Bonan Zhao

A hallmark of effective teaching is that it grants learners not just a collection of facts about the world, but also a toolkit of abstractions that can be applied to solve new problems. How do humans teach abstractions from examples? Here, we applied Bayesian models of pedagogy to a necklace‐building task where teachers create necklaces to teach a learner “motifs” that can be flexibly recombined to create new necklaces. In Experiment 1 (N = 151), we find that human teachers produce necklaces that are simpler (i.e., have lower algorithmic complexity) than would be expected by chance, as indexed by a model that samples uniformly from all necklaces that contain the target motifs. This tendency to select simpler examples is captured by a pedagogical sampling model that tries to maximize the learner's belief in the true motifs by prioritizing examples that have fewer alternative interpretations. In Experiment 2 (N = 295), we find that simplicity is beneficial. Human learners recover the underlying motifs better when teachers produce simpler sequences, as predicted by the pedagogical sampling model. However, humans learn best from human teachers rather than from model‐generated examples, which suggests that human teachers have additional expectations about how learners will interpret examples that are not captured by standard models of teaching. Our work provides a principled framework to understand when and why teachers use simple examples to convey abstract knowledge.

Successful innovation hinges on balancing exploring new ideas and exploiting good known ones. A rational innovator should be state-sensitive, effectively switching to exploitation when the best available idea reaches some standard. We tackle innovation with a discovery-by-recombination game under additive reward growth, and compare the optimal state-dependent policy with a state-independent policy. Our experiment reveals that participants made state-dependent decisions, exploring more in rounds with early successes, albeit being told of the same true success probability. In contrast, the optimal state-dependent policy switches to exploitation earlier. This suggests that participants' state-sensitivity may be driven by ad-hoc subjective probabilities. Participants also deviated from optimality through excessive exploration, switching multiple times between exploration and exploitation, and their switching points also differed from the theoretical optimum.

A hallmark of effective teaching is that it grants learners not just a collection of facts about the world, but also a toolkit of abstractions that can be applied to solve new problems. How do humans transmit and acquire generalizable abstractions from examples? Here, we applied Bayesian models of pedagogy to a necklace-building task where teachers create necklaces to teach a learner ``motifs'' that can be flexibly recombined to create new necklaces. In Experiment 1 (N = 151), we find that human teachers produce necklaces that are simpler (i.e., have lower algorithmic complexity) than would be expected by chance, as indexed by a model that samples uniformly from all necklaces that contain the target motifs. This tendency to select simpler examples is partially captured by a pedagogical sampling model that tries to maximize the learner's belief in the underlying motifs. In Experiment 2 (N = 295), we find that simplicity is beneficial. Human learners recover the underlying motifs better when teachers produce simpler sequences, and they learn best from human teachers rather than from model-generated examples. Our results suggest that the computational principles that underlie effective communication and teaching may also provide a first step towards understanding the transmission of culturally-specific abstractions.

Humans have the remarkable ability to learn new categories from few examples, but how few examples can we actually learn from? Recent studies suggest it may be possible to learn more novel concepts than the number of examples. Previous approaches to such less-than-one-shot (LO-shot) learning used soft labels to provide weighted mappings from each example to multiple categories. Unfortunately, people find soft labels unintuitive and this approach did not provide plausible, cognitively-grounded mechanisms for LO-shot learning at scale. We propose a new paradigm that leverages well-established learning strategies: reducing complex stimuli to primitives, learning by discrimination, and generalizing to novel compositions of features. We show that participants can learn 22 categories from just 4 examples, shedding light on the mechanisms involved in LO-shot learning. Our results provide valuable insights into the human ability to learn many categories from limited examples, and the strategies people employ to achieve this impressive feat.

