Search of Associative Memory: A Tutorial

Contents

• Introduction
  • Retrieval Structure
• Recognition
  • Item Strength and List Length Effects in Recognition
  • A Recognition Example
• Recall
  • The Recall Process
  • The Sampling Probability
  • The Recovery Probability
  • Item Strength and List Length Effects in Recall
  • A Recall Example
• SAM Tutorial Questions

1. Contextual elements (identify context/setting item occurs in);
2. Item information (identify the item encoded in the image);
3. Iter-item information (links one image to the others).

1. Context cues which represent an episode (e.g. the list you just studied, breakfast this morning);
2. Item cues which represent items (e.g. words, pictures, or sentences);
3. Category cues which represent categories (e.g. a metal when steel and iron were on the study list, a flower when rose and daisy were on the study list).

1. Coding and rehearsal at study (and any additional learning that occurs at time of test);
2. The match of the cue used a test with the cue used at study;
3. Pre-experimental associations.

Assumptions about the setting of the retrieval strengths:

1. The retrieval structure contains images of all presented items rather than all items in memory
2. A context cue has strengths to each image in proportion to the time spent rehearsing that item
3. An item cue has strengths to each image in proportion to the time spent rehearsing those items together. This leads to high self strengths, relatively high strengths to items that were rehearsed together, and small residual strengths to items not studied together.
4. A category cue has a high strength to images of items from that category and small residual strengths to images from other categories.
5. Variability is added to each of the strengths (to avoid perfect performance) by replacing each element of the retrieval structure with a value sampled from a three point distribution given by:

   Final Value = (1-v) Starting Value, p=1/3
                       Starting Value, p=1/3
                 (1+v) Starting Value, p=1/3
   

In recognition the yes/no decision is based on the integration of the activation of all images, putting SAM in the class of Global Matching Models. A familiarity value is calculated using equation 1. This familiarity value is then compared against a criterion. If it is above criterion the model responds "old", that is, it indicates that the cue set has retrieved something from memory. If the familiarity value is below criterion the model responds "new".

    (1)

where

Qj are the cues
Ik are the images of the list items
M is the number of cues
N is the number of images
Wj are the weighting factors reflecting the amount of attention allotted to each cue (often set to 1.0).
is the strength between Qj and Ik.

The activation of each image is the product of retrieval strengths from each of the cues to that image. Consequently, an image will only be highly active if it is has strong retrieval strengths to all of the cues. The familiarity value is the sum of these activations.

In a single item recognition task a context cue (C) and an item cue (Ij) are used to probe memory. If we assume that the attentional weights are all set to 1, equation 1 simplifies to:

    (2)

Only list items contribute non-negligible activations (i.e., the sum in the familiarity equation is computed over N list items). Therefore, an item is familiar only to the degree it activates list items. The model gives better than chance recognition performance because:

1. The strength of a target to its own image will usually be higher than the strength of a distractor to that image;
2. Interitem strengths will be higher for targets than for distractors because the list items will be rehearsed together during study.

The length effect in recognition occurs because the familiarity is summed over all of the items in the list. While the mean difference between target and distractor familiarity will remain the same as length increases, the variance will increase leading to a decrease in d'.

A Recognition Example

where I1, I2 and I3 are items that appeared on the list (targets) and D1 and D2 did not appear on the list (distractors).

Calculating the activations of each of the images and summing produces:

If we set the criterion to 0.36, I1 and I3 will be correctly labelled "old" (a hit), I2 will be labelled "new" when in fact it did appear on the list (a miss), D1 will be correctly labelled "new" (a correct rejection) and D2 will be labelled "old" when it did not appear on the list (a false alarm).

Recall

1. Probe cues are chosen according to a retrieval plan which may be affected by prior knowledge and strategies.
2. An image is sampled from the active set.
3. An attempt is made to recover the name of the image.
4. If the name is recovered it is evaluated to determine whether to respond. The search continues, repeating steps 1-3, until a maximum number of failures has been reached.

The Sampling Probability

    (3)

The numerator is the activation of a given image. The denominator is the summed activation across all images (i.e., the total activation of long term store - the same value of familiarity used in recognition judgements). So the probability of sampling a given image is proportional to its strength to the probe cues. The product rule ensures the sampled image is generally an item strongly connected to all cues, allowing the use of multiple cues to focus the memory search.

At the start of free recall the only cue available is the context cue. When all Wj are set to 1.0, and the context cue alone is used to probe memory:

    (4)

Once an item has been retrieved it can also be used as a cue, giving:

    (5)

The Recovery Probability

    (6)

When context alone is the cue:

    (7)

When context and an item cue, Ij are used:

    (8)

Equations 6, 7, and 8 are general expressions for correct recovery assuming each cue has an independent chance of producing recovery. Equations 3 to 8 describe what happens in a single cycle of a search. Retrieval consists of a series of such cycles.

Item Strength and List Length Effects in Recall

The effect of list length occurs in the sampling phase. A longer list means a greater total activation which results in a smaller sampling probability.

A Recall Example

Suppose in the first cycle of the memory search I3 is sampled. I3 has a probability of 0.5 of being sampled so this is a likely scenario. Now moving to the recovery phase we see that I3 has a 0.5507 probability of being recovered. Suppose that on this cycle I3 is not recovered. Consequently the search does not output a response on this cycle. Now the process goes back to the sampling phase. We still have only the context cue (since I3 was not recovered during cycle one), and so the calculations will be identical. Suppose we again sample I3. In the recovery phase of the second cycle, however, the name of I3 is recovered so we can output I3. Now we have an additional cue, so the calculations change since our cue set will now include this new cue.

The probability of sampling I3 has increased making it very likely that we will sample it again. In fact as the number of items we have recalled increases, it becomes progressively less likely that we will sample other items, a property that is consistent with the experimental data. The process continues as above until some maximum number of failures has been reached.

In cued recall both a context cue and an item cue are provided and both are used as probes. As in free recall, the search continues until a maximum number of failures is reached.

SAM Tutorial Questions

1. Run the SAM recognition simulator with the standard parameters and note the d' value (use the prop. figure), the mean familiarity for targets and distractors and the variances for targets and distractors.
2. Simulate a list of 16 items and adjust the criterion appropriately. How does d' change and why?
3. Simulate a list of weak and strong items. How does d' change for the weak items? Why?
4. How would you expect increasing the context strength to affect recognition performance? Conduct simulations to verify your answer.
5. Repeat questions 1-4 for cued recall.