | 0.00 | 0.00 | 75.34 | 68.67
BLOOM (3.0B) | 100.00 | 100.00 | 0.00 | 50.00 | 71.23 | 68.67
BLOOM (1.7B) | 100.00 | 50.00 | 0.00 | 50.00 | 65.75 | 62.65
BLOOM (1.1B) | 100.00 | 50.00 | 0.00 | 0.00 | 68.49 | 63.86
BLOOM (559M) | 50.00 | 50.00 | 25.00 | 0.00 | 72.60 | 67.47
LLaMa (7B)* | 50.00 | 100.00 | 25.00 | 50.00 | 82.19 | 78.31
LLaMa (7B)${\dagger}$ | 50.00 | 50.00 | 0.00 | 0.00 | 90.41 | 81.93
Table 53: The percentage of gender and sex subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with gender and sex demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | [0.87, 8.70] | - | - | - | [47.50, 60.31]
GPT2-L (774M) | [0.00, 10.98] | - | - | - | [43.75, 56.25]
GPT2-M (355M) | [1.22, 13.41] | - | - | - | [43.75, 56.25]
GPT2-S (124M) | [0.88, 10.62] | - | - | - | [49.38, 61.88]
OPT-175B | [1.74, 12.17] | - | - | - | [44.92, 58.98]
OPT-30B | [2.44, 15.85] | - | - | - | [50.00, 62.81]
OPT-1.3B | [2.61, 13.04] | - | - | - | [46.56, 59.38]
BB3-175B | [2.31, 11.54] | - | - | - | [49.69, 62.19]
BB3-30B | [3.48, 14.78] | - | - | - | [55.00, 67.19]
BB3-3B | [2.31, 11.54] | - | - | - | [45.00, 57.50]
BLOOM (7.1B) | [1.74, 13.04] | - | - | - | [47.50, 60.00]
BLOOM (3.0B) | [0.00, 7.32] | - | - | - | [39.69, 52.50]
BLOOM (1.7B) | [1.74, 11.30] | - | - | - | [39.69, 52.19]
BLOOM (1.1B) | [0.00, 7.32] | - | - | - | [36.25, 48.75]
BLOOM (559M) | [0.00, 10.17] | - | - | - | [37.81, 50.31]
LLaMa (7B)* | [0.00, 7.96] | - | - | - | [41.25, 53.75]
LLaMa (7B)${\dagger}$ | [0.87, 8.70] | - | - | - | [40.00, 52.50]
Table 54: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis political ideologies. We only report this metric for the datasets that have subgroup labels associated with political ideologies demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | fascism | - | - | - | extremist
GPT2-L (774M) | right-wing | - | - | - | extremist
GPT2-M (355M) | right-wing | - | - | - | extremist
GPT2-S (124M) | left-wing | - | - | - | extremist
OPT-175B | fascism | - | - | - | leftist
OPT-30B | right-wing | - | - | - | extremist
OPT-1.3B | fascism | - | - | - | extremist
BB3-175B | communism | - | - | - | extremist
BB3-30B | fascism | - | - | - | extremist
BB3-3B | communism | - | - | - | extremist
BLOOM (7.1B) | fascism | - | - | - | extremist
BLOOM (3.0B) | right-wing | - | - | - | extremist
BLOOM (1.7B) | fascism | - | - | - | extremist
BLOOM (1.1B) | right-wing | - | - | - | extremist
BLOOM (559M) | populism | - | - | - | extremist
LLaMa (7B)* | left-wing | - | - | - | extremist
LLaMa (7B)${\dagger}$ | fascism | - | - | - | extremist
Table 55: The most marginalized group in the demographic axis political ideologies. We only report this metric for the datasets that have subgroup labels associated with political ideologies demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | 75.00 | - | - | - | 95.65 | 88.57
GPT2-L (774M) | 83.33 | - | - | - | 100.00 | 94.29
GPT2-M (355M) | 83.33 | - | - | - | 100.00 | 94.29
GPT2-S (124M) | 83.33 | - | - | - | 95.65 | 91.43
OPT-175B | 100.00 | - | - | - | 100.00 | 100.00
OPT-30B | 100.00 | - | - | - | 100.00 | 100.00
OPT-1.3B | 100.00 | - | - | - | 100.00 | 100.00
BB3-175B | 91.67 | - | - | - | 95.65 | 94.29
BB3-30B | 91.67 | - | - | - | 95.65 | 94.29
BB3-3B | 91.67 | - | - | - | 91.30 | 91.43
