# The Emergence of Organizing Structure in Conceptual Representation

Brendan Lake, NYU
Neil D. Lawrence, Amazon Research Cambridge and University of Sheffield
Joshua B. Tenenbaum, MIT

Cognitive Science

#### Abstract

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form—where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach can learn intuitive organizations, including a tree for animals and a ring for the color circle, it assumes a strong inductive bias that considers only these particular forms, and each form is explicitly provided as initial knowledge. Here we introduce a new computational model of how organizing structure can be discovered, utilizing a broad hypothesis space with a preference for sparse connectivity. Given that the inductive bias is more general, the model’s initial knowledge shows little qualitative resemblance to some of the discoveries it supports. As a consequence, the model can also learn complex structures for domains that lack intuitive description, as well as predict human property induction judgments without explicit structural forms. By allowing form to emerge from sparsity, our approach clarifies how both the richness and flexibility of human conceptual organization can coexist.

  @Article{the-emergence-of-organizing-structure-in-conceptual-representation, title = {The Emergence of Organizing Structure in Conceptual Representation}, journal = {Cognitive Science}, author = {Brendan Lake and Neil D. Lawrence and Joshua B. Tenenbaum}, year = {2018}, month = {00}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2018-01-09-the-emergence-of-organizing-structure-in-conceptual-representation.md}, url = {http://inverseprobability.com/publications/the-emergence-of-organizing-structure-in-conceptual-representation.html}, abstract = {Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form—where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach can learn intuitive organizations, including a tree for animals and a ring for the color circle, it assumes a strong inductive bias that considers only these particular forms, and each form is explicitly provided as initial knowledge. Here we introduce a new computational model of how organizing structure can be discovered, utilizing a broad hypothesis space with a preference for sparse connectivity. Given that the inductive bias is more general, the model's initial knowledge shows little qualitative resemblance to some of the discoveries it supports. As a consequence, the model can also learn complex structures for domains that lack intuitive description, as well as predict human property induction judgments without explicit structural forms. By allowing form to emerge from sparsity, our approach clarifies how both the richness and flexibility of human conceptual organization can coexist.}, key = {Lake:emergence18}, doi = {10.1111/cogs.12580}, linkpdf = {http://inverseprobability.com/publications/papers/2018-01-09-the-emergence-of-organizing-structure-in-conceptual-representation.pdf}, OPTgroup = {} }
 %T The Emergence of Organizing Structure in Conceptual Representation %A Brendan Lake and Neil D. Lawrence and Joshua B. Tenenbaum %B %C Cognitive Science %D %F the-emergence-of-organizing-structure-in-conceptual-representation %J Cognitive Science %P -- %R 10.1111/cogs.12580 %U http://inverseprobability.com/publications/the-emergence-of-organizing-structure-in-conceptual-representation.html %X Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form—where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach can learn intuitive organizations, including a tree for animals and a ring for the color circle, it assumes a strong inductive bias that considers only these particular forms, and each form is explicitly provided as initial knowledge. Here we introduce a new computational model of how organizing structure can be discovered, utilizing a broad hypothesis space with a preference for sparse connectivity. Given that the inductive bias is more general, the model's initial knowledge shows little qualitative resemblance to some of the discoveries it supports. As a consequence, the model can also learn complex structures for domains that lack intuitive description, as well as predict human property induction judgments without explicit structural forms. By allowing form to emerge from sparsity, our approach clarifies how both the richness and flexibility of human conceptual organization can coexist. 
 TY - CPAPER TI - The Emergence of Organizing Structure in Conceptual Representation AU - Brendan Lake AU - Neil D. Lawrence AU - Joshua B. Tenenbaum PY - 2018/01/09 DA - 2018/01/09 ID - the-emergence-of-organizing-structure-in-conceptual-representation SP - EP - DO - 10.1111/cogs.12580 L1 - http://inverseprobability.com/publications/papers/2018-01-09-the-emergence-of-organizing-structure-in-conceptual-representation.pdf UR - http://inverseprobability.com/publications/the-emergence-of-organizing-structure-in-conceptual-representation.html AB - Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form—where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach can learn intuitive organizations, including a tree for animals and a ring for the color circle, it assumes a strong inductive bias that considers only these particular forms, and each form is explicitly provided as initial knowledge. Here we introduce a new computational model of how organizing structure can be discovered, utilizing a broad hypothesis space with a preference for sparse connectivity. Given that the inductive bias is more general, the model's initial knowledge shows little qualitative resemblance to some of the discoveries it supports. As a consequence, the model can also learn complex structures for domains that lack intuitive description, as well as predict human property induction judgments without explicit structural forms. By allowing form to emerge from sparsity, our approach clarifies how both the richness and flexibility of human conceptual organization can coexist. ER - 
 Lake, B., Lawrence, N.D. & Tenenbaum, J.B.. (2018). The Emergence of Organizing Structure in Conceptual Representation. Cognitive Science :-