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Computational Neuroscience

Spikuit models knowledge dynamics using simplified neural mechanisms.

Neurons and Spikes

graph LR
    A[input] --> B[accumulate] --> C{threshold?} --> D[fire!] --> E[propagate]
    D -.->|leak / decay| B
  • Biological neurons communicate through discrete electrical pulses (action potentials)
  • A neuron accumulates input, fires when it crosses a threshold, then resets
  • In Spikuit: a Spike = a review event; firing propagates signal to connected knowledge

Synaptic Plasticity (STDP)

"Neurons that fire together wire together" — Hebb, 1949

Spike-Timing-Dependent Plasticity refines Hebb's rule with temporal direction:

  • Pre fires before post (causal) → connection strengthens (LTP)
  • Post fires before pre (reverse) → connection weakens (LTD)
  • Magnitude decays exponentially with |dt|
  • In Spikuit: edge weights update based on co-fire timing within tau_stdp days (default: 7)

Leaky Integrate-and-Fire (LIF)

  • Neurons accumulate input (integration) and gradually lose charge (leak)
  • High pressure = the system is telling you this concept needs review
  • In Spikuit: neighbor reviews push pressure up, time decays it exponentially

Spreading Activation

graph LR
    subgraph activated [" "]
        dog(("dog")):::fired -->|primed| cat(("cat")):::primed
        dog -->|primed| bone(("bone")):::primed
        dog -->|primed| walk(("walk")):::primed
    end
    subgraph not_activated [" "]
        algebra(("algebra")):::inactive
    end

    classDef fired fill:#E53935,color:#fff,stroke:#B71C1C
    classDef primed fill:#FFF9C4,stroke:#F9A825,color:#333
    classDef inactive fill:#EEEEEE,stroke:#BDBDBD,color:#666
    style activated fill:none,stroke:#E0E0E0,stroke-dasharray:4
    style not_activated fill:none,stroke:#E0E0E0,stroke-dasharray:4
  • Activating a concept in memory primes related concepts (Collins & Loftus, 1975)
  • In Spikuit: reviewing one node sends activation to graph neighbors via APPNP (Personalized PageRank)

Sleep-Inspired Consolidation

Memory consolidation during sleep involves multiple phases:

  • Slow-Wave Sleep (SWS): Replays and strengthens important memories
  • Synaptic Homeostasis (SHY): Globally downscales synaptic weights to prevent saturation (Tononi & Cirelli, 2003)
  • REM: Reorganizes and abstracts — detects patterns across memories

In Spikuit: consolidate runs a 4-phase plan: Triage (classify synapses) → SHY (decay weak connections) → SWS (prune dead weight) → REM (detect consolidation opportunities).

References

  • Hodgkin, A. L. & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117(4), 500–544.
  • Hebb, D. O. (1949). The Organization of Behavior. Wiley.
  • Bi, G. & Poo, M. (1998). Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal of Neuroscience, 18(24), 10464–10472.
  • Collins, A. M. & Loftus, E. F. (1975). A spreading-activation theory of semantic processing. Psychological Review, 82(6), 407–428.
  • Tononi, G. & Cirelli, C. (2003). Sleep and synaptic homeostasis: a hypothesis. Brain Research Bulletin, 62(2), 143–150.
  • Tononi, G. & Cirelli, C. (2014). Sleep and the price of plasticity: from synaptic and cellular homeostasis to memory consolidation and integration. Neuron, 81(1), 12–34.