systems. This paper introduces a novel computational cognitive model that maps latent mental models to observable behaviors, allowing the system to detect changes in users' mental models from their actions. We propose an inference framework to dynamically adjust to the user's evolving understanding and decision-making processes. An empirical experiment demonstrates the framework's ability to accurately detect shifts in users' mental models based on their interactions. The results indicate a consistent improvement in prediction accuracy and a decrease in variance over time, suggesting the model's potential for real-time application in designing adaptive interactive Workshop Proceedings
An intelligent interactive system needs to adapt to the
behaviors of its users. It should understand their intentions,
and anticipate what’s coming next. A user’s interactive
behavior is shaped by their mental model, the user’s
knowledge and beliefs of the interactive system [
However, a problem in inferring mental models is that
they are not static during interaction. For example, as users
become more experienced, their mental models change [
Consider a hypothetical scenario involving a multisensor smart scanner that can obtain ultrasound and radio frequency readings of boxes at a warehouse. Suppose that diferent contents produce diferent sensor readings. Harry, a novice operator yet to learn to read radio frequencies, relies solely on ultrasound to determine the content. Accordingly, the scanner should provide hints on how to interpret ultrasound readings. If Harry suddenly scans for radio frequency data, it will likely be a mistake, and the scanner should intervene to avert it.
Harry practices reading radio frequency data and associating the readings with the contents. At some point, his mental model – an internal representation of the dynamics and facts of the external task – evolves to have a closer correspondence with reality. If the AI of the scanner does not pick up on this evolution, it will continue to recognize Harry’s actions as mistakes and ofer inefective or detrimental hints. Therefore, intelligent interactive systems must accurately infer user’s changing mental models to provide useful adaptation. 11.6.2024 Vaasa, Finland ∗Corresponding author. †These authors contributed equally.
CEUR
ceur-ws.org only understood ultrasound readings. Now he starts to scan for radio frequencies. Is this a mistake, or has he learned how to read radio frequencies?
In this paper, we propose a computational model of interaction that accounts for how changes in the mental model lead to changes in interactive behavior. We then define a framework to infer and quantify the mental model from observed behavior and demonstrate how to detect changes in parameter value from behavioral data with an empirical experiment. In summary, this paper contributes to the computational modeling of interactive behavior by proposing: • a computational model of how interactive behavior emerges from quantified mental models; • an inference framework to detect these changes from observed behavior.
In human-computer interaction, mental models represent
how the interaction is internally interpreted and
reconstructed by the users [
Interactive systems are often designed to adapt to user
needs and habits to create an intuitive user experience.
The classic approach is to collect behavioral data, such as
keystrokes, mouse movements, or system logs, and analyze
it for patterns [
Parameterized, computational models of interaction have
been proposed to explain the user’s decision-making
process during an interaction [
However, these models have not addressed cases where the latent factors change. A user could gain knowledge and experience during an interaction to become more skillful, which would be reflected in the mental model. Failure to account for such changes would render any interactive system’s adaptation inefective or even detrimental. Consequently, our present work formalizes a computational framework for interaction that detects changes in mental models based on observed user behavior. This would be important for creating intelligent interactive systems and collaborative AI that are truly adaptive to the users.
We view the user of an interactive system as an agent
trying to solve a Partially Observable Markov Decision
Process (POMDP) [
The interaction process between an agent and a POMDP environment can now be described in Figure 2. In a POMDP, the agent cannot know the environment state directly. Instead, it observes the state and forms an internal representation of the state as a belief ∈ , with being the set of all possible beliefs. The agent aims to find an optimal policy ∶ → to guide its choice of action that maximizes the expected discounted rewards over time. Specifically, the interaction takes place as follows.
1. Initial Belief State: The interaction starts with the agent having an initial belief state, 0() representing the agent’s initial knowledge about the environment, ∈ , ∈ . 2. Action Selection: At each time step , the agent selects an action ∈ based on its current belief state () according to a policy to maximize the expected reward. 3. Environment Response: The environment transitions from to +1 according to ( , , +1 ) = ( +1 | , ). This is not directly observable by the agent. 4. Observation: The agent receives an observation +1 ∈ , generated according to the observation model Ω: ( +1 , , +1 ) = ( +1 | +1 , ). 5. Belief Update: The agent performs Bayesian update of its belief to +1 () with observation +1 , action , and previous belief () , and revises knowledge about the environment. 6. Reward: The agent receives a reward ( , , +1 ) based on the state transition. 7. Repetition: Steps 2 through 6 are repeated, with the agent continually updating its belief state and selecting actions until a terminal condition is reached.
