# Interactions of Linguistic and Domain Overhypotheses in Category Learning

Luann C. Jung<EMAIL_ADDRESS>
Department of Computer Science and Engineering, MIT

Haiyan Wang<EMAIL_ADDRESS>
Department of Statistics, Kansas State University

###### Abstract

For humans learning to categorize and distinguish parts of the world, the set
of assumptions (overhypotheses) they hold about potential category structures
is directly related to their learning process. In this work we examine the
effects of two overhypotheses for category learning: 1) the bias introduced by
the presence of linguistic labels for objects; 2) the conceptual ‘domain’
biases inherent in the learner about which features are most indicative of
category structure. These two biases work in tandem to impose priors on the
learning process; and we model and detail their interaction and effects. This
paper entails an adaptation and expansion of prior experimental work Ivanova
Hofer (2020) that addressed label bias effects but did not fully explore
conceptual domain biases. Our results highlight the importance of both the
domain and label biases in facilitating or hindering category learning.

Keywords: category learning; word learning; overhypotheses; label bias; domain
bias; Bayesian modeling

## Introduction

How do conceptual knowledge and language work together to affect the way we
partition the world into categories? Some researchers Lupyan . (2007) claim
that verbal labels facilitate category learning by helping learners pick out
relevant category dimensions. However, others Brojde . (2011) have shown
contrasting results that indicate that the presence of words can actually slow
down learning.

Recent work (Ivanova & Hofer, 2020) developed a Bayesian computational model
that reconciles these conflicting results. The authors argued that word labels
impose a set of priors on the learning process. Thus, if the word-induced
prior aligns with the true category structure, then words will facilitate
learning. If the word-induced prior does not align with the true structure,
they will make learning harder by biasing the learner toward irrelevant
stimulus features. However, although this ‘label effect’ is explored in depth
by the authors, domain priors are not.

In this work, we alter and expand upon an existing Bayesian framework model
Ivanova Hofer (2020) for examining the effects of linguistic overhypotheses on
category learning. Particularly, we examine the interaction between linguistic
“label-based” priors and “domain-based” conceptual priors. By modeling the
interactions between general concept priors and word-induced priors, we attain
a more accurate representation of the priors involved in category learning.
For example, how do priors that drive the belief that shape is more likely to
be a determinant of category than texture compare and interact with priors
induced by labels?

This work centers around examining and implementing these domain and label
biases into a hierarchical Bayesian model. Through this model, we can better
understand how learning is driven by interactions between language-independent
and language-dependent biases. Specifically, we show that these two different
biases both affect category learning, with the degree of each one’s effect
being variable and learnable.

## Prior Work

Efforts have been made in prior works to describe the effect of labels on
category learning.

A study conducted by lupyan2007 presented participants with two ‘alien’
stimuli and had them learn to distinguish between which aliens to approach and
which to avoid in a supervised learning setup. The distinguishing feature
between the categories was shape, and the authors performed experiments by
providing participants with labels for the aliens (‘leebish’ and ‘grecious’)
that aligned with category membership. These labels did not provide additional
information about category membership to the participants (and thus could not
be considered as features themselves). The study yielded results that the
labels facilitated category learning and posited that the reason was because
the labels helped to emphasize features where object variance aligned with
category membership.

However, another study by Brojde . (2011) communicated doubts about the
beneficial nature of labels in category learning. Specifically, the authors
found that providing shape-based labels with data that is categorized based on
other dimensions such as texture or hue actually hindered category learning.
This provided a contrasting view to the label advantage effect of linguistic
labels on learning. Hence, brojde2011 concluded that instead of emphasizing
category-distinguishing differences across all features, labels serve to bring
the participants’ attention towards dimensions that have been ‘historically
relevant’ for classification.

To reconcile these two views, ivanovahofer proposed that verbal labels serve
as overhypotheses for the learner in category learning. They assert that
learners have a set of biases imposed by, for example, words whose meanings
are characteristic of certain categories. Thus, when labels are used in the
learning process they can either facilitate or hinder learning depending on
whether the priors induced by the overhypotheses align with the true category
structure. However, their model does not account for the potential conceptual
domain biases that a learner may have. Specifically, in their model, the
absence of label biases is considered a ‘no bias’ situation, which they
acknowledge is not truly representative of the learner due to the fact that
even without any label biases the learner may still have inherent domain
biases.

Figure 1: Six example objects for category learning that vary among numerous
features (e.g. shape, texture, color, size, and position).

