#  How Old is GPT?: The $\mathtt{HumBEL}$ Framework for Evaluating Language
Models using Human Demographic Data

Anthony Sicilia
Intelligent Systems Program
University of Pittsburgh
<EMAIL_ADDRESS>
&Jennifer C. Gates
Independent Researcher
<EMAIL_ADDRESS>
&Malihe Alikhani
Intelligent Systems Program
Computer Science Department
University of Pittsburgh
<EMAIL_ADDRESS>

###### Abstract

While large pre-trained language models (LMs) find greater use across NLP,
existing evaluation protocols do not consider how LM language use aligns with
particular human demographic groups, which can be an important consideration
in conversational AI applications. To remedy this gap, we consider how LM
language skills can be measured and compared to human sub-populations. We
suggest clinical techniques from Speech Language Pathology, which has well-
established norms for acquisition of language skills, organized by (human)
age. We conduct evaluation with a domain expert (i.e., a clinically licensed
speech language pathologist), and also propose automated techniques to
substitute clinical evaluation at scale. We find LM capability varies widely
depending on task with GPT-3.5 mimicking the ability of a typical 6-9 year old
at tasks requiring inference about word meanings and simultaneously
outperforming a typical 21 year old at memorization. GPT-3.5 (InstructGPT)
also has trouble with social language use, exhibiting less than 50% of the
tested pragmatic skills. It shows errors in understanding particular word
parts-of-speech and associative word relations, among other lexical features.
Ultimately, findings reiterate the importance of considering demographic
alignment and conversational goals when using these models as public-facing
tools. Our framework will be publicly available via code, data, and a python
package.

##  1 Introduction

Large pre-trained language models (LMs) like GPT make excellent tools for use
in conversational agents due to their near human-like language skill in text-
generation (Uchendu et al., 2021; Clark et al., 2021) and certain types of
reasoning (Rajani et al., 2019; West et al., 2022). Still, LMs do fall short
in conversational application where considering the demographic information of
interlocutors is a requirement for success. Cultural code-switching, for
example, is an important consideration when designing conversational agents in
the healthcare domain for older black adults Harrington et al. (2022). Also,
in the education domain, alignment of teachable agents with the social
capabilities of student age groups plays a significant factor in the student’s
success Ogan et al. (2012). Indeed, conversational common sense and social
capabilities innately depend on the demographic of the interlocutors, since
these capabilities are dependent on things like cultural norms Geertz (1975).
Unfortunately, biases in the training data inherited by LMs can prevent
development of language skills that align with particular demographics Lucy
and Bamman (2021), and evaluation of such alignment has not been well-studied.
To fill this gap, we propose the novel $\mathtt{HumBEL}$ evaluation
framework,111$\mathtt{Hum}$an demographic $\mathtt{B}$ased
$\mathtt{E}$valuation of $\mathtt{L}$Ms which uses expert-in-the-loop
statistical evaluation techniques to quantify the demographic similarity of
LMs to specific groups of interlocutors.

Figure 1: $\mathtt{HumBEL}$ uses data from human clinical exams to align
language model evaluation with human sub-populations; i.e., via age estimates.
It proposes both clinician-in-the-loop and automated evaluations.

$\mathtt{HumBEL}$ evaluates alignment of LMs with human populations by
administering tests designed by domain-experts and applying novel statistical
techniques, so key differences between an LM and a human sub-population are
revealed (Figure 1). While $\mathtt{HumBEL}$ is generally applicable to
(categorical) demographic features, we focus in this work on human age groups,
using clinical tests for diagnosing human language disorders (i.e., from
Speech Language Pathology). In effect, we evaluate LMs in the same way
clinical experts evaluate humans of varying age groups, using data to assign a
typical human age222Age equivalents are designed for comparison with human
sub-populations to study alignment of language use in specific skills. Please,
use care in interpretation; i.e., see Limitations. based on task performance,
and providing both clinician-in-the-loop and automated methods for achieving
this goal. Model alignment with an age group at a task can then be used to
test robustness in matching conversation applications.

To demonstrate $\mathtt{HumBEL}$, we evaluate InstructGPT. Our key findings
demonstrate gaps in common sense knowledge about noun relationships, social
language use, inferential language tasks, and a general inconsistency in
language skills compared to normal human development: failures in social and
inferential capability are akin to error patterns of a typical 3-7 year old,
while success at recollection surpasses a typical 21 year old. Ultimately, our
results suggest interlocutor age and conversational goal are important
considerations when using this model in conversational applications.

In the rest of this paper, we introduce our new proposal. In particular, we
contribute:

  1. 1.

(§ 2.1) protocols for evaluation of LMs by domain experts (i.e., Speech
Language Pathologists), using common clinical exams that estimate human age
equivalent of a LM’s performance with detailed clinician error analyses

  2. 2.

(§ 2.2) statistical tools for automation of clinical techniques at scale via
metrics for determination of human age equivalent and procedures for error
analysis motivated by clinical practice

  3. 3.

(§ 3) detailed evaluation of a current state-of-the-art LM (GPT-3.5) using
these protocols

  4. 4.

experimental code and a python package for future researchers to easily apply
these protocols

  5. 5.

publicly available data, including clinician annotations of GPT-3.5 errors

Next, we describe $\mathtt{HumBEL}$ in detail.

##  2 The $\mathtt{HumBEL}$ Framework: Human Age Based Evaluation of Language
Models

As just discussed, the $\mathtt{HumBEL}$ framework consists of two evaluation
protocols. The first (preferred) evaluation protocol describes techniques to
administer a clinical exam to a LM via prompting, so that results can be
carefully analyzed by a clinically licensed Speech Language Pathologist. The
second describes automated alternatives, which are easier to conduct more
frequently and at scale.

###  2.1 Clinical Evaluation by Speech Language Pathologist

In this section, we use examples from the commonly used CELF5 (Preschool)
clinical exam (Wiig et al., 2013) to describe our protocols.333 Note, any
examples of test materials provided during discussion are adaptions of the
original materials per publishing agreement with Pearson, Inc. While these
examples are different from the original materials, they are designed to
convey similar qualitative insight to the reader; e.g., the LM prompt or types
of errors made by the LM.,444Clinical Evaluation of Language Fundamentals,
Fifth Edition, CELF-5 Copyright © 2013 NCS Pearson, Inc. Reproduced with
permission. All rights reserved.,555Clinical Evaluation of Language
Fundamentals, Fifth Edition, CELF-5 is a trademark, in the US and/or other
countries, of Pearson Education, Inc. or its affiliates(s). This test is used
throughout our paper, but our ideas generalize to other common clinical tests.

####  2.1.1 Description of Exam

As noted, we use the common clinical exam CELF5 (Wiig et al., 2013) as an
example. CELF5 is composed of multiple sub-tests which assess syntactic,
semantic, and pragmatic use of language in 5-8 year olds. Each test consists
of 24-40 questions.

  1. 1.

Word Classes (WC) presents 3-4 words and asks test subject to identify the two
words that go together best. It measures semantic knowledge and ability to
apply this knowledge to determine and rank word associations.

  2. 2.

Formulated Sentences (FS) presents 1-2 words and asks subject to provide a
sentence which uses the(se) word(s). It measures syntactic and semantic
correctness of the provided sentence.

  3. 3.

Recalling Sentences (RS) presents a sentence and asks subject to repeat the
sentence. It measures memorization and reproduction ability.

  4. 4.

Understanding Spoken Paragraphs (USP) presents a story and asks subject
questions about the story. It primarily measures recollection ability with
occasional need for inference.

  5. 5.

Pragmatics Profile (PP) analyzes social error patterns in test subjects,
observed during administration of other sub-tests and general interaction. We
use the full profile to make an age estimate, and a smaller checklist (PPC)
which better targets current LM capabilities.

SLP |  QA |  Comp
---|---|---
Carefully consider the following words and tell me the two words that go together best: "[W]", "[X]", "[Y]", "[Z]". |  Instruction: Carefully consider the following words and tell me the two… Student: |  Among the words "[W]", "[X]", "[Y]", and "[Z]", the two words that go together best are
Table 1: Examples from different prompt protocols for the Word Classes test.
SLP follows CELF5 directives exactly.${}^{\text{\ref{TOU}}}$ QA adds a
mechanism to inform the LM of its speaker role. Comp re-frames as a likely
seen prefix (i.e., in training). We test these and 70+ other prompt/parameter
variations. See sensitivity analysis in Appendix D.

