Concept learning as motor program induction: A large-scale empirical study

Concept learning as motor program induction: A large-scale empirical study Brenden M. Lake Ruslan Salakhutdinov Joshua B. Tenenbaum Department of Brain and Cognitive Sciences Massachusetts Institute of Technology Department of Statistics University of Toronto Department of Brain and Cognitive Sciences Massachusetts Institute of Technology Abstract more structured representations that can generalize in deeper and more flexible ways. Concepts have been characterized in terms of “intuitive theories,” which are mental explana- tions that underly a concept (e.g., Murphy & Medin, 1985), or “structural description” models, which are compositional representations based on parts and relations (e.g., Winston, 1975; Hummel & Biederman, 1992). In the latter framework, the concept “Segway” might be represented as two wheels connected by a platform, which supports a motor, etc. Most recently, research in AI and cognitive science has empha- sized rich generative representations. Concepts like “house” can vary in both the number and configuration of their parts (windows, doors, balconies, etc.), much like the variable syn- tactic structure of language. This has lead researchers to model objects and scenes using generative grammars (Wang et al., 2006; Savova, Jakel, & Tenenbaum, 2009; Zhu, Chen, & Yuille, 2009) or programs (Stuhlmuller, Tenenbaum, & Goodman, 2010). A different tradition has focused more on rapid learning and less on conceptual richness. People can acquire a concept from as little as one positive example, contrasting with early work in psychology and standard machine learning that has focused on learning from many positive and negative exam- ples. Bayesian analyses have shown how one-shot learning can be explained with appropriately constrained hypothesis spaces and priors (Shepard, 1987; Tenenbaum & Griffiths, 2001), but where do these constraints come from? For sim- ple prototype-based representations of concepts, rapid gen- eralization can occur by just sharpening particular dimen- sions or features, as described in theories of attentional learn- ing (Smith, Jones, Landau, Gershkoff-Stowe, & Samuelson, 2002) and overhypotheses in hierarchical Bayesian models (Kemp, Perfors, & Tenenbaum, 2007). From this perspective, prior experience with various object concepts may highlight the most relevant dimensions for whole classes of concepts, like the “shape bias” in learning object names (as opposed to a “color” or “material bias”). It is also possible to learn new features over the course of learning the concepts (Schyns, Goldstone, & Thibaut, 1998), and recent work has combined dimensional sharpening with sophisticated methods for fea- ture learning (Salakhutdinov, Tenenbaum, & Torralba, 2011). Despite these different avenues of progress, we are still far from a satisfying unified account. The models that explain how people learn to perform one-shot learning are restricted to the simplest prototype- or feature-based representations; they have not been developed for more sophisticated repre- sentations of concepts such as structural descriptions, gram- mars, or programs. There are also reasons to suspect that these richer representations would be difficult if not impos- Human concept learning is particularly impressive in two re- spects: the internal structure of concepts can be representation- ally rich, and yet the very same concepts can also be learned from just a few examples. Several decades of research have dramatically advanced our understanding of these two aspects of concepts. While the richness and speed of concept learn- ing are most often studied in isolation, the power of human concepts may be best explained through their synthesis. This paper presents a large-scale empirical study of one-shot con- cept learning, suggesting that rich generative knowledge in the form of a motor program can be induced from just a single example of a novel concept. Participants were asked to draw novel handwritten characters given a reference form, and we recorded the motor data used for production. Multiple drawers of the same character not only produced visually similar draw- ings, but they also showed a striking correspondence in their strokes, as measured by their number, shape, order, and direc- tion. This suggests that participants can infer a rich motor- based concept from a single example. We also show that the motor programs induced by individual subjects provide a pow- erful basis for one-shot classification, yielding far higher accu- racy than state-of-the-art pattern recognition methods based on just the visual form. Keywords: concept learning; one-shot learning; structured representations; program induction The power of human thought derives from the power of our concepts. With the concept “car,” we can classify or even imagine new instances, infer missing or occluded parts, parse an object into its main components (wheels, windows, etc.), reason about a familiar thing in an unfamiliar situation (a car underwater), and even create new compositions of concepts (a car-plane). These abilities to generalize flexibly, to go beyond the data given, suggest that human concepts must be represen- tationally rich. Yet it is remarkable how little data is required to learn a new concept. From just one or a handful of exam- ples, a child can learn a new word and use it appropriately (Carey & Bartlett, 1978; Markman, 1989; Bloom, 2000; Xu & Tenenbaum, 2007). Likewise, after seeing a single “Seg- way” or “iPad,” an adult can grasp the meaning of the word, an ability called “one-shot learning.” A central challenge is thus to explain these two remarkable capacities: what kinds of representations can support such flexible generalizations, and what kinds of learning mechanisms can acquire a new con- cept so quickly? The greater puzzle is putting them together: how can such flexible representations be learned from only one or a few examples? Over the last couple of decades, the cognitive science of concepts has divided into different traditions, focused largely on either the richness of concepts or on learning from sparse data. In contrast to the simple representations popular in early cognitive models (e.g., prototypes; Rosch, Simpson, & Miller, 1976) or conventional machine learning (e.g., sup- port vector machines), one tradition has worked to develop