Spontaneous thought separates into clusters of negative, positive, and flexible thinking

Spontaneous thought is an umbrella term for the phenomena of mind-wandering, daydreaming, and involuntary autobiographical memory¹. These are task-unrelated, stimulus-independent thoughts that spontaneously arise over the course of daily life, and can occupy up to 60% of an individual’s waking hours². A defining feature of mind-wandering is that thoughts flow freely between topics without staying on any one concept for too long³. In contrast, when thought patterns become repetitively focused on content of self-referential negative valence, individuals may be said to be ruminating or worrying, generally known as repetitive negative thinking (RNT)⁴. Although most people ruminate and worry from time to time, individuals who excessively engage in RNT patterns are at a higher risk for the development and maintenance of internalizing psychopathologies, such as depression, anxiety, and post-traumatic stress disorder^5,6,7. Accordingly, RNT is a transdiagnostic behavior that may confer risk for psychiatric disorders.

Cognitive models of spontaneous thought (like mind-wandering or RNT) posit that opportunity for mind-wandering is in continuous competition for mental resources⁸. Because mind-wandering and rumination are memory-retrieval processes, easier-to-activate memory chunks (for instance, unattained goals, or highly arousing, negative memories) may be more readily recalled during an unrelated task, potentially decreasing task performance. Based on these principles, researchers have successfully predicted when individuals would become distracted by mind-wandering thoughts during a task—i.e., when their performance would worsen—as well as which thoughts would cause distraction⁹. Further evidence of how spontaneous thought may impact measurable behavior has been presented in several recall paradigms. Individuals with high self-reported perseverative-thinking scores are less likely to be affected by primacy and recency effects during cued-recall¹⁰. They are also generally less accurate in their recall, struggle to inhibit task-irrelevant information of negative valence^11,12,13, and are more likely to freely recall negative words, and to continue to recall negative words following the first recall¹⁴. Together, this collection of studies speaks to the impact of RNT on measurable behavior and to the salience and strength of RNT thoughts during task performance and daily functioning.

To date, the primary means of assessing RNT has been through self-report measures such as the Ruminative Response Scale (RRS)¹⁵ or the Penn State Worry Questionnaire (PSWQ)¹⁶. These trait-based self-report instruments approximate how frequent and problematic patients believe their spontaneous negative cognitions to be, and to explore how they perceive their abilities to engage or disengage from these repetitive thoughts. However, these tools are likely impacted by retrospective report and memory recall biases^{17,18,19,20,21}, and they cannot provide meaningful insight into the dynamic cognitive mechanisms that give rise to RNT. Indeed, one of the challenges of studying mind-wandering and RNT from a mechanistic perspective is that they occur in the absence of observable behavior, and the act of assessment can interrupt the mind-wandering or RNT process of interest. Consequently, there is a need for tasks and models that may capture the dynamics of RNT without relying on self-report.

One long-standing procedure for assessing RNT is the free association method. First developed in the context of experimental psychology^22,23 and psychoanalysis^24,25, free-association paradigms have recently been formalized into behavioral paradigms to probe mechanisms of mind-wandering and RNT. While spontaneous mind-wandering is unlikely to rely on the exact same mechanisms as deliberate word-association, there is evidence to suggest that spontaneous inner dialogue impacts language valence and structure^26,27, and can be identified in ecological momentary assessment written data²⁸. Indeed, prior research has shown that individuals with high self-reported RNT²⁹, stress³⁰, and negative mood^31,32 scores will recall or spontaneously bring up more negative words that they likely also think about repeatedly in their day-to-day life¹⁴. One such example is the Free Association of Semantics Task (FAST)¹⁴. The FAST asks participants to engage in quick word-associations to generate word-chains that parallel the spontaneous trains of thought that individuals often experience in daily life. Using this task in combination with Markov chain analysis¹⁴, it was found that individuals with high self-reported rumination scores were more likely to spontaneously transition into negative thoughts, and more likely to stay within negative-valenced thoughts than individuals with low rumination scores¹⁴. A limitation of this prior work was the reliance on Markov chain analysis³³, which does not specify thought-transition dynamics beyond changes in valence.

