C.P. Dolan and P. Smolensky. Tensor product production system: a modular architecture and representation. Connection Science, 1(1):53--68, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... designs (including synergistic hybrids of ANN and AI designs) for intelligent systems [20] 28] 32] 34] 35] 46] 92] 95] 99] Examples of such systems include: neural architectures for database query processing [10] generation of context free languages [100] rule based inference [12], 72] 88] 94] computer vision [4] 58] natural language processing [6] 13] learning [19] 31] 89] and knowledge based systems [43] 75] We strongly believe that a judicious and systematic exploration of the design space of such systems is essential for understanding the nature of ....

C. P. Dolan and P. Smolensky, "Tensor product production system: A modular architecture and representation," Connection Sci., vol. 1, pp. 53--58, 1989.

....are also required, so the size of the excursion space is 2 (C V )T . This is somewhat larger than the grandmother binding node state space if T = V , but can be much smaller if T is small. 4. 3 Tensor product binding Smolensky, Dolan, and others have used tensor products to represent bindings [3]. Each constant is associated with an activation pattern over one set of O(log C) nodes, and similarly for variables. These activation patterns need to have at least one node set to 1. Let fl i be the index of the i th node used for representing constants, and i be the index of the i th node ....

C. P. Dolan and P. Smolensky. Tensor product production system: a modular architecture and representation. Connection Science, 1:53--68, 1989.

....by presenting two compositional schemes for generating representations for complex expressions; tensor product representations and the Recurrent Auto Associative Memory (RAAM) 2.4. 4 The tensor product representational scheme The basic idea behind the tensor product representational scheme (Dolan and Smolensky, 1989; Smolensky, 1990) is that any concept with constituent structure (e.g. the sentence John loves Mary ) can be represented by combining the representations for all the constituents, associated with the role the constituent plays in the complex concept (e.g. John agent] loves relation] ....

Dolan, C. P. and Smolensky, P. (1989). Tensor product production system -- a modular architecture and representation. Connection Science, 1(1).

....by Fu (1989, 1991) and Hayashi (1990) Towell (1991) also describes several alternatives to the n of m method described earlier. The work of Gallant (1988) was an important early example of integrating connectionist and rule based approaches. Other examples of integrated approaches include Dolan and Smolensky (1989), Touretzky and Hinton (1998) and Sun (1991) Hybrid AI systems have become quite popular in the recent years, and several such systems are discussed in Dinsmore (1992) Although explicit rule extraction is the focus of this work, there are other ways to combat the problem of network opacity. ....

Dolan, C. P., & Smolensky, P. (1989). Tensor product production system: a modular architecture and representation. Connection Science, 1, 53--68.

....meaning. 6 Chapter 1 The issue of binding one token with another, as in AGE:4, has been difficult in neural network systems. The issues surrounding this will not be described here, but the approach taken appears to overcome a number of the problems. We use a method that is similar to Smolenski [9] but instead of using continuous tensor products, we use binary tensors, an approach discounted by Smolensky for no obvious reason. In the present system the aim is to bind two tokens together, so that they do not get confused with the representation used when the conjuction of tokens is ....

C P Dolan, P Smolensky (1989), Tensor product production system: a modular architecture and representation, Connection Science, No. 1, p 53-68.

.... be able to detect a pattern independent of translation over the input layer (Rumelhart, Hinton Williams, 1986; Honavar Uhr, 1988; 1989) Gates control and coordinate the flow of signals between different functional modules in CN implementations of production systems (Touretzky Hinton, 1988; Dolan Smolensky, 1989). The meta pi network (Hampshire Waibel, 1989) incorporates structures that enable the network to integrate conflict arbitrated sub networks for speaker independent speech recognition. Several simple control structures have been employed to regulate the form and content of the internal ....

Dolan, C. P., & Smolensky, P. (1989). Tensor Product Production System: A Modular Architecture and Representation. Connection Science, 1, 53-68.

....Networks planned by the journal Knowledge Based Systems. external stimuli. One of the main technical difficulties in building hybrid modes is the well known dynamic variable binding problem [1 4] Many hybrid models proposed partial solution to this problem for example: DCPS [5] TPPS [6], ROBIN [7] COMPOSIT [8] CONSYDERR [9] but all of these impose strong representational limitations and or rely on neural elements of high complexity. Subsequently, Shastri and Ajjanagadde [10,11] henceforth S A) proposed another form of dynamic variable binding using temporal synchrony of ....

Dolan,C P and Smolensky, P `Tensor product production system: A modular architecture and representation' Connection Science. Vol 1 (1989)

.... binding [6] of representation vectors, with exact unbinding [6] As an cognitive modelling [2,3,4] and for memory in aim of many neural network models is to provide a connectionist implementations of production system distributed representation of the concepts involved, it is architectures [1]. A tensor product network has a rank: the desirable for the representation vectors to have a high rank of each network used in the experiments described in proportion of non zero components. This can be achieved the papers just cited was 2 or 3; we will introduce tensor in a systematic way by ....

