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🧬 Biological Systems β€” Overview

Spector Memory draws on computational neuroscience research to implement simplified, performance-optimized approximations of biological memory mechanisms. Each package in spector-memory maps to a neuroscience concept, implementing mathematical models inspired by peer-reviewed cognitive science β€” particularly Anderson's ACT-R architecture (1993) β€” and optimized for microsecond-scale agent memory operations.

The Brain–Code Mapping

graph TB
    subgraph "Encoding & Storage"
        STE["🧩 Synapse<br/>Synaptic Tags & Scoring<br/><i>Bloom filter + binary layout</i>"]
        CT["🧠 Cortex<br/>4-Tier Memory Stores<br/><i>Working β†’ Episodic β†’ Semantic β†’ Procedural</i>"]
    end

    subgraph "Emotional & Importance Modulation"
        DA["⚑ Dopamine<br/>Surprise Detection<br/><i>Welford Z-score β†’ importance</i>"]
        AM["❀️ Amygdala<br/>Emotional Valence<br/><i>-128 to +127 coloring</i>"]
    end

    subgraph "Retrieval Dynamics"
        HB["πŸ›‘ Habituation<br/>Anti-Filter Bubble<br/><i>Repetition penalty</i>"]
        IN["🚫 Inhibition<br/>Suppression Set<br/><i>Inhibition of return</i>"]
        IF["πŸ”€ Interference<br/>Deduplication<br/><i>Proactive/retroactive</i>"]
    end

    subgraph "Association & Learning"
        HE["πŸ”— 3-Layer Cognitive Graph<br/>Hebbian + Entity + Temporal<br/><i>Off-heap graph structures</i>"]
    end

    subgraph "Consolidation & Planning"
        HP["πŸ’€ Hippocampus<br/>Sleep Consolidation<br/><i>ReflectDaemon cycle</i>"]
        PR["πŸ“‹ Prospective<br/>Future Intents<br/><i>Scheduled reminders</i>"]
        MM["πŸ” Metamemory<br/>Self-Reflection<br/><i>Confidence calibration</i>"]
    end

    DA --> STE
    AM --> STE
    STE --> CT
    CT --> HE
    HE --> HP

    style HE fill:#e74c3c,color:white
    style DA fill:#f39c12,color:white
    style HP fill:#9b59b6,color:white
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Systems at a Glance

System Brain Region Key Concept Spector Implementation Reference
[[Cortex Memory--Cortex]] Prefrontal, Hippocampus, Neocortex, Basal Ganglia Multi-store memory model 4-tier off-heap stores (Working, Episodic, Semantic, Procedural)
[[Synapse Memory--Synapse]] Synaptic junction Synaptic tagging & capture 64-bit Bloom filter tag encoding, 32B binary header
[[Dopamine Memory--Dopamine]] Ventral tegmental area Prediction error signaling Welford Z-score surprise detection, flashbulb encoding
[[Amygdala Memory--Amygdala]] Amygdala Emotional memory modulation Signed valence byte (-128 to +127), emotional filtering
[[3-Layer Graph Memory--Hebbian]] Cortical networks, Hippocampus Hebbian learning, STDP, episodic sequences Off-heap HebbianGraph, EntityGraph, TemporalChain
[[Habituation Memory--Habituation]] Sensory cortex Response decrement to repetition Exponential penalty on repeated recall
[[Inhibition Memory--Inhibition]] Prefrontal cortex Inhibition of return SuppressionSet with TTL-based suppression windows
[[Interference Memory--Interference]] Hippocampus Proactive/retroactive interference Similarity-based deduplication during ingestion
[[Hippocampus Memory--Hippocampus]] Hippocampus Sleep consolidation & replay ReflectDaemon: decay, compaction, episodic→semantic promotion
[[Prospective Memory--Prospective]] Prefrontal cortex Prospective memory Scheduled future intent reminders
[[Metamemory Memory--Metamemory]] Prefrontal cortex Metacognitive monitoring Confidence calibration, recall quality estimation
[[Sync Memory--Sync]] β€” (engineering) Persistence & replication WAL + mmap-backed partitions

Key Mathematical Models

Temporal Decay (Power Law of Forgetting)

Spector approximates the power law of forgetting using precomputed decay buckets β€” avoiding expensive Math.pow() calls in the hot loop:

$$R(t) = a \cdot t^{-d}$$

Where $R(t)$ is retrieval strength, $t$ is time since encoding, and $d$ is the configurable decay exponent (default: 0.15). Research since Wixted (2004) has established that forgetting follows a power law, not the exponential curve originally proposed by Ebbinghaus (1885). Spector discretizes this into 12 buckets spanning 5+ years, with a configurable permastore floor (default: 0.10) β€” see Scoring Pipeline).

