🎓 Theoretical Foundations¶

Spector Memory's cognitive scoring pipeline is a simplified, hardware-optimized approximation of established cognitive science models. This page maps each component of the scoring formula to its theoretical origin, documents the simplifications made for performance, and identifies where future work could close the gap.

The Scoring Formula¶

Spector's core scoring formula (from CognitiveScorer.java):

Where:

• \(\alpha = 0.6\) — weight for context relevance (spreading activation)
• \(\beta = 0.4\) — weight for base-level activation
• \(\text{similarity}\) — cosine similarity between query and memory embeddings
• \(\text{importance}\) — Z-score surprise detection + ICNU hints from the LLM
• \(\text{decay}(t)\) — power-law temporal decay from 12-bucket lookup table
• \(S^{0.3}\) — storage strength boost from Bjork's Two-Factor model

ACT-R Lineage¶

The Full ACT-R Activation Equation¶

Anderson's ACT-R architecture (1993, 1998) defines memory activation as:

Where:

• \(B_i\) (Base-level activation): How accessible the memory is based on recency and frequency of use
• \(\sum_j W_j \cdot S_{ji}\) (Spreading activation): How much the current context activates this memory
• \(\epsilon\) (Noise): Stochastic variability in retrieval

The base-level activation is computed as:

Where \(t_1, t_2, \ldots, t_n\) are the times since each of the \(n\) past retrievals of item \(i\), and \(d\) is the decay exponent (typically ~0.5 in ACT-R).

What Spector Implements (Simplified ACT-R)¶

The Gap: What We Lose¶

The primary simplification is in base-level activation. Full ACT-R's \(\ln(\sum t_j^{-d})\) captures the spacing effect — memories recalled at spaced intervals are stronger than memories recalled in rapid succession. Spector's recallCount-based reconsolidation does not distinguish between 3 recalls in 1 minute and 3 recalls over 3 months.

Planned Phase 4: Implement recall-timestamp tracking using a compact ring buffer (last 8 recall timestamps per memory, stored in a fixed 64-byte slot). This would enable the full ACT-R base-level computation while maintaining SIMD alignment.

Power Law of Forgetting¶

The Research Progression¶

Why Power Law > Exponential¶

The exponential curve (\(e^{-\lambda t}\)) predicts that forgetting is essentially complete within weeks. Empirical data shows this is wrong — memories persist much longer than exponential models predict.

The power law (\(t^{-d}\)) matches observed human forgetting data because:

1. Slow tail: The power law has a "fat tail" — old memories decay very slowly, matching the permastore observation
2. Initial rapid drop: Recent memories are still forgotten quickly, consistent with short-term memory dynamics
3. Scale invariance: The same functional form works from seconds to decades

Spector's Implementation¶

Spector uses a precomputed 12-bucket lookup table derived from the power law:

R(t) = a · t^{-d}    where d = 0.15 (configurable via DecayConfig)

Bucket values are computed at construction time by DecayConfig.computeBuckets() and stored as a static float[] array. At scoring time, the decay lookup is a single array access — DECAY_BUCKETS[bucket] — costing ~7 CPU cycles.

Three presets are available via DecayConfig:

Two-Factor Memory (Bjork & Bjork, 1992)¶

The Theory¶

Bjork & Bjork's New Theory of Disuse (1992)² proposes that every memory has two independent strengths:

• Retrieval Strength \(R(t)\): How easily the memory can be accessed right now. Decays with time.
• Storage Strength \(S(t)\): How deeply the memory is encoded. Only increases through successful retrieval.

The key insight is desirable difficulty: when retrieval is hard (low \(R\)), successful recall produces the largest boost to \(S\). This is why spaced repetition works — forcing difficult retrievals builds stronger long-term memories.

Spector's Implementation¶

ΔS = sGain × (1 - R(t))     // max boost when retrieval is hard
S' = min(S + ΔS, sMax)       // bounded growth

Final score modifier: S^{sExponent}

Configured via TwoFactorConfig:

A memory with \(S=5.0\) gets a \(5^{0.3} = 1.62\times\) multiplier. The default \(S=1.0\) has no effect (\(1^{0.3} = 1.0\)).

Comparison With Other AI Memory Systems¶

Key Differentiators¶

1. Spector is the only system that combines power-law decay, Two-Factor strengthening, AND emotional valence in a single scoring formula
2. Stanford Generative Agents uses additive scoring (\(0.99^{\Delta hours}\) for recency) — effectively exponential decay, which drops to near-zero within weeks
3. Full ACT-R has the most theoretically rigorous base-level activation, but doesn't model emotional memory. Spector adds valence/arousal as an extension
4. Mem0/Letta have no temporal dynamics — every memory is equally accessible regardless of age

References¶