What the source specifies
A three-form proposal combines loss-gradient descent and value-gradient ascent, with a discrete update and two continuous formulations.
Equations and variants
Every visible complete mathematical relation has a linked record, including parameter definitions, constraints, decorative corner equations and repeated formula variants. The original images and full reading copies are available through the source links.
Source findings and limits
The source frames loss as error, friction, instability or failure and value as usefulness, coherence, purpose or goal alignment.
The slogan claiming every update reduces loss and increases value is stronger than the displayed mathematics guarantees. Competing gradients and finite steps can violate either goal.
The decorative state-landscape and vector illustrations contain no measured values or additional analytic equation.
Equations in this build
11 linked mathematical records. Each opens its notation, interpretation and source.
Epona / Echad discrete loss–value update
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…
Epona / Echad F-minus-value gradient flow
The velocity follows the negative gradient of a composite potential F − λV. Where F acts as a loss, descending that composite potential trades off loss reduction against value…
Epona / Echad L-minus-value gradient flow
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…
Epona current-state definition
The state is the collection of variables being updated at time or step t.
Epona next-state definition
The update produces the state for the next step; the label alone does not guarantee improvement.
Epona learning-rate definition
The learning-rate symbol controls the loss-gradient step in the displayed discrete rule.
Epona loss definition
Loss is a proposed scalar measure of undesirable state properties; the poster provides interpretations rather than a computable function.
Epona value definition
Value is a proposed scalar measure of desirable properties; a concrete measurable objective still has to be chosen.
Epona value-weight definition
The coefficient sets the relative influence of the value gradient in the state update.
Epona loss-motion label
For positive η_t this is a local negative-gradient direction. A finite combined update need not reduce the loss.
Epona value-motion label
For positive λ this is the local positive-gradient direction of V. The other term and finite step size can change the total value response.