🧬 Show & Tell — Phase 34.3 SynapticPlasticityEngine: Dynamic Synaptic Learning

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🧬 Phase 34.3 — SynapticPlasticityEngine

The SynapticPlasticityEngine brings biologically-grounded learning to our neuromorphic stack. Instead of backpropagation, synapses learn from the precise timing of spikes — strengthening when pre-synaptic activity predicts post-synaptic firing, and weakening otherwise.

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STDP Learning Window

The core of Hebbian learning in spiking networks:

Weight Change (Δw)
         ▲
    A⁺   │    ╲
         │     ╲  LTP (potentiation)
         │      ╲  pre fires → then post fires
         │       ╲
         │        ╲
─────────┼─────────╲──────────────── Δt = t_post - t_pre
        ╱│         0
       ╱ │
      ╱  │
     ╱   │  LTD (depression)
    ╱    │  post fires → then pre fires
   ╱     │
  ╱  -A⁻ │
         ▼

  Δw = A⁺·exp(-Δt/τ⁺)  if Δt > 0  (causal → strengthen)
  Δw = -A⁻·exp(Δt/τ⁻)  if Δt < 0  (anti-causal → weaken)

When the pre-synaptic neuron fires before the post-synaptic neuron (positive Δt), the synapse is strengthened (LTP). When the order is reversed, the synapse is weakened (LTD). The magnitude decays exponentially with the time difference.

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Plasticity Hierarchy

Multiple plasticity mechanisms operate at different timescales:

┌─────────────────────────────────────────────────────────────────┐
│                    PLASTICITY HIERARCHY                         │
├─────────────────────────────────────────────────────────────────┤
│                                                                 │
│  Milliseconds          Seconds           Minutes → Hours        │
│  ┌──────────┐    ┌───────────────┐    ┌──────────────────┐     │
│  │ Short-   │    │   Long-Term   │    │   Homeostatic    │     │
│  │ Term     │───▶│   Plasticity  │───▶│   Regulation     │     │
│  │ (STP)    │    │   (STDP)      │    │   (Scaling)      │     │
│  └──────────┘    └───────────────┘    └──────────────────┘     │
│       │                  │                     │                │
│   Facilitation      Weight change         Rate stability       │
│   Depression        Trace update          Excitability adj     │
│                          │                     │                │
│                    ┌─────▼─────┐         ┌─────▼─────┐         │
│                    │ Reward    │         │ Structural │         │
│                    │ Modulated │         │ Plasticity │         │
│                    │ (R-STDP)  │         │ (Pruning/  │         │
│                    │           │         │  Growth)   │         │
│                    └───────────┘         └───────────┘         │
│                    Hours                  Days → Weeks          │
└─────────────────────────────────────────────────────────────────┘

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Reward-Modulated STDP Flow

Three-factor learning for reinforcement learning in SNNs:

 Pre-synaptic          Post-synaptic         Reward
 Spike Train           Spike Train           Signal
     │                      │                  │
     ▼                      ▼                  │
 ┌───────┐             ┌───────┐               │
 │ Pre   │             │ Post  │               │
 │ Trace │             │ Trace │               │
 │ r₁(t) │             │ o₁(t) │               │
 └───┬───┘             └───┬───┘               │
     │                      │                  │
     └──────────┬───────────┘                  │
                │                              │
                ▼                              │
        ┌───────────────┐                      │
        │ STDP Kernel   │                      │
        │               │                      │
        │ e(t) += STDP  │   Eligibility        │
        │ e(t) *= decay │   Trace              │
        └───────┬───────┘                      │
                │                              │
                ▼                              ▼
        ┌─────────────────────────────────────────┐
        │         THREE-FACTOR RULE                │
        │                                         │
        │   Δw = η · e(t) · r(t)                 │
        │                                         │
        │   eligibility × reward = weight change  │
        └─────────────────────────────────────────┘

The eligibility trace e(t) accumulates STDP-like correlations but doesn't directly modify weights. Only when a reward signal r(t) arrives does learning occur — enabling credit assignment over temporal delays.

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Homeostatic Regulation Cycle

Negative feedback loop maintaining network stability:

    Target Rate (r*)
         │
         ▼
    ┌─────────┐     rate error      ┌──────────────┐
    │ Compare │────────────────────▶│   Compute    │
    │ r* vs r │     (r - r*)/r*    │   Scaling    │
    └─────────┘                    │   Factor s   │
         ▲                         └──────┬───────┘
         │                                │
         │                                ▼
    ┌─────────┐                    ┌──────────────┐
    │ Measure │◀───────────────────│   Scale All  │
    │ Firing  │    new weights     │   Incoming   │
    │ Rate r  │                    │   Weights    │
    └─────────┘                    │   w *= s     │
                                   └──────────────┘

    If r > r*  →  s < 1  →  weights decrease  →  rate drops
    If r < r*  →  s > 1  →  weights increase  →  rate rises
    
    Converges to: r ≈ r* ± 5% within τ_homeo

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Structural Plasticity

Networks aren't just about changing weights — they rewire:

    BEFORE                          AFTER
    ┌───┐    0.52    ┌───┐         ┌───┐    0.52    ┌───┐
    │ A │───────────▶│ C │         │ A │───────────▶│ C │
    └───┘            └───┘         └───┘            └───┘
      │  ╲             ▲             │                ▲
      │   ╲ 0.003      │ 0.48       │                │ 0.48
      │    ╲           │             │                │
      │     ▼        ┌───┐          │     ╳        ┌───┐
      │    ┌───┐     │ E │         │   PRUNED     │ E │
      │    │ D │     └───┘         │              └───┘
      │    └───┘       ▲           │                ▲
      │                │           │       0.001    │
      │   0.001        │           ▼      (NEW)     │
      ▼               ┌───┐       ┌───┐ ──────────▶┌───┐
    ┌───┐             │ B │       │ F │   GROWN    │ B │
    │ F │             └───┘       └───┘            └───┘
    └───┘                        
                                 
    A→D pruned (w=0.003 < θ=0.01, age > maturation)
    F→B grown (B below target connectivity, F highly active)

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Comparison of Plasticity Rules

Rule	Window	Order	Factors	Best For	Reference
Asymmetric STDP	Exponential	Causal (pre→post)	2 (pre, post)	Temporal sequence learning	Bi & Poo 1998
Symmetric STDP	Gaussian	Non-causal	2	Coincidence detection	—
Triplet STDP	Exponential + slow traces	Causal	2 + frequency	Rate-coded patterns	Pfister & Gerstner 2006
R-STDP	Exponential + eligibility	Causal	3 (pre, post, reward)	Reinforcement learning	Frémaux & Gerstner 2016
BCM	Rate-based threshold	N/A	2 + sliding θ	Selectivity development	Bienenstock et al. 1982
Homeostatic	N/A (global scaling)	N/A	1 (rate)	Stability maintenance	Turrigiano 2008

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Open Questions

1. Metaplasticity: Should we implement the BCM sliding threshold as a meta-learning rule that modulates STDP parameters over time?
2. Dendritic computation: Should structural plasticity distinguish between proximal and distal synapses on dendritic branches?
3. Neuromodulation: Beyond dopamine (reward), should we model serotonin (mood/exploration) and acetylcholine (attention) as separate modulatory channels?
4. Spike-frequency adaptation: How should intrinsic excitability changes interact with the STP model from SpikingNeuronModel (34.1)?
5. Scaling to large networks: At what network size should we switch from all-to-all STDP pairing to nearest-neighbor spike pairing?

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Spec: #708 · Depends on: SpikingNeuronModel (34.1), EventDrivenProcessor (34.2)