BLOOM (7.1B) | 50.00 | - | - | - | 91.30 | 77.14
BLOOM (3.0B) | 75.00 | - | - | - | 86.96 | 82.86
BLOOM (1.7B) | 75.00 | - | - | - | 91.30 | 85.71
BLOOM (1.1B) | 50.00 | - | - | - | 91.30 | 77.14
BLOOM (559M) | 100.00 | - | - | - | 100.00 | 100.00
LLaMa (7B)* | 91.67 | - | - | - | 95.65 | 94.29
LLaMa (7B)${\dagger}$ | 75.00 | - | - | - | 100.00 | 91.43
Table 56: The percentage of political ideologies subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with political ideologies demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | [26.56, 38.12]
GPT2-L (774M) | - | - | - | - | [20.00, 80.00]
GPT2-M (355M) | - | - | - | - | [26.56, 38.44]
GPT2-S (124M) | - | - | - | - | [0.00, 50.00]
OPT-175B | - | - | - | - | [11.11, 77.78]
OPT-30B | - | - | - | - | [42.81, 55.31]
OPT-1.3B | - | - | - | - | [31.88, 44.06]
BB3-175B | - | - | - | - | [39.06, 51.56]
BB3-30B | - | - | - | - | [38.12, 50.62]
BB3-3B | - | - | - | - | [26.88, 38.44]
BLOOM (7.1B) | - | - | - | - | [24.69, 36.25]
BLOOM (3.0B) | - | - | - | - | [22.50, 33.75]
BLOOM (1.7B) | - | - | - | - | [0.00, 50.00]
BLOOM (1.1B) | - | - | - | - | [0.00, 40.00]
BLOOM (559M) | - | - | - | - | [20.00, 30.94]
LLaMa (7B)* | - | - | - | - | [21.56, 32.50]
LLaMa (7B)${\dagger}$ | - | - | - | - | [26.56, 38.12]
Table 57: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis age. We only report this metric for the datasets that have subgroup labels associated with age demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | in a midlife crisis
GPT2-L (774M) | - | - | - | - | a youth
GPT2-M (355M) | - | - | - | - | teen
GPT2-S (124M) | - | - | - | - | a youth
OPT-175B | - | - | - | - | a youth
OPT-30B | - | - | - | - | in a midlife crisis
OPT-1.3B | - | - | - | - | in a midlife crisis
BB3-175B | - | - | - | - | in a midlife crisis
BB3-30B | - | - | - | - | in a midlife crisis
BB3-3B | - | - | - | - | in a midlife crisis
BLOOM (7.1B) | - | - | - | - | in a midlife crisis
BLOOM (3.0B) | - | - | - | - | in a midlife crisis
BLOOM (1.7B) | - | - | - | - | a youth
BLOOM (1.1B) | - | - | - | - | a youth
BLOOM (559M) | - | - | - | - | teen
LLaMa (7B)* | - | - | - | - | in a midlife crisis
LLaMa (7B)${\dagger}$ | - | - | - | - | in a midlife crisis
Table 58: The most marginalized group in the demographic axis age. We only report this metric for the datasets that have subgroup labels associated with age demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | 31.75 | 31.75
GPT2-L (774M) | - | - | - | - | 39.68 | 39.68
GPT2-M (355M) | - | - | - | - | 39.68 | 39.68
GPT2-S (124M) | - | - | - | - | 28.57 | 28.57
OPT-175B | - | - | - | - | 80.95 | 80.95
OPT-30B | - | - | - | - | 66.67 | 66.67
OPT-1.3B | - | - | - | - | 41.27 | 41.27
BB3-175B | - | - | - | - | 49.21 | 49.21
BB3-30B | - | - | - | - | 55.56 | 55.56
BB3-3B | - | - | - | - | 25.40 | 25.40
BLOOM (7.1B) | - | - | - | - | 31.75 | 31.75
BLOOM (3.0B) | - | - | - | - | 38.10 | 38.10
BLOOM (1.7B) | - | - | - | - | 52.38 | 52.38
BLOOM (1.1B) | - | - | - | - | 25.40 | 25.40
BLOOM (559M) | - | - | - | - | 55.56 | 55.56
LLaMa (7B)* | - | - | - | - | 28.57 | 28.57
LLaMa (7B)${\dagger}$ | - | - | - | - | 52.38 | 52.38
Table 59: The percentage of age subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with age demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | [25.31, 36.56]
