Apalancamiento de una cartera riesgosa con dos activos

5.2.3.1 Fixed feedforward connections

As mentioned previously, all fixed connection weights are hand-wired.

Both PS units and TA units have feedforward excitatory connections into the RO units. The network architecture can be classified into two main task-associated pathways—a pathway task-associated with the dog detection task, and a pathway associated with the bird detection task. Each PS unit is connected to both Dog and Bird response sets (Fig. 5.3). According to the experimental instructions, a stimulus input can be associated with two response categories—

(a) a positive detection to Task A, or (b) a negative detection to Task B (e.g. a

‘Dog’ input can be interpreted as ‘presence of a dog’ and ‘absence of a bird’).

Therefore, each stimulus input is associated with two different response sets.

The connections between PS and RO have asymmetric pathways by modalities. Specially, the connection weights from visual percept stimulus (PSVIS) are stronger than the connection weights from the auditory percept stimulus (PSAUD). This is due to the observation that all ages were quicker in responding to visual targets than auditory targets in the bimodal CMTS study.

This asymmetry is applied to both pure and mixed networks.

Figure 5.3. Feedforward connections between Percept Stimulus layer and

Response Output layer in (a) mixed networks and (b) pure networks. Black connections

represent stronger visual PS-RO pathways; grey connections represent weaker auditory

PS-RO pathways.

Task attribute units have excitatory feedforward connections to the RO units of the corresponding categories. The connection strengths are the same between the two task-associated pathways (TADOG to RODY&DN vs. TABIRD to ROBY&BN pathways); however, within each category pathway, the connection weights are different for the ‘Yes’ pathway and for the ‘No’ pathway. Task attribute units are strongly connected to the corresponding ‘Yes’ units, since the task instruction was to make a positive response for target detection, and weakly connected to the corresponding ‘No’ units (Fig. 5.4). Therefore, there is a bias towards making a positive response. This asymmetry is applicable to both pure and mixed networks.

Figure 5.4. Feedforward connections from Task Attribute (TA) units to

Response-Output (RO) units in mixed networks—stronger connections to the corresponding ‘Yes’

units and weaker connections to the corresponding ‘No’ units. The lateral inhibitory

connections are symmetrical between the TA units. In pure networks, one of the

task-associated pathway is omitted.

5.2.3.2 Lateral Inhibition connections

Units at the task attribute level and the response output level have reciprocal lateral inhibition connections to the other units in the same level.

Mayr and Keele (2000) have argued that when two tasks are competing against each other, selection of the task-relevant attribute is likely to be accompanied by the inhibition of the competing task-irrelevant attributes (Mayr & Keele, 2000). At the response output level, it has been suggested that, on stop-signal tasks, there are likely to be inhibitory interactions between go and stop responses to facilitate response decision (Boucher, Palmeri, Logan, & Schall, 2007; Verbruggen & Logan, 2008). The inclusion of lateral inhibition also promotes settling among the RO units and increases the likelihood that only one response output reaches the response threshold.

The lateral inhibition connections between the TA units are symmetrical (Fig. 5.5, upper panel), since the tasks are presumed to have equal strengths.

The lateral inhibition connections are also symmetrical between the response sets (RODOG vs. ROBIRD), but are asymmetrical within the response set (Yes/No) (Fig. 5.5, lower panel). Competing response sets (RODOG vs. ROBIRD) strongly inhibit each other, thereby enabling the network to settle into one response set only. In comparison, the ‘Yes’ unit strongly inhibits the ‘No’ unit within the same response set (e.g. ROBY strongly inhibits ROBN). It is assumed that once the Yes unit is activated, it is relatively easy to inhibit the ‘No’ unit. In contrast, the ‘No’

unit only weakly inhibits the ‘Yes’ unit within the same response set. As a consequence, settling to a ‘No’ response requires a greater number of cycles.

This asymmetric inhibition is also an optimal strategy for bi-selection trials. Bi-selection trials involve stimuli with two competing PS units (e.g. DA paired with BV). On these trials, even when an appropriate task is selected, the competition between the RO units within the response set is strong since the PS units send positive input to both Yes and No responses with the same response set.

Selection is optimised if the processing is biased towards the ‘Yes’ response.

The stronger lateral inhibition from Yes to No, coupled with the stronger TA unit to ROYES pathway, means that the network requires weaker evidence from the perceptual stimulus to make a ‘Yes’ response than a ‘No’ response on bi-selection trials.

Figure 5.5. Lateral inhibitory connections in the mixed networks. Upper network

shows the symmetrical lateral inhibitions between TA units. Lower network shows lateral

inhibition between RO units—strong inhibitory connections between response sets;

strong inhibitory connection from ‘Yes’ to ‘No’, and a weaker inhibitory connection

from ‘No’ to ‘Yes’ within a response set. In the pure networks (not shown here), there is

no lateral inhibition at TA level, and only the asymmetric lateral inhibition within the

response set.

5.2.3.3 Priming connections between PS and TA (PS2TA)

Other than the fixed excitatory and inhibitory connections mentioned earlier, there are also temporary feedforward connections from the PS units to the TA units (Fig. 5.2, dashed line). These connections create the n-1 stimulus-task primes. These connections are formed through hebbian-like learning mechanism between the activated PS unit(s) and the TA units (both activated and inhibited units) at the end of each trial. These temporary connections are the only connections that undergo associative learning; however, unlike learning that results in fixed structural changes that affect all future behaviours, the learning here lasts for one trial only. The same priming connections were also present in Gilbert and Shallice’s models, and were crucial to account for the

interference component of switch costs. If any identical percept stimulus unit is reactivated on a following trial, the percept stimulus unit(s) will send activation to the task attribute unit(s) relevant to the n-1 trial. It should be noted that both excited and inhibited TA units have temporary priming connections with the PS units, and therefore the primes can either have positive input or negative input to the TA units.

On a task-repetition trial, the priming effect is facilitative since it increases the activation of the relevant task attribute, and decreases activation of the competing TA unit. In contrast, on a task-switch trial, the priming effect would be interfering since the prime is likely to send positive input to the competing TA unit, and negative input to the task-relevant TA unit.

The priming connection weights are the product of the activation values between the PS and TA units at the end of the n-1 trial (Equation 1).

𝑊_"# = Irate×𝑎_#×𝑎_" (Equation 1)

The aj is the activation of the PS unit, and the ai is the activation of the TA unit. Irate is the learning rate of the weight change, which determines the magnitude of the priming effect. These connections are rewired, rather than updated, after each trial. Therefore, the memory of the connection lasts for one trial only. Since our studies only looked at n-1 trial effect, no other assumptions are made about other potential higher-order trial sequence effects, although higher order effects might be present.