In the current work, we conceptualized free word-association in terms of the unconstrained navigation within a multidimensional semantic space. We then explored the dynamics of stuck thought by applying concepts of attractor space from dynamical systems theory. Dynamic systems modelling and attractor space dynamics have previously been applied in psychology to successfully model neural activity and behavior related to imagery, ambiguity resolution, and pattern completion³⁴. Furthermore, in the context of spontaneous thought dynamics, the Attention-to-Thought model employed dynamic systems approaches to predict differential temporal trajectories of internal attention, working memory, and emotion using experimental simulations³⁵, but has yet to be applied to human subjects’ data. As described in this previous work, an attractor space represents a stable state that a dynamical system will tend to gravitate toward³⁴. As such, we operationalized RNT as the impact of one or more negatively-valenced attractor spaces on these otherwise unconstrained semantic trajectories. If RNT is indeed defined by the presence of strong, negatively-valenced, attractor spaces, this would manifest by individuals staying within or repeatedly returning to negative topics during a free word association task.

Here, we applied an attractor-state dynamic model to 3 independent empirical datasets from a written free-association paradigm. Using dynamic and attractor state modelling and word-association data, we modeled thought trajectories and identified distinct patterns of thought likely associated with mind-wandering and RNT. Our approach enabled us to find the semantic locations that individuals revisited during trains of thought, as well as determine the presence and strength of negative attractor locations. We found that output measures reliably cluster into two distinct “stuck thought” patterns, a protective positive thinking pattern, and a pure mind-wandering pattern. This model provides information about stuck spontaneous thought not captured in self-report measures and proves as a potentially promising diagnostic tool for state-based RNT severity and presentation³⁶.

Participants

An a priori power analysis was conducted using G*Power version 3.1.9.7³⁷ to determine the minimum sample size required to test the study hypotheses. Results indicated the required sample size to achieve 90% power for detecting a medium effect in individual-level measures (not trial or cluster-level), at a significance criterion of α = 0.05, was N = 59 for a 4-predictor multiple linear regression model. While the analysis strategy was expanded after data collection, recruitment goals were kept at N = 59. Accordingly, three samples were collected. First, we collected data from a sample of freshmen and sophomore undergraduate students from Emory University (N = 72). After data cleaning, 65 participants from this sample were included in the final analysis. These participants were recruited through the SONA system and received course credit in exchange for their time (about 1 h). Our second and third community samples were collected online using Prolific (N = 100 and N = 300). All online participants were located in the United States of America and individuals who partook in our first online data collect were screened out and unable to participate in our second online data collect. After data cleaning, 79 participants and 222 participants, respectively, were included in the analyses. Note that our N = 222 sample fell slightly short of our recruitment goal of 250. Prolific participants received $12/hour as compensation for their time. All data collection, storage, and usage took place in accordance with and under the approval of Emory University’s Institutional Review Board. All participants provided written consent and agreed to have their de-identified data published. For a full breakdown of our participants’ demographics, see Table 1.

Task

Participants completed an written free word-association paradigm, heavily inspired by the FAST¹⁴. First, a seed word was displayed on the screen. Next, participants were allowed 4.5 s to type in a word related to the displayed seed word. This time interval was chosen after an online pilot dataset (N = 42), collected on Prolific, revealed that participants took an average of 3.01 s (SD = 1.24) to come up with and type in a word during this task. A standard deviation was added to that average, and rounded up, to account for slower participants. However, crucially, more time was not granted to prevent individuals from self-editing their answers and encouraging them to submit their first thought as an answer. With this manipulation, we hope to be capturing spontaneous thought patterns, as they arise. Upon submission of the first word, participants continued submitting related words until they reached 10-word submissions per seed word. Notably, each word had to be related to the immediately prior word, not the original seed word. For instance, when presented with the seed word “spouse”, a participant initially thought of “together”, then “apart”, and then “alone”. Here “alone” is more related to “apart” than “spouse”. If a participant failed to submit a new word within the time allotted (4.5 s), the previous word automatically re-submitted. Participants were instructed not to submit proper nouns, names of places or brands, numbers, or acronyms. Subjects completed two practice sequences before moving on to the actual task. A total of 21 seed words were presented, and 210 words were manually (by the participant) or automatically (by the program after 4.5 s) submitted. According to the Affective Norms for English Words (ANEW) database³⁸, a third of the seed words were negative in valence, another third were neutral, and the final third were positive. Seed words were presented in a random order.

