The Child As Hacker: Building More Human-Like Models of Learning by Joshua S
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The child as hacker: Building more human-like models of learning by Joshua S. Rule Submitted to the Department of Brain and Cognitive Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Cognitive Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2020 © Massachusetts Institute of Technology 2020. All rights reserved. Author...................................................................... Department of Brain and Cognitive Sciences September 5, 2020 Certified by. Joshua B. Tenenbaum Professor of Computational Cognitive Science Thesis Supervisor Accepted by................................................................. Rebecca Saxe John W. Jarve (1978) Professor of Brain and Cognitive Sciences Associate Head, Department of Brain and Cognitive Sciences Affiliate, McGovern Institute for Brain Science Chairman, Department Committee on Graduate Theses 2 The child as hacker: Building more human-like models of learning by Joshua S. Rule Submitted to the Department of Brain and Cognitive Sciences on September 5, 2020, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Cognitive Science Abstract Cognitive science faces a radical challenge in explaining the richness of human learning and cognitive development. This thesis proposes that developmental theories can address the challenge by adopting perspectives from computer science. Many of our best models treat learning as analogous to computer programming because symbolic programs provide the most compelling account of sophisticated mental representations. We specifically propose that learning from childhood onward is analogous to a style of programming called hacking— making code better along many dimensions through an open-ended and internally-motivated set of diverse values and activities. This thesis also develops a first attempt to formalize and assess the child as hacker view through an in-depth empirical study of human and machine concept learning. It introduces list functions as a domain for psychological investigation, demonstrating how they subsume many classic concept learning tasks while opening new avenues for exploring algorithmic thinking over complex structures. It also presents HL, a computational learning model whose representations, objectives, and mechanisms reflect core principles of hacking. Existing work on concept learning shows that learners both prefer simple explanations of data and find them easier to learn than complex ones. The child as hacker, by contrast, suggests that learners use mechanisms that dissociate hypothesis complexity and learning difficulty for certain problem classes. We thus conduct a large-scale experiment exploring list functions that vary widely in difficulty and algorithmic content to help identify structural sources of learning difficulty. We find that while description length alone predicts learning, predictions are much better when accounting for concepts’ semantic features. These include the use of internal arguments, counting knowledge, case-based and recursive reasoning, and visibility—a measure we introduce to modify description length based on the complexity of inferring each symbol in a description. We further show that HL’s hacker-like design uses these semantic features to better predict human performance than several alternative models of learning as programming. These results lay groundwork for a new generation of computational models and demonstrate how the child as hacker hypothesis can productively contribute to our understanding of learning. Thesis Supervisor: Joshua B. Tenenbaum Title: Professor of Computational Cognitive Science 3 4 Acknowledgments First thanks go to Josh Tenenbaum and Steve Piantadosi. Chapters 1–2 contain material taken from a paper we wrote together (Rule et al., in press), but every page profits from their influence. They are the reason the rest of this thesis uses we rather than I. They not only contributed their effort and ideas, but they taught me how to contribute myown. Who I am as a scientist deeply reflects what I have learned from them. Thank you both for believing in the importance of our work and for guiding me to make it far better than it would have been otherwise. Josh, thank you for teaching me to use nagging doubts as stepping stones to new insights and for being the first to invite me into the awe-inspiring and life-changing community that is MIT. Steve, thank you for teaching me to try the simplest possible thing first, ideally in the next half-hour, and for repeatedly helping me distill the sea of my confusion into a clear hypothesis. I cannot imagine better people to shape this work than my thesis committee. Susan Carey, you transformed my thinking about the depths to be mined in understanding the young mind. Thank you for teaching me that what is actual is possible, that