A dynamical attractor computes reward prediction in the basal forebrain
Phasic ensemble bursting in subcortical neuromodulatory systems such as the basal forebrain (BF) provides a powerful format for broadcasting reward-prediction signals. These bursts encode reward prediction by varying population amplitude, yet their internal structure, reflected in cell-to-cell amplitude relationships, remains conserved. How neural circuits reconcile these competing constraints remains unknown. Here we show that BF bursting is generated by a dynamical attractor: burst structure is imposed not by feedforward inputs but by recurrent circuit dynamics, while burst amplitude is determined by approximately linear integration across concurrent inputs. Optogenetic activation of BF neurons expressing natriuretic peptide receptor 3 (Npr3) outside the behavioral task reproduced the low-dimensional dynamics of natural cue-evoked bursting, preserving the temporal envelope and cell-to-cell amplitude relationships across stimulation patterns. Critically, unilateral activation of non-overlapping Npr3 populations in either hemisphere recruited the full bilateral ensemble into the same native trajectory, showing that restricted inputs can nevertheless recruit the full ensemble. Matched ipsilateral and contralateral onset latencies exceeding 25 ms implicated recurrent interactions beyond the BF. Despite the conserved structure, population burst amplitude varied with stimulation strength and summed approximately linearly across concurrent unilateral inputs. This linear summation extended to natural sensory input during behavior: adding Npr3 stimulation to auditory cues increased cue-evoked burst amplitude, improved detection, and reduced subsequent reward responses, consistent with stronger reward prediction producing smaller reward prediction errors. Thus, a low-dimensional dynamical attractor preserves a shared BF burst structure across diverse inputs while integrating concurrent inputs into a scalar burst amplitude that encodes reward prediction.