Extended Data Fig. 9: Decision-making models validate the combined effect of noise and rate signal.

For both models, we postulated multiple normal subpopulation (a) or multiple DDM neurons (b) converging to a “post-synaptic” neuron/region that is activated by either of the inputs (see methods, [equation 2]). (a) An illustration of the ‘normal’ model: example distributions of the sum of FR of k identically and independently distributed (i.i.d) neurons with similar mean FR and high standard deviation (σ_L, orange) or low standard deviation (σ_G, blue). The probability of random crossing of a threshold (dashed black line) under the noisier distribution (high standard deviation, σ_L) is larger than under the less noisy distribution (quantified by the red and green filled areas, respectively). See methods under normal model. (b) An illustration of the DDM model (with μ = 1, σ = 2.3, see methods). Crossing the positive boundary (green and yellow traces) was modelled as exploitation and crossing the negative one (orange trace) was modelled as exploration. (c) The probability of exploration increases with the noise level (σ) in both models. (d) The ratio of the noise levels (\(\frac{{\sigma }_{L}}{{\sigma }_{G}}\), y axis, see methods [equations 1,3]) that is associated with the average probability of exploration experimentally observed in the loss \(({p}_{{loss}}=0.25)\) and gain \(({p}_{{gain}}=0.06)\) as a function of n subpopulations (Gaussian model) or n neurons (DDM). The ratio decreases and reaches a plateau with n. Notice that in this framework and for equal mean exploitation signal, the ratio between standard deviations of models with equal probabilities only depends on the probabilities in each condition. Similarly, the ratio between EE signals can be described in terms of the probabilities and standard deviations in each condition. (e) Noise-level ratio \(\left(\frac{{\sigma }_{L}}{{\sigma }_{G}}{colormap}\right)\) for different exploration rates in the loss and gain conditions, assuming equal signal strength and a large enough subpopulation. White dots mark the actual choice probabilities of single participants. White cross marks the mean and SE across our participants, overlaid by 2D kernel density contours. Black dots mark the expected choice probabilities for the experimentally measured noise ratio in amygdala neurons (the 75^th percentile, see methods). Shown for both models (DDM also shown in main Fig. 5l). The noise-level \(\left(\frac{{\sigma }_{L}}{{\sigma }_{G}}\right)\) is computed from the CV. (f) Same as (e) but with the noise-level \(\left(\frac{{\sigma }_{L}}{{\sigma }_{G}}\right)\) computed from the std(ISI) instead of the CV. Notice that in all four cases (e,f), the participants’ mean behaviour (white cross) