I study how children, adults, and machines
learn to represent the world

In many tasks, human behavior is far noisier than is optimal. Yet when asked to behave randomly, people are typically too predictable. We argue that these apparently contrasting observations have the same origin: the operation of a general-purpose local sampling algorithm for probabilistic inference. This account makes distinctive predictions regarding random sequence generation, not predicted by previous accounts—which suggests that randomness is produced by inhibition of habitual behavior, striving for unpredictability. We verify these predictions in two experiments: people show the same deviations from randomness when randomly generating from non-uniform or recently-learned distributions. In addition, our data show a novel signature behavior, that people's sequences have too few changes of trajectory, which argues against the specific local sampling algorithms that have been proposed in past work with other tasks. Using computational modeling, we show that local sampling where direction is maintained across trials best explains our data, which suggests it may be used in other tasks too. While local sampling has previously explained why people are unpredictable in standard cognitive tasks, here it also explains why human random sequences are not unpredictable enough.

People often display essentialist biases, which can lead them to underestimate within-species variability. This bias is especially pronounced when traits are described as advantageous for survival. However, it is unclear whether this bias is limited to the specified trait or encompasses complex trait interactions. We used Markov Chain Monte Carlo with People (MCMCp) to analyze people's representations of biological variability, using ladybeetles as a model species. Participants either received contextual information about the benefits of ladybeetle color for survival, or survival-irrelevant information. Overall, participants held consistent beliefs about ladybeetle features, but those with survival-relevant context produced lighter and larger ladybeetles; this difference was consistent with survey responses. However, we found no significant interaction between MCMCp variability and essentialism scores, given our context manipulation. We discuss potential explanations for these results and highlight advantages of MCMCp for assessing biological variability, particularly when studying the development of essentialist biases.

People must often make inferences about, and decisions concerning, a highly complex and unpredictable world, on the basis of sparse evidence. An "ideal" normative approach to such challenges is often modeled in terms of Bayesian probabilistic inference. But for real-world problems of perception, motor control, categorization, language comprehension, or common-sense reasoning, exact probabilistic calculations are computationally intractable. Instead, we suggest that the brain solves these hard probability problems approximately, by considering one, or a few, samples from the relevant distributions. By virtue of being an approximation, the sampling approach inevitably leads to systematic biases. Thus, if we assume that the brain carries over the same sampling approach to easy probability problems, where the "ideal" solution can readily be calculated, then a brain designed for probabilistic inference should be expected to display characteristic errors. We argue that many of the "heuristics and biases" found in human judgment and decision-making research can be reinterpreted as side effects of the sampling approach to probabilistic reasoning.

The brain must make inferences about, and decisions concerning, a highly complex and unpredictable world, based on sparse evidence. An “ideal” normative approach to such challenges is often modeled in terms of Bayesian probabilistic inference. But for real-world problems of perception, motor control, categorization, language understanding, or commonsense reasoning, exact probabilistic calculations are computationally intractable. Instead, we suggest that the brain solves these hard probability problems approximately, by considering one, or a few, samples from the relevant distributions. Here we provide a gentle introduction to the various sampling algorithms that have been considered as the approximation used by the brain. We broadly summarize these algorithms according to their level of knowledge and their assumptions regarding the target distribution, noting their strengths and weaknesses, their previous applications to behavioural phenomena, as well as their psychological plausibility.

Uncovering how categories develop through childhood is crucial for cognitive science. However, even for simple domains, categories can be complex, making it challenging to access them experimentally, especially in developmental studies. Markov-Chain Monte Carlo with People (MCMCp) is a statistically-based procedure that allows us to elicit category members from participants' implicit categories. However, due to the complexity of the paradigm, MCMCp has been limited to experiments with adult populations. Here, we develop and validate a child-friendly method for applying MCMCp, producing the first MCMCp experiment to elicit category examples from children. Comparing fruit category members for five-year-olds and seven-year-olds, we find generally consistent representative fruits and a developmental progression of initially broad and overlapping fruit categories to more differentiated distributions.