After completing the written free-association paradigm, participants were presented with all the unique words that they submitted (no duplicates were shown), and asked to provide a rating on each submission. For each word, participants were asked “do you believe you think about [word] more than you should in your daily life?” (“perceived overthinking” rating). Participants’ answers on “perceived overthinking” ranged from “Not at all” (0) to “Very much” (100). See Fig. 1 for a full task breakdown. Participants were also asked “do you enjoy thinking about [word] in your daily life?” (“perceived enjoyment” rating). Participants’ answers on “perceived enjoyment” ranged from “Not at all” (0) to “Very much” (100).

Participants were presented with 21 seed words (7 positive, 7 neutral, 7 negative, according to the ANEW database). One seed word at a time, participants were asked to come up with 11-word-long word chains. Participants had 4.5 s to come up with new words. Each word submission needed to be associated with the immediately prior word. Upon completing the word-association portion of the task, participants were asked to provide ratings for each word-submission answering the question: “do you believe you think about this concept more than you should in your daily life?”. Rating scale ranged from “not at all” to “very much so”.

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Once the task portion of the study was completed, participants filled out several self-report measures: the RRS (containing three subscales: Brooding, Reflection, and Depression)¹⁵, the PSWQ¹⁶, the Perceived Stress Scale (PSS)³⁹, the Dysfunctional Attitudes Scale (DAS)⁴⁰, the Positive and Negative Affect Schedule (PANAS)⁴¹, and the Dimensional Anhedonia Rating Scale (DARS)⁴². These tools were chosen in order the test the validity, specificity, and sensitivity of our model outputs. The study took a total of 50–60 min to complete and was coded in JsPsych⁴³ and ran locally (in person sample) or remotely, on Pavlovia (online sample).

Data Preprocessing

Data was manually checked for spelling mistakes and other errors. Submissions that contained proper nouns, names of places and brands, numbers, unintelligible words, or acronyms were treated as “late word submissions” and substituted with the previous word in the sequence. Two-word expressions or phrasal verbs were substituted by one-word synonyms. An average of 4.3% of the word-submissions had to be substituted during data cleaning. Data was cleaned by trained staff and checked by a supervisor (MM). After data cleaning, participants who had failed to submit more than 1/3 of words within the 4.5 s time limit (meaning, submitted less than 138 unique words) were excluded from the analysis for missing data. This was our only exclusion criteria. 7 participants in Sample 1, 21 from Sample 2, and 78 participants from Sample 3 were removed due to missing data or poor data quality, as described above.

The cleaned data were then embedded using a pre-trained GloVe model⁴⁴, trained with 2 billion tweets/27 billion tokens, which yielded 25 dimensional vectors for each submitted word. These vectors were numerical representations of the word location in a multidimensional semantic space. Principal Component Analysis was then used to reduce the number of dimensions to 3 in order to alleviate computational requirements of subsequent analyses and after extensive model selection procedures.

Data Modeling

Three models were developed for this study. All models (described below) were fit at the trial level using 1000 iterations of a Nelder-Mead optimization method that aimed to minimize sum of squared error. Akaike Information Criterion (AIC) were computed as measures of model fit. Model fits were averaged across participants and compared across models.

Linear Model

Our linear model assumed that participants were spontaneously traveling a multidimensional semantic space in a simple, unconstrained, and non-creative manner. These individuals’ trains of thoughts would not have been influenced by the presence of attractor locations, but would have displayed some inflexibility or lack of creativity⁴⁵. Because of the nature of our 3D semantic space, true mind-wandering would likely lead individuals to travel between semantic spaces in a more flexible, non-linear fashion. This model was equipped to capture both non-creative and non-RNT spontaneous thought.

The equation (1) describes the position in the 3D semantic space of each word submission (k_t) in a word-chain at every time t. All word chains were 11 words long (there were 11 timepoints or ts in each word chain). All word chains started at the provided seed word (k₀), and were update based on a single term m ((min [-100,,100]), unidimensional—assuming the same slope across all three dimensions). m was estimated at the trial level, and initialized at random values between ([-100,,100]) during optimization. Smaller values of m indicated less creative spontaneous thought.

Sinusoidal Model

Our sinusoidal model assumed that truly free mind-wandering would lead individuals to travel back and forth between ideas in any and all semantic areas, in a non-linear fashion. Accordingly, our sinusoidal model aimed to capture unconstrained thinking that could revisit previous semantic areas within a word chain.

