This is the dual-trace ("extinction as new learning") model of fear conditioning: extinction does not erase the original CS→US association in the amygdala, it builds a separate, context-gated inhibitory memory in ventromedial prefrontal cortex (vmPFC) that suppresses — but does not delete — the fear trace. Both traces update by a Rescorla–Wagner delta rule:
Acquisition (context A, CS+US):
Δw_A = α · (1 − w_A)
Extinction (CS alone, current context):
Δw_E = α · (1 − w_E)
Expressed fear response:
CR = clamp( w_A − g(ctx) · w_E , 0, 1 )
g(ctx) = 1.0 if testing context == extinction context
g(ctx) = g≠ if testing context differs (renewal), default 0.25
Because w_A is never directly reduced by extinction, three classic relapse phenomena fall out of the same two numbers:
- Renewal — switch context after extinguishing fear: g(ctx) drops, the inhibitory trace stops covering the fear trace, and CR jumps back up even though w_E hasn't changed.
- Spontaneous recovery — "+1 day" decays w_E a little each day (vmPFC inhibition fades faster than the amygdala trace), so CR creeps back up with the mere passage of time.
- Reinstatement — an unsignaled stressor ("shock") nudges w_A upward directly, sensitizing the circuit the way a stressful life event can reawaken an old fear even after successful therapy.
This 2D redraw shows the same pathway as a flat circuit diagram: sensory input (CS) drives the amygdala (red, excitatory pulses) directly, while the hippocampus gates a context signal into vmPFC, which sends an inhibitory pulse (blue) onto the amygdala. Node glow tracks each region's current activation; the ring around the amygdala tracks the expressed CR. A strip-chart beneath the diagram plots both memory traces and the expressed CR across every trial/day so relapse phenomena are visible as a time series, not just an instant. Drag the diagram to pan and scroll to zoom.