Ross W Gayler
I am attempting to develop a practical connectionist mechanism for compositional and analogical memory. This is concerned with the ability to recognise and predict situations and objects in terms of the pattern of relationships between their component parts independently of the precise identity of the component parts. Current standard connectionist techniques have limited capacity to deal with patterns of relationships and consequently have difficulty recognising novel configurations of familiar components or recognising familiar patterns of relationship when the components being related are novel. Human analogical reasoning is the extreme example of the neural functionality I am striving for. I believe that cognition is based on sensorimotor planning and that analogical retrieval is needed to allow the application of sensorimotor schemas to novel and abstract situations. I argue that high-level perception and all cognition are fundamentally the same process and are implemented by this neural mechanism of compositional, analogical memory.
Supervisors: Catherine A. Brown and John D. Bain
Phone: +61 413 111 303
Address: Melbourne
Australia
Supervisors: Catherine A. Brown and John D. Bain
Phone: +61 413 111 303
Address: Melbourne
Australia
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Papers by Ross W Gayler
Video DOI:10.5281/zenodo.5560797
Slides DOI:10.5281/zenodo.5552219
Source DOI:10.5281/zenodo.5561063
The August 2010 workshop focused on what may now be the major issue in connectionism and computational cognitive neuroscience: the debate between proponents of localist representations (e.g. Page 2000), in which a single unit or population of units encodes one (and only one) item, and proponents of distributed representations, in which all units participate in the encoding of all items (see Plate 2002 for an overview). The aim of this workshop was to bring together researchers working with a wide range of compositional connectionist models, independent of application domain (e.g. language, logic, analogy, web search), with a focus on what commitments (if any) each model makes to localist or distributed representation. We solicited submissions from both localist and distributed modellers, as well as those whose work bypasses this distinction or challenges its importance. We expected vigorous and exciting debate on this topic, and we were not disappointed.
Video DOI:10.5281/zenodo.5560797
Slides DOI:10.5281/zenodo.5552219
Source DOI:10.5281/zenodo.5561063
The August 2010 workshop focused on what may now be the major issue in connectionism and computational cognitive neuroscience: the debate between proponents of localist representations (e.g. Page 2000), in which a single unit or population of units encodes one (and only one) item, and proponents of distributed representations, in which all units participate in the encoding of all items (see Plate 2002 for an overview). The aim of this workshop was to bring together researchers working with a wide range of compositional connectionist models, independent of application domain (e.g. language, logic, analogy, web search), with a focus on what commitments (if any) each model makes to localist or distributed representation. We solicited submissions from both localist and distributed modellers, as well as those whose work bypasses this distinction or challenges its importance. We expected vigorous and exciting debate on this topic, and we were not disappointed.
Coming from a completely different direction, I have been developing a connectionist memory architecture to support high level cognition (Gayler, 2000). Surprisingly, this architecture is also based on simultaneous transformation and recognition and is abstractly isomorphic to the perceptual invariance architectures. The similarity between the perceptual and cognitive architectures suggests that there may be a fundamental unity between them. The difference lies in the details; the perceptual architectures use localist representations and a fixed palette of geometric transformations, while the cognitive architecture uses distributed connectionist representations capable of representing recursive structures, and transformations that are arbitrary structural substitutions. I propose that the architectures could be unified and devote the remainder of this presentation to exploring how this may enable the recognition of composite objects.
The perceptual architectures mentioned earlier recognise a single item at a time. They can be persuaded to attend to multiple items serially, but they do not allow for representation of the relations between items. These architectures do represent the relations between the elements (pixels or feature vectors) within an item, but these relations are fixed. Each item is recognised holistically and treated as atomic (having no internal compositional structure). Thus, multi-level composite items can not be represented.
The representational advantage offered by the distributed approach is that transformations are “first-class” entities, having the same status as the content mapped by the transformations. This means that representations of transformations can be included in the representations of objects. In particular, two serially fixated items and the attentional transformation between the fixations could be represented on the same set of connectionist units used to represent just one item. Thus, it should be possible to represent complex entities as a network of components with transformations between them. This leads naturally to graph structures as representations of objects – a common choice in computer vision systems.
The process advantage of such an approach is that it should be possible to build a connectionist memory that simultaneously recalls multiple items while settling on mappings between them. These mappings would serve to unify the retrieved items into a representation of a novel composite object. Memory systems of this sort should be able to recognise novel compositions of familiar components as readily as they recognise the components themselves. The distributed connectionist implementation of this recognition process can be construed as an indirect implementation of Pelillo's (1999) approximate graph matching via replicator equations, by embedding his algorithm in a fixed high-dimensional vector space.
Arathorn, D. W. (2002). Map-seeking circuits in visual cognition: A computational mechanism for biological and machine vision. Stanford, CA, USA: Stanford University Press.
Gayler, R. W. (2000). Multiplicative Binding, Representation Operators & Analogical Inference. Presented at Cognitive Science Conference. Melbourne, Australia.
Hinton, G. E. (1981). A parallel computation that assigns canonical object-based frames of reference. Proceedings of the Seventh International Joint Conference on Artificial Intelligence Vol. 2. Vancouver BC, Canada.
Lashley, K. S. (1942). The problem of cerebral organization in vision. Biological Symposia, 7, 301-322.