## Concept Overhypotheses

The need for modeling of not only the label biases in category learning but
also the domain biases is the impetus for this work. When a learner considers
a category learning task, they tend to have some form of conceptual prior over
which features are more indicative of category membership.

An example of this can be demonstrated by looking at Fig 1. Learners faced
with these six objects for classification may have some inherent domain biases
when learning the categories. For example, English speakers (a language where
most nouns for objects are based on shape) tend to be more likely to classify
objects by their shape than other features such as texture Landau . (1988). In
the example in Fig 1, there are numerous features that the data can be
partitioned by: shape, texture (hairless or furry), color (light or dark),
size, and position (lying down, upright), among others. Focusing on each of
these features as deterministic for categorization yields a different set of
final categories.

The conceptual domain biases that learners have when learning to categorize
objects ultimately interplay with biases they develop when given linguistic
labels for objects. One example of this is the case when a learner approaches
the aforementioned category learning task with a conceptual bias that objects
like these are more likely to be categorized by shape. Then, when provided
with labels “furry” and “hairless,” they develop a label bias towards texture
being the diagnostic feature (according to their understanding of the meanings
of the labels). These biases (whether contrasting or constructive) both have
effects on the learner’s learning of category structure, especially in the
early stages of supervised learning.

To better understand the processes by which humans perform these category
learning tasks, we aim to account for the conceptual biases learners have
about which dimensions are more informative of category membership in addition
to any label-induced biases they may acquire.

## Model Setup

In this model, we consider a learning scenario where the goal is to learn to
categorize object exemplars into $C$ disjoint categories. These exemplars
possess $F$ perceptual dimensions (i.e. features) along which they may vary.
The categories themselves vary along at least one of the $F$ features.

${\vec{\alpha_{d}}}$${\vec{\alpha_{l}}}$${domain\;bias_{1}}$${domain\;bias_{2}}$${label\;bias_{1}}$${label\;bias_{2}}$${bias_{1}}$${bias_{2}}$${\Sigma_{1}}$${\Sigma_{2}}$${{\mu_{1,1}}}$${{\mu_{1,2}}}$${{\mu_{2,1}}}$${{\mu_{2,2}}}$${{y_{1,1}}}$${{y_{1,2}}}$${{y_{2,1}}}$${{y_{2,2}}}$$\scriptstyle{\omega}$$\scriptstyle{\omega}$$\scriptstyle{1-\omega}$$\scriptstyle{1-\omega}$
Figure 2: Illustration of the model structure with $F=C=2$. From the top down,
$\omega$ and all $\vec{\alpha}$’s are fixed parameters; all biases,
$\Sigma$’s, and $\mu$’s are stochastic variables; and all $y$ values are
observed during learning.

We focus on two types of bias that affect the way the learner evaluates and
learns from the exemplars: 1) the bias induced in the learner by the presence
of linguistic labels for the data; 2) the inherent domain bias of the learner.
These domain and label biases were integrated into the model by considering a
vector of bias parameters for each of the two biases. More specifically, the
domain bias is parameterized by a vector $\vec{\alpha_{d}}$ that determines
the learner’s relative domain biases over each of the $F$ features. Likewise,
the label bias is parameterized in the same manner by a vector
$\vec{\alpha_{l}}$.

The domain bias itself is a vector $\vec{p}$ containing $F$ values sampled
from a Dirichlet distribution with parameter $\vec{\alpha_{d}}$. Similarly,
the label bias is a vector $\vec{k}$ sampled from a Dirichlet distribution
with aforementioned parameter $\vec{\alpha_{l}}$:

$\begin{split}\vec{p}=(p_{1},...,p_{F})^{T}\sim\textrm{Dirichlet}(\vec{\alpha_{d}}),\\\
\vec{k}=(k_{1},...,k_{F})^{T}\sim\textrm{Dirichlet}(\vec{\alpha_{l}}).\end{split}$

These bias vectors $\vec{p}$ and $\vec{k}$ serve as overhypotheses during
learning. The model also takes parameters $w$ and $s$ which serve to constrain
how the domain and label biases interact. Particularly, $w$ and $s$ provide
the mean and standard deviation that are used to sample a weight $\omega$ that
will define a convolution of the domain and label biases;

$\omega\sim\textrm{Normal}(w,s)\;\textrm{truncated at 0}.$

By sampling $\omega$ from a truncated normal distribution centered at $w$ with
lower bound zero, we are essentially choosing an estimate $w$ of how much
belief the learner places on the domain bias and then adding a small amount of
noise. This can capture to some extent the variability in how much more
important a learner may consider the domain bias compared to the label bias or
vice versa.