The equation (2) describes the position in the 3D semantic space of each word submission (({k}_{t})) in a word-chain at every time t. All word chains started at the provided seed word (k₀). Two parameters were fit, A ((Ain [-50,,50])) and f ((fin (0,,50])). A captured the amplitude of our word chains. Greater values of this parameter indicated higher unconstrained creativity. f captured the frequency of our word chains. In this case, smaller values of f indicated less constrained thought, and a lower tendency to revisit previous ideas.

Convergent Dynamic Model

Finally, our convergent dynamic model assumed that individuals attempted to travel the multidimensional semantic space while in the presence of one or more attractor locations that influenced them to revisit previous topics across chains or become stuck in negatively-valenced semantic areas.

The equation (3) describes the position of each word submission (k_t) in a word-chain at every time t. This equation enables us to find the location towards which individuals may have been traveling at each word chain (estimated attractor location, (hat{k}), (hat{k}in left(left[-200,,200right],,left[-200,,200right],, left[-200,,200right]right)), initialized at random) and the adjustment rate coefficient, or rate of approach to that location ((mu ,,mu in (0,,25]), unidimensional, initialized at random). The meaning of (hat{k}) and μ can only be interpreted in the context of other observations. They cannot be interpreted on their own. In trials where individuals started and ended around the attractor location, (hat{k}), a small μ indicated “stuckness”. In trials where individuals traveled long distances and ended very close to the attractor location, (hat{k}), a large value of μ indicated “stuckness”. We computed additional information for each attractor location, (hat{k}), to further understand the quality of the word chains.

First, to calculate participant’s tendencies to revisit previously explored topics, we used kernel density estimates. This technique enabled us to compute the distribution densities at each participant’s (hat{k}{{rm{s}}}). Higher kernel densities meant higher topic-revisiting behaviors, while lower kernel densities meant lesser topic-revisiting behaviors. Next, we computed valence ratings and “perceived overthinking” ratings associated with the attractor locations. Valence ratings for each word submission were obtained from the ANEW database and “perceived overthinking” ratings were obtained from each participant. To estimate valence and “perceived overthinking” at each attractor location, we computed a weighted average where values of “perceived overthinking” and valence associated with words that appeared closer in space to (hat{k}) were weighted more heavily than the rating values of those words that appeared far from (hat{k}) in the semantic space. Finally, we estimated the Euclidian distance from (hat{k}) at the end of each word-chain. Ending close to (hat{k}) indicated increasingly stuck thought.

Actual data fitting procedures followed the parameter recovery pipeline, meaning that all trials were fit using 1000 iterations of a Nelder-Mead optimization method. AICs were computed for each trial and averaged within participants. At the participant level, the convergent dynamic model fit significantly better than the simple linear model and the sinusoidal model across all samples. Accordingly, subsequent analyses were conducted using parameters estimated from the convergent dynamic model.

Parameter Recovery

During model development, we conducted parameter recoveries to explore best optimization methods, iteration needs, and parameter ranges. Using all models separately, we first generated 100 data observations (word-chains) using random parameter values within our desired parameter bounds. Next, we tried to recover those parameter values using 1000 iterations of the Nelder-Mead optimization method. All model parameters recovered strongly at rates ranging from r = 0.82 to r = 1, all p < 0.001 (see Fig. 2).

Three models were developed for this study: a simple linear model, a sinusoidal model, and a convergent dynamic model. a Reveals the robust parameter recovery rates (all r > 0.8) that parameter values across all models demonstrated. The y axis indicates the r-values (obtained from 100 data simulations) of the correlations between the parameters used to simulate data and the recovered parameters following optimization. b Displays AIC values associated with our 3 models after fitting them to our data. Significance is assumed based on the criteria that ({triangle }_{{AIC}} > 3.) In box plot: the middle line represents the distribution median, the top line represents the third quartile (75th percentile), and the bottom line represents the first quartile (25th percentile). As can be observed in the image, our convergent dynamic model fit our behavioral data significantly better than the other two models. c Presents the complete scatter plots of the regressions reported in a. All y-axes present the actual parameter values that were used to conduct data simulations, and the x-axes present the recovered parameters.