The agent can use reinforcement learning to find the
strategy that maximizes the future-discounted cumulative
reward: () = max { (, ) + ∑ ( ′|, ) ( ′)}. It has
been theorized and shown empirically that as long as the
POMDP formalism correctly models the task environment
and the relevant parts of human cognition, an optimal policy
approximates that of human behavior. This is known as
computational rationality [
Given that the true state is not directly observable, the agent forms its belief , a probability distribution over all possible states in the environment at . We propose that the agent performs a Bayesian update to obtain using its mental model, :̂ +1 ∝ (̂ , ), (1)
In Equation 1, the mental model is a (probabilistic) function that updates the agent’s belief given observation and previous belief. Thus the mental model ̂ can be viewed as the (imperfect) transition function of an individual agent. An ideal agent with the perfect knowledge and expertise of the interactive environment would have the true mental model identical to . In reality, even given the same observation, agents with diferent mental models ̂ would have diferent ways to update their beliefs.
We can use the framework in Sections 3.1 and 3.2 to simulate agents with diferent mental models and use them to generate simulated behavior. When a human user interacts to generate real data, it can then be compared to the simulated data to determine the likely mental model of the human user.
Suppose that the mental model has the probability distribution ( )̂ . From Sections 3.1 and 3.2 we know how an agent with a mental model ̂ would behave. Consequently, we also know the conditional probability distribution of ( ∣ )̂ , given an observed behavior data . Bayes’ rule can then be used to invert the conditional probability and ifnd: ( ̂∣ ) ∝ ( ∣ )̂ ⋅ ( )̂ , (2)
Finding the likelihood ( ∣ )̂ is dificult, both
analytically and empirically. Instead, we use a likelihood-free
Approximate Bayesian Computation (ABC) [
Equation 2 gives us a probabilistic estimate of mental models, which alone is insuficient in detecting potential changes in mental models. To algorithmically determine whether, given observed data, the mental model has changed significantly, we need to quantify changes in the posterior distribution ( ̂ ∣ ). Depending on the specificities of the interaction, we can choose from various methods, as summarized in Table 1.
Which quantification method to use depends on the characteristics of mental models. Suppose we have a categorical mental model, which is the case we could use maximum a posteriori estimate (MAP) to determine the values of ,̂ and detect any changes.
1. Calculate Posterior Distribution
For each category in the mental model categories (i.e. Equation 2):
Posterior[] = Likelihood[] × Prior[] Normalize the Posterior for each category by dividing by the sum of all Posterior values:
Posterior[] ←
Posterior[] ∑ ′∈ Posterior[ ′] Threshold Monitoring
Description Utilize statistical distance measures (e.g., KL divergence, Total Variation distance, Wasserstein distance) to quantify the diference between successive posterior distributions of the mental model ( ( ̂∣ )) to assess how one distribution diverges from another.
Define a threshold for a significant change, based on domain knowledge, statistical criteria, or adaptive methods.
Validate this threshold through simulations or historical data to ensure it efectively diferentiates between routine updates and significant model changes.
Continuously or periodically calculating the distance measure between the current and previous posterior distributions, storing past distributions for comparison. If the distance exceeds the threshold, infer a significant change in the mental model has occurred.
We use an experiment to demonstrate how the framework outlined in Section 3 quantifies and detects changes in the latent mental models of human participants interacting with an interactive system. We change the instructions given to the participants during the experiment to mimic changes in mental models and showcase how the model prediction successfully reflects these changes.
We recruited 10 participants online1, of which 8 identified as females, and 2 as males, coming from 5 diferent nations. They are between the ages of 20 and 48, averaging at 29. The participants were paid compensation for taking part in the experiment.
We conducted our experiment remotely using a webpage designed to simulate a hypothetical scenario where participants interact with the simulation environment and make decisions based on feedback and prior instructions. Participants interact by clicking buttons which are logged as experiment data.
Scenario Picture a warehouse of unmarked boxes containing electric and electronic waste, including used batteries, LED lights, and household appliances. To identify what each box contains, there’s an advanced scanner equipped with ultrasound, X-ray tomography, magnetic resonance imaging (MRI), and radio frequency sensors. The warehouse manager can select a sensor to scan a box and get specific results. Each type of waste generates unique readings on the sensors. By scanning a box, the manager aims to determine its specific contents. Specifically, each waste has four features: ultrasound, x-ray, MRI, and radio frequency. Each feature value can be either high or low.
The scenario is represented on a webpage, and the participants play the role of warehouse manager. In each task, the participant is presented with a box of unknown contents, and given a goal of finding particular contents. The participant must scan the box for the four features and decide whether to open the box or abandon it, given their mental model of what contents produce what sorts of scanner readings, and what their goal is.
The experiment is carried out as follows: • Each participant performs 12 rounds of tasks. • During each round, the webpage refreshes and randomly generates a box as described above. • During each round, each participant is randomly assigned a type of waste to look for. • The participant scans the box, and decides whether to accept or reject it.
Each participant is rewarded points for accepting the box containing the assigned waste or rejecting the box not containing it. If a participant wrongly accepts or rejects a box, a penalty is applied. Scanning a feature will also cost points. Therefore participants are instructed to act economically to make the right decision with minimal costs.
The 10 participants are divided into 2 groups of 5. In round 1, we give each group a table containing the probability of finding each waste given a set of features. • Group 1: the probabilities of finding each waste given all features except radio frequency; • Group 2: the probabilities of finding each waste given all features except MRI.