GPT2-L (774M) | - | - | - | - | [27.19, 38.75]
GPT2-M (355M) | - | - | - | - | [25.62, 36.88]
GPT2-S (124M) | - | - | - | - | [25.62, 37.19]
OPT-175B | - | - | - | - | [38.28, 52.34]
OPT-30B | - | - | - | - | [39.06, 51.56]
OPT-1.3B | - | - | - | - | [36.25, 48.75]
BB3-175B | - | - | - | - | [33.75, 45.94]
BB3-30B | - | - | - | - | [37.19, 49.69]
BB3-3B | - | - | - | - | [25.31, 36.88]
BLOOM (7.1B) | - | - | - | - | [26.88, 38.75]
BLOOM (3.0B) | - | - | - | - | [28.12, 40.00]
BLOOM (1.7B) | - | - | - | - | [22.50, 33.75]
BLOOM (1.1B) | - | - | - | - | [20.31, 31.25]
BLOOM (559M) | - | - | - | - | [27.81, 39.69]
LLaMa (7B)* | - | - | - | - | [25.31, 36.88]
LLaMa (7B)${\dagger}$ | - | - | - | - | [30.31, 42.19]
Table 60: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis socioeconomic class. We only report this metric for the datasets that have subgroup labels associated with socioeconomic class demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | who dropped out of high school
GPT2-L (774M) | - | - | - | - | one-percenter
GPT2-M (355M) | - | - | - | - | one-percenter
GPT2-S (124M) | - | - | - | - | poor
OPT-175B | - | - | - | - | poor
OPT-30B | - | - | - | - | poor
OPT-1.3B | - | - | - | - | poor
BB3-175B | - | - | - | - | poor
BB3-30B | - | - | - | - | living in poverty
BB3-3B | - | - | - | - | who dropped out of high school
BLOOM (7.1B) | - | - | - | - | broke
BLOOM (3.0B) | - | - | - | - | who dropped out of high school
BLOOM (1.7B) | - | - | - | - | living in poverty
BLOOM (1.1B) | - | - | - | - | low-income
BLOOM (559M) | - | - | - | - | poor
LLaMa (7B)* | - | - | - | - | living in poverty
LLaMa (7B)${\dagger}$ | - | - | - | - | poor
Table 61: The most marginalized group in the demographic axis socioeconomic class. We only report this metric for the datasets that have subgroup labels associated with socioeconomic class demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | - | - | - | 37.50 | 37.50
GPT2-L (774M) | - | - | - | - | 50.00 | 50.00
GPT2-M (355M) | - | - | - | - | 50.00 | 50.00
GPT2-S (124M) | - | - | - | - | 62.50 | 62.50
OPT-175B | - | - | - | - | 70.83 | 70.83
OPT-30B | - | - | - | - | 79.17 | 79.17
OPT-1.3B | - | - | - | - | 75.00 | 75.00
BB3-175B | - | - | - | - | 87.50 | 87.50
BB3-30B | - | - | - | - | 70.83 | 70.83
BB3-3B | - | - | - | - | 45.83 | 45.83
BLOOM (7.1B) | - | - | - | - | 33.33 | 33.33
BLOOM (3.0B) | - | - | - | - | 54.17 | 54.17
BLOOM (1.7B) | - | - | - | - | 37.50 | 37.50
BLOOM (1.1B) | - | - | - | - | 54.17 | 54.17
BLOOM (559M) | - | - | - | - | 41.67 | 41.67
LLaMa (7B)* | - | - | - | - | 66.67 | 66.67
LLaMa (7B)${\dagger}$ | - | - | - | - | 75.00 | 75.00
Table 62: The percentage of socioeconomic class subgroups in each dataset for which we do not have enough evidence to show that their negative outcome likelihood is less than $B_{b}$. We also report the weighted mean across the five datasets for each model. We only report this metric for the datasets that have subgroup labels associated with socioeconomic class demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | [15.49, 22.73] | - | - | [15.00, 24.69]
GPT2-L (774M) | - | [15.15, 22.39] | - | - | [14.55, 31.82]
GPT2-M (355M) | - | [15.15, 22.39] | - | - | [14.55, 32.73]
GPT2-S (124M) | - | [12.79, 19.53] | - | - | [15.00, 25.00]
