Read the equation
The continuous state moves downhill on L − λV. Expanding the gradient gives −∇L + λ∇V when λ is independent of state. This is the continuous counterpart of the poster’s goal of balancing failure reduction and value seeking.
Its role in the build
The Megamind Equation Atlas
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
Read dX_t/dt as the quantity being defined or updated by this relation.
Uses a derivative or gradient to describe a rate of change or a direction of variation.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
The adjacent discrete rule scales only the loss term by η_t; a common Euler time step would scale the entire right-hand side. The two printed forms are retained separately rather than silently treating them as identical.
Original context
Read the surrounding source passage
The Megamind Equation Atlas: The continuous state moves downhill on L − λV. Expanding the gradient gives −∇L + λ∇V when λ is independent of state. This is the continuous counterpart of the poster’s goal of balancing failure reduction and value seeking. The Epona / Echad Equation: The continuous state moves downhill on L − λV. Expanding the gradient gives −∇L + λ∇V when λ is independent of state. This is the continuous counterpart of the poster’s goal of balancing failure reduction and value seeking.
Exact original notation
dX_t/dt = −∇ [ L(X_t) − λ V(X_t) ]
Related builds
Sources & provenance
dX_t/dt = −∇ [ L(X_t) − λ V(X_t) ]
dX_t/dt = −∇ [ L(X_t) − λ V(X_t) ]