Spaced Reinforcement

Every time a memory is recalled, it receives a strength boost. The size of the boost depends on two factors: how long it has been since the last recall (spacing effect) and how many times the memory has been recalled before (diminishing returns). This models the well-established spacing effect from cognitive psychology — distributed practice is more effective than massed practice.

The Boost Formula

spacingMultiplier = min(3.0, 1.0 + log2(1 + daysSinceLastAccess))
diminishingFactor = 1.0 / (1.0 + 0.1 * recallCount)
boost = 0.05 * spacingMultiplier * diminishingFactor

Spacing Multiplier

The spacing multiplier rewards longer gaps between recalls. It uses a logarithmic function that grows quickly at first and then plateaus:

spacingMultiplier = min(3.0, 1.0 + log2(1 + daysSinceLastAccess))

The cap at 3.0 prevents unreasonably large boosts for very old memories recalled after months of absence.

Diminishing Factor

The diminishing factor reduces the boost for memories that have already been recalled many times. Each additional recall provides less marginal benefit:

diminishingFactor = 1.0 / (1.0 + 0.1 * recallCount)

This prevents any single memory from being boosted indefinitely through repeated recall. It also penalizes "cramming" — recalling the same memory many times in quick succession yields diminishing returns.

Example Scenarios

The optimal strategy is clear: recall memories at spaced intervals rather than repeatedly in the same session.

Strength Update

After computing the boost, the memory's strength is updated:

new_strength = min(1.0, current_strength + boost)

Strength is capped at 1.0. A memory that is already at maximum strength still benefits from the decay rate improvement (see below).

Decay Rate Improvement

Each recall also improves the memory's decay rate, making it more resistant to future forgetting:

new_decay_rate = decay_rate + 0.10 * (0.999 - decay_rate)

This formula asymptotically approaches 0.999 (the slowest possible decay). The improvement is proportional to how far the current rate is from the maximum.

Memories with lower decay rates (faster forgetting) benefit more from each recall. Over many recalls, even an observation (initial decay 0.950) can approach the permanence of an insight (0.997).

Combined Effect

Over multiple recalls, spaced reinforcement produces compounding benefits:

1. Strength increases — Each recall adds a boost
2. Decay slows — Each recall improves the decay rate
3. Effective half-life extends — The combination of higher strength and slower decay means the memory persists much longer

A decision memory (strength 0.85, decay 0.995) recalled 5 times over 2 months might have:

• Strength: ~0.92 (after boosts minus decay between recalls)
• Decay rate: ~0.997 (improved from 0.995)
• Effective half-life: ~8 months (up from ~4.5 months)