Human learning does not stop at solving a single problem. Instead, we seek new challenges, define new goals, and come up with new ideas. What drives people to disrupt the existing conceptual landscape and create new things? Here, we examine the decision to create new things under different levels of potential returns. We formalize innovation as stochastically recombining existing ideas, where successful and more complex combinations generate higher returns. This formalization allows us to cast innovation-seeking as a Markov decision process, and derive optimal policies under different settings. Data collected through an online behavioral experiment confirm our prediction that people should invest more time and effort in seeking innovations when they know the chances of success are high and the potential new ideas would be rewarding. However, people also deviate from being optimal, both innovating more and less than they should in different settings.

To tackle a hard problem, it is often wise to reuse and recombine existing knowledge. Such an ability to bootstrap enables us to grow rich mental concepts despite limited cognitive resources. Here we present a computational model of conceptual bootstrapping. This model uses a dynamic conceptual repertoire that can cache and later reuse elements of earlier insights in principled ways, modelling learning as a series of compositional generalizations. This model predicts systematically different learned concepts when the same evidence is processed in different orders, without any extra assumptions about previous beliefs or background knowledge. Across four behavioural experiments (total n = 570), we demonstrate strong curriculum-order and conceptual garden-pathing effects that closely resemble our model predictions and differ from those of alternative accounts. Taken together, this work offers a computational account of how past experiences shape future conceptual discoveries and showcases the importance of curriculum design in human inductive concept inferences.

An open question regarding how people develop their models of the world is how new candidates are generated for consideration out of infinitely many possibilities. We discuss the role that evolutionary mechanisms play in this process. Specifically, we argue that when it comes to developing a global world model, innovation is necessarily incremental, involving the generation and selection among random local mutations and recombinations of (parts of) one's current model. We argue that, by narrowing and guiding exploration, this feature of cognitive search is what allows human learners to discover better theories, without ever grappling directly with the problem of finding a ``global optimum'', or best possible world model. We suggest this aspect of cognitive processing works analogously to how blind variation and selection mechanisms drive biological evolution. We propose algorithms developed for program synthesis provide candidate mechanisms for how human minds might achieve this. We discuss objections and implications of this perspective, finally suggesting that a better process-level understanding of how humans incrementally explore compositional theory spaces can shed light on how we think, and provide explanatory traction on fundamental cognitive biases including anchoring, probability matching and confirmation bias.

Human learning and generalization benefit from bootstrapping: we arrive at complex concepts by starting small and building upon past successes. In this paper, we examine a computational account of causal conceptual bootstrapping, and describe a novel experiment in which the sequence of training data results in a dramatic order effect: participants succeed in identifying a compound concept only after experiencing training data in a “helpful” order. Our computational model represents causal relations as reusable, modular programs, which can themselves be “chunked” and flexibly reused to tackle more complex tasks. Our specific approach is based in combinatory logic and adaptor grammars, building on previous theories that posit a “language of thought” for concept representation, but making the learning process more sensitive to a learner’s experiences than any partic- ular choice of conceptual primitives. Crucially, we demonstrate that a caching mechanism like that used in adaptor grammars is key to explain human-like bootstrapping patterns in causal generalization.

How do people decide how general a causal relationship is, in terms of the entities or situations it applies to? What features do people use to decide whether a new situation is governed by a new causal law or an old one? How can people make these difficult judgments in a fast, efficient way? We address these questions in two experiments that ask participants to generalize from one (Experiment 1) or several (Experiment 2) causal interactions between pairs of objects. In each case, participants see an agent object act on a recipient object, causing some changes to the recipient. In line with the human capacity for few-shot concept learning, we find systematic patterns of causal generalizations favoring simpler causal laws that extend over categories of similar objects. In Experiment 1, we find that participants’ inferences are shaped by the order of the generalization questions they are asked. In both experiments, we find an asymmetry in the formation of causal categories: participants preferentially identify causal laws with features of the agent objects rather than recipients. To explain this, we develop a computational model that combines program induction (about the hidden causal laws) with non-parametric category inference (about their domains of influence). We demonstrate that our modeling approach can both explain the order effect in Experiment 1 and the causal asymmetry, and outperforms a naïve Bayesian account while providing a computationally plausible mechanism for real-world causal generalization.