Using the weight $\omega$, we can define $\omega\vec{p}+(1-\omega)\vec{k}$, a
convolution of the two biases which is the total bias that the learner has
when learning. Using $\omega$ and $1-\omega$ as the weights for the biases
enforces that increased weight given to the domain bias corresponds to equally
decreased weight for the label bias (and vice versa). The final bias values
for each feature $i$ are transformed further using a power law function
$r(p_{i},k_{i})$ scaled between -1 and 1 as follows:

$r(p_{i},k_{i})=2(\omega p_{i}+(1-\omega)k_{i})^{\frac{1}{\gamma}}-0.5).$

Since the domain and label biases $\vec{p}$ and $\vec{k}$ were both drawn from
Dirichlet distributions, they satisfy that $\sum_{i=1}^{C}{p_{i}}=1$ and
$\sum_{i=1}^{C}{k_{i}}=1$. Accordingly, the convolution of $\vec{p}$ and
$\vec{k}$ still maintains the same property $\sum_{i=1}^{C}{\omega
p_{i}+(1-\omega)k_{i}}=1$. This allows for the domain and label biases to be
considered with different weight, but still aligns with the so-called
‘conservation of belief’ where if the learner is biased towards a particular
feature then they are less likely to discover category distinctions based on
other features.

Figure 3: Left panel: Nonlinear effect of different $\gamma$ values on the
relationship between overall bias and correlations of category means. The rate
of change for correlation values gets more extreme as bias approaches 0. Thus,
a change in the bias closer to 0 results in a larger change in the
distribution of the sampled category means. Right panel: A surface plot of the
correlation between category means versus biases $p_{1}$ and $k_{1}$ for
$p_{1}\in[0.2,0.5]$ and $k_{1}\in[0,0.5]$. The resultant non-additive effect
of the biases $p$ and $k$ is reflected in the nonlinear surface plot.

Using the function $r(p_{i},k_{i})$ to scale and transform the bias gives the
correlation between the category means for the $i$th feature. More
specifically, the correlation between the means of categories $m$ and $n$ for
feature $i$ is defined as follows $\forall m,n\in 1,\ldots,C$:

$\operatorname{corr}\left(\mu_{i,m},\mu_{i,n}\right)=\left\\{\begin{array}[]{ll}r\left(p_{i},k_{i}\right)&\text{
if }m\neq n\\\ 1&\text{ otherwise. }\end{array}\right.$

Figure 4: Average accuracy of the model over 4 learning blocks compared to
previous studies’ results. The model ($w=0.3,s=0.03$) results corroborate
previous findings. Specifically, the presence of a ‘right bias’ facilitates
category learning (higher accuracies) while the presence of a ‘wrong bias’
hinders learning (lower accuracies) compared to the ‘no bias’ case.
Additionally, the model shows that in general, a wrong label bias results in
greater hindrance to learning compared to a wrong domain bias (the same
applies for right biases). This occurs because for these settings of $w$ and
$s$, the domain weight $\omega$ is less than the label weight $1-\omega$.

The transformation $r$ serves to account for the need for nonlinear
correlation values as discussed in ivanovahofer, where linear correlation
values produce very little difference between right-bias, none-bias, and
wrong-bias conditions. By using a power law function with parameter $\gamma$
we can specify how conservatively the learner generates hypotheses. When
$\gamma$ is close to to 1 (linear), the learner is more likely to learn
category structures that do not align with their biases. In contrast, larger
values of $\gamma$ specify that the learner will primarily consider category
structure hypotheses that align with their biases. The nonlinear
transformation also augments the additive nature of the label and domain
biases to result in a non-additive final effect (Fig 3).

From here, the model infers the category means and variances for each feature.
Let $\vec{\sigma_{i}}$ be the vector of the variances of the $i$th feature for
all $C$ categories:

$\vec{\sigma_{i}}^{2}=(\sigma_{i,1}^{2},...,\sigma_{i,C}^{2})^{T}.$

Using the correlation values obtained from the biases, we can define a
covariance matrix $\Sigma_{i}$ for each feature $i$:

$\Sigma_{i}=diag(\vec{\sigma_{i}})\cdot R_{i}\cdot diag(\vec{\sigma_{i}}),$

where $R_{i}$ is the correlation matrix with entry $(m,n)$ being
$\textrm{corr}(\mu_{i,m},\mu_{i,n})$.

