State-change cost using two norms

Read the equation

The first term measures average absolute component change and the second measures the sum of squared changes. With positive coefficients, both are nonnegative. For a fixed total absolute change, the squared term penalizes concentrating that change in a few large components more than spreading it evenly.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

• The division by 16 presumes the intended sixteen-component subset.

Original context

## 5.2 Surprise Component

```
Surprise = α₁ · ||ΔΨ||₁/16 + α₂ · ||ΔΨ||₂²
```

**Where**:
- `||ΔΨ||₁` = L1 norm (sum of absolute differences)
- `||ΔΨ||₂²` = squared L2 norm
- `α₁, α₂` = weighting coefficients (default 0.5 each)

**Explanation**: Surprise measures how much the state changed. L1 captures sparse, large changes; L2 captures distributed changes.

## 5.3 Uncertainty Component

```
Uncertainty = 1 - b²
```

**Where**:
- `b` = normalization factor

**Explanation**: When the state vector is large (high activity), b is small, so uncertainty is high. Calm, focused states have low uncertainty.

Surprise = α₁ · ||ΔΨ||₁/16 + α₂ · ||ΔΨ||₂²

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