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Clustering and Statistical Analyses

Based on our pre-registered analysis, unsupervised k-means clustering was conducted on three primary variables on interest: 1. rate of approach, 2. final distance to (hat{k}), and 3. valence at (hat{k}). Clustering was conducted independently in all three samples, at the trial level. Optimal number of clusters was obtained using the knee method (Kneed python package) based on inertia (a measure of dispersion of clusters) and the gap statistic (a measure of distance between clusters). Across all samples, 4 clusters represented the optimal solution including after cluster-size correction to ensure statistical power. We ran one-way ANOVAs to compute between cluster differences across all variables. Mix linear models and a canonical correlation were also conducted to explore the relationship between individually averaged parameter values and self-report measures (see Supplemental Fig. 1).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Study Design and Pre-Registration

An initial sample of 72 (due to missing data, 65 usable) in-person participants (Sample 1) and a second sample of 100 (79 usable) online participants (Sample 2) completed the written free-association paradigm and several self-report measures. These two samples were used to conduct exploratory analyses aimed at unearthing distinct patterns of spontaneous thought. Exploratory analyses revealed results that were both theory-congruent and yielded results that replicated across samples. The most harmonious and theory-driven analysis (described in this paper) was then selected for pre-registration⁴⁶ prior to a final replication. This pre-registration hypothesized that the clustering algorithm described in this paper would continue to yield the results observed in the prior two samples, in a larger dataset. Indeed, a final online sample of 300 (222 usable) participants (Sample 3) replicated the results obtained in the previous samples, confirming our pre-registered analysis.

Association Between Self-Report Questionnaires and Word Submissions

After preprocessing data from the free word-association paradigm, we first analyzed the relationship between trait worry (PSWQ) and rumination (RRS), self-reported stress (PSS) and mood (PANAS), and the collected word-submissions. In line with previous studies, we expected to observe a negative association between these self-report measures and word-submission valence, and a positive association between these measures and reported “perceived overthinking”. When controlling for age and sex (and including data from Samples 1, 2, and 3) we found negative correlations between word-submission valence (smaller values = more negative valence) and self-report measures of rumination (r(364) = −0.10, p = 0.047, 95% CI [−0.20, −0.004]), worry (r(364) = −0.10, p = 0.047, 95% CI [−0.20, −0.008]), depressed mood (r(364) = −0.18, p = 0.0004, 95% CI [−0.28, −0.08]), and stress (r(364) = −0.17, p = 0.001, 95% CI [−0.26, −0.06]). We also found positive correlations linking a higher reporting that individuals thought about the words they submitted during the task more than they “should” in daily life (“perceived overthinking” ratings) and self-report measures of rumination (r(364) = 0.27, p < 0.001, 95% CI [0.17, 0.38]), worry (r(364) = 0.32, p < 0.001, 95% CI [0.19, 0.40]), depressed mood (r(364) = 0.41, p < 0.001, 95% CI [0.31, 0.51]), and stress (r(364) = 0.34, p < 0.001, 95% CI [0.22, 0.43]). See Fig. 3 for further details. Together, these analyses help confirm the reliability of our samples, as they successfully replicate previous findings. Furthermore, our samples count on a wide range of trait-rumination and worry tendencies, enabling us to test our core hypotheses along a comprehensive range of symptom severities (RRS: M = 47.8, SD = 14.3, Range = 22–88; PSWQ: M = 47.6, SD = 9.3, Range = 16–67; PSS: M = 23.0, SD = 9.4, Range = 0–43; PANAS negative: M = 20.0, SD = 8.3, Range = 10–45).

In line with previously reported findings, our data (N = 366) revealed that individuals with more elevated measures of negative mood (PANAS negative), stress (PSS), rumination (RRS), and worry (PSWQ) also brought up more negative words (based on the ANEW database) during the task, and words that they “believed they thought about more than they should in their day to day life” (“perceived overthinking” rating). In relation to Valence: RRS, r(364) = −0.10, p < 0.05, 95% CI [−0.20, −0.004]; PSWQ, r(364) = −0.10, p < 0.05, 95% CI [−0.20, −0.008]; PANAS, r(364) = −0.18, p < 0.001, 95% CI [−0.28, −0.08]; PSS, r(364) = −0.17, p = 0.001, 95% CI [−0.26, −0.06]. In relation to “Perceived Overthinking”: RRS, r(364) = 0.27, p < 0.001, 95% CI [0.17, 0.38]; PSWQ, r(364) = 0.32, p < 0.001, 95% CI [0.19, 0.40]; PANAS, r(364) = 0.41, p < 0.001, 95% CI [0.31, 0.51]; PSS, r(364) = 0.34, p < 0.001, 95% CI [0.22, 0.43].