computational models must make contact with empirical facts (the more, the better), and for demonstrating how a deep understanding of learning builds on all the fields I love most: mathematics, psychology, philosophy, and computer science. Laura Schulz, thank you for challenging me to take seriously the richness, inventiveness, and raw power of children’s learning and for telling me flat out that not every contribution I made had to come in the form of amodel. I needed to hear that. I am also immensely grateful to the broader intellectual community that has introduced me to cognitive science. Cocosci and Colala have simultaneously sharpened and broad- ened my thinking about the mind. Special thanks to the program inductors—especially Eyal Dechter, Eric Schulz, Lucas Morales, Kevin Ellis, Max Nye, Zenna Taveres, Luc Cary, and Andrés Campero. I am also grateful for many good conversations with Liz Spelke, Tomer Ullman, John McCoy, Andrew Cropper, Josh Hartshorne, Max Kleiman-Weiner, Tim O’Donnell, and Brenden Lake. My time in BCS owes much to the dedicated work of Denise Heintze, Kris Kipp, Sierra Vallin, and Julianne Gale Ormerod and the generous funding of 5 the NSF Graduate Fellowship, the Stark Graduate Fellowship, and the Leventhal Fellowship. Many others have deeply shaped my own cognitive development, including: Bob Wengert, Gerald DeJong, Dan Roth, Paul Drelles, Gordon Brown, Keith Hamilton, Bob Parker, and Ted Malt. Special thanks to Max Riesenhuber for his role in my decision to pursue academic research, his support and friendship over the years, and his challenging me to apply to MIT in the first place. Michel Selva, thank you for wise advice and friendly counsel. I am nearly overwhelmed when I think of the debt of gratitude I owe to my dearest friends. Thanks to the Champaign crew—Alyssa Combs, Micah & Priscilla Putman, Josh & Julie Birky, and Josh & Jess Kober—your friendship has often been felt deepest when needed most. To Aidan & Sarah McCarthy, Austin & Becca Ward, Caleb & Lauren Hintz, Bre & Wes Rieth, Matt & Lynnae Terrill, Kevin & Kelsey McKenzie, and Meg & Adam Norris: thank you for loving me well and for making Aletheia Church my spiritual family in Cambridge. Donny Fisher, thank you for keeping me sane, too, through the many miles we have walked together. I hope there are many more. My family has been a constant and inexhaustible source of support. Adam, I am so glad we share the field of cognitive science, as well as a love of walking wild places fast and far. Oresta, thank you for catching my throw-away jokes on family calls and ensuring I had sufficient ice cream to study productively. AJ & Ariel were a constant source ofen- couragement during our time in Boston. Shelley, Daniel, Kim, & Matt have loved me and my family even as my own attention has been consistently devoted to model runs, writing, and analysis. Mom, Dad, Jim, & Laura: I would not be writing these words without your help. Mom & Dad, I thank you especially for your support, prayers, and willingness to do anything that might help me. Ana and Forest, you are by far the most successful mod- els of intelligence I have collaborated on to date. You bring me so much joy. Thank you for teaching me how little I really understand about the mind. Amy, I cannot even begin to describe how grateful I am for you or this thesis would be at least twice as long as it is. You have helped me to be more than I could be on my own and to do what, at times, I did not think possible. You are more than I have ever hoped for. You take my breath away. Soli Deo gloria 6 Contents 1 Introduction 15 1.1 Three observations about learning . 20 1.2 Knowledge as code . 23 1.3 Learning as programming . 25 2 The child as hacker 29 2.1 From programming to hacking . 29 2.1.1 The many values of hacking . 31 2.1.2 The many activities of hacking . 32 2.1.3 The intrinsic motivation of hacking . 32 2.1.4 Putting it all together . 34 2.2 Hacking early arithmetic . 36 2.3 Hacking intuitive theories . 42 2.4 Hacking and other metaphors . 44 2.4.1 The child as scientist . 44 2.4.2 Resource rationality & novelty search . 47 2.4.3 Workshop and evolutionary metaphors . 48 2.5 Prospects for a computational account of learning . 50 3 List functions as a domain for psychological investigation 53 3.1 The domain of list functions . 57 3.2 Capturing classic domains and developmental case studies . 73 3.3 Conclusion . 80 7 4 HL: A hacker-like model of learning 81 4.1 Representation: Term rewriting as a model of mental representations . 84 4.1.1 Meaning through conceptual role . 84 4.1.2 The value of domain-specific languages . 86 4.1.3 Term rewriting . 97 4.2 Learning Mechanisms: Learning as iterative meta-programming . 102 4.2.1 Hypothesis-and-goal-driven search . 103 4.2.2 Hacking as iterative revision . 104 4.2.3 HL’s learning mechanisms . 108 4.2.4 Chaining mechanisms into meta-programs . 112 4.2.5 Monte Carlo tree search .