####  2.1.2 Exam Administration via Prompting

Prompting is the standard technique in which textual output is generated from
LMs. We use prefix prompting, in which input text is provided to the LM and
the LM is sampled based on this input to complete the text. In this way,
questions from the 5 discussed tests can be administered to the LM and the LM
response (i.e., the text-completion) can be evaluated by the clinician with
relevant observations noted for each question. Since estimation of age
equivalents assumes precise adherence to the CELF5 protocols for
scoring/evaluation, we adhere to these as much as possible. We do identify two
primary limitations in administering CELF5 to common LMs and provide solutions
below:

  1. 1.

First, LMs are optimized for text-completion rather than instruction
following,666InstructGPT works towards bridging this gap, but results indicate
this problem is not solved by InstructGPT alone. making typical administration
of the test challenging. To control for performance drops induced by this, we
use multiple prompt formats (see Table 1). The SLP protocol follows the CELF5
directives exactly, while the QA and Comp protocols should be better tailored
for LMs. Sensitivity analysis (Appendix D) with 70+ additinoal configurations
suggests prompt and parameter variations do not significantly impact LM
performance.

  2. 2.

Secondly, LMs lack the ability to perceive visually and take action in an
embodied setting. Therefore, we limit the types of tests administered (i.e.,
those in § 2.1.1) and tailor these tests for a language-only medium when
appropriate (see Appendix A). Investigation of the impact of this choice is
left for future work. Indeed, the necessity of visual/embodied stimuli to
inform lexical semantics has been hypothesized Bisk et al. (2020) and CELF5
scores may be used in the future to provide a principled answer.

###  2.2 Automation of Clinical Techniques

In this part, we describe automated techniques for two important aspects of
the clinical exam: (1) qualitative analysis of errors through detailed
clinician notes and (2) determination of human age equivalent for the LM on a
language task. We use the Word Classes test (WC) from the CELF5 exam as an
example application.

####  2.2.1 Data

We build a large-scale WC test (WC large) by combining two publicly available
data sources:

  1. 1.

Word Associations: We build associated word pairs using cue and association
words from the WAX dataset (Liu et al., 2022a) collected from human annotators
by presenting a cue and asking for spontaneous associations (with
explanation). This dataset is transformed into a large-scale version of the WC
test by randomly sampling two additional association words for each human
labeled word pair and presenting the quadruple to a subject using the existing
WC prompt protocols. All four test words (i.e., the target pair and two
additional associations) are presented in random order and filtered to prevent
overlap in target pairs by chance.

  2. 2.

Age Norms: In clinical exams, human developmental standards are determined
from exam score data (i.e., age norms) that indicate the age at which one
expects the observed score in a human population. To do this automatically for
new WC questions, we use a test-based age-of-acquisition (AoA) dataset (Dale
and O’rourke, 1976; Brysbaert and Biemiller, 2017), which determines the AoA
of 40K English words. Word AoA is determined by the age at which 50% of a
human population knows the word according to a definition matching test (see
Appendix B). We call this test Def in experiments (§ 3). For WC large, AoA is
the max AoA of the target words (i.e., the typical age at which a human can
select the target pair without guessing).

Applying AoA estimates to the word association data leads to about 10K new WC
questions with accompanying explanations and projected age norms. See Appendix
B for more statistics on WC large.

####  2.2.2 Automated Analysis of Errors

We isolate some influential factors in typical word acquisition by humans
based on discussion with a licensed Speech Language Pathologist; i.e., these
question/response features were deemed useful for analyzing errors in notes
during clinical exams. We limit our analysis to those that can be
automatically determined777We use the spacy package. and tailor our
description of these features to the WC test. More details on feature
extraction are provided in Appendix E.

  1. 1.

Parts of Speech (POS): Unordered parts of speech of the target word pair can
play a factor in correctness of a subject response. Typically, intended word
POS can be inferred from the target pair explanations; otherwise, "X" is used.

  2. 2.

Relation: The WAX dataset (Liu et al., 2022a) also contains relation
categories for word associations. In humans, particular relation types are
more challenging depending on test subject age.

  3. 3.

Morphological Complexity: Morphological Features in the Universal Dependencies
framework (Nivre et al., 2016) describe lexical and grammatical properties of
particular word forms. We define complexity via the count of unique features
across both words in a target pair. High means 4+ features, medium means 3-4,
and low means < 2\. So, these categories indicate complexity of word forms in
a pair, relative to the base semantics of the pair’s lemmas.

  4. 4.

Explanations: Explanations or other cues provided with an answer provide
valuable information to evaluating clinicians, including signals of
confidence, reasoning, and social skills. We use the presence of an
explanation as a simple binary feature of the LM response. While prompts are
not designed to elicit explanations, the LM in § 3 provides one more than half
the time.

##### Statistical Tests

In lieu of detailed notes, we propose a variety of statistical tests to
determine association and impact of the various features just discussed. The
$\chi^{2}$-statistic provides a basic test for the association of each feature
with the occurrence of an LM error. Furthermore, specific hypotheses about the
impact of particular parts-of-speech, relations, and other features can be
estimated using a Linear Probability Model (LPM). For example, an LPM allows
us to estimate the effect size

$\begin{split}&\mathbf{Pr}\\{\text{LM error}\mid\text{Relation=Function}\\}\\\
&\quad-\mathbf{Pr}\\{\text{LM error}\mid\text{Relation}\ \neq\
\text{Function}\\}.\end{split}$ (1)

while controlling for other features such as typical human age-of-acquisition
for the word pair and any other features included in the model. For details on
both testing procedures see Appendix F. Example applications are provided in
later results (§ 3).

####  2.2.3 Automated Determination of LM Age

##### Test Divergence

We base our first test for LM age on a statistic called the test divergence
(Sicilia and Alikhani, 2022). For an evaluation function $h$ and language
model LM the test-divergence is:

$\begin{split}&\mathbf{TD}_{a}(\texttt{LM})=\mathbf{E}[\lvert
h(D)-h(\hat{D})\rvert];\\\
&\qquad(D,C)\sim\mathbb{G}_{a};\quad\hat{D}\sim\texttt{LM}(C).\end{split}$ (2)

Here, $\mathbb{G}_{a}$ is called the goal distribution and typically
represents a distribution of human dialogues. We incorporate new dependence on
the age $a$, restricting the age of the humans in the population. With this
interpretation, $D$ is a random human dialogue about the context $C$ and
$\hat{D}$ is a dialogue sampled from the language model about this same
context; context can be a prompt, an image, both (for perceptually grounded
models), or any other information source which grounds the dialogue. In this
paper, $C$ will correspond to a test question (or, equivalent LM prompt) in
the WC large dataset and $h$ will indicate whether the response $D$ (or
$\hat{D}$) is correct. $C$ follows a uniform distribution over questions in WC
large where AoA (§ 2.2.1) is either (1) exactly equal to $a$, or (2) $\leq a$.
We disambiguate between these two cases throughout.

##### The $\mathbf{TD}$ Test for LM Age

Granted the test-divergence as a test statistic, we are interested in the
following null $H_{0}$ and alternative $H_{A}$ hypotheses:

> $H_{0}:$ LM errors align with age group $a$
> $H_{A}:$ LM errors fail to align with age group $a$

Thus, we grant the LM benefit of the doubt and reject the model LM aligns with
an age group if we establish evidence against this claim. Formally, we define
alignment when a models error patterns are within a tolerance $\gamma$: i.e.,
if $\mathbf{TD}_{a}(\texttt{LM})\leq\gamma$. In English, this means the
expected difference between the LM performance and human (aged $a$)
performance on each test question is no more than the tolerance $\gamma$ where
tolerance allows us to account for any (human) subjectivity in question
responses. Then, with this, we can rewrite our hypotheses:

> $H_{0}:\mathbf{TD}_{a}(\texttt{LM})\leq\gamma$
> $H_{A}:\mathbf{TD}_{a}(\texttt{LM})>\gamma$.

In turn, a test at confidence $100\times(1-\alpha)\%$ rejects the null if the
$p$-value is bounded by $\alpha$

$p=\mathbf{Pr}(\widehat{T}_{a}-\gamma\leq T_{a}-\gamma\mid H_{0})\leq\alpha$
(3)

where $\widehat{T}_{a}$ is the observed estimate of
$\mathbf{TD}_{a}(\texttt{LM})$ (i.e., an empirical average) and $T_{a}$ is the
r.v. representing this empirical average. For the WC large dataset, $n\cdot
T_{a}$ is a Binomial random variable and probability under the Binomial
distribution gives the $p$-value exactly. In other circumstances, the test
outcome may be continuous or the test $h$ may be learned from data as
suggested by Bruni and Fernández (2017), in which case Hoeffding’s or PAC type
inequalities can bound $p$-values, respectively. See Shalev-Shwartz and Ben-
David (2014) for reference on a variety on these inequalities.

##### The Mean Test for LM Age

As we will see in later results, the statistic/test just described will often
be preferred because it incorporates information about individual question
outcomes, making it more sensitive to correlation between $h(D)$ and
$h(\hat{D})$. Still, we may not always have access to the individual human
question outcomes $h(D)$. Instead, we might only know the average outcome
$\mu_{a}=\mathbf{E}[h(D)]$ with $D\sim\mathbb{G}_{a}$. Following the same
logic as before, we can use this limited information to test the LM age as
follows:

> $H_{0}:\mathbf{E}[R]=n\cdot\mu_{a}$
> $H_{A}:\mathbf{E}[R]<n\cdot\mu_{a}$.

where $R$ is the empirical sum of correct GPT responses
$\sum_{i}h(\hat{D}_{i})$ and $n$ is the question count. Note, this leads to a
standard Binomial test.

##### A Proxy for Unlabeled Data

In Appendix F, we explore additional proxies for totally unlabeled human and
LM question responses, including theoretical justification and
experimentation. For example, these techniques may be of interest in long
essay-format examinations where question outcomes require nuanced human
evaluation.

##  3 Experimental Results: Applying $\mathtt{HumBEL}$ to InstructGPT

In this part, we apply the framework just described to evaluate the
performance of InstructGPT (GPT 3.5) according to human demographic alignment.

###  3.1 Clinical Evaluation Results

Test |  InstructGPT |  Clinician Observation
---|---|---
WC |  Among the words "car", "water", "stroller", and "boat", the two words that go together best are "car" and "boat". This is because they are both types of transport. |  Misses functional "goes in" relation for "boat" and "water"
WC |  Among the words "singing", "loving", "touching", and "tasting" the two words that go together best are "singing" and "loving." This is because both words involve using your voice and express affection. |  Misses the categorical "sense" relation for "touching" and "tasting"
USP |  Melanie was thrilled and nervous at the same time because it was her first day at a new summer camp. |  Does not infer concerns about camp instructors being nice
USP |  Melanie greeted Miss Grace because she was happy to see her. |  Did not infer specific context: she was old camp instructor
USP |  ["throw-and-chase" is] a game where one person throws a ball and the other person goes to chase it. |  Not fact based. Fact-based answer is easily found in context
Table 2: Examples of inferential and other language application errors by InstructGPT in CELF5 exam. Explanations are provided by the evaluating clinician. Examples are adapted for publication per agreement with Pearson.${}^{\text{\ref{TOU}}}$ Prompt | WC | WC∗ | FS | RS | USP | PPC
---|---|---|---|---|---|---
SLP | 3% | 50% | 94% | 88% | 93% |
QA | 28% | 50% | 85% | 96% | 93% | 47%
Comp | 35% | 60% | 90% | 100% | 88% |
Table 3: Test scores reported as percent of highest possible score. For CELF5 age equivalents, see Table 4. Prompt | WC | WC∗ | FS | RS | USP | PP
---|---|---|---|---|---|---
SLP | 3:2 | 7:5 | 21:5+ | 21:5+ | - |
QA | 5:3 | 7:5 | 12:7 | 21:5+ | - | < 3
Comp | 5:11 | 8:10 | 15:1 | 21:5+ | - |
Table 4: Age equivalent (year:month) for scores in Table 3. Age is unavailable
for USP. Figure 2: Accuracy of InstructGPT (GPT-3.5) on WC large and Def.; AoA
is defined in § 2.2.1. Solid line tests all pairs at most the AoA, while
dotted tests pairs exactly at the AoA.  Figure 3: Legend as in Figure 2.
Vertical axis shows $p$-values from mean tests. Red dashed line is
$\alpha=0.05$. $\mu_{a}$ is estimated based on Dale and O’rourke (1976),
accounting for chance and subjectivity of gold associations. For details, see
Appendix C.

We show CELF5 test scores and age equivalents for InstructGPT,888The exact
OpenAI LM is ”text-davinci-002” sampled via nucleus sampling top_p=0.95,
temp=1, max_tokens=256. We also explore the recommended ”factual” setting –
top_p=1 and temperature=0 – for WC, which is arguably a fact-oriented task,
but observe slightly worse results. Additional analysis of parameter
sensitivity is provided in Appendix D. in Tables 3 and 4, respectively.
Notice, we include a modified Word Classes test WC∗. While official clinical
evaluation stipulates the evaluator should prematurely conclude the WC test if
4 sequential incorrect answers are provided, this stopping rule (ceiling) is
based on human developmental standards (i.e., easier words are presented
earlier), which GPT may not follow. For comparison, WC∗ reports evaluation
without a ceiling.

The key qualitative takeaways from clinician observations are discussed next.
Where possible, we also incorporate quantitative results from the question
outcomes for added support.

##### Recollection vs. Inference

InstructGPT excels at memorization tasks, but seems to have trouble making new
inferences. Of all the tests, Word Classes (WC) most requires the ability to
make new inferences from existing (lexical semantic) knowledge. This is also
the task that InstructGPT performs worst at, demonstrating alignment with the
ability of a 6 year old. While InstructGPT was generally more successful on
other tasks, the evaluating clinician observed errors in USP (Comp protocol)
were also frequently due to trouble drawing inferences. Better inferences were
noted using the SLP protocol, but sometimes these were not fact based (i.e.,
impossible to determine from context). When InstructGPT provided explanations
for answers on WC, the clinician observed flawed or irrelevant logic in more
than 59% of cases. See Table 2 for examples of inferential and other language
application errors. Note, this pitfall of GPT also induces a large variation
in scores (e.g., from age equivalent over 21 to under 4) which is certainly
atypical of human norms. Rarely (if ever) would a human evaluation exhibit
such variation. Despite some negatives, the impressive proficiency of GPT at
recollection suggests it would excel in conversational applications requiring
rote information extraction. In applications requiring inference about word
meanings, one might consider communicating the error patterns of GPT,
depending on target interlocutor age and conversational goals.

##### Difficult Relations

InstructGPT has particular trouble with functional roles, categories, and
antonyms. In particular, on Word Classes (WC), the evaluating clinician
identified multiple errors for each of these relation types. For functional
roles, InstructGPT fails to recognize relationships like "[X] goes in [Y]" or
"[X] used for [Y]". It also failed to recognize categories like "body parts"
and "senses" as well as dichotomous pairs used to describe the same concept;
e.g., "brief" and "long".${}^{\text{\ref{TOU}}}$ Table 2 shows additional
examples.

##### Atypical Semantic Errors

According to human developmental standards, InstructGPT understands some
"hard" words better than "easy" words. In particular, the clinician observed
error patterns in semantic knowledge which were distinct from typical patterns
in children. While InstructGPT failed frequently at comparatively "easy" word
relations (e.g., shirt and jacket), it succeeded at "harder" relations (e.g.,
copious and teem).${}^{\text{\ref{TOU}}}$ In the data, this is exemplified by
WC and the modified test WC∗. The difference in scores implies InstructGPT
accumulated sequential errors early in the test on "easy" word relations,
while still succeeding later on "hard" relations. This example hits home the
necessity of considering human demographics in evaluation, since GPT does not
appear to conform to human preconceptions of how knowledge builds. This
disconnect can lead to significant misunderstandings in conversational
applications.

##### Social Error Patterns

InstructGPT often fails to consider context, leading to issues in social
capability. In particular, the clinician observed key behaviors of InstructGPT
based on the Pragmatics Checklist (PPC). InstructGPT said illogical things
given the surrounding context and displayed misunderstanding of directions and
goals. For example, some cases are exemplified during WC and USP in Table 2.
Clinician also observed GPT provided too much information when answering
questions. Mostly, these issues in social language capability are related to
poor understanding/use of context as determined by the clinician. For PP,
these contextual issues are exacerbated by an LMs limited interactive
capabilities (e.g., inability to use potentially non-verbal aspects of
language). We consider how these factors affect PP scores in Appendix A.
Overall, the limited social capabilities of instruction following models “out-
of-the-box” suggests further work is needed to adapt these models to
conversational applications. We do expect chat models (e.g., gpt-3.5-turbo) to
have better social capabilities and leave this study for future work.

###  3.2 Automated Evaluation Results

Figure 4: Expected increase in probability of GPT error on WC large task when
property of the word pair (or response) holds. Estimates based on LPM and are
significant at confidence 99% (with Bonferroni correction) except H4.
Estimates are near true effect size for large samples (see Appendix F). Figure
5: Bounds on $p$-values for $\mathtt{TD}$ and Means test. Red dotted line is
significance level 0.05.

Performance of InstructGPT999Intended answer is automatically extracted using
the first uttered test words (2 for WC large and 1 for Def). On CELF5, the
clinician noted the intended word pair was always the first two test words
uttered by GPT, while (later) explanations may include other test words. Human
evaluation of the rule on WC large ($n=108$) showed 100% intent recovery. on
WC large and Def is provided in Figure 2 with $p$-values from a mean test for
LM age in Figure 3. We provide performance of human annotators on a 1%
($n=108$) sample of WC large in Appendix Table 5.

##### Overall Performance

Coarse-grained results for InstructGPT are generally consistent with the
clinical evaluation results in § 3.1. Accuracy, which is equivalent to the WC∗
score in Table 3, is consistent with the clinical evaluation based on a 95%
confidence interval.101010Via Hoeffding’s inequality with $n=40$ examples
tested in WC∗, the two-sided interval has lower bound of 39%. It is notable
that WC large may be more difficult, as exhibited by human disagreements (see
Table 5). Overall, the general takeaways of the clinical exam can be confirmed
in these coarse-grained results. For example, InstructGPT appears to succeed
at the recollection task Def, which only requires recalling a definition, and
perform worse at the inference task WC large. Also, GPT shows a spike in
performance when word pair AoA is 19 (exactly), demonstrating unnatural word
acquisition compared to human age standards.

##### Automated Determination of LM Age

Based on the $p$-values in Figure 3, we determine InstructGPT to align with
ages 9 and 11 for the WC large task, depending on whether $\mathbb{G}_{a}$
contains questions with word pair AoA exactly $a$ or $\leq a$, respectively.
This can be seen by excluding all ages where the means test rejects the null
that GPT aligns with age group $a$ (i.e., by dipping below the dashed red line
of significance). When word pair AoA is exactly 19, the means test succeeds in
identifying the aforementioned "unnatural" spike in performance by correctly
failing to reject the null that GPT is aged 19. Overall, the means test
findings on WC large are consistent with the clinical evaluation.

##### Automated Analysis of Errors

In Appendix Figure 7, we visualize the influential factors on language errors
discussed in § 2.2.2 and determine each has statistically significant
association with the errors of InstructGPT. We also consider 6 hypotheses
about the role of these factors on the likelihood of error for InstructGPT.
These hypotheses were formulated through discussion with the evaluating
clinician and tested with an LPM. Notably, many results (Figure 4) confirm
insights from the CELF5 examination (§ 3.1):

  * •

H1: InstructGPT has more trouble when the associated pair includes an adverb
or adjective. Clinician observations indicate trouble with modifiers in CELF5
examination. This hypothesis is confirmed in Figure 4 where we estimate a 3.5%
increase in probability of error when at least one word in the pair is an
adjective or adverb. Note, testing for other clinician observations (e.g.,
trouble with basic nouns) was not significant.

  * •

H2: InstructGPT has more trouble when the associated pair do not share POS.
Distinct POS can indicate more complex relationships across word pairs, which
is a noted problem for GPT in CELF5 evaluation. This hypothesis is confirmed
with a similar effect size as H1.

  * •

H3: InstructGPT has more trouble with particular relation types. Building on
the last hypothesis, we isolate "easy" word pair relations including {action,
location, phrase, and synonym }, so the remaining "hard" word pair relations
overlap with types of relations our clinician noted as difficult for GPT.
Unknown relations are assumed to be hard. Results in Figure 4 confirm this
hypothesis where we estimate a relatively large 11% increase in error
probability for "hard" relations.

  * •

H4: InstructGPT has more trouble with morphologically complex words. As
before, assuming the complexity of a word is tied to its count of
morphological features, we would expect GPT to have trouble with words having
medium or high morphological feature count. We estimate an effect size similar
to H1 and H2.

  * •

H5: GPT does worse when it explains. Clinician evaluation on the Pragmatics
checklist reveals untrustworthy, illogical explanations by GPT. Testing at
scale reveals GPT has more errors when it attempts to explain its reasoning
with a relatively large estimated effect size of 6%.

  * •

H6: InstructGPT has more trouble as the word pair AoA increases. While we
include word pair AoA in our analysis as a potential confounder for which to
control, it is also interesting to see how this variable impacts the
performance of GPT. We estimate a 0.5% increase in probability of error for
each unit increase in AoA; e.g., a word pair AoA of 19 would cause 5% greater
chance of error than an AoA of 9.

###  3.3 Simulated Results with $\mathbf{TD}$ Test for Age

In the last section, we used the Means test for LM age because we did not have
access to sample human question outcomes from different age groups and can
only estimate the test parameter $\mu_{a}$. Next, we simulate data to show the
benefit of the $\mathbf{TD}$ test when access to human outcomes is available.

##### Setup

Figure 5 shows results applying tests to LM and human samples GPT v.H as well
as two (same age) human samples H v.H. Ideally, a test should fail to reject
the null for all H v.H experiments and be sensitive for GPT v.H experiments,
rejecting the null when appropriate. To conduct tests and study variation, we
require multiple human samples. Since we only have one (used to define WC
large), we simulate human test performance with a random variable $H_{i}$
defined:

$H_{i}=\begin{cases}h(\hat{D}_{i})&\text{with probability}\ \rho,\\\
\text{Bernoulli}\Big{(}\frac{\mu-\rho\mathbf{E}[h(\hat{D}_{i})]}{1-\rho}\Big{)}&\text{else}\end{cases}$
(4)

So, we have $\mathbf{Pr}(H_{i}=1)=\mu$ regardless, and $\rho$ controls the
extent to which the model LM and the sampled human agree. For all experiments
in Figure 5, we conduct 25 trials. $H_{i}$ is simulated using Eq. (4),
$h(\hat{D}_{i})$ is given by GPT performance on WC large, and questions for
age $a$ comprise all questions whose AoA is less than or equal to $a$. We
estimate $\mu$ and $\gamma$ from data.111111$\mu$ is lower bound of a 95%
Hoeffding interval around the acc. in Table 5; $\gamma$ is disagreement across
sim. samples of $H_{i}$.

##### Failure of Means Test

As the agreement parameter $\rho$ between the sampled human and the model LM
increases, tests using the $\mathbf{TD}$ statistic adapt appropriately,
failing to reject at higher and higher ages. So, using $\mathbf{TD}$ allows us
to account for context well. In comparison, the result of the means test is
unchanged, demonstrating a benefit of using the $\mathbf{TD}$ statistic (when
possible).

##  4 Related Works

##### Psycho-linguistic Study of LMs

Recent work is not devoid of appeal to psychology and linguistics, which is
much of the basis for the clinical techniques from Speech Language Pathology
that we propose. Sahu et al. (2021) use Bloom’s Taxonomy (Bloom, 1956) to add
contextual information in LM prompts and improve question answering
capability. Hovy and Yang (2021) develop a taxonomy of social factors to
consider in evaluation of LMs. Most similar to our work, Cong (2022) evaluate
GPT-3 using psycholinguistic tests, and Chang and Bergen (2022) use word age-
of-acquisition to study development of LM word knowledge (throughout training)
compared to human development. $\mathtt{HumBEL}$ differs significantly from
these works, directly measuring the alignment of an LM with a human sub-
population, and providing systematic techniques for automatic and clinician-
in-the-loop answers to this question. As such, it gives a concise solution to
the broad goal of aligning LM evaluation with human demographic groups.