Recent advancements in natural language processing by large language models (LLMs), such as GPT-4, have been suggested to approach Artificial General Intelligence. And yet, it is still under dispute whether LLMs possess similar reasoning abilities to humans. This study evaluates GPT-4 and various other LLMs in judging the profoundness of mundane, motivational, and pseudo-profound statements. We found a significant statement-to-statement correlation between the LLMs and humans, irrespective of the type of statements and the prompting technique used. However, LLMs systematically overestimate the profoundness of nonsensical statements, with the exception of Tk-instruct, which uniquely underestimates the profoundness of statements. Only few-shot learning prompts, as opposed to chain-of-thought prompting, draw LLMs ratings closer to humans. Furthermore, this work provides insights into the potential biases induced by Reinforcement Learning from Human Feedback (RLHF), inducing an increase in the bias to overestimate the profoundness of statements.

Human cognition is fundamentally noisy. While routinely regarded as a nuisance in experimental investigation, the few studies investigating properties of cognitive noise have found surprising structure. A first line of research has shown that inter-response-time distributions are heavy-tailed. That is, response times between subsequent trials usually change only a small amount, but with occasional large changes. A second, separate, line of research has found that participants' estimates and response times both exhibit long-range autocorrelations (i.e., 1/f noise). Thus, each judgment and response time not only depends on its immediate predecessor but also on many previous responses. These two lines of research use different tasks and have distinct theoretical explanations: models that account for heavy-tailed response times do not predict 1/f autocorrelations and vice versa. Here, we find that 1/f noise and heavy-tailed response distributions co-occur in both types of tasks. We also show that a statistical sampling algorithm, developed to deal with patchy environments, generates both heavy-tailed distributions and 1/f noise, suggesting that cognitive noise may be a functional adaptation to dealing with a complex world.

Elicitation methods, such as asking people to produce the deciles of a distribution, are standard practices in policy or applied statistics. However, these approaches often only capture a rough outline of what people know. We investigated whether tasks in which participants generate random sequences of items can be used to elicit people's implicit beliefs about the distribution of these items. Because it remains unclear if, and at what level of detail, people represent distributions, we applied both decile elicitation and random generation tasks to uncover the kinds of environmental statistics investigated by Griffiths and Tenenbaum (2006). We found that random generation is competitive with decile elicitation in predicting participants' expectations. Both random generation and decile elicitation revealed that people know the rough shapes of environmental distributions. Random generation, however, goes beyond decile elicitation in establishing the novel finding that people are aware of fine details of environmental distributions.

Capturing the structure of human conceptual knowledge is a challenging but fundamental task. The most prominent approach, Multidimensional Scaling (MDS), usually requires many similarity judgments, which leads to long experiments, and only provides a representation of a fixed set of stimuli. In contrast, we present a more flexible method that can generalize to novel stimuli. This method uses a child-friendly task that allows researchers to uncover the development of categories with fewer participant judgments. We evaluate this approach on simulated data and find that it can accurately reveal representations even when trained on data generated by groups that categorize differently. We then analyze data from the World Color Survey and find that we can recover language-specific color organization. Finally, we use the method in a novel developmental experiment and find age-dependent differences in how fruit categories are structured. These results suggest that our method is widely applicable in developmental tasks.

Uncovering how categories develop through childhood is crucial for cognitive science. However, even for simple domains, categories can be complex, making it challenging to access them experimentally. Here, we use an experimental method that allows us to produce exemplars from children's implicit categories (Markov Chain Monte Carlo with People, MCMCP). Instead of querying pre-specified materials, MCMCP adaptively selects which stimuli to present, allowing us to focus on the most informative exemplars. We use MCMCP to uncover age-dependent differences in the category organization of fruits in a pre-registered online experiment. Comparing five-year-olds, seven-year-olds, and adults, we find a developmental progression of initially broad and overlapping fruit categories to more differentiated distributions. Furthermore, we find that across age groups, apple and grape categories exhibit bi-modal color distributions. We discuss these results in the context of theories of randomness reduction over the lifespan and shape biases in category induction.