Olshausen, B. A., Anderson, C. H., & Van Essen, D. C. (1993). A neurobiological model of visual attention and invariant pattern recognition based on dynamic routing of information. The Journal of Neuroscience, 13, 4700-4719.
Pelillo, M. (1999). Replicator equations, maximal cliques, and graph isomorphism. Neural Computation, 11, 1933-1955.
The purpose of this paper is to alert credit risk modelers to the relationships between TSD and common scorecard development concepts and to provide a toolbox of simple techniques and interpretations.
initially dissimilar source and target are effectively very similar after mapping.
Similarity (the angle between vectors) is central to the mechanics of VSA/HDC. Introductory papers (e.g. [8]) necessarily devote space to vector similarityand the effect of the primitive operators (sum, product, permutation) on similarity. Most VSA examples rely on static similarity, where the vector representations are fixed over the time scale of the core computation (which is usually a single-pass, feed-forward computation). This emphasises encoding methods (e.g.
[12, 13]) that create vector representations with the similarity structure required by the core computation. Random Indexing [13] is an instance of the vector embedding approach to representation [11] that is widely used in NLP and ML. The important point is that the vector embeddings are developed in advance and then used as static representations (with fixed similarity structure) in the
subsequent computation of interest.
Human similarity judgments are known to be context-dependent (see [3] for a brief review). It has also been argued that similarity and analogy are based on the same processes [6] and that cognition is so thoroughly context-dependent that representations are created on-the-fly in response to task demands [2]. This seems extreme, but doesn’t necessarily imply that the base representations are context-dependent as long as the cognitive process that compares them is
context-dependent, which can be achieved by having dynamic representations that are derived from the static base representations by context-dependent transforms (or any functionally equivalent process).
An obvious candidate for a dynamic transformation function in VSA is substitution by binding, because the substitution can be specified as a vector and dynamically generated (see Representing substitution with a computed mapping in [8]). This implies an internal degree of freedom (a register to hold the substitution vector while it evolves) and a recurrent VSA circuit to provide the dynamics to evolve the substitution vector.
These essential aspects are present in [4], which finds the maximal subgraph isomorphism between two graphs represented as vectors. This is implemented as a recurrent VSA circuit with a register containing a substitution vector that evolves and settles over the course of the computation. The final state of the substitution vector represents the set of substitutions that transforms the static base representation of each graph into the best subgraph isomorphism to the static base representation of the other graph. This is a useful step along the path to an analogical memory system.
Interestingly, the subgraph isomorphism circuit can be interpreted as related to the recently developed Resonator Circuits for factorisation of VSA representations [9], which have internal degrees of freedom for each of the factors to be calculated and a recurrent VSA dynamics that settles on the factorisation. The graph isomorphism circuit can be interpreted as finding a factor (the substitution vector) such that the product of that factor with each of the graphs is the
best possible approximation to the other graph. This links the whole enterprise back to statistical modelling, where there is a long history of approximating matrices/tensors as the product of simpler factors [10].
References
1. Blokpoel, M., Wareham, T., Haselager, P., van Rooij, I.: Deep Analogical Inference as the Origin of Hypotheses. The Journal of Problem Solving 11(1), 1–24 (2018)
2. Chalmers, D.J., French, R.M., Hofstadter, D.R.: High-level perception, representation, and analogy: A critique of artificial intelligence methodology. Journal of Experimental & Theoretical Artificial Intelligence 4(3), 185–211 (1992)
3. Cheng, Y.: Context-dependent similarity. In: Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence (UAI’90), pp. 27–30. Cambridge, MA, USA (1990)
4. Gayler, R.W., Levy, S.D.: A distributed basis for analogical mapping. In: Proceedings of the Second International Conference on Analogy (ANALOGY-2009), pp. 165–174. New Bulgarian University, Sofia, Bulgaria (2009)
5. Gentner, D.: Structure-mapping: A theoretical framework for analogy. Cognitive Science 7(2), 155–170 (1983)
6. Gentner, D., Markman, A.B.: Structure mapping in analogy and similarity. American Psychologist 52(1), 45–56 (1997)
7. Gust, H., Krumnack, U., Kühnberger, K.-U., Schwering, A.: Analogical Reasoning: A core of cognition. KI - Künstliche Intelligenz 1(8), 8–12 (2008)
8. Kanerva, P.: Hyperdimensional computing: An introduction to computing in distributed representation with high-dimensional random vectors. Cognitive Computation 1, 139–159 (2009)
9. Kent, S.J., Frady, E.P., Sommer, F.T., Olshausen, B.A.: Resonator Circuits for factoring high-dimensional vectors. http://arxiv.org/abs/1906.11684 (2019)
10. Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Review 51(3), 455–500 (2009)
11. Pennington, J., Socher, R., Manning, C.D.: GloVe: Global vectors for word representation. In: Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp. 1532–1543. Association for Computational Linguistics, Doha, Qatar (2014)
12. Purdy, S.: Encoding data for HTM systems. http://arxiv.org/abs/1602.05925 (2016)
13. Sahlgren, M.: An introduction to random indexing. In: Proceedings of the Methods and Applications of Semantic Indexing Workshop at the 7th International Conference on Terminology and Knowledge Engineering (TKE 2005), Copenhagen, Denmark (2005)