##### LM Evaluation and Human-Likeness

Automated metrics for evaluation of generated text include metrics based on
$n$-grams such as BLEU (Papineni et al., 2002), ROUGE (Lin, 2004), and CIDEr
(Vedantam et al., 2015) as well as metrics based on neural models (Sellam et
al., 2020; Zhang et al., 2019; Inan et al., 2021). Bruni and Fernandez (2017)
also propose a (learned) adversary to discriminate between human and generated
text. Text discrimination (by humans or models) has appeared in other works as
well (Ippolito et al., 2020; Dou et al., 2022). Human annotation and
evaluation, of course, remains the gold-standard. Our work is most related to
those works considering evaluation of human-likeness (and properties thereof).
For example, our techniques target commonsense knowledge, inference, and
social factors as studied in a variety of works (Nair et al., 2020; Kassner
and Schütze, 2020; Liu et al., 2022b). Our work builds on broad goals of
evaluating human-likeness not only in the types of tasks we test, but also in
the communication of the results to the practitioner, presenting qualitative
and quantitative results in terms of human demographic information.

##### SLP Tasks

It is worthwhile to note that many of the tasks we consider have existing
counterparts appearing in the NLP literature. For example, USP is a narrative
QA task Kočiský et al. (2018) and WC is, in some respects, akin to the word
association tests used to evaluate distributional semantic modelling of words
Bolukbasi et al. (2016); Caliskan et al. (2017); Liu et al. (2022b). Our work
extends this literature by incorporating clinician-in-the-loop feedback for
the design and evaluation of these tasks, and furthermore, is the first to
incorporate human demographic data for comparison of LM performance to human
sub-populations.

##  5 Conclusion

We present $\mathtt{HumBEL}$, which approaches the goal of evaluation aligned
with human demographics by using novel clinician-in-the-loop statistical
techniques to evaluate language models. Our framework moves beyond measuring
superficial coherence of large language models, instead working towards a
human-explainable way to test LMs for language use and context relevance
(Clark, 1996), and to compare this language use to human subpopulations. For
example, our techniques provide insight on the utility of LMs for inference,
information-extraction, and social applications. Furthermore, in building
connections between human and LM development, diverse research communities may
find LMs useful for studying language disorders in humans as well. We make the
code and data of our framework publicly available, so future researchers can
make use of our suite of automated statistical techniques, and protocols for
clinician evaluation.

## Acknowledgements

Thanks to Sulare Telford Rose, Ph.D., CCC-SLP for her helpful comments and
feedback.

## Limitations

First and foremost, we wish to be careful about claiming our proposed
techniques ascribe an intellectual age to any AI model. It is not yet clear
whether the tests for human language ability we use are an appropriate "all-
in-one" assessment for artificial intelligence, especially considering the
vast range of specific tasks in the literature at which artificial agents can
achieve super-human performance. While the tasks we study are good indicators
of general language skills in humans, connections between our framework and
performance generalization of AI models on untested reasoning and social
language tasks are unknown. For example, factors such as overfitting,
adversarial robustness, stochasticity, and prompt sensitivity can all play a
new distinct role for AI models. Thus, it is better to take care and interpret
our framework as designed to investigate alignment of LM language use/skills
to the language use/skills of particular human demographic groups on
particular language tasks. As noted, there is still significant benefit to
this more careful interpretation, since our framework serves to assess model
fit in conversational AI with consideration of interlocutor demographics and
goals.

Second, the nature of language models produces a gap in evaluation protocols
between children and these models. While we take a number of steps to
alleviate these issues, there is still need for this gap to be bridged
completely; i.e., so that normative age data is most accurate. Taking clinical
evaluation to perceiving and embodied models is one possibility. One can also
consider collecting new normative data on tasks designed for a language-only
medium, or, consider using fine-grained metrics more commonly used by SLPs;
e.g., preferring percentile rank among same age peers over age equivalents.

Third, we do not explicitly consider inter-annotator (i.e., inter-clinician
agreement). The CELF5 exam does already come with estimates of inter-clinician
agreement on evaluations with humans, but it is possible that working with
language models produces new challenges that will ultimately invalidate this
estimate. Fourth, more human data is needed to test statistics like the test
divergence on real world data. Finally, our work does not explore in-depth
automated analyses on other problem areas of LMs such as social language;
i.e., while our clinician-in-the-loop analysis does consider pragmatics, our
automated analysis focuses on inference.

## Ethics Statement

The proposed approach does not explicitly evaluate societal biases inherited
by language models, so any harm or bias associated with these models should be
considered separately. General methods that propose to mitigate harms can help
to resolve these issues, along with careful human evaluations.

For readers or users of our framework to gain access to test questions, they
may need to purchase licenses from the company, university, or research lab
that publishes and produces these tests. Our use of the CELF5 examination is
consistent with our publishing agreement with Pearson, Inc.

Our human subject board approved our protocol. Human subjects participated
voluntarily and were compensated according to the regulations approved by our
human subject review board.

