Reward coding can preserve choice probabilities and change signed prediction errors in a model with equal rates, zero initial values, and zero decay targets

We proved a feedback code identity for a learning model with two actions. One rate controls chosen value learning, unchosen value decay, and the choice trace. Initial values and decay targets are zero in both codes. A change from feedback 0 and 1 to feedback -1 and 1 preserves every choice probability when the two choice coefficients and their domain are mapped. The signed reward prediction error also gains a term from the chosen choice trace. In OpenNeuro ds004295 version 1.0.0, all 46 task records from 23 people showed an error difference beyond a shift and scale. The choice probabilities agreed within 1.23e-15 across 12,880 trials. The median residual norm fraction after an affine error fit was 0.27718. Adding the chosen choice trace and an unmodulated feedback baseline gave equal linear design spaces. The largest checked full design gap was below 7.29e-15. This permits a coding invariant partial signed error test under a fixed error model. We did not analyze EEG voltage or establish a neural effect. The package provides the proof, audit tool, source bytes, hashes, fits, traces, validation, and repeat instructions.

reinforcement learning · reward prediction error · feedback coding · choice trace · model identifiability · linear design · OpenNeuro