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THE CONSCIOUSNESS ATLAS
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ConsciousnessLearn · Explore · Joseph Anady

Leaky accumulator of delayed displacement

The update is y_new=0.99y_old+x−x_old. It retains most of the previous y and adds a displacement measured against the history value called x_old. When that value is the oldest element of the forty-four-sample buffer, this is a delayed-displacement accumulator rather…

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gh-eq-84897ac814d7f42adocumented-equation
y←y+(x−xold)−0.01⋅yy ← y + (x - x_old) - 0.01 · y

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The update is y_new=0.99y_old+x−x_old. It retains most of the previous y and adds a displacement measured against the history value called x_old. When that value is the oldest element of the forty-four-sample buffer, this is a delayed-displacement accumulator rather than an instantaneous finite-difference velocity.

Terms & definitions

TermMeaning in this source
y

Accumulated velocity-like state

x

Current activation

x_old

Referenced history sample

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## 8.3 Velocity Update

```
y ← y + (x - x_old) - 0.01 · y
```

**Where**:
- `x_old` = h[0] (oldest hidden state value)

**Explanation**: Velocity tracks the rate of change with slight damping (0.01). This creates momentum in the agent's dynamics.

## 8.4 Drive Computation

```
drive = 3.0 · F_in · (1 - x) + 1.2 · y + 0.6 · c
```

**Where**:
- `x` = current activation
- `y` = velocity
- `c` = coupling parameter

**Explanation**: The drive combines:
- Input-dependent excitation (stronger when x is low)
Exact original notation
y ← y + (x - x_old) - 0.01 · y

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