Then, we assume that the learner considers the category means for each feature
as adhering to a Normal prior distribution with covariance matrix
$\Sigma_{i}$:

$\vec{\mu_{i}}=(\mu_{i,1},...,\mu_{i,C})^{T}\sim\textrm{Normal}(0,\Sigma_{i})$

These category means $\vec{\mu_{i}}$ and category variances
$\vec{\sigma_{i}}^{2}$ (which are subject to some perceptual noise
$\sigma_{s}^{2}$) are inferred by the learner based on observed category
exemplars $y$. In this model, we make the simplifying assumption that the
learner considers exemplars to be sampled from a Multivariate Normal
distribution as follows:

$\vec{y_{i}}=(y_{i,1},...,y_{i,C})^{T}\sim\textrm{MVN}(\vec{\mu_{i}},diag(\vec{\sigma_{i}}^{2})+\sigma_{s}^{2}I_{C}),$

where $\vec{y_{i}}$ contains the learner’s estimated values of feature $i$ in
all categories.

Through this model setup, graphically visualized in Fig 2, we can explore the
combined effect that conceptual domain priors and linguistic label priors have
on category learning.

$w=0.2,s=0$ | $w=0.3,s=0.03$ | $w=0.5,s=0$
---|---|---
Figure 5: Heatmaps showing the average accuracy for each model for three
different settings of $w$ and $s$. Note that when $w=0.5$ with no additional
variance the domain and label biases are considered equally by the learner, so
the accuracies are symmetric along the anti-diagonal. When $w=0.2$ or $w=0.3$,
the learner places less belief in the domain bias compared to the label bias
and this imbalance is reflected in the resulting accuracies.

## Model Fitting

#### Data

To fit the model, simulated data was generated in a manner to approximate the
experiments in brojde2011. A total of 16 exemplars were generated with 8 in
each of two categories. These simulated data varied along 2 dimensions, which,
for simplification will subsequently be referred to as the “texture” and
“shape” features. In the data, the shape feature was diagnostic of category.

#### Biases

The model was fitted 9 separate times to consider a variety of possible
interactions between domain and label biases. We establish three levels of
bias: the bias-induced prior aligns with the true category structure (“right
bias”), the bias-induced prior does not align with the true category structure
(“wrong bias”), and no priors are induced by the bias (“none bias”). The 9
fitted models consisted of all combinations of {right, none, wrong} domain
bias and {right, none, wrong} label bias.

#### Markov Chain Monte Carlo

As in lupyan2007, brojde2011, and ivanovahofer, each model was given all 16
exemplars as observed data in every learning block. The models were fitted to
the data using PyMC3, a Python-based probabilistic programming language
Salvatier . (2016).

In the fitting process, a Markov chain Monte Carlo (MCMC) simulation-based
approach is used to obtain a Markov chain of values of the posterior
distribution of the category means given the observed data. During the MCMC
sampling, the No-U-Turn Sampler (NUTS) is used to generate posterior samples
of the category means. NUTS is especially useful in our model due to its
ability to handle many continuous parameters, a situation where other MCMC
algorithms work very slowly. It computes the model gradients via automatic
differentiation of the log-posterior density to find the regions where higher
probabilities are present.

## Results

We evaluated the performance of the 9 fitted models by classifying the
observed exemplars into the two categories. This was done by comparing the
exemplars’ feature values to the learner’s estimated feature means and
standard deviations of each category.

Bias | $\vec{\alpha}$
---|---
Right | (1, 10)
None | (10, 10)
Wrong | (10, 1)
Table 1: Settings of $\vec{\alpha}$ for each class of bias

In the model, some parameters were held as constants. These were the
perceptual noise $(\sigma_{s}^{2}=1)$ and the nonlinear transform parameter
$(\gamma=10)$.

We also established settings of $\vec{\alpha_{d}},\vec{\alpha_{l}}\in$ {(1,
10), (10, 1), (10, 10)} according to Table 1 to represent the domain and label
biases. In setting these $\vec{\alpha}$s we are choosing a fixed
representation for the overhypotheses. However, it is notable that in
principle, these overhypotheses can be learned from data Kemp . (2007).

#### Comparison of Models

The model was able to demonstrate the effects of the domain and label biases
on learning.

At a basic level, holding the domain bias constant at ‘none’ produced results
that align with those in ivanovahofer, where we see that ‘right label bias‘
facilitated learning while ‘wrong label bias‘ hindered it (Fig 4).