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Dynamic Systems Model Development

We tested three primary models: a simple linear model, a sinusoidal model, and a convergent dynamic model. Based on participant-level Akaike Information Criterion (AIC)⁴⁷ and assuming significance based on a ({triangle }_{{AIC}} > 3), the convergent dynamic model (({{AIC}}_{{conv}}) = 24.3, ({triangle }_{{conv}}({AIC}))= 0, ({w}_{{conv}}left({AIC}right)=0.90)) fit significantly better than the simple linear model (({{AIC}}_{{line}}) = 35.3, ({triangle }_{{line}}({AIC}))= 11, ({w}_{{line}}left({AIC}right)=0.0037)) and the sinusoidal model (({{AIC}}_{sin }) = 28.8, ({triangle }_{sin }({AIC}))= 4.5, ({w}_{sin }left({AIC}right)=0.095)) across all samples (See Fig. 2b). Accordingly, the convergent dynamic model was used for further analyses.

Unsupervised Clustering of Spontaneous Thought Trajectories

We next tested the parameters of our convergent dynamic model using an exploratory clustering algorithm. Adjustment rate coefficient (or rate of approach), valence at attractor location, and Euclidean proximity to attractor location were used to conduct unsupervised k-means clustering. Other measures, such as tendency to revisit the attractor location or “perceived overthinking” rating associated with the attractor location, were used to validate and interpret our clusters. Figure 4 shows the results of clustering on variables of interest, while Fig. 5 provides a graphical depiction of the distinct thought trajectory dynamics representative of each cluster.

All y-axes display standardized variables, where M = 0, and SD = 1. All error bars represent standard error of the mean (SEMs). (top left) Displays cluster average, model-estimated adjustment rate coefficients (μ). Larger values indicate faster approach to attractor location. (top middle) Displays cluster average trial distance to model-estimated attractor locations ((hat{k})). Smaller values indicate closer proximity to attractor location – more stuck thought. (top right) Displays cluster average valence associated with model-estimated attractor locations ((hat{k})). Larger values indicate more positive words. (bottom left) Displays cluster kernel density estimates associated with model-estimated attractor locations ((hat{k})). Larger values indicate higher revisiting patterns. (bottom middle) Displays cluster average “perceived pathology” ratings associated with model-estimated attractor locations ((hat{k})). Larger values indicate higher “perceived pathology”, meaning higher reporting that individuals thought about attractor locations “more than they should” in their daily lives.

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Axes represent our 3-dimensional semantic space. Dots are model-estimated attractor locations ((hat{k})). Dot size represents average kernel estimates at attractor location (larger indicates more revisiting). Dot color represents valence at attractor location (red indicates negative valence, blue indicates positive valence). Arrows (11 for each cluster, representing 11 words submitted in each word-chain) represent average thought trajectories that participants engaged in during trials in each cluster.

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Using the elbow method on various model statistics, our algorithm yielded a four optimal clusters solution that replicated across all three samples. For a breakdown of all cluster parameters, see Table 2. Cluster 1 displayed a pattern similar to mind-wandering, where individuals were not quickly approaching an attractor location (small μ), nor did they end close to it at the end of the word-chains. Attractor locations in cluster 1 were rated as neutral in valence and rarely revisited, as evidenced by their associated low kernel densities. These findings are further validated by participants’ self-reporting that they did not “think about the words they submitted more than they should” in their daily life (“perceived overthinking” rating). Of note, neither kernel density nor “perceived overthinking” ratings were used for clustering, but nevertheless aligned with the intuitions that the model-estimated parameters are based on. Taken together, this pattern appears most akin to tradition definitions of mind-wandering: characterized by easy transitions between thoughts, slow/meandering progression across the semantic space, and minimal reports of subjective distress related to thought content.

Cluster 2 revealed a pattern consistent with protective, positive thinking, where individuals slowly traveled (small μ) towards a positively-valenced attractor location. Word-chains in this clustered closely approached the attractor location and were sometimes revisited. Across all groups, this cluster revealed the lowest “perceived overthinking” ratings, indicating that people indeed did not believe that they thought about the positive attractor locations in this cluster more than they “should” in their daily life. The thinking pattern displayed in this cluster best parallels a way of thinking that focuses on pleasant experiences or outcomes and is often linked to protective benefits that can keep psychopathology at bay.

