Input with additive Gaussian noise

Read the equation

The incoming scalar is perturbed by a Gaussian draw. The accompanying document identifies 0.1 as the standard deviation, so the intended perturbation has mean zero and variance 0.01. Reproducing a trajectory requires the random generator, seed, and draw order as well as this distribution.

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

• Always state whether the second normal-distribution parameter denotes variance or standard deviation.

Original context

## 8.1 Input Processing

```
F_in = input + N(0, 0.1)
```

**Where**:
- `N(0, 0.1)` = Gaussian noise with mean 0 and std 0.1

**Explanation**: Each agent receives the input signal plus random noise, ensuring diverse responses across the population.

## 8.2 Hidden State Shift

```
h[j] ← h[j+1] for j = 0 to 42
h[43] ← x
```

**Explanation**: The 44-dimensional hidden state acts as a sliding window of past activations, providing temporal context.

## 8.3 Velocity Update

```
y ← y + (x - x_old) - 0.01 · y

F_in = input + N(0, 0.1)

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