Noise in behavior is often considered a nuisance: Although the mind aims for the best possible action, it is let down by unreliability in the sensory and response systems. Researchers often represent noise as additive, Gaussian, and independent. Yet a careful look at behavioral noise reveals a rich structure that defies easy explanation. First, in both perceptual and preferential judgments sensory and response noise may potentially play only minor roles, with most noise arising in the cognitive computations. Second, the functional form of the noise is both non-Gaussian and nonindependent, with the distribution of noise being better characterized as heavy-tailed and as having substantial long-range autocorrelations. It is possible that this structure results from brains that are, for some reason, bedeviled by a fundamental design flaw, albeit one with intriguingly distinctive characteristics. Alternatively, noise might not be a bug but a feature. Specifically, we propose that the brain approximates probabilistic inference with a local sampling algorithm, one using randomness to drive its exploration of alternative hypotheses. Reframing cognition in this way explains the rich structure of noise and leads to the surprising conclusion that noise is not a symptom of cognitive malfunction but plays a central role in underpinning human intelligence.

Many models of cognition assume that people can generate independent samples, yet people fail to do so in random generation tasks. One prominent explanation for this behavior is that people use learned schemas. Instead, we propose that deviations from randomness arise from people sampling locally rather than independently. To test these explanations, we teach people one- and two-dimensional arrangements of syllables and ask them to generate random sequences from them. Although our results reproduce characteristic features of human random generation, such as a preference for adjacent items and an avoidance of repetitions, we also find an effect of dimensionality on the patterns people produce. Furthermore, model comparisons revealed that local sampling accounted better for participants' sequences than a schema account. Finally, evaluating the importance of each models' constituents, we show that the local sampling model proposed new states based on its current trajectory, rather than an inhibition-of-return-like principle.

Recent computational advancements show that human performance often aligns with Bayesian models in complex domains like vision and language. However, humans also make systematic errors in probability reasoning, such as the unpacking effect or conjunction fallacy, which seem to contradict Bayesian principles. These errors can be explained by the brain's use of sampling algorithms like Markov Chain Monte Carlo (MCMC) and Metropolis-coupled Markov chain Monte Carlo (MC3). These algorithms generate samples that depend on previous ones, explaining cognitive biases like the anchoring effect. They produce patterns in cognitive time series, such as Lévy distributed distances between samples and 1/f noise, which are key for understanding human inference. The Bayesian sampler concept incorporates uncertainty into sampling, leading to conservatism in probability judgments. The Bayesian Amortised Sequential Sampler (BASS) model explains perceptual biases by reusing samples between decisions and estimates, offering insights for designing efficient machine intelligence.

Cognitive science is often concerned with questions about our representations of concepts and the underlying psychological spaces in which these concepts are embedded. One method to reveal concepts and conceptual spaces experimentally is Markov chain Monte Carlo with people (MCMCP), where participants produce samples from their implicit categories. While MCMCP has allowed for the experimental study of psychological representations of complex categories, experiments are typically long and repetitive. Here, we contrasted the classical MCMCP design with a linked variant, in which each participant completed just a short run of MCMCP trials, which were then combined to produce a single sample set. We found that linking produced results that were nearly indistinguishable from classical MCMCP and often converged to the desired distribution faster. Our results support linking as an approach for performing MCMCP experiments within broader populations, such as in developmental settings where large numbers of trials per participant are impractical.

People must often make inferences about, and decisions concerning, a highly complex and unpredictable world, on the basis of sparse evidence. An "ideal" normative approach to such challenges is often modeled in terms of Bayesian probabilistic inference. But for real-world problems of perception, motor control, categorization, language comprehension, or common-sense reasoning, exact probabilistic calculations are computationally intractable. Instead, we suggest that the brain solves these hard probability problems approximately, by considering one, or a few, samples from the relevant distributions. By virtue of being an approximation, the sampling approach inevitably leads to systematic biases. Thus, if we assume that the brain carries over the same sampling approach to easy probability problems, where the "ideal" solution can readily be calculated, then a brain designed for probabilistic inference should be expected to display characteristic errors. We argue that many of the "heuristics and biases" found in human judgment and decision-making research can be reinterpreted as side effects of the sampling approach to probabilistic reasoning.

