Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a (...) single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models. Key Words: additive clustering; Bayesian inference; categorization; concept learning; contrast model; features; generalization; psychological space; similarity. (shrink)
The debate between A-theory and B-theory in the philosophy of time is a persistent one. It is not always clear, however, what the terms of this debate are. A-theorists are often lumped with a miscellaneous collection of heterodox doctrines: the view that only the present exists, that time ﬂows relentlessly, or that presentness is a property (Williams 1996); that time passes, tense is unanalysable, or that earlier than and later than are deﬁned in terms of pastness, presentness, and futurity (Bigelow (...) 1991); or that events or facts (as opposed to language) are “tensed” (Mellor 1993). B-theorists then argue that the A-theory is incoherent, using variants on J.M.E. McTaggart’s argument for the unreality of time (McTaggart 1927, ch. 33). (shrink)
Recent progress in artificial intelligence has renewed interest in building systems that learn and think like people. Many advances have come from using deep neural networks trained end-to-end in tasks such as object recognition, video games, and board games, achieving performance that equals or even beats that of humans in some respects. Despite their biological inspiration and performance achievements, these systems differ from human intelligence in crucial ways. We review progress in cognitive science suggesting that truly human-like learning and thinking (...) machines will have to reach beyond current engineering trends in both what they learn and how they learn it. Specifically, we argue that these machines should build causal models of the world that support explanation and understanding, rather than merely solving pattern recognition problems; ground learning in intuitive theories of physics and psychology to support and enrich the knowledge that is learned; and harness compositionality and learning-to-learn to rapidly acquire and generalize knowledge to new tasks and situations. We suggest concrete challenges and promising routes toward these goals that can combine the strengths of recent neural network advances with more structured cognitive models. (shrink)
In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement Bayesian (...) inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition. (shrink)
Hierarchical Bayesian models (HBMs) provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘paradigms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher‐level theory change may be driven by the impact of evidence on lower levels. HBMs capture features described in the Kuhnian tradition, particularly the idea that (...) higher‐level theories guide learning at lower levels. In addition, they help resolve certain issues for Bayesians, such as scientific preference for simplicity and the problem of new theories. *Received July 2009; revised October 2009. †To contact the authors, please write to: Leah Henderson, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 32D‐808, Cambridge, MA 02139; e‐mail: [email protected] (shrink)
Hierarchical Bayesian models (HBMs) provide an account of Bayesian inference in a hierarchically structured hypothesis space. Scientific theories are plausibly regarded as organized into hierarchies in many cases, with higher levels sometimes called ‘para- digms’ and lower levels encoding more specific or concrete hypotheses. Therefore, HBMs provide a useful model for scientific theory change, showing how higher-level theory change may be driven by the impact of evidence on lower levels. HBMs capture features described in the Kuhnian tradition, particularly the idea (...) that higher-level theories guide learning at lower levels. In addition, they help resolve certain issues for Bayesians, such as scientific preference for simplicity and the problem of new theories. (shrink)
We applaud Millikan's psychologically plausible version of the causal theory of reference. Her proposal offers a significant clarification of the much-debated relation between concepts and beliefs, and suggests positive directions for future empirical studies of conceptual development. However, Millikan's revision of the causal theory may leave us with no generally satisfying account of concept individuation in the mind.
Rogers & McClelland (R&M) criticize models that rely on structured representations such as categories, taxonomic hierarchies, and schemata, but we suggest that structured models can account for many of the phenomena that they describe. Structured approaches and parallel distributed processing (PDP) approaches operate at different levels of analysis, and may ultimately be compatible, but structured models seem more likely to offer immediate insight into many of the issues that R&M discuss.