References: Wixted, J.T. (2004). The psychology and neuroscience of forgetting[^15]; Ebbinghaus, H. (1885). Über das GedÀchtnis[^13]

Reconsolidation (Spacing Effect)

Each recall shifts the decay bucket backward, simulating how retrieved memories become more durable:

$$\text{adjustedBucket} = \text{rawBucket} - \lfloor \text{recallCount} / 3 \rfloor$$

Reference: Bjork & Bjork (1992). A New Theory of Disuse[^14]

Surprise Detection (Dopamine Prediction Error)

The importance signal uses a Z-score from Welford's online statistics:

$$\text{importance} = \alpha \cdot \sigma\left(\frac{x - \mu}{\sigma}\right) + \beta \cdot \text{temporalNovelty}$$

Where $\sigma()$ is the sigmoid function, $\alpha = 0.6$, $\beta = 0.4$.

Reference: Schultz, W. (1997). A neural substrate of prediction and reward[^3]

Hebbian Edge Strengthening

Co-ingested memories strengthen their bidirectional edge:

$$w_{ij}(t+1) = w_{ij}(t) + \Delta w$$

With decay during consolidation: $w_{ij}(t+1) = 0.9 \cdot w_{ij}(t)$

Reference: Hebb, D.O. (1949). The Organization of Behavior[^5]

STDP β€” Spike-Timing Dependent Plasticity

Directed causal edges are strengthened when tag A is recalled before tag B:

$$\Delta w = \begin{cases} A_+ \cdot e^{-\Delta t / \tau_+} & \text{if } \Delta t > 0 \text{ (causal)} \ -A_- \cdot e^{\Delta t / \tau_-} & \text{if } \Delta t < 0 \text{ (anti-causal)} \end{cases}$$

Reference: Bi & Poo (2001). Synaptic modification by correlated activity[^6]

Scoring Formula (ACT-R Lineage)

Spector's core scoring formula is a simplified, hardware-optimized approximation of the ACT-R activation equation (Anderson, 1993):

$$\text{ACT-R: } A_i = \underbrace{B_i}_{\text{base-level}} + \underbrace{\sum_{j} W_j \cdot S_{ji}}_{\text{spreading activation}} + \epsilon$$

Spector's approximation:

$$\text{Spector: } \text{score} = \underbrace{\alpha \cdot \text{similarity}}_{\approx \sum W_j S_{ji}} + \underbrace{\beta \cdot \text{importance} \cdot \text{decay} \cdot S^{0.3}}_{\approx B_i}$$

Where:

  • Similarity β‰ˆ ACT-R's spreading activation from current context
  • Importance Γ— decay β‰ˆ ACT-R's base-level activation $B_i$
  • $S^{0.3}$ (storage strength) β‰ˆ Bjork's two-factor model (1992)[^14]
  • Ξ±, Ξ² = relative weighting of context vs. base-level (default: 0.6, 0.4)

References: Anderson, J.R. (1993). Rules of the Mind[^16]; Anderson, J.R. & Lebiere, C. (1998). The Atomic Components of Thought[^17]

Habituation Penalty

Repeated recall of the same memory incurs an exponentially increasing penalty:

$$\text{penalty}(n) = 1 - e^{-\gamma \cdot n}$$

Where $n$ is the number of times the memory appeared in recent results and $\gamma$ controls penalty steepness.

Reference: Thompson & Spencer (1966). Habituation: A model phenomenon[^7]

Design Principles

  1. Grounded in research: Each system implements a mathematical model inspired by peer-reviewed cognitive science, optimized for microsecond-scale agent memory operations. The scoring formula is a simplified, hardware-optimized approximation of the ACT-R activation equation (Anderson, 1993)[^16], with extensions for emotional valence (McGaugh, 2004)[^4] and storage strength (Bjork & Bjork, 1992)[^14].

  2. Independent testability: Each biological system is a standalone package with its own unit tests. Systems compose via dependency injection, not inheritance.

  3. Graceful degradation: Every system is optional. Disabling surprise detection, habituation, or graph augmentation produces a functional (if less intelligent) memory system.

