(A–C) We simulate the output of each encoder to repeated cycles of the probe environment. In the case of discretization (panel A), we use a simple entropy coding procedure to map optimal response levels onto spike patterns, as shown by the spike rasters. In the case of temporal filtering (panel B) and stimulus selection (panel C), we measure properties of the response . When encodings are optimized for inference (dark blue traces), abrupt changes in the mean of the stimulus distribution (panels A-C, left) are followed by transient increases in spike rate (discretization, panel A) and response variability (filtering, panel B; stimulus selection, panel C). In the case of temporal filtering, these changes are additionally marked by decreases in the temporal correlation of the response. In contrast, the response properties of encoders optimized for stimulus reconstruction (light green traces) remain more constant over time. Abrupt changes in variance (panels A-C, right) are marked by changes in baseline response properties. Responses show transient deviations away from baseline when encodings are optimized for inference, but remain fixed at baseline when encodings are optimized for reconstruction. In all cases, encodings optimized for inference maintain lower baseline firing rates, lower baseline variability, and higher baseline correlation than encodings optimized for stimulus reconstruction. Spike rates (panel A) are averaged over 500 cycles of the probe environment. Response variability (panels B-C) is computed at each timepoint across 800 cycles of the probe environment. Temporal correlation (panel B) is computed between consecutive timepoints across 800 cycles of the probe environment. (D–E) Encoding schemes impact both the accuracy (panel D) and speed (panel E) of inference. In all cases, the dynamics of inference are symmetric for changes in mean (points lie along the diagonal) but asymmetric for changes in variance (points lie off the diagonal). Encodings decrease the accuracy of estimating high-variance states (panel D), and they alter the speed of responding to changes in both mean and variance. The response to upward versus downward switches (dotted box) separates encoding schemes based on whether they are faster (right of dotted vertical line) or slower (left of dotted vertical line) to respond to increases versus decreases in variance. Speed and accuracy are measured from the trial-averaged trajectories of shown in Figure 3E, Figure 4D (), and Figure 5C () (Materials and methods).