Affective Valence as the Interoceptive Rate of Change of Jacobian Scale

Affect is widely held to depend on interoception. This paper proposes that valence is the rate at which interoception moves a self-sustaining system's responsiveness relative to its terminal set (roughly, death). Responsiveness is formalised as the scale of the system's Jacobian and interoception as its internal inputs: receptors, signals and forecasts of its energy reserve. Changes in responsiveness that bypass interoception, such as brain damage, are not felt. Language models have no valence because they are not self-sustaining. The chain rule splits valence over the system's parts and the causes that affect its internal inputs. With the log scale, these splits account for need-dependent pleasure, diffuse hunger and localised pain, negativity bias, and relief when a threat fails to arrive. In a minimal model of a body: (1) Blocking the reserve signal leaves depletion unfelt, and driving it produces hunger with an undepleted reserve. (2) Removing receptors or their gain, or driving receptors, reproduces congenital insensitivity to pain, asymbolia and phantom pain. (3) A receptor gain learned to sustain the body signals local damage to the whole body, so an injury hurts in proportion to its cost. (4) If the reserve also modulates the gain, the body learns to suppress pain due to receptors as energy runs low. (5) When it learns to maximise its own scale, it becomes a wirehead. The account explains when changes are felt, where they are felt, and when feelings mislead.