C.P. Dolan and P. Smolensky, Tensor product production system: A modular architecture and representation, Connection Science 1 (1989) 53-68.

.... in building hybrid modes has been the well known dynamic variable binding problem [Feldman (1982) Barnden(1984) Malsburg (1986) and Fodor Pylyshyn (1988) Many hybrid models proposed partial solution to the dynamic variable binding problem for example: Touretzky Hinton (1988) Dolan Smolensky (1989), Lange Dyer (1989) Smolensky (1990) Barnden Srinivas (1991) Sun (1992) but all of these impose strong representational limitations and or rely on neuronal elements of high complexity. A research paper of the Department of Artificial Intelligence numbered RP93 666. Recently Shastri ....

C. P. Dolan and P. Smolensky. Tensor product production system: A modular architecture and representation. Connection Science, 1.

....by presenting two compositional schemes for generating representations for complex expressions; tensor product representations and the Recurrent Auto Associative Memory (RAAM) 2.4. 4 The tensor product representational scheme The basic idea behind the tensor product representational scheme (Dolan Smolensky 1989; Smolensky 1990) is that any concept with constituent structure (e.g. the sentence John loves Mary ) can be represented by combining the representations for all the constituents, associated with the role the constituent plays in the complex concept (e.g. John agent] loves relation] ....

Dolan, C. P. and Smolensky, P. (1989). Tensor product production system -- a modular architecture and representation. Connection Science, 1(1):53--68.

....used in various ways to represent structured objects. Smolensky 5 CADAMjContent addressable distributed associative memory. 6 TODAMjTheory of distributed associative memory. 7 CHARMjComposite holographic associative recall model. A framework for distributed representation schemes [1990] Dolan and Smolensky [1989], and Dolan [1989] use role filler schemes. Nested structures can be represented, but the size of patterns increases exponentially with the depth of nesting. Tensor products bindings are one extreme of using the pairwise products of pattern elements: every possible product is used, and each forms ....

....structured objects. Smolensky 5 CADAMjContent addressable distributed associative memory. 6 TODAMjTheory of distributed associative memory. 7 CHARMjComposite holographic associative recall model. A framework for distributed representation schemes [1990] Dolan and Smolensky [1989] and Dolan [1989] use role filler schemes. Nested structures can be represented, but the size of patterns increases exponentially with the depth of nesting. Tensor products bindings are one extreme of using the pairwise products of pattern elements: every possible product is used, and each forms one element of the ....

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Dolan, C. P. and P. Smolensky (1989). Tensor product production system: a modular architecture and representation. Connection Science 1(1), 53--68.

....connectionist solutions to the dynamic binding problem using a variety of techniques. These include the use of dynamic connections (Feldman, 1982) parallel constraint satisfaction (Touretzky Hinton, 1988) position specific encoding (Barnden Srinivas, 1991) tensor product representations (Dolan Smolensky, 1989) and signatures (Lange Dyer, 1989) Shastri Ajjanagadde, 1992) compares and contrasts these other approaches with the temporal synchrony approach used in this paper. The system described in (Shastri Ajjanagadde, 1990b) has the limitation that any predicate in the reasoner can be ....

:53--68.

....unlike symbolic systems, most of connectionist systems obtain propagation of initial bindings from one group of nodes to the other through explicit links between them. Although various connectionist systems have been proposed to achieve symbolic inference, for example: Touretzky Hinton (1988) Dolan Smolensky (1989), Lange Dyer (1989) Smolensky (1990) Barnden Srinivas (1991) Sun (1992) Shastri Ajjanagadde (1993) only a few have dealt closely with knowledge representation issues such as pseudo bindings, binding generation, consistency checking, and unification. Specifically, the example system we ....

C. P. Dolan and P. Smolensky. Tensor product production system: A modular architecture and representation. Connection Science, 1.

....of experiments with networks using random representation vectors. 2 Tensor Product Networks in STAR Tensor product networks have been used for purposes like the modelling of variable binding and for working memory structures in connectionist implementations of production system architectures [2,9]. They have the property, sometimes an advantage, of being oneshot learning systems. A tensor product network has a rank: all networks used in the experiments described in this paper were of rank 3, and we will describe tensor product networks in terms of the rank 3 case. 2.1 Representing and ....

C.P. Dolan and P. Smolensky, Tensor product production system: A modular architecture and representation, Connection Science 1 (1989) 5368.

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C.P. Dolan and P. Smolensky. Tensor product production system: a modular architecture and representation. Connection Science, 1(1):53--68, 1989.

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Dolan, C.P. and Smolensky, P. (1989). Tensor product production system: A modular architecture and representation. Connection Science, 1:53-58.

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Dolan, C. P. & Smolensky, P. (1989). Tensor product production system: a modular architecture and representation. Connection Science, 1:53--58.

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