Epona / Echad discrete loss–value update

Read the equation

The next state combines a step opposite the loss gradient with a step in the direction of the value gradient. The learning rate η_t scales the loss term, while λ independently scales the value term in this printed discrete formula. These two directions can conflict, so reducing loss and increasing value on every update is not guaranteed.

Its role in the build

The Megamind Equation Atlas

Terms & definitions

How it works

1. Read X_{t+1} as the quantity being defined or updated by this relation.

2. Uses a derivative or gradient to describe a rate of change or a direction of variation.

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

Assumptions & limits

• Differentiable loss and value functions, compatible state coordinates and suitable step sizes are required. An Euler step for the adjacent continuous gradient flow would multiply both gradient terms by the time step; equivalence requires a stated rescaling of λ.

Original context

The Megamind Equation Atlas: The next state combines a step opposite the loss gradient with a step in the direction of the value gradient. The learning rate η_t scales the loss term, while λ independently scales the value term in this printed discrete formula. These two directions can conflict, so reducing loss and increasing value on every update is not guaranteed.

The Epona / Echad Equation: The next state combines a step opposite the loss gradient with a step in the direction of the value gradient. The learning rate η_t scales the loss term, while λ independently scales the value term in this printed discrete formula. These two directions can conflict, so reducing loss and increasing value on every update is not guaranteed.

X_{t+1} = X_t − η_t ∇L(X_t) + λ ∇V(X_t)

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