Outlist CMR (CMR-DE)

Out-of-list context mixing for repetitions

Outlist CMR (also called CMR-DE, “Distinct Encoding”) provides an alternative approach to handling repeated items. Instead of using position-based encoding, it maintains item-based encoding but introduces out-of-list context to distinguish presentations.

The Mechanism

When an item appears for the second time, the model mixes its contextual input with an “out-of-list” context unit. This creates temporal separation between the two presentations:

• First presentation: Normal context integration
• Repetition: Context input mixed with a unique out-of-list unit

The out-of-list context makes the second presentation’s trace partially distinct from the first.

Why Out-of-List Context?

The theoretical motivation is that seeing something familiar triggers a different mental state than seeing something new:

• “I’ve seen this before” is itself part of the encoding context
• The repetition carries information about being a repetition
• This meta-cognitive state affects how the item is encoded

Mathematical Specification

First Presentation

Standard encoding: \[\mathbf{c}^{IN}_i = M^{FC} \mathbf{f}_i\] \[\mathbf{c}_{new} = \rho \mathbf{c}_{old} + \beta_{enc} \mathbf{c}^{IN}_i\]

Repetition (item already encoded)

Mixed context input: \[\mathbf{c}^{mix} = \alpha \cdot \mathbf{c}^{IN}_i + (1-\alpha) \cdot \mathbf{c}^{out}\]

where: - \(\mathbf{c}^{IN}_i = M^{FC} \mathbf{f}_i\) (item’s normal context) - \(\mathbf{c}^{out}\) = next available out-of-list context unit - \(\alpha\) = mfc_trace_sensitivity (balance parameter)

Then integrate: \[\mathbf{c}_{new} = \rho \mathbf{c}_{old} + \beta_{enc} \mathbf{c}^{mix}\]

Expanded Context Space

To support out-of-list context, the context vector is expanded:

• Standard size: \(N + 1\) (items + start-of-list)
• Expanded size: \(2N + 1\) (items + out-of-list + start-of-list)

Each repetition consumes a new out-of-list unit.

Parameters

Parameter	Symbol	Description
mfc_trace_sensitivity	\(\alpha\)	Balance between item context and out-of-list context

• \(\alpha = 1.0\): No out-of-list mixing (equivalent to standard CMR)
• \(\alpha = 0.5\): Equal mix of item and out-of-list context
• \(\alpha = 0.0\): Only out-of-list context (complete distinction)

Usage

from jaxcmr.models.outlist_cmr import CMR
import jaxcmr.components.context as TemporalContext

params = {
    "encoding_drift_rate": 0.5,
    "start_drift_rate": 0.5,
    "recall_drift_rate": 0.5,
    "learning_rate": 0.5,
    "primacy_scale": 2.0,
    "primacy_decay": 0.8,
    "shared_support": 0.05,
    "item_support": 0.25,
    "choice_sensitivity": 0.6,
    "mfc_trace_sensitivity": 0.7,  # Out-of-list mixing ratio
    "stop_probability_scale": 0.05,
    "stop_probability_growth": 0.2,
    "learn_after_context_update": True,
    "allow_repeated_recalls": False,
}

# Must use expanded context
model = CMR(
    list_length=16,
    parameters=params,
    context_create_fn=TemporalContext.init_expanded,  # Required!
)

Comparison: Positional vs Outlist

Aspect	Positional CMR	Outlist CMR
Feature layer	Position-based	Item-based
Distinction mechanism	Different position = different trace	Out-of-list context unit
Memory structure	Positions in MCF	Items in MCF (standard)
Context size	Standard	Expanded (2N+1)
Recall identifies	Position	Item

Predictions

Context Similarity

With \(\alpha < 1\): - First and second presentations have partially distinct contexts - Lower \(\alpha\) = more distinct - Transitions from repetition don’t strongly cue first presentation

Spacing Effects

The out-of-list mixing happens regardless of spacing. This differs from drift-based models where spacing affects context overlap directly.

Implementation

Key code from experience_item:

def experience_item(self, item_index):
    item = self.items[item_index]
    context_input = self.mfc.probe(item)

    # Check if item was already encoded
    new_context = lax.cond(
        self.recallable[item_index],  # Already studied?
        # Repetition: mix with out-of-list context
        lambda: self.context.integrate_with_outlist(
            context_input, self.mfc_sensitivity, self.encoding_drift_rate
        ),
        # First presentation: standard integration
        lambda: self.context.integrate(context_input, self.encoding_drift_rate),
    )
    ...

The integrate_with_outlist method in TemporalContext handles the mixing:

def integrate_with_outlist(self, inlist_input, ratio, drift_rate):
    # Mix in-list input with next available out-of-list unit
    context_input = normalize_magnitude(
        (normalize_magnitude(inlist_input) * ratio)
        + (self.outlist_input * (1 - ratio))
    )
    # Then standard integration...

Theoretical Connections

This model relates to:

• Encoding specificity: Each encoding event has unique contextual features
• Global matching models: Items can match based on overall similarity, not just local context
• Recognition memory: The “old” signal at repetition affects encoding

The out-of-list context can be interpreted as an “already seen” tag that becomes part of the memory trace.