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Figure 2: (a) Circular convolution. (b) Circular convolution illustrated as a compressed outer product forn = 3. Each of the small circles represents an element of the outer product of z and y, e.g., the middle bottom one is z2y;. The elements of the circular convolution of x and y are the sums of the outer product elements along the wrapped diagonal lines. A distributed representation for nested relational structures requires a solution to the bindin; problem. The representation of a relation such as bite(spot, jane) (“Spot bit Jane.” must bind ‘Spot’ to the agent role and ‘Jane’ to the object role. In order to represent nestec structures it must also be possible to bind a relation to a role, e.g., bite(spot , jane) anc the antecedent role of the cause relation.

Figure 2 (a) Circular convolution. (b) Circular convolution illustrated as a compressed outer product forn = 3. Each of the small circles represents an element of the outer product of z and y, e.g., the middle bottom one is z2y;. The elements of the circular convolution of x and y are the sums of the outer product elements along the wrapped diagonal lines. A distributed representation for nested relational structures requires a solution to the bindin; problem. The representation of a relation such as bite(spot, jane) (“Spot bit Jane.” must bind ‘Spot’ to the agent role and ‘Jane’ to the object role. In order to represent nestec structures it must also be possible to bind a relation to a role, e.g., bite(spot , jane) anc the antecedent role of the cause relation.

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MACY/FAC, a computer models of this process, has two stages(Gentner and Forbus, 1991). The first stage selects a few likely analogs from a large number of potential analogs. The second stage searches for an optimal (or at least good) mapping between each selected story and the probe story and outputs those with the best mappings. Two stages are necessary because it is too computationally expensive to search for an optimal mapping between the probe and all stories in memory. An important requirement for a first stage is that its performance scale well with both the size and number of episodes in long-term memory. This prevents the first stage of MAC/FAC from considering any structural features.
MACY/FAC, a computer models of this process, has two stages(Gentner and Forbus, 1991). The first stage selects a few likely analogs from a large number of potential analogs. The second stage searches for an optimal (or at least good) mapping between each selected story and the probe story and outputs those with the best mappings. Two stages are necessary because it is too computationally expensive to search for an optimal mapping between the probe and all stories in memory. An important requirement for a first stage is that its performance scale well with both the size and number of episodes in long-term memory. This prevents the first stage of MAC/FAC from considering any structural features.
Table 1: (a) Scores from the fast (MAC) similarity estimator in MAC/FAC. (b) Scores from an ideal structure-sensitive similarity estimator, e.g., SME as used in MAC/FAC. A simplified view of the overall similarity scores from MAC and the full MAC/FAC is shown in Table 1. There are four conditions — the two structures being compared can be similar in structure and/or in object attributes. In all four conditions, the structures are assumed to involve similar relations — only structural and object attribute similarities are varied. Ideally, the responses to the mixed conditions should be flexible, and controlled by which aspects of similarity are currently considered important. Only the relative values of the scores are important, the absolute values do not matter.
Table 1: (a) Scores from the fast (MAC) similarity estimator in MAC/FAC. (b) Scores from an ideal structure-sensitive similarity estimator, e.g., SME as used in MAC/FAC. A simplified view of the overall similarity scores from MAC and the full MAC/FAC is shown in Table 1. There are four conditions — the two structures being compared can be similar in structure and/or in object attributes. In all four conditions, the structures are assumed to involve similar relations — only structural and object attribute similarities are varied. Ideally, the responses to the mixed conditions should be flexible, and controlled by which aspects of similarity are currently considered important. Only the relative values of the scores are important, the absolute values do not matter.
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