  4. Performance-first biology: Biological accuracy is constrained by microsecond latency requirements. Where exact models are too expensive (e.g., continuous exponential decay), we use precomputed approximations (decay buckets, Bloom filter tags).

Explore Each System

References

[^1]: Atkinson, R.C. & Shiffrin, R.M. (1968). Human memory: A proposed system and its control processes. In Psychology of Learning and Motivation, 2, 89–195. doi:10.1016/S0079-7421(08)60422-3

[^2]: Frey, U. & Morris, R.G.M. (1997). Synaptic tagging and long-term potentiation. Nature, 385, 533–536. doi:10.1038/385533a0

[^3]: Schultz, W. (1997). A neural substrate of prediction and reward. Science, 275(5306), 1593–1599. doi:10.1126/science.275.5306.1593

[^4]: McGaugh, J.L. (2004). The amygdala modulates the consolidation of memories of emotionally arousing experiences. Annual Review of Neuroscience, 27, 1–28. doi:10.1146/annurev.neuro.27.070203.144157

[^5]: Hebb, D.O. (1949). The Organization of Behavior: A Neuropsychological Theory. New York: Wiley.

[^6]: Bi, G. & Poo, M. (2001). Synaptic modification by correlated activity: Hebb's postulate revisited. Annual Review of Neuroscience, 24, 139–166. doi:10.1146/annurev.neuro.24.1.139

[^7]: Thompson, R.F. & Spencer, W.A. (1966). Habituation: A model phenomenon for the study of neuronal substrates of behavior. Psychological Review, 73(1), 16–43. doi:10.1037/h0022681

[^8]: Klein, R.M. (2000). Inhibition of return. Trends in Cognitive Sciences, 4(4), 138–147. doi:10.1016/S1364-6613(00)01452-2

[^9]: Underwood, B.J. (1957). Interference and forgetting. Psychological Review, 64(1), 49–60. doi:10.1037/h0044616

[^10]: Rasch, B. & Born, J. (2013). About sleep's role in memory. Physiological Reviews, 93(2), 681–766. doi:10.1152/physrev.00032.2012

[^11]: Einstein, G.O. & McDaniel, M.A. (1990). Normal aging and prospective memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 16(4), 717–726. doi:10.1037/0278-7393.16.4.717

[^12]: Nelson, T.O. & Narens, L. (1990). Metamemory: A theoretical framework and new findings. In Psychology of Learning and Motivation, 26, 125–173. doi:10.1016/S0079-7421(08)60053-5

[^13]: Ebbinghaus, H. (1885). Über das GedÀchtnis: Untersuchungen zur experimentellen Psychologie. Leipzig: Duncker & Humblot. English translation: Memory: A Contribution to Experimental Psychology (1913).

[^14]: Bjork, R.A. & Bjork, E.L. (1992). A new theory of disuse and an old theory of stimulus fluctuation. In From Learning Processes to Cognitive Processes: Essays in Honor of William K. Estes, 2, 35–67.

[^15]: Wixted, J.T. (2004). The psychology and neuroscience of forgetting. Annual Review of Psychology, 55, 235–269. doi:10.1146/annurev.psych.55.090902.141555

[^16]: Anderson, J.R. (1993). Rules of the Mind. Hillsdale, NJ: Erlbaum.

[^17]: Anderson, J.R. & Lebiere, C. (1998). The Atomic Components of Thought. Mahwah, NJ: Erlbaum.

[^18]: Park, J.S. et al. (2023). Generative Agents: Interactive Simulacra of Human Behavior. UIST '23. doi:10.1145/3586183.3606763

[^19]: Hu, Y. et al. (2025). MemoryOS: Cognitive-Inspired Memory Architecture for AI Agents. arXiv:2506.06326.

[^20]: McClelland, J.L., McNaughton, B.L. & O'Reilly, R.C. (1995). Why there are complementary learning systems in the hippocampus and neocortex. Psychological Review, 102(3), 419–457. doi:10.1037/0033-295X.102.3.419

[^21]: Baddeley, A.D. (2000). The episodic buffer: a new component of working memory? Trends in Cognitive Sciences, 4(11), 417–423. doi:10.1016/S1364-6613(00)01538-2

[^22]: Bahrick, H.P. (1984). Semantic memory content in permastore: Fifty years of memory for Spanish learned in school. JEP: General, 113(1), 1–29. doi:10.1037/0096-3445.113.1.1

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