## References

  * Battey et al. (2019) Heather S Battey, David R Cox, and Michelle V Jackson. 2019.  On the linear in probability model for binary data.  _Royal Society open science_ , 6(5):190067.
  * Bisk et al. (2020) Yonatan Bisk, Ari Holtzman, Jesse Thomason, Jacob Andreas, Yoshua Bengio, Joyce Chai, Mirella Lapata, Angeliki Lazaridou, Jonathan May, Aleksandr Nisnevich, Nicolas Pinto, and Joseph Turian. 2020.  Experience Grounds Language.  In _Conference on Empirical Methods in Natural Language Processing (EMNLP)_.
  * Bloom (1956) Benjamin Samuel Bloom. 1956.  Taxonomy of educational objectives: The classification of educational goals.  _Cognitive domain_.
  * Bolukbasi et al. (2016) Tolga Bolukbasi, Kai-Wei Chang, James Y Zou, Venkatesh Saligrama, and Adam T Kalai. 2016.  Man is to computer programmer as woman is to homemaker? debiasing word embeddings.  _Advances in neural information processing systems_ , 29.
  * Bruni and Fernández (2017) Elia Bruni and Raquel Fernández. 2017.  Adversarial evaluation for open-domain dialogue generation.  In _Proceedings of the 18th Annual SIGdial Meeting on Discourse and Dialogue_ , pages 284–288, Saarbrücken, Germany. Association for Computational Linguistics.
  * Bruni and Fernandez (2017) Elia Bruni and Raquel Fernandez. 2017.  Adversarial evaluation for open-domain dialogue generation.  In _Proceedings of the 18th Annual SIGdial Meeting on Discourse and Dialogue_ , pages 284–288.
  * Brysbaert and Biemiller (2017) Marc Brysbaert and Andrew Biemiller. 2017.  Test-based age-of-acquisition norms for 44 thousand english word meanings.  _Behavior research methods_ , 49(4):1520–1523.
  * Caliskan et al. (2017) Aylin Caliskan, Joanna J Bryson, and Arvind Narayanan. 2017.  Semantics derived automatically from language corpora contain human-like biases.  _Science_ , 356(6334):183–186.
  * Chang and Bergen (2022) Tyler A. Chang and Benjamin K. Bergen. 2022.  Word acquisition in neural language models.  _Transactions of the Association for Computational Linguistics_ , 10:1–16.
  * Clark et al. (2021) Elizabeth Clark, Tal August, Sofia Serrano, Nikita Haduong, Suchin Gururangan, and Noah A. Smith. 2021.  All that’s ‘human’ is not gold: Evaluating human evaluation of generated text.  In _Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 7282–7296, Online. Association for Computational Linguistics.
  * Clark (1996) Herbert H Clark. 1996.  _Using language_.  Cambridge university press.
  * Cong (2022) Yan Cong. 2022.  Psycholinguistic diagnosis of language models’ commonsense reasoning.  _CSRR 2022_ , page 17.
  * Dale and O’rourke (1976) Edgar Dale and Joseph O’rourke. 1976.  The living word vocabulary, the words we know: A national vocabulary inventory.
  * Diamond and Evans (1973) James Diamond and William Evans. 1973.  The correction for guessing.  _Review of educational research_ , 43(2):181–191.
  * Dou et al. (2022) Yao Dou, Maxwell Forbes, Rik Koncel-Kedziorski, Noah A Smith, and Yejin Choi. 2022\.  Is gpt-3 text indistinguishable from human text? scarecrow: A framework for scrutinizing machine text.  In _Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pages 7250–7274.
  * Freund et al. (2004) John E Freund, Irwin Miller, and Marylees Miller. 2004.  _John E. Freund’s Mathematical Statistics: With Applications_.  Pearson Education India.
  * Geertz (1975) Clifford Geertz. 1975.  Common sense as a cultural system.  _The Antioch Review_ , 33(1):5–26.
  * Gomila (2021) Robin Gomila. 2021.  Logistic or linear? estimating causal effects of experimental treatments on binary outcomes using regression analysis.  _Journal of Experimental Psychology: General_ , 150(4):700.
  * Harrington et al. (2022) Christina N Harrington, Radhika Garg, Amanda Woodward, and Dimitri Williams. 2022\.  “it’s kind of like code-switching”: Black older adults’ experiences with a voice assistant for health information seeking.  In _Proceedings of the 2022 CHI Conference on Human Factors in Computing Systems_ , pages 1–15.
  * Hayes (2019) Alex Hayes. 2019.  consistency and the linear probability model.
  * Horrace and Oaxaca (2003) William C Horrace and Ronald L Oaxaca. 2003.  New wine in old bottles: A sequential estimation technique for the lpm.  _Available at SSRN 383102_.
  * Hovy and Yang (2021) Dirk Hovy and Diyi Yang. 2021.  The importance of modeling social factors of language: Theory and practice.  In _Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 588–602, Online. Association for Computational Linguistics.
  * Inan et al. (2021) Mert Inan, Piyush Sharma, Baber Khalid, Radu Soricut, Matthew Stone, and Malihe Alikhani. 2021.  Cosmic: A coherence-aware generation metric for image descriptions.  _arXiv preprint arXiv:2109.05281_.
  * Ippolito et al. (2020) Daphne Ippolito, Daniel Duckworth, Chris Callison-Burch, and Douglas Eck. 2020.  Automatic detection of generated text is easiest when humans are fooled.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 1808–1822.
  * Kassner and Schütze (2020) Nora Kassner and Hinrich Schütze. 2020.  Negated and misprimed probes for pretrained language models: Birds can talk, but cannot fly.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 7811–7818, Online. Association for Computational Linguistics.
  * Kočiský et al. (2018) Tomáš Kočiský, Jonathan Schwarz, Phil Blunsom, Chris Dyer, Karl Moritz Hermann, Gábor Melis, and Edward Grefenstette. 2018.  The NarrativeQA reading comprehension challenge.  _Transactions of the Association for Computational Linguistics_ , 6:317–328.
  * Lin (2004) Chin-Yew Lin. 2004.  Rouge: A package for automatic evaluation of summaries.  In _Text summarization branches out_ , pages 74–81.
  * Liu et al. (2022a) Chunhua Liu, Trevor Cohn, Simon De Deyne, and Lea Frermann. 2022a.  WAX: A new dataset for word association eXplanations.  In _Proceedings of the 2nd Conference of the Asia-Pacific Chapter of the Association for Computational Linguistics and the 12th International Joint Conference on Natural Language Processing (Volume 1: Long Papers)_ , pages 106–120, Online only. Association for Computational Linguistics.
  * Liu et al. (2022b) Ruibo Liu, Ge Zhang, Xinyu Feng, and Soroush Vosoughi. 2022b.  Aligning generative language models with human values.  In _Findings of the Association for Computational Linguistics: NAACL 2022_ , pages 241–252, Seattle, United States. Association for Computational Linguistics.
  * Lucy and Bamman (2021) Li Lucy and David Bamman. 2021.  Gender and representation bias in gpt-3 generated stories.  In _Proceedings of the Third Workshop on Narrative Understanding_ , pages 48–55.
  * Nair et al. (2020) Sathvik Nair, Mahesh Srinivasan, and Stephan Meylan. 2020.  Contextualized word embeddings encode aspects of human-like word sense knowledge.  In _Proceedings of the Workshop on the Cognitive Aspects of the Lexicon_ , pages 129–141, Online. Association for Computational Linguistics.
  * Nivre et al. (2016) Joakim Nivre, Marie-Catherine de Marneffe, Filip Ginter, Yoav Goldberg, Jan Hajič, Christopher D. Manning, Ryan McDonald, Slav Petrov, Sampo Pyysalo, Natalia Silveira, Reut Tsarfaty, and Daniel Zeman. 2016.  Universal Dependencies v1: A multilingual treebank collection.  In _Proceedings of the Tenth International Conference on Language Resources and Evaluation (LREC’16)_ , pages 1659–1666, Portorož, Slovenia. European Language Resources Association (ELRA).
  * Ogan et al. (2012) Amy Ogan, Samantha Finkelstein, Elijah Mayfield, Claudia D’adamo, Noboru Matsuda, and Justine Cassell. 2012.  " oh dear stacy!" social interaction, elaboration, and learning with teachable agents.  In _Proceedings of the SIGCHI conference on human factors in computing systems_ , pages 39–48.
  * Papineni et al. (2002) Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. 2002.  Bleu: a method for automatic evaluation of machine translation.  In _Proceedings of the 40th annual meeting of the Association for Computational Linguistics_ , pages 311–318.
  * Rajani et al. (2019) Nazneen Fatema Rajani, Bryan McCann, Caiming Xiong, and Richard Socher. 2019.  Explain yourself! leveraging language models for commonsense reasoning.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 4932–4942, Florence, Italy. Association for Computational Linguistics.
  * Sahu et al. (2021) Pritish Sahu, Michael Cogswell, Ajay Divakaran, and Sara Rutherford-Quach. 2021\.  Comprehension based question answering using bloom’s taxonomy.  In _Proceedings of the 6th Workshop on Representation Learning for NLP (RepL4NLP-2021)_ , pages 20–28.
  * Sellam et al. (2020) Thibault Sellam, Dipanjan Das, and Ankur Parikh. 2020.  BLEURT: Learning robust metrics for text generation.  In _Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics_ , pages 7881–7892, Online. Association for Computational Linguistics.
  * Shalev-Shwartz and Ben-David (2014) Shai Shalev-Shwartz and Shai Ben-David. 2014.  _Understanding machine learning: From theory to algorithms_.  Cambridge university press.
  * Sicilia and Alikhani (2022) Anthony Sicilia and Malihe Alikhani. 2022.  LEATHER: A framework for learning to generate human-like text in dialogue.  In _Findings of the Association for Computational Linguistics: AACL-IJCNLP 2022_ , pages 30–53, Online only. Association for Computational Linguistics.
  * Szekely (1989) Gabor J Szekely. 1989.  Potential and kinetic energy in statistics.  _Lecture Notes, Budapest Institute_.
  * Székely and Rizzo (2013) Gábor J Székely and Maria L Rizzo. 2013.  Energy statistics: A class of statistics based on distances.  _Journal of statistical planning and inference_ , 143(8):1249–1272.
  * Uchendu et al. (2021) Adaku Uchendu, Zeyu Ma, Thai Le, Rui Zhang, and Dongwon Lee. 2021.  TURINGBENCH: A benchmark environment for Turing test in the age of neural text generation.  In _Findings of the Association for Computational Linguistics: EMNLP 2021_ , pages 2001–2016, Punta Cana, Dominican Republic. Association for Computational Linguistics.
  * Vedantam et al. (2015) Ramakrishna Vedantam, C Lawrence Zitnick, and Devi Parikh. 2015.  Cider: Consensus-based image description evaluation.  In _Proceedings of the IEEE conference on computer vision and pattern recognition_ , pages 4566–4575.
  * West et al. (2022) Peter West, Chandra Bhagavatula, Jack Hessel, Jena Hwang, Liwei Jiang, Ronan Le Bras, Ximing Lu, Sean Welleck, and Yejin Choi. 2022.  Symbolic knowledge distillation: from general language models to commonsense models.  In _Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies_ , pages 4602–4625, Seattle, United States. Association for Computational Linguistics.
  * White (1980) Halbert White. 1980.  A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity.  _Econometrica: journal of the Econometric Society_ , pages 817–838.
  * White (1982) Halbert White. 1982.  Maximum likelihood estimation of misspecified models.  _Econometrica: Journal of the econometric society_ , pages 1–25.
  * Wiig et al. (2013) Elisabeth H Wiig, Eleanor Messing Semel, and Wayne Secord. 2013.  _CELF 5: Clinical evaluation of language fundamentals_.  Pearson/PsychCorp.
  * Zhang et al. (2019) Tianyi Zhang, Varsha Kishore, Felix Wu, Kilian Q Weinberger, and Yoav Artzi. 2019\.  Bertscore: Evaluating text generation with bert.  _arXiv preprint arXiv:1904.09675_.