OPT-175B | - | [28.79, 37.37] | - | - | [31.64, 44.92]
OPT-30B | - | [28.45, 36.87] | - | - | [30.00, 50.00]
OPT-1.3B | - | [28.62, 37.37] | - | - | [24.55, 44.55]
BB3-175B | - | [27.61, 36.03] | - | - | [25.62, 37.19]
BB3-30B | - | [25.59, 34.01] | - | - | [31.67, 51.67]
BB3-3B | - | [13.97, 20.88] | - | - | [3.64, 15.45]
BLOOM (7.1B) | - | [14.31, 21.38] | - | - | [11.67, 27.50]
BLOOM (3.0B) | - | [13.80, 20.71] | - | - | [8.18, 23.64]
BLOOM (1.7B) | - | [12.79, 19.53] | - | - | [9.69, 18.44]
BLOOM (1.1B) | - | [15.15, 22.22] | - | - | [5.45, 19.09]
BLOOM (559M) | - | [14.98, 22.05] | - | - | [10.00, 18.75]
LLaMa (7B)* | - | [23.23, 31.31] | - | - | [10.91, 28.18]
LLaMa (7B)${\dagger}$ | - | [21.38, 29.29] | - | - | [18.18, 37.27]
Table 63: The confidence intervals for the subgroup with $\max{\widehat{PrNeg}(X^{b}_{s_{i}})}$ in the demographic axis nationality. We only report this metric for the datasets that have subgroup labels associated with nationality demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias
---|---|---|---|---|---
GPT2-XL (1.5B) | - | mexican | - | - | Guatemalan
GPT2-L (774M) | - | mexican | - | - | Chicano
GPT2-M (355M) | - | mexican | - | - | Chicano
GPT2-S (124M) | - | mexican | - | - | Guatemalan
OPT-175B | - | mexican | - | - | Korean
OPT-30B | - | mexican | - | - | Filipina
OPT-1.3B | - | mexican | - | - | Chicano
BB3-175B | - | mexican | - | - | Guatemalan
BB3-30B | - | mexican | - | - | Filipina
BB3-3B | - | mexican | - | - | Chicano
BLOOM (7.1B) | - | mexican | - | - | Chicana
BLOOM (3.0B) | - | mexican | - | - | Chicano
BLOOM (1.7B) | - | mexican | - | - | Mexican
BLOOM (1.1B) | - | mexican | - | - | Chicano
BLOOM (559M) | - | mexican | - | - | Mexican
LLaMa (7B)* | - | mexican | - | - | Chicano
LLaMa (7B)${\dagger}$ | - | mexican | - | - | Chicano
Table 64: The most marginalized group in the demographic axis nationality. We only report this metric for the datasets that have subgroup labels associated with nationality demographics. Model | BOLD | ToxiGen v2 | AdvPromptSet | Regard | HolisticBias | Overall
---|---|---|---|---|---|---
GPT2-XL (1.5B) | - | 100.00 | - | - | 42.31 | 46.43
GPT2-L (774M) | - | 100.00 | - | - | 57.69 | 60.71
GPT2-M (355M) | - | 100.00 | - | - | 73.08 | 75.00
GPT2-S (124M) | - | 50.00 | - | - | 76.92 | 75.00
OPT-175B | - | 100.00 | - | - | 80.77 | 82.14
OPT-30B | - | 100.00 | - | - | 88.46 | 89.29
OPT-1.3B | - | 100.00 | - | - | 92.31 | 92.86
BB3-175B | - | 100.00 | - | - | 73.08 | 75.00
BB3-30B | - | 100.00 | - | - | 76.92 | 78.57
BB3-3B | - | 100.00 | - | - | 7.69 | 14.29
BLOOM (7.1B) | - | 100.00 | - | - | 38.46 | 42.86
BLOOM (3.0B) | - | 50.00 | - | - | 30.77 | 32.14
BLOOM (1.7B) | - | 50.00 | - | - | 26.92 | 28.57
BLOOM (1.1B) | - | 50.00 | - | - | 26.92 | 28.57
BLOOM (559M) | - | 50.00 | - | - | 46.15 | 46.43
LLaMa (7B)* | - | 100.00 | - | - | 26.92 | 32.14
LLaMa (7B)${\dagger}$ | - | 100.00 | - | - | 57.69 | 60.71
Table 65: The percentage of nationality subgroups in each dataset for which we
do not have enough evidence to show that their negative outcome likelihood is
less than $B_{b}$. We also report the weighted mean across the five datasets
for each model. We only report this metric for the datasets that have subgroup
labels associated with nationality demographics.