Assignment 3: Context Maintenance and Retrieval (CMR)

Assignment 3: Context Maintenance and Retrieval (CMR)#

Overview#

In this assignment, you will implement the Context Maintenance and Retrieval (CMR) model as described in Polyn, Norman, & Kahana (2009). CMR is a context-based model of memory search, extending the Temporal Context Model (TCM) to explain how temporal, semantic, and source context jointly influence recall. You will fit your implementation to Murdock (1962) free recall data and evaluate how well the model explains the observed recall patterns.

Data Format and Preprocessing#

The dataset consists of sequences of recalled items from multiple trials of a free recall experiment. Each row represents a participant’s recall sequence from a single list presentation.

Numbers (1, 2, …, N): Serial position of recalled items.
88: Denotes errors (recalls of items that were never presented)
Example:
```
6 1 4 7 10 2 8  
10 9 6 8 2 1 88  
10 7 9 8 1  
```
This represents three recall trials. Each row contains the order in which items were recalled for one list.

Model Description#

You will implement and fit a Context Maintenance and Retrieval (CMR) model that consists of:

1. Encoding Stage: Context Representation#

Each studied item is associated with a context representation composed of:
- Temporal context (slowly drifting across time).
- Semantic context (pre-existing associative relations).
- Source context (internal or external cues such as task or modality).
When an item is presented, its item features interact with the current context. Context is gradually updated via:

\[ c_i = \rho_i c_{i-1} + \beta c_{in} \]

where:
- \(c_i\) is the context at position \(i\),
- \(\rho_i\) scales how much prior context persists,
- \(\beta\) controls the drift rate of context,
- \(c_{in}\) represents the new item-driven input.
Semantic context is pre-defined by prior associations, while temporal and source contexts evolve dynamically.

2. Retrieval Stage: Memory Search#

Recall is modeled as a probabilistic competition where activated context cues retrieve stored items:

Activation of Memory Traces#

Each item has an activation score based on how well it matches the current context:

\[ f_{in} = M_{CF} c_i \]

where:
- \(M_{CF}\) represents learned context-to-item associations.
- Higher \(f_{in}\) means a greater probability of recall.
Items compete for recall through a leaky, competitive accumulation process:

\[ x_s = (1 - \tau \kappa - \tau \lambda N) x_{s-1} + \tau f_{in} + \epsilon \]

where:
- \(\kappa\) controls memory decay,
- \(\lambda\) determines inhibition between competing items,
- \(\tau\) sets the speed of evidence accumulation.
Once an item crosses a recall threshold, it is recalled and updates context, influencing subsequent recalls.

3. Fitting the Model#

The following three key parameters should be optimized to best match human recall data:

Context Drift Rate (\(\beta\)): How quickly temporal and source context updates.
Memory Decay (\(\kappa\)): Governs how quickly items lose activation.
Inhibition (\(\lambda\)): Controls competition between retrieved items.

Implementation Tasks#

Step 1: Implement Context Evolution#

Implement temporal and source context updates during study.
Encode semantic relations using a fixed association matrix.

Step 2: Implement the Recall Process#

Compute retrieval strengths using context-to-item activation.
Implement the competitive accumulation process.
Simulate context reinstatement from retrieved items.

Step 3: Load and Process Data#

Read in the recall dataset and parse trials correctly.
Compute observed recall probabilities for comparison.

Step 4: Fit Model Parameters#

Optimize \(\beta\) (context drift), \(\kappa\) (memory decay), and \(\lambda\) (inhibition) to best match recall patterns.

Step 5: Generate Key Plots#

For each combination of list length and presentation rate, generate the following plots:

Plot 1: Probability of First Recall as a Function of Serial Position#

X-axis: Serial position in the presented list.
Y-axis: Probability that the item is the first item recalled.
Overlay model predictions on observed data.

Plot 2: Conditional Recall Probability as a Function of Lag#

X-axis: Lag (\(l\)) (distance between successive recalls).
Y-axis: Probability of recalling an item at position \(i+l\) after recalling \(i\).
Overlay model predictions on observed data.

Plot 3: Overall Probability of Recall as a Function of Serial Position#

X-axis: Serial position in the presented list.
Y-axis: Probability of recall at any output position.
Overlay model predictions on observed data.

Each plot should include:

Observed human recall data (solid line).
Model predictions (dashed line).
Error bars (95% confidence intervals).

Step 6: Evaluate the Model#

Write a brief discussion (3-5 sentences) addressing:
- Does the model explain the data well?
- Which patterns are well captured?
- Where does the model fail, and why?
- Potential improvements or limitations of CMR.

Grading Criteria#

Model Implementation (50%):
- Correct encoding, retrieval, and stopping rule logic.
- Accurate probability calculations.
- Clear and well-documented code.
Plot Accuracy (45%):
- 15% for each of the three required plots.
- Must correctly overlay observed data and model predictions.
Interpretation and Discussion (5%):
- Thoughtful analysis of model fit.
- Identifies strengths and weaknesses of CMR.

Submission Instructions#

Submit a Google Colaboratory notebook (or similar) that includes:
- Your full implementation of the CMR model.
- Markdown cells explaining your code, methodology, and results.
- All required plots comparing model predictions to observed data.
- A short written interpretation of model performance.

Good luck, and happy modeling!