##  Appendix A CELF5 Testing Modifications

As noted in the main text, we typically adhere to the administration of the
CELF5 exam (Wiig et al., 2013) exactly as prescribed in the examination manual
and booklet. Changes discussed in the main text are due to the nature of LMs,
which have narrow training objectives and an inability to visually perceive or
act in an embodied environment.

##### Visual Stimuli

Besides what is discussed in the main text, one of the key ways we modify exam
administration is by removing any visual stimuli. For example, Word Classes
(WC) has accompanying visual stimuli (i.e., an image), which is presented with
each of the words. Formulated sentences (FS) also uses a visual stimulus to
restrict the sentence content. Depending on the test, these stimuli may either
help or hurt performance, if perceptually grounded models were tested on the
same tasks.

##### Non-Verbal and Interactive Evaluation

The other primary restriction comes from an inability to judge the capability
of an LM’s non-verbal skills and interactive behaviors as they relate to
social language use; i.e., this impacts the pragmatics profile PP and
checklist PPC. For example, the clinician could not evaluate non-verbal cues
like eye contact, voice intonation, and body language. The clinician also
could not evaluate interactive capabilities like whether the subject uses
communicative strategies to elicit attention from the clinician or effectively
resolve interruptions during conversation. We considered two main options for
results reported in the main text: penalizing the LM for not being able to
exhibit these key social capabilities by its very nature, or restricting the
scoring process to those skills that could possibly be achieved by the LM
without visual processing and embodied action. Notably, the latter option
invalidates the validity of age equivalents. For PPC, results in the main text
report the latter option, since we do not make an age equivalent estimation in
this case, and we restrict consideration to 15 of the 32 possible checklist
items. For PP, since we report age estimates, reported results use the former
option; i.e., using all test items and penalizing the LM for errors in non-
verbal/interactive language skills. Notably though, if we restrict
consideration to language-only skills (7 of 50 possible skills) and
incorrectly determine the age estimate by extrapolating the score (i.e.,
assuming the subject would achieve the same average score if it had been
tested on the remaining skills), we still arrive at the published age
equivalent. So our choices here are not of much consequence in the current
case. Future work should be careful to reconsider such issues, and the impact
of including non-verbal/interactive language skills on social assessments.

##  Appendix B Word AoA: Determination and Statistics

Recall, we use a test-based age-of-acquisition dataset (Dale and O’rourke,
1976; Brysbaert and Biemiller, 2017) to determine word age-of-acquisition
(AoA) of 40K English words. Age is determined by U.S. K-12 grade-level and
adapted to typical age equivalents (discussed later). Word grade-level is
determined via multiple-choice test in which target word definitions are
provided and subjects select the target amongst multiple alternatives. A word
is assigned to the earliest level at which 67-80% of subjects answer
correctly, equating to about 50% of subjects "knowing" the word at this level
(accounting for chance). A word’s AoA is then inferred from grade-level via
typical grade-to-age mapping for U.S. K-12; i.e., $\text{age}=\text{grade}+5$.
Tests were given to U.S. (Midwest) students across a range of socio-economic
and racial backgrounds with each specific word-meaning administered to about
200 subjects. Word and word pair AoA is visualized in Figure 8 and 9. As noted
in the main text, besides WC large, we also test GPT-3.5 on this multiple-
choice test for matching word definitions which we call Definitions (Def).
Alternatives are selected randomly and prompt follows the Comp format: Among
the words "[W]", "[X]", "[Y]", and "[Z]", the word that most means "[Defn.]"
is.

##  Appendix C Estimating Human Mean Correctness

In experiments, we use a similar approach as Dale and O’rourke (1976) to
estimate $\mu_{a}$ from word AoA, while accounting for guessing (and in our
case, subjectivity of the task). From test results of Dale and O’rourke
(1976), we make a reasonable assumption that about 50% of humans at a
particular age level know a word at this age level. For a human to be correct
on the WC task, they must both know the target words and agree with the
annotation. To compute probability for the latter, we estimate probability of
agreement from Table 5 using the upperbound of a 95% Hoeffding interval for
the reported % disagreement (to be conservative).121212Agreement is 100 less
the % disagreement. Results without the upperbound – i.e., instead, using the
exact observed disagreement– are slightly different, but generally consistent
with our takeaways in the main text. See Figure 6. Then, assuming agreement
and knowledge are independent, this means 38% of humans aged $a$ will be
correct based on knowledge. Finally, accounting for guessing using the score
correction of Diamond and Evans (1973), this means we should expect about 47%
of humans aged $a$ to answer correctly.

Figure 6: Results in Figure 3, re-reported without using a Hoeffding interval
to estimate disagreement. Key results (i.e., lowest age estimate) differs only
by a grade level.

##  Appendix D Sensitivity Analysis: Prompts and Parameters

Although testing for the impact of various prompts and parameters is
impractical when evaluation is done by a clinician, our automated version of
the WC test provides a more practical alternative to explore the impact of
these model choices. We test different parameter settings for nucleus sampling
(i.e., $\texttt{top\\_p}\in\\{0.8,0.9,0.95\\}$) and temperature scaling (i.e.,
$\texttt{temp}\in\\{0,0.5,0.7,1\\}$) as well as 11 different prompts with
varying aspects of the key prompt differences highlighted in Table 1. All in
all, we test differences in GPT performance of a total of 77 different
prompt/parameter settings on sample of 100 examples from WC large. The
standard deviation in the LM scores was only 3% and a $\chi^{2}$ test for
independence between the settings and the error rates indicates there is no
statistically significant association between the settings and the error
rates. In other words, GPT performance was not significantly impacted by
different prompt/parameter settings.

##  Appendix E Feature Extraction for Error Analysis

  1. 1.

Part of Speech (POS) While word POS is dependent on context, the explanations
in the WAX dataset (Liu et al., 2022a) provide an opportunity to infer the
annotator’s intended POS for the word association. In particular, we can apply
open-source POS parsers131313We use the spacy package. to the annotator
explanation. This strategy assumes an explanation uses a word in the same POS
as intended for the word association. In case an annotator does not use the
full word pair, we use "X" for unknown. Results in Figure 7 suggest GPT-3.5
error rates can vary widely based on the pairs POS, exhibiting particular
association with adverbs, adjectives, and pairs having distinct POS.

  2. 2.

Relation The WAX dataset also contains relation categories for word
associations. Recall, the results of the clinical exam suggested particular
relations are challenging for GPT-3.5 and the results in Figure 7 seem to
suggest this as well; e.g., as in the clinical exam, functional relations are
hard for GPT-3.5 to identify.

  3. 3.

Morphological Complexity We also consider Morphological Features within the
Universal Dependencies framework (Nivre et al., 2016), which describe semantic
and grammatical properties of words. We define morphological complexity as the
total number of morphological features attached to at least one of the the
words in the association. High corresponds to more than 4 features, medium
corresponds 3-4 features, and low corresponds to 2 or less features. Our
working assumption is that the number of features is a loose indicator of the
complexity of the a word’s meaning and can thus introduce challenges for
GPT-3.5. The results in Figure 7 do appear to confirm this hypothesis.

  4. 4.

Explanations Lastly, we consider if GPT-3.5 provides an (unprompted)
explanation of its reasoning behind an answer. Interestingly, this occurs more
times than not on the WC large dataset. While our intuition may tell us this
means GPT-3.5 is more confident in the answer, the clinical evaluation
actually demonstrated that GPT-3.5 often provided illogical explanations that
may appear off-topic or overly complex to humans. Results in Figure 7 seem to
confirm these findings, indicating that explanations typically led to worse
performance at identifying associations.

##  Appendix F Overview of Statistical Tools

###  F.1 $\chi^{2}$ Test

The $\chi^{2}$ test is commonly used to determine statistical association
between two categorical variables (Freund et al., 2004). In our case, the two
categorical variables are (1) the occurrence of a language application error
by GPT and (2) one of the categorical features of the word pair discussed in §
2.2.2. The test uses a contingency table; i.e., a table of counts formed by
letting one of the variables define the columns, the other variable define the
rows, and filling each element with the number of occurrences observed for
each pair of categories. Then, the test uses the statistic

$\chi^{2}=\sum\nolimits_{i=1}^{k}\frac{(\text{observed}_{i}-\text{expected}_{i})^{2}}{\text{expected}_{i}}$
(5)

where $k$ is the number of elements in the contingency table,
$\text{observed}_{i}$ is the observed frequency of each element of the table,
and $\text{expected}_{i}$ is the expected frequency under the assumption that
the two categorical variables are independent (i.e., the null hypothesis).
Aptly, the distribution of the statistic is asymptotically $\chi^{2}$ and a
$p$-value can be calculated accordingly. We use a Bonferroni correction to
control for multiple testing (i.e., across the multiple features we present as
well as those not presented).