In contrast to Clusters 1 and 2, Clusters 3 and 4 presented two distinct patterns of stuck thinking (i.e., RNT). Cluster 3 revealed individuals that traveled slowly (small μ) towards a negative attractor location, and frequently reached it. While this behavior was similar to Cluster 2, unlike Cluster 2, these attractor locations were rated as being negatively valenced and had higher “perceived overthinking” ratings. This pattern is similar to definitions of RNT that focus on individuals’ tendencies to stay within negative-valenced ideas once they start thinking about them and lack an ability to engage in flexible adaptive thinking. These individuals may experience their moods spiraling downward when they begin engaging in RNT, as many other negative thoughts can come to their minds.

Finally, Cluster 4 captured an “obsession-like” thinking pattern, in which individuals quickly approached (large μ) a negatively-valenced attractor location, that they repeatedly revisited during the task and believed that they “thought about more than they should in their daily life”. This pattern of thinking closely resembles potentially more obsessive RNT, where individuals keep quickly travelling to one negative topic that they are particularly stuck on, regardless of where they start the train of thought. These are individuals that not only transition towards negative-valenced ideas fast, but they are uniquely bothered by one topic.

Note that there was no significant association between trial clustering and trial’s seed word valence (Cramer’s V = 0.004, p = 0.56), indicating a lack of association between a trial’s forced beginning and the participant’s chosen end. In other words, individuals that were repeatedly stuck in, for instance, negative-valence attractor locations, travelled there regardless of what valence seed-word they started at.

Associations between Thought-Trajectory Clusters and Self-Report Measures of Trait Rumination and Internalizing Psychopathology

Despite well-documented inconsistencies in the correlations between clinical self-report measures and parameter values of learning, decision-making, and other behavioral tasks⁴⁸, we performed an exploratory analysis to determine how the four clusters related to commonly-used retrospective self-report measures of psychopathology (trait-rumination, trait-worry, perceived stress, and negative mood). Of note, to avoid type-I errors⁴⁹, we attempted to replicate our findings across samples, rather than merging them together. When controlling for sex and age, the frequency of trials in cluster 1 (“mind-wandering-like”) did not significantly correlate with any clinical self-report measures of mood, stress, or perseverative thinking (t(63–220) = −1.80–0.97, p = 0.16–.68, η² = 0.001–0.03). Frequency of trials in cluster 2 (“protective positive thinking”) negatively correlated with measures of negative mood (t(77–220) = −2.88–−2.40, p = 0.037–0.0005, η² = 0.02–0.20) and stress (t(77–220)= −2.81–−2.07, p = 0.036, η² = 0.01–0.06) in our Samples 2 and 3, and worry (t(220) = −2.42, p = 0.05, η² = 0.01) only in Sample 3. Correlation analyses linking self-report measures and frequency of trials clustered into cluster 3 (our inflexible stuck thinking cluster) were more heterogeneous across samples. While all correlation coefficients yielded effects in the expected directions, only a minority of those relationships were statistically significant, none of them in Sample 3, our largest, likely most-powered, sample. Positive mood negatively correlated with cluster 3 frequency (t(63)= −2.04, p = 0.05, η² = 0.06) in Sample 1, and both stress (t(77) = 2.22, p = 0.02, η² = 0.008) and negative mood (t(77) = 2.15, p = 0.01, η² = 0.02) significantly positively correlated with cluster 3 clustering frequency in Sample 2. Finally, frequency of trials clustered into cluster 4 (our revisiting stuck thinking cluster) positively correlated with measures of rumination (t(220) = 2.58, p = 0.05, η² = 0.006), worry (t(220) = 2.59, p = 0.03, η² = 0.007), negative mood (t(220) = 2.91, p = 0.009, η² = 0.007) and stress (t(220) = 2.69, p = 0.04, η² = 0.007) only in Sample 3.

A 4-level linear mixed effects model, separately conducted in each sample, further explored whether repeated cluster membership was related to clinical self-report measures. No consistent patterns linking clinical self-report measures and our parameter-estimated clusters were found (see Supplemental Materials).

