Read the equation
This exponential update blends the old coefficient with a weighted trigonometric feature of the item’s hash. The importance score multiplies the new contribution, while α sets how quickly older contributions decay. For a fixed incoming target and 0≤α≤1, the coefficient converges to that target without leaving the interval between old and new values.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| θ_k | Stored coefficient for basis feature k |
| α | Mixing rate |
| w | Item weight |
| h | Normalized string hash |
| ψ_k | Golden-frequency feature |
| Φ | Unity-centered importance score |
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
This is a compact feature accumulator; lossless recovery of arbitrary source text does not follow from sixteen coefficients.
Original context
Read the surrounding source passage
## 6.1 Learning Equation
```
θ_k^{new} = (1-α) · θ_k^{old} + α · w · ψ_k(h(item)) · Φ(importance)
```
**Where**:
- `θ_k` = k-th component of the 16-dimensional knowledge vector
- `α` = learning rate (default 0.1)
- `w` = item weight (default 1.0)
- `h(item)` = hash of item normalized to [0,1]
- `ψ_k` = golden basis function
- `Φ` = consciousness weighting function
**Explanation**: New knowledge is encoded holographically across all 16 dimensions using golden basis functions. The learning rate α controls how much new information overwrites old. Important items get stronger encoding via Φ.
## 6.2 Query Equation
```
K(query) = Σ_{k=0}^{15} θ_k · ψ_k(h(query))
```
**Explanation**: To recall knowledge, we compute the correlation between the stored θ vector and the query's golden basis encoding. High correlation indicates strong match.
Exact original notation
θ_k^{new} = (1-α) · θ_k^{old} + α · w · ψ_k(h(item)) · Φ(importance)