###  F.2 Linear Probability Model

Consider a $n\times 1$ vector of dependent variables $Y$ and a $n\times m$
matrix of independent variables $X$ where $n$ is the number of observations
and $m$ is a number of features for each observation. In our case, $Y$ is a
binary vector indicating the occurrence of a GPT language application error
and $X$ is a matrix ($m=4$) with the 3 categorical features (discussed in §
2.2.2), and the last column being the word pair AoA (§ 2.2.1). With this
notation, the Linear Probability Model (LPM) assumes a conditional probability
function modeled by:

$\mathbf{Pr}(Y=1|X)=\begin{cases}1,&\quad X\beta>1\\\ 0,&\quad X\beta<0\\\
X\beta,&\quad\text{else}\end{cases}$ (6)

where $\beta$ is an unknown parameter vector of implied dimension. Supposing
$\mathbf{Pr}(X\beta>1)=\mathbf{Pr}(X\beta<0)=0$, the LPM reduces to the
assumption: $\mathbf{Pr}(Y=1|X)=X\beta$, in which case, the standard OLS
estimate

$\hat{\beta}=(X^{\mathrm{T}}X)^{-1}X^{\mathrm{T}}Y$ (7)

provides a consistent estimator for the true parameter $\beta$ (Horrace and
Oaxaca, 2003). Furthermore, using techniques for heteroscedasticity (i.e.,
unequal variance of errors) like White’s robust covariance matrix (White,
1980) allows us to conduct hypothesis testing for significance of the
coefficient estimates (Horrace and Oaxaca, 2003). We use these techniques for
the coefficient estimates and statistical tests in § 3 Figure 4. As before, we
employ a Bonferroni correction to control for multiple testing.

Hum. Acc. | A1 $\neq$ A2 | $\kappa$ | GPT Acc. |  $\neq$ Hum.
---|---|---|---|---
84% | 15% | 0.82 | 56% | 40%
Table 5: Sample ($n=108$) WC large scores of 2 annotators aged 19+ (left) and
InstructGPT (right). For annotators, % disagreement and Cohen’s $\kappa$ is
reported. For GPT, average % disagreement with annotators is reported.
Annotators were students prompted using the same directives as GPT
experimentation; i.e., which two words go together best? Figure 7: Proportion
plot for features associated with InstructGPT errors on WC large. Association
is significant at confidence 99% according to $\chi^{2}$ test of independence
with a Bonferroni correction for multiple testing. Infrequent categories not
shown. Figure 8: AoA of individual words from dataset of Dale and O’rourke
(1976) used to create WC large. Figure 9: AoA of word pairs in WC large. Some
expected accumulation in higher ages occurs (i.e., from taking a max). Figure
10: $\mathbf{TD}$ v. Energy. Split shows how samples are grouped within each
data point. Dotted line is line of best fit.

##### Drawbacks of LPMs

Notably, the LPM has been criticized by some because it is a somewhat fragile
model of the Bernoulli process governing $Y$ (Gomila, 2021). For example, one
may ask if the coefficient estimate makes sense in case $X\beta>1$ or
$X\beta<0$ is a probable outcome: how should this be interpreted? Indeed,
mathematically, this is a failure case. When the presumed model is not true
(i.e., when there are data such that $X\beta>1$) the least square estimates
for the LPM coefficients in Eq. (7) are biased (Horrace and Oaxaca, 2003).
Further, in all cases, the LPM induces heteroscedasticity in the errors
(Horrace and Oaxaca, 2003). Although, as previously noted, this is a minor
concern, granted the existence of easy resolutions like heteroscedasticity
robust covariance matrices. With these two concerns, critics typically suggest
a general linear model like logistic regression. Such models directly consider
the Bernoulli nature of $Y$, restricting output to probabilities in $[0,1]$.
Coefficient estimation is done using MLE, which has nice properties w.r.t
consistency even if the model is mis-specified (White, 1982). For a brief
introduction to drawbacks and benefits of LPMs, we recommend the blog post by
Alex Hayes (Hayes, 2019). Next, we elaborate on our own considerations in
choosing an LPM over logistic regression.

##### Why we choose the LPM

We choose to report results from an LPM for a few reasons:

  1. 1.

First, the model is not obviously wrong in our case. Among, about 10K data
points we sample, not a single point falls into the problem cases: $X\beta>1$,
$X\beta<0$. Thus, under recommended testing procedures, one cannot refute
correctness of the model with data (Horrace and Oaxaca, 2003; Battey et al.,
2019).

  2. 2.

Secondly, analysis using a logistic regression model leads to the same general
conclusions discussed in § 3 — both in terms of significance and
interpretation of the effect sizes. So, our takeaways would be identical had
we reported a logistic regression model.

  3. 3.

Lastly, and most importantly, the LPM results are far more interpretable. As
noted in the main text, LPM coefficients may be interpreted as a relative
increase in probability (see Eq. 1), whereas logistic regression coefficients
represent relative increase in the log odds (i.e., where odds is the ratio of
success probability $Y=1$ to failure probability $Y=0$). The LPM is obviously
more intuitive to a wider audience.

So, in our case, the LPM is a relatively risk free way to increase
interpretability, and as such, we use it to report our results.

###  F.3 Energy Statistic: A Proxy for $\mathbf{TD}$ when Data is Unlabeled

For any independent random variables $A$ and $B$, the discrete energy distance
is defined $\varepsilon_{01}(A,B)$:

$=2\mathbf{E}[1\\{A\neq B\\}]-\mathbf{E}[1\\{A\neq
A^{\prime}\\}]-\mathbf{E}[1\\{B\neq B^{\prime}\\}]$ (8)

where $A^{\prime}$ is an i.i.d copy of $A$, $B^{\prime}$ is an i.i.d. copy of
$B$, and $1\\{\cdot\\}$ is the indicator function; i.e., it returns 1 for true
arguments and 0 otherwise. The discrete energy distance is a modification of
the energy distance sometimes called the statistical energy. It was first
proposed by Szekely (1989) and was studied extensively by Székely and Rizzo
(2013) in the case where $A$ and $B$ are continuous variables admitting a
probability density function. The discrete case is studied in greater detail
by Sicilia and Alikhani (2022) and linked to the test divergence $\mathbf{TD}$
discussed in § 2.2.3.

Typically, energy is computed with respect to a coarsening function; i.e., to
increase sensitivity of the metric for large sets (e.g., as in dialogue and
text generation). In particular, if the random variables are all
$\mathcal{D}$-valued, the coarsening function is a map
$c:\mathcal{D}\to\mathcal{D}$ such that $c(\mathcal{D})=\\{c(d)\mid
d\in\mathcal{D}\\}$ is finite and $\lvert
c(\mathcal{D})\rvert<\lvert\mathcal{D}\rvert$. In experiments, Sicilia and
Alikhani (2022) define the coarsening function $c$ via $k$-means clustering
using real-valued vector representations of dialogues (e.g., from model latent
space) and report the energy $\varepsilon_{01}(c(A),c(B))$. In our case, we
use vector representations from the OpenAI API141414text-embedding-ada-002 and
conduct $k$-means with $k=\min\\{\lfloor.05\times n\rfloor,50\\}$ and $n$ the
total number of observations in the energy computation. For a test question
(and answer) $x$ the response $c(x)$ is defined by the cluster of $x$; i.e.,
one uses an arbitrary question to represent the whole of each cluster and then
assign this question as the output $c(x)$. We show how the energy distance can
be used as a proxy for the test divergence $\mathbf{TD}$ in the next part.

##### Energy as Proxy

In Figure 10, we show the relationship between the discrete energy distance
and the test-divergence $\mathbf{TD}$151515Here, $\mathbf{TD}$ is computed
using the gold associations from WC large to ensure (human) explanations match
the human test answers; i.e., $\mathbf{TD}$ becomes the error rate on WC
large. using the human explanations and GPT explanations to compute the
energy. In particular, this illustrates the efficacy of energy as a proxy
metric for $\mathbf{TD}$ when we only have easy access to textual data without
test outcomes (e.g., as in long-form essay questions). Energy appears to
exhibit a linear relationship when we split the data by AoA or POS.