Computational models of analogy

Gentner, Dedre; Forbus, Kenneth D.

doi:10.1002/wcs.105

Cited by 124 publications

(132 citation statements)

References 64 publications

(117 reference statements)

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“…In this section we introduce some models that either have been influential or are closely related to the work presented here. For comprehensive surveys see [11,15], where computational models of analogy are categorize as symbolic, connectionist, or symbolic-connectionist hybrids.…”

Section: Related Workmentioning

confidence: 99%

“…However, in contrast to SMT and other symbolic models, the AMU satisfies semantic constraints, thereby allowing the model to handle the problem of similar but not identical compositional structures. Satisfying semantic constraints reduces the number of potential correspondence mappings significantly, to a level that is psychologically more plausible [7,16] and computationally feasible [15].…”

Section: Related Workmentioning

confidence: 99%

“…However, LISA has a complex architecture that represents propositions in working memory by dynamically binding roles to their fillers, and encoding those bindings in long-term memory. It is unclear whether this model scales well and is able to handle complex analogies [7,15,54].…”

Section: Related Workmentioning

confidence: 99%

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Analogical Mapping with Sparse Distributed Memory: A Simple Model that Learns to Generalize from Examples

Emruli

Sandin

2013

Cogn Comput

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We present a computational model for the analogical mapping of compositional structures that combines two existing ideas known as holistic mapping vectors and sparse distributed memory. The model enables integration of structural and semantic constraints when learning mappings of the type x i → y i and computing analogies x j → y j for novel inputs x j . The model has a one-shot learning process, is randomly initialized and has three exogenous parameters: the dimensionality D of representations, the memory size S and the probability χ for activation of the memory. After learning three examples the model generalizes correctly to novel examples. We find minima in the probability of generalization error for certain values of χ, S and the number of different mapping examples learned. These results indicate that the optimal size of the memory scales with the number of different mapping examples learned and that the sparseness of the memory is important. The optimal dimensionality of binary representations is of the order 10 4 , which is consistent with a known analytical estimate and the synapse count for most cortical neurons. We demonstrate that the model can learn analogical mappings of generic two-place relationships and we calculate the error probabilities for recall and generalization.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Analogical Mapping with Sparse Distributed Memory: A Simple Model that Learns to Generalize from Examples

Emruli

Sandin

2013

Cogn Comput

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“…Current theories of analogical mapping (for a review, see Gentner & Forbus, 2011) provide mechanisms by which analogical mapping can create new relational structure; however, none have directly addressed the question of whether and how prior information about the source could be altered through the process of mapping. On the basis of the present findings, it appears that This document is copyrighted by the American Psychological Association or one of its allied publishers.…”

Section: Discussionmentioning

confidence: 99%

When reasoning modifies memory: Schematic assimilation triggered by analogical mapping.

Vendetti¹,

Wu²,

Rowshanshad³

et al. 2014

Journal of Experimental Psychology: Learning, Memory, and Cogni

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Analogical mapping highlights shared relations that link 2 situations, potentially at the expense of information that does not fit the dominant pattern of correspondences. To investigate whether analogical mapping can alter subsequent recognition memory for features of a source analog, we performed 2 experiments with 4-term proportional analogies (A:B::C:D), using problems based on cartoon figures varying on 4 visual dimensions. The source analog (A:B) was encoded before the reasoner was told which dimension was relevant to the analogy. After encoding, the A:B pair disappeared, 1 randomly selected dimension was specified as the basis for an analogical decision, and the target (C:D) was presented. A decision about the validity of the analogy was then made, after which memory for the A:B pair was assessed by a recognition test. In Experiment 1, we found that participants' recognition memory was reduced for lures involving a feature change on a dimension initially inconsistent with the analogical decision relative to a change on a dimension that had been consistent with it. The results of Experiment 2 revealed that this memory decrement occurred only when the change in the initially inconsistent feature caused the lure to be coherent with the overall schematic pattern of relational correspondences. These findings suggest that analogical reasoning can trigger changes in the memory representation of a source analog stored in memory such that subsequent recognition is guided by a relational schema.

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“…Integral Biomathics involves reconceptualising what mathematics is and its role in science, granting a place to, while clarifying, the relationship between the non-mathematical concepts of philosophical biology (Sober, 2000;Griffiths, 2002;Godfrey-Smith, 2014), qualitative mathematics (Smith, 1983;Sacks, 1985;Rudolph, 2014) that provides insight but no precise predictions, analogical computation (Damper, 2001;Kokinov and French, 2002;Gentner and Forbus, 2011) and formal models that do facilitate precise predictions. In particular, philosophical biology and philosophical anthropology are far more than descriptive and concerned with justifying the reality of life and living beings, thereby revealing how misguided are efforts to examine these only in terms of received mathematical ideas.…”

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confidence: 99%

Integral Biomathics reloaded: 2015

Simeonov¹,

Cottam

2015

Progress in Biophysics and Molecular Biology

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Recap and antrorseMany biological phenomena do not have adequate mathematical representations. This is because living systems use structures that are not yet grasped by our present conceptions of mathematics and computation. In particular they are circularly organized and they use recursions. Mathematics and computation at the present time deal only superficially with circular organization or the consequences of recursion. We just have not yet found a way to adequately deal with such matters 1 ! Current approaches to complex problems rely on modelling, but one aspect of the problem is that they rely on a single form of mathematics, switching from it to another to address the next aspect, and so on. All this switching is an indication of how inadequate our mathematical tools are to date (ODE/PDE systems, stochastic models, discrete state-transition systems, topological algebra, etc.). Biological systems function at all these levels simultaneously. Yet, the real problem is that even the simplest recursions are beyond our capacity to analyse at the present time. It is not biology that is too messy to be modelled; it is our use of current mathematical paradigms that are not able to adequately address these biological problems (Root-Bernstein, R. S., 2012). These paradigms are keeping biology within the fixed boundaries of physics, the domain of nonliving matter. Despite being the most advanced mathematics-based natural sciences discipline, physics is currently experiencing its own crisis when trying to overcome the dichotomy between its major theories (Smolin, 2006) and remains not sufficiently developed to explain living systems. Is this a chance in disguise?We believe that further advances in the sciences -physical, biological, social -require new levels of integration across the domains. It is a commonplace to seek a "paradigm shift" (Kuhn, 1962) to advance the frontiers of a scientific domain. Such shift can also uplift the network of interdisciplinary connections among existing research areas. However, we are seeking more than a shift that advances the network of the complex dynamical system of knowledge. We seek to advance the nature of the links of this network by encouraging the development of mathematical and computational methods that will at once change the shapes of the nodes and the links, thus performing a simultaneous "quantum jump" in multiple disciplines, to enable a new integration and rationalization of knowledge: Integral Biomathics. The major implications of this new paradigm for reinventing and re-engineering mathematics and computation address the life sciences and medicine. They encompass meanwhile also the foundations of creativity and cognitive processes in the sciences and the arts, as well as the phenomenology of consciousness in general.

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Computational models of analogy

Cited by 124 publications

References 64 publications

Analogical Mapping with Sparse Distributed Memory: A Simple Model that Learns to Generalize from Examples

Analogical Mapping with Sparse Distributed Memory: A Simple Model that Learns to Generalize from Examples

When reasoning modifies memory: Schematic assimilation triggered by analogical mapping.

Integral Biomathics reloaded: 2015

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