Towards a more flexible language of thought: Bayesian grammar updates after each concept exposure

Recent approaches to human concept learning have successfully combined the power of symbolic, infinitely productive rule systems and statistical learning to explain our ability to learn new concepts from just a few examples. The aim of most of these studies is to reveal the underlying language structuring these representations and providing a general substrate for thought. However, describing a model of thought that is fixed once trained is against the extensive literature that shows how experience shapes concept learning. Here, we ask about the plasticity of these symbolic descriptive languages. We perform a concept learning experiment that demonstrates that humans can change very rapidly the repertoire of symbols they use to identify concepts, by compiling expressions that are frequently used into new symbols of the language. The pattern of concept learning times is accurately described by a Bayesian agent that rationally updates the probability of compiling a new expression according to how useful it has been to compress concepts so far. By portraying the language of thought as a flexible system of rules, we also highlight the difficulties to pin it down empirically.

Figure 1

The context-free grammar for language $\mathsf{P}$. Language ${\mathsf{P}}^{\oplus }$ has an extra rule: $\mathrm{B}\mathrm{O}\mathrm{O}\mathrm{L}\to (\mathrm{B}\mathrm{O}\mathrm{O}\mathrm{L}\oplus \mathrm{B}\mathrm{O}\mathrm{O}\mathrm{L}).$

Figure 2

Example of a concept $\mathcal{C}$, as shown in the experiment. Variables in $\mathsf{Vars}=\{x_1,x_2,x_3,x_4\}$ correspond to the presence of a color light in the object ($x_1=$ green, $x_2=$ blue, $x_3=$ red, $x_4=$ orange). Items (valuations) belonging to $\mathcal{C}$ are highlighted with bold border. $\mathcal{C}$ may be described by $x_1\wedge x_2$. As in a traffic light, each color is fixed to each position.

Figure 3

Concept learning time (a) and difficulty predicted (b, c) for the two test concepts (${\mathcal{C}}^5$ and ${\mathcal{C}}^6$). Error bars are s.e.m. across subjects.

Figure 4

Learning times and model predictions for target and control groups (see Table 1 for concept details). The predicted difficulties of each model were calculated using $d_{\mathcal{C}}$. Error bars are s.e.m.

Figure 5

Evolution of Dirichlet parameters of different rules after each concept experienced by the target group.