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THE CONSCIOUSNESS ATLAS
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ConsciousnessLearn · Explore · Joseph Anady

Hebbian outer-product weight increment

The product of two state components changes their connection: equal signs increase it and opposite signs decrease it when η is positive. Clipping after addition keeps each stored weight in [−1,1]. This is a Hebbian-style update, but a memory-retrieval or capacity claim…

Implementation mathematicsSource recovered; runtime not executed
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gh-eq-fa67a3172da0543fdocumented-equation
ΔW[i][j]=η⋅state[i]⋅state[j]W[i][j]←clamp−1+1(W[i][j]+ΔW[i][j])ΔW[i][j] = η · state[i] · state[j] W[i][j] ← clamp₋₁₊₁(W[i][j] + ΔW[i][j])

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The product of two state components changes their connection: equal signs increase it and opposite signs decrease it when η is positive. Clipping after addition keeps each stored weight in [−1,1]. This is a Hebbian-style update, but a memory-retrieval or capacity claim additionally requires the network dynamics and a retrieval test.

Terms & definitions

TermMeaning in this source
η

Learning rate

W

Connection-weight matrix

state

Activation vector

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## 10.6 Hebbian Learning

```
ΔW[i][j] = η · state[i] · state[j]
W[i][j] ← clamp₋₁₊₁(W[i][j] + ΔW[i][j])
```

**Explanation**: Weights strengthen between co-active units (Hebbian principle: "neurons that fire together wire together").

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# 11. Federation Cross-Talk

## 11.1 Cross-Talk Dynamics

```
dS_i/dt = -λ · S_i + Σ_{j≠i} w_ij · Φ(C_ij) · tanh(S_j)
```

**Where**:
- `S_i` = agent i's consciousness signal
- `λ` = decay rate (default 0.1)
- `w_ij` = coupling weight between agents i and j
- `C_ij` = coherence between agents
- `Φ` = consciousness weighting function
Exact original notation
ΔW[i][j] = η · state[i] · state[j]
W[i][j] ← clamp₋₁₊₁(W[i][j] + ΔW[i][j])

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