Using a previously established word-association paradigm designed to capture spontaneous thinking patterns, we fit a dynamic convergent model to estimate attractor locations in a multidimensional semantic space and their associated rates of approach (adjustment rate coefficients). We successfully used clustering algorithms to capture four distinct thought trajectories that match onto previously theorized spontaneous thinking patterns and further provide a more nuanced understanding of stuck spontaneous thought, such as RNT, rumination, and worry. Across three independent samples, we observed unstuck, mind-wandering-like thinking³, protective positive thinking^50,51, and two forms of stuck thought that may have relevant clinical implications. To our knowledge, these results offer the first empirical demonstration of previously hypothesized thought dynamics that may underlie RNT.

From our resulting four clusters, Cluster 1 displayed a pattern similar to free mind-wandering where individuals did not travel towards a negative attractor location quickly or revisit topics, but rather freely and flexibly navigated a semantic space³. Cluster 2 displayed a pattern of protective positive thinking, during which individuals stayed in positive-valenced attractor locations that they sometimes revisited^50,51. Cluster 3 showed individuals engaging in RNT-like thinking, as trains of thought in this cluster were inflexible, slowly traveled and stayed among negative ideas, but did not often re-visit topics⁶. Finally, Cluster 4 revealed another form of RNT. In this cluster, trains of thought quickly and creatively traveled towards a negative attractor location that was very often revisited, potentially akin to obsessive thinking⁵².

In addition to providing a computational framework for conceptualizing and measuring free and stuck thought, our results also point to new potential targets for treatment. Namely, that RNT may be distinctly composed of racing-thought patterns that frequently revisit a topic, or slower, inflexible, perseverative thinking of diverse negative ideas. Although significant more work is needed, and our findings ought to be compared to other state measures of stuck thought (like ecological momentary assessment), these distinct forms of RNT could possibly point towards distinct underlying biological markers and may benefit from different treatment options.

Additional strengths of this work include a high degree of reliability and construct validity of our results, as evidenced by robust replication and convergence with variables that were not used for clustering. Specifically, kernel density estimates provided further evidence that our model was capturing free and stuck thought, and participant-reported “perceived overthinking” ratings aligned with our standardized measures of valence at the attractor locations and were elevated in our model-estimated stuck thought clusters. Finally, our study provides insights not captured in self-report measures of RNT, extending the literature in a meaningful way. While self-report measures of mood, stress, and RNT showed some significant associations with our model’s results, those significant links did not often replicate across samples. We are excited by these results as they suggest a reasonable connection between trait-based self-report measures and state severity of RNT, but further demonstrate the need for state-dependent measures of psychopathology severity beyond individuals’ conscious awareness. In this way, this work contributes to the growing body of evidence suggesting that self-report clinical measures and computational psychiatry modeling likely capture distinct, both valuable, features of psychopathology^48,53.

Limitations

Although the current work has many strengths, there are also several limitations to be considered. Most importantly, our parameter estimation process would be strengthened by increasing our computational power, which would enable us to use more efficient optimization techniques, hence sample from a larger parameter space. Specifically, we sampled our attractor location coordinates from [−200, 200] and our rate of change coefficient from [0, 20], a vast majority of these trials did not appear to max out our parameter space, but we could sample a larger parameter space. Relatedly, future work could explore how hierarchical or Bayesian estimation methods may strengthen our parameter estimation. Future work should also explore how stable/sensitive our model is in tracking changes in thinking patterns from individuals who are, for instance, undergoing treatment for depression or RNT. Additionally, future iterations of this work should also consider different word-embedding models that can account for homographs, and different data collection strategies that may reduce the need for word-substitutions during data cleaning. We also used normative measures of valence (drawn from the ANEW database) instead of individually provided measures, as we initially intended to⁴⁶. Our original method of collecting individual valence ratings (“perceived enjoyment”) did not successfully tap into the construct of interest as most individuals reported on something akin to the “utility” of thinking about the concepts they submitted, rather than their valence. Individual measures of valence could be highly informative of these thinking patterns and strengthen our work. Furthermore, thought dynamics are highly complex processes that likely could be captured by models not explored in the present paper. More work is needed to determine the ideal complexity and formulation of each cluster’s dynamics. Finally, while our results appear reliable and valid, the clinical implications of cluster memberships ought to be further studied to better understand their diagnostic utility. Indeed, we lacked confirmed clinical diagnoses on our participants, and two of our samples were likely underpowered to detect significant correlations between model-estimated parameters and clinical measures.

Taken together, we provide support for a conceptual model of spontaneous free and stuck thought and preliminary evidence towards a potential future measure of RNT state severity.