Generalization is at the core of human intelligence. When the relationship between continuous-valued data is generalized, generalization amounts to function learning. Function learning is important for understanding human cognition, as many everyday tasks and problems involve learning how quantities relate and subsequently using this knowledge to predict novel relationships. While function learning has been studied in psychology since the early 1960s, this thesis argues that questions regarding representational characteristics have not been adequately addressed in previous research. Previous accounts of function learning have often proposed one-size-fits-all models that excel at capturing how participants learn and extrapolate. In these models, learning amounts to learning the details of the presented patterns. Instead, this thesis presents computational and empirical results arguing that participants often learn abstract features of the data, such as the type of function or the variability of features of the function, instead of the details of the function. While previous work has emphasized domain-general inductive biases and learning rates, I propose that these biases are more flexible and adaptive than previously suggested. Given contextual information that sequential tasks share the same structure, participants can transfer knowledge from previous training to inform their generalizations. Furthermore, this thesis argues that function representations can be composed to form more complex hypotheses, and humans are perceptive to, and sometimes generalize according to these compositional features. Previous accounts of function learning had to postulate a fixed set of candidate functions that form a participants' hypothesis space, which ultimately struggled to account for the variety of extrapolations people can produce. In contrast, this thesis's results suggest that a small set of broadly applicable functions, in combination with compositional principles, can produce flexible and productive generalization.

We propose that when humans learn sets of relationships, they can learn the abstract structure or type of a family of relationships and exploit that knowledge to improve their ability to learn and generalize in the future, especially in the face of sparse or ambiguous data. In two experiments we found that participants choose patterns and extrapolate in ways consistent with sets of previously learned relations, as measured by extrapolation judgments and forced-choice tasks. We take these results to suggest that humans can detect shared abstract relations and apply this learned regularity to perform rapid and flexible generalization.

Function learning research has highlighted the importance of human inductive biases that facilitate long-range extrapolations. However, most previous research is focused on aggregate errors or single-criterion extrapolations. Thus, little is known about the underlying psychological space in which continuous relationships are represented. We ask whether people can learn the distributional properties of new classes of relationships, using Markov Chain Monte Carlo with People, and find that (1) people are able to track not just the expected parameters of a linear function, but information about the variability of functions in a specific context and (2) in many cases these spaces over parameters exhibit multiple modes.

In function learning experiments, where participants learn relationships from sequentially presented examples, people show a strong tacit expectation that most relationships are linear, and struggle to learn and extrapolate from non-linear relationships. In contrast, experiments with similar tasks where data are presented simultaneously – typically using scatterplots – have shown that human learners can discover and extrapolate from complex non-linear trends. Do people have different expectations in these task types, or can the results be attributed to effects of memory and data availability? In a direct comparison of both paradigms, we found that differences between task types can be attributed to data availability. We show that a simple memory-limited Bayesian model is consistent with human extrapolations for linear data for both high and low data availability. However, our model underestimates the participants' ability to infer non-monotonic functions, especially when data is sparse. This suggest that people track higher-order properties of functions when learning and generalizing.

GPflow is a Gaussian process library that uses TensorFlow for its core computations and Python for its front end. The distinguishing features of GPflow are that it uses variational inference as the primary approximation method, provides concise code through the use of automatic differentiation, has been engineered with a particular emphasis on software testing and is able to exploit GPU hardware.

Chess experts remember meaningful chess positions better than novices (de Groot, 1978; Chase & Simon, 1973). This can be explained with a larger number of chunks in experts' long-term memory (Gobet & Simon, 1998). These chunks are mainly based on visual representations—that is, pieces on squares. However, a recent experiment highlighted that experts prefer to group chess positions by abstract similarities that cannot be explained purely visually (Linhares & Brum, 2007). Based on these data it was claimed that chess expertise, in addition to chunks, crucially relies on abstraction and analogies. These data and the conclusions were heavily criticized because the instructions strongly biased the participants to group positions in a certain way (Bilalic & Gobet, 2009). Here, we successfully replicated this experiment with less explicit instructions. In addition, we collected category labels for the groupings that allowed us to explore the abstract principles that participants used.