Mathematical Psychology
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Interference Models of WM

Interference models of working memory explain forgetting not through temporal decay but through representational overlap and competition among stored items, with similarity between items as the key determinant of memory loss.

P(retrieve i | cue) = S(target, cue) / [S(target, cue) + Σ S(competitorⱼ, cue)]

Interference models of working memory (WM) propose that forgetting occurs because stored representations compete with and degrade one another, rather than fading over time. This class of models, with roots in the interference theory of McGeoch (1932) and Underwood (1957), has been revitalized in the WM literature by work from Oberauer, Lewandowsky, Nairne, and others who argue that purely temporal accounts of WM forgetting are unnecessary.

Retroactive and Proactive Interference

Retroactive interference (RI) occurs when new information disrupts memory for older information. Proactive interference (PI) occurs when older information disrupts memory for newer information. In WM tasks, both forms of interference are readily observed. The Nairne (1990) feature model formalizes interference as feature overwriting: when a new item shares features with a stored item, the shared features in the older trace are replaced by the new item's values:

Feature Overwriting trace(i, feature j) = new_value with probability p_overwrite, else original_value

The probability of overwriting depends on the similarity between the interfering item and the stored trace. Highly similar items produce more interference because they share more features that are vulnerable to overwriting.

Oberauer's Interference Model

Oberauer and Kliegl (2006) developed a formal interference model of WM in which items are bound to positions (or contexts) in a distributed representational space. Interference arises from two sources: feature overwriting (as in Nairne's model) and superposition (multiple items sharing the same representational space). The model uses a softmax choice rule for retrieval:

Retrieval Competition P(retrieve item i | cue) = e^(a · sim(i, cue)) / Σⱼ e^(a · sim(j, cue))

where the sum includes all items that are associated with the cue context. This softmax retrieval rule captures the graded competition between items that characterizes WM retrieval.

Similarity and Confusability

A key prediction of interference models is that the similarity between items determines the amount of forgetting. Phonologically similar items in verbal WM produce more order errors (the phonological similarity effect), and visually similar items in visual WM produce more swap errors. The relationship between similarity and interference is typically modeled using an exponential similarity function: sim(i,j) = e^(−d(i,j)/s), where d is the distance between item representations and s is a scaling parameter.

Evidence Against Pure Decay

Several lines of evidence favor interference over decay in WM. Lewandowsky, Duncan, and Brown (2004) showed that in serial recall, the number of items intervening between study and test predicts forgetting but the duration of the retention interval does not (when rehearsal is controlled). Oberauer and Lewandowsky (2008) demonstrated that filled delays produce forgetting only to the extent that the filler material is similar to the memory items. These findings are naturally explained by interference but are problematic for decay-based accounts such as TBRS.

Interference as a Feature, Not a Bug

From a functional perspective, interference can be adaptive. In a dynamic environment, old information that conflicts with new information is often outdated. By allowing new representations to overwrite old ones, the cognitive system automatically updates its contents to reflect the most recent state of the world, implementing a form of rational information management.

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References

  1. Nairne, J. S. (1990). A feature model of immediate memory. Memory & Cognition, 18, 251-269.
  2. Oberauer, K., & Kliegl, R. (2006). A formal model of capacity limits in working memory. Journal of Memory and Language, 55, 601-626.
  3. Lewandowsky, S., Duncan, M., & Brown, G. D. A. (2004). Time does not cause forgetting in short-term serial recall. Psychonomic Bulletin & Review, 11, 771-790.

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