func (g *EnergyGenerator) langevinStep(x []float64) []float64 · Langevin dynamics: x_new

Read the equation

This relation defines Langevin dynamics: x_new in the source section “func (g *EnergyGenerator) langevinStep(x []float64) []float64 · Langevin dynamics: x_new”. Takes a square root, requiring a nonnegative real radicand when interpreted over the reals. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read Langevin dynamics: x_new as the quantity being defined or updated by this relation.

2. Takes a square root, requiring a nonnegative real radicand when interpreted over the reals.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

// langevinStep performs one Langevin dynamics step
func (g *EnergyGenerator) langevinStep(x []float64) []float64 {
	grad := g.computeEnergyGradient(x)

	xNew := make([]float64, len(x))
	for i := range x {
		// Langevin dynamics: x_new = x - step_size * grad + sqrt(2 * step_size * temp) * noise
		noise := rand.NormFloat64()
		xNew[i] = x[i] - g.stepSize*grad[i] + math.Sqrt(2*g.stepSize*g.temperature)*noise
	}

	return xNew
}

// Forward performs forward pass (energy computation)
func (g *EnergyGenerator) Forward(input []float64) (*generators.GeneratorOutput, error) {
	state := g.GetState()

Langevin dynamics: x_new = x - step_size * grad + sqrt(2 * step_size * temp) * noise

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