In addition, the other models fitted with various label and domain biases for
$w=0.3,s=0.03$ (Fig 4) show that the label bias has a stronger effect (whether
positive or negative) on learning. This aligns with the expected results due
to the tested settings of $w$ and $s$ generating a domain weight $\omega$ that
is less than the label weight $1-\omega$.

When looking at the average accuracies yielded by each of the 9 fitted models,
we see a reflection of the hypothesized effects of the domain and label biases
(Fig 5). When the two biases are considered with equal weight by the learner,
the resulting accuracy matrix for the different combinations of domain and
label bias is symmetric along the anti-diagonal (Fig 5). This aligns with the
expectation that when the learner considers the two biases equally while
learning, changes in one bias have very similar effects to equivalent changes
in the other bias on overall accuracy.

$w=0.2,s=0$ | $w=0.3,s=0.03$ | $w=0.5,s=0$
---|---|---
Figure 6: Interaction plots for three different settings of $w$ and $s$
showing average accuracy by model. When $s=0$, the lines are basically
parallel and indicate minimal interaction between the domain and label biases.
However, of particular interest is the introduction of a nonzero $s$ value (as
is the case when $w=0.3$). In this case, the additional variability in
$\omega$ makes the lines in the plot begin to deviate from parallel.

However, for unequal weights (e.g. when $w=0.2$ and $w=0.3$ in Fig 5), the
effect of changes in one bias (label bias in the example) is shown to be
stronger than equivalent changes in the other bias. Additionally, the
inclusion of a nonzero $s$ when $w=0.3$ introduces noise to the bias weights –
a scenario more representative of a real human learner.

Finally, another important observation from the results is demonstrated in Fig
7. Within each particular bias type and class (e.g. right domain bias),
changing the other bias from ‘wrong’ to ‘none’ to ‘right’ generally increases
accuracy. However, within a particular setting of both bias types and classes
(e.g. wrong domain bias and wrong label bias), the accuracy trends vary when
parameter $w$ is changed. For example, when domain bias and label bias are
both wrong, increasing $w$ (and therefore $\omega$, the degree to which the
learner believes their domain bias) decreases accuracy. However, when there is
no domain bias and wrong label bias, increasing $w$ has negligible effect on
the accuracy. These results all align with our initial hypotheses about the
behavior of the domain and label biases.

The model also attempts to capture the interactions between the domain and
label biases. The convolution of the two biases and the decision to put both
on the same level of the Bayesian hierarchical framework was informed by
adhesion to the principle of ‘conservation of belief’ where increased belief
or weight placed in one type of bias should result in a corresponding decrease
in others. Although the initial convolution was additive, the final
contribution of the combined biases to the correlations between the category
means is not linear (Fig 3). This could potentially lead to interaction
effects between the two biases. However, such interactions were minimal in our
simulation results.

|  | $w=0.2,s=0$ | $w=0.3,s=0.03$ | $w=0.5,s=0$
---|---|---|---|---
|  | GEE | GLMER | GEE | GLMER | GEE | GLMER
Effect | Df | p-value | F-value | p-value | F-value | p-value | F-value
Block | 1 | 0 | 1896.8 | 0 | 1824.6 | 0 | 1784.3
Label Bias | 2 | 0 | 249.2 | 4.00e-15 | 205.2 | 1.83e-09 | 124.8
Domain Bias | 2 | 0.016 | 22.4 | 5.49e-05 | 57.9 | 3.33e-10 | 121.5
block:Label Bias | 2 | 5.13e-05 | 65.9 | 3.69e-04 | 55.2 | 0.099 | 16.5
block:Domain Bias | 2 | 0.941 | 0.5 | 0.177 | 12.0 | 0.021 | 25.0
Label Bias:Domain Bias | 4 | 0.931 | 1.3 | 0.741 | 2.7 | 0.583 | 3.8
Table 2: Results from mixed effects logistic regression and generalized
estimation equation with logit link and exchangeable correlation structure.
The interaction effect of label and domain bias is not significant from either
the GEE and GLMER models.

As seen in Fig 6, changes in the model parameters $w$ and $s$ (and therefore
weight parameter $\omega$) demonstrate mildly different levels of interaction
between domain and label biases. For the cases when $s=0$ ($w=0.2$ and
$w=0.5$), the lines in the plot do not intersect at any point. This indicates
that there are no significant interactions between the domain and label biases
when the learner’s belief in their domain bias is not subject to any
variation.

Finally, parallel to the procedure used in ivanovahofer, we simulated
individual-level predictions with 75 participants per setting of domain and
label biases class combinations in each learning block. These were analyzed
using a mixed effects logistic regression model that was fitted using the
glmer command from the lme4 package Bates . (2015) with formula:

$accuracy\sim(label+domain+block)^{2}+(1|object),$

and a generalized estimating equation (GEE) model with observations from the
same object having an exchangeable correlation structure and formula:

$accuracy\sim(block+label+domain)^{2}$ (1)

These two models have identical correlation matrices, but GEE provides a test
for the fixed effects while glmer does not. We used both models to assess
whether the interaction effect between the label and domain biases is
significant.

We concluded that the interaction effect for the model fitted with different
settings of $(w,s)$ was not statistically significant based on both the
$p$-values from the GEE model and the F-statistics from the mixed model as
shown in Table 2. This quantitatively confirms the patterns we observed in the
interaction plot (Fig 6) where there are not significant interactions between
domain and label biases (at least at the level of weight variation $s$
tested). Although the examples modeled did not show significant interaction
between biases, the use of more complex data and therefore more complex bias
priors could very likely amplify any domain-label interactions. We did observe
significant effects for block & label, block & domain, and main effects of
block, label, and domain. Some of these effects were also reported by
brojde2011.

## Discussion

#### Domain weight flexibility

In this work, the additional parameters $w$ and $s$ that further parameterize
the domain bias weight $\omega$ served an important role in making the
learner’s consideration of domain vs label biases flexible. It appears very
reasonable that these parameters are also learnable in category learning tasks
– i.e. learners learn to either emphasize or discount their domain bias as
they go through the supervised learning process, thus altering their $\omega$.

#### Importance of parameters $w$ and $s$

Different learners have different inherent degrees of belief in the two
biases. This variability is able to be partially captured by the noise
introduced by the $s$ parameter. Hence, the capability to adjust $s$ is
important for estimating different types of learners.

Beyond these smaller variations between learners, learners may also vary
wildly in their preference for domain or label belief. One key example of this
is in comparing adult learners to infant learners. Infants will have less
developed understanding of word meanings and therefore the label bias effect
may be negligible for them (high $\omega$). On the contrary, adults may be
strongly influenced by label biases because they understand the structure
underlined by the labels (high $1-\omega$). The model can account for these
differences by adjusting the magnitude of $w$, which is where the distribution
of $\omega$ is centered, to model learners with vastly different beliefs in
the two biases.

#### Limitations

It is important to acknowledge the limitations of this model. Although the
model detailed in this work provides an implementation of the domain and label
biases, additional data collection to tune the model’s assumptions was outside
of the scope of this project and thus was not conducted.

Additionally, the model is just one implementation of the possible combined
behaviors of the label and domain biases. Hence, alternative implementations
may be worth investigating to compare and contrast results.

Figure 7: Dot plot of the average model accuracies and standard errors for
each of the 9 model fittings for three different settings of ($w,s$): (0.2,
0), (0.3, 0.03), and (0.5, 0). We can see that the different values of $w$
have slightly different effects on the magnitude and direction of the accuracy
trends for any fixed domain bias and label bias.

### Future Research

Given the limitations detailed previously, a key future direction to consider
for this work is adjusting the structure of the Bayesian hierarchical model.
In this work, we discussed that the convolution of the domain and label biases
is additive. Despite this additive implementation, we use a combination of the
nonlinear transformation and the learners’ variations $s$ in the degree to
which they believe in their domain biases to introduce potential interactions
between the biases. However, as we saw in Fig. 6, these interactions are still
minimal. One way to further model more complex interactions between the domain
and label biases when category learning is to consider the domain bias on a
separate level from the label bias. This is particularly relevant given our
assumption about the label bias for this work: that the label biases are
generated by the learner’s understanding of word meanings and their alignment
with certain dimensions. Since the label bias depends in part on the learner’s
understanding of the domain, the label biases and domain biases may be more
interconnected than defined in this model. Considering the domain bias on a
different level of the hierarchical framework or using it to put priors on the
label bias (which would then propagate down to generate priors for the
category mean correlations) would be interesting ways to implement the domain
and label biases differently.

Finally, data collection to compare the simulated results of this model with
human data is an important next step for further verifying the conclusions
generated in this work.

Overall, this paper clarifies and conceptualizes the importance of considering
both label and domain biases in category learning. By representing the biases
as overhypotheses that impose priors over the learning process, we are able to
model the effects each bias has on learning, as well as show how they
interact.

## Acknowledgments

Thanks to Anna Ivanova and Matthias Hofer for participating in discussion at
the early stages of this project.

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