After round 5, all participants are given a new table containing the probabilities of finding each waste given all features, with no features withheld. These tables represent the participants’ mental models ( ̂ in our computational model). The mental models of the initial 5 rounds belong to those participants not having learned to associate certain features with the underlying probabilities. We assign 1̂ to the initial mental model of Group 1, and 2̂ to that of Group 2. The new mental model assigned after round 5 is 0̂.
ult. high x-ray high
MRI high radio batt. 0.7 lights 0.3 app 0.6
A snippet of the table given to Group 1 is shown in Table 2. Using this knowledge, if a participant obtains the corresponding readings, they would know that the likelihood of finding a battery is 0.65. Taking into consideration the action costs, they can calculate the expected reward and decide whether they would accept the box.
The switch at round 5 is designed to model users acquiring a new mental model during an interaction after gaining knowledge and expertise about the environment and correctly associating all features with the probabilities.
Summary Statistics The experiment data gathered are the sequence of actions performed by each participant, recorded as a list of button IDs. To eliminate unnecessary randomness, we transform the data using summary statistics: we ignore any repetitions in the action and its order. As a result, we are only concerned with whether each sensor has been used, and whether the participant decides to accept or reject the box.
Inference 10 participants each performed 12 tasks to
generate 12 results of button clicks. In total 60 sequences are
collected and transformed by summary statistics into sets
of boolean variables. Each result records the status of the 6
buttons, with 1 corresponding to the button being clicked,
and 0 otherwise. For example, if a participant chooses to
scan the X-ray and MRI, and rejects the box, the resultant
data would be: [
As described in Section 3.4, the mental model can be
quantified as a categorical variable. We divide the unit
interval into thirds so that each third corresponds to one
of three mental models 0̂, 1̂ and 2̂. We create simulated
agents with the three mental models to produce simulated
data. For each ,̂ we use Proximal Policy Optimization with
the default parameters [
Using the mechanism in Section 3, our model samples possible values of and compares the simulated results with participant data to produce a probabilistic distribution of values. We use MAP estimates to determine their values, as outlined in Section 3.4. For each round of tasks each participant performs, we sample the corresponding simulated result 200 times.
We can calculate the accuracy of our inference: the percentage of the 200 inferred that matches the correct mental model ̂ , = 0, 1, 2 . Averaged over all participants, we thus obtained 12 average prediction accuracies throughout the iteration. The result is presented in Figure 4.
We plot the results in Figure 4. We observe the model’s average prediction accuracy for each participant’s mental model across the 12 rounds. The red, vertical dotted line marks the switching of ̂ as participants receive the new table after round 5.
Furthermore, we also calculate the standard deviation of the inferred values of mental models for each round, and average over all participants. The result is shown in the Figure 5. The switching of ̂ is also marked by a red, vertical dotted line.
We can discover several trends in the results as shown in Figures 4 and 5. The accuracy of model prediction of mental model ̂ increases per round (Figure 4). This is due to the Bayesian update of the model incorporating the results from previous rounds into the following rounds as prior information. Consequently, the inference improves in accuracy as confoundments are gradually resolved. This is also shown in the decrease of standard deviations in Figure 5. In earlier rounds, there is relatively little information and more confoundments, leading to greater uncertainty in inference results. As evidence accumulates and confoundments are resolved, uncertainty also decreases.
Importantly, both figures show a drastic change between rounds 5 and 6, when the mental models ̂ are switched. The accuracy goes down and the standard deviation slightly increases. This means that at round 6, the priors from previous rounds still have a strong influence on the inference results, and the model clings to the prediction that the data were produced by agents with the old mental model (either 1̂ or 2̂). However, as can be seen in Figures 4 and 5, evidence accumulates due to our model’s Bayesian setup, suggesting that a new mental model was likely behind the observed data. Towards the later rounds, accuracy has recovered and the model now firmly predicts the new mental model 0̂. Similar trends can also be observed in average standard deviations, as the value goes up slightly after round 5 before continuing to descend.
In this paper, we present a formal, computational model to infer a user’s mental model during interaction. It can detect changes in the mental model and dynamically updates the inference once suficient evidence is accumulated. The experiment demonstrates a consistent trend of improving accuracy and decreasing variance in the model predictions. The model can be a starting point for building an intelligent interactive system that truly understands its users.
Currently, the model needs to run ABC and sample at
each round of inference, as outlined in section 3. This makes
the model too slow to be implemented in real applications.
Consequently, a key improvement would be to make the
model more lightweight and eficient so that inferences and
adaptations can be implemented in real-time. One idea
worth exploring is amortizing the inference by pre-training
the model using simulation [
The entire inference framework must also be tested with real HCI tasks, such as menu search and typing. To do so we need to define both the computational model of interaction and the mental model. This would also allow us to compare our proposed approach to existing methods and conduct statistical analysis with more participants. To do so would likely require insights from psychology, behavioral science, etc., and is beyond the scope of this work.
This research has been supported by the Academy of Finland (grant 330347).