A distributed basis for analogical mapping

We are concerned with the practical feasibility of the neural basis of analogical mapping. All existing connectionist models of analogical mapping rely to some degree on localist representation (each concept or relation is represented by a dedicated unit/neuron). These localist solutions are implausible because they need too many units for human-level competence or require the dynamic re-wiring of networks on a sub-second time-scale. Analogical mapping can be formalised as finding an approximate isomorphism between graphs representing the source and target conceptual structures. Connectionist models of analogical mapping implement continuous heuristic processes for finding graph isomorphisms. We present a novel connectionist mechanism for finding graph isomorphisms that relies on distributed, high-dimensional representations of structure and mappings. Consequently, it does not suffer from the problems of the number of units scaling combinatorially with the number of concepts or requiring dynamic network re-wiring.

[1]  Chris Eliasmith,et al.  Integrating structure and meaning: a distributed model of analogical mapping , 2001, Cogn. Sci..

[2]  Geoffrey E. Hinton.  Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems , 1991 .

[3]  C. Eliasmith.  Cognition with neurons: A large-scale, biologically realistic model of the Wason task , 2005 .

[4]  Markus Werning,et al.  Compositionality and Biologically Plausible Models , 2009 .

[5]  Kaleem Siddiqi,et al.  Matching Hierarchical Structures Using Association Graphs , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Paul Smolensky,et al.  Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems , 1990, Artif. Intell..

[7]  Paul Thagard,et al.  Analogical Mapping by Constraint Satisfaction , 1989, Cogn. Sci..

[8]  Alexander Katovsky,et al.  Category Theory , 2010, Arch. Formal Proofs.

[9]  G. Kane.  Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol 1: Foundations, vol 2: Psychological and Biological Models , 1994 .

[10]  D. Gentner,et al.  Advances in Analogy Research: Integration of Theory and Data from the Cognitive, Computational, and Neural Sciences , 1997, Cognitive Psychology.

[11]  Ross W. Gayler,et al.  Multiplicative Binding, Representation Operators & Analogy , 1998 .

[12]  Ross W. Gayler.  Vector Symbolic Architectures answer Jackendoff's challenges for cognitive neuroscience , 2004, ArXiv.

[13]  Marcello Pelillo,et al.  Replicator Equations, Maximal Cliques, and Graph Isomorphism , 1998, Neural Computation.

[14]  Tony A. Plate,et al.  Holographic Reduced Representation: Distributed Representation for Cognitive Structures , 2003 .

[15]  Panos M. Pardalos,et al.  The maximum clique problem , 1994, J. Glob. Optim..

[16]  Geoffrey E. Hinton,et al.  A general framework for parallel distributed processing , 1986 .

[17]  M. Page,et al.  Connectionist modelling in psychology: A localist manifesto , 2000, Behavioral and Brain Sciences.

[18]  John E. Hummel,et al.  Distributed representations of structure: A theory of analogical access and mapping. , 1997 .

[19]  Pentti Kanerva,et al.  Binary Spatter-Coding of Ordered K-Tuples , 1996, ICANN.

[20]  Boicho N. Kokinov,et al.  Associate Memory-Based Reasoning: How to Represent and Retrieve Cases , 1988, AIMSA.

[21]  M. Pelillo,et al.  Payoff-Monotonic Game Dynamics and the Maximum Clique Problem , 2006 .

[22]  Pentti Kanerva,et al.  Hyperdimensional Computing: An Introduction to Computing in Distributed Representation with High-Dimensional Random Vectors , 2009, Cognitive Computation.

[23]  Ross W. Gayler,et al.  “ Lateral Inhibition ” in a Fully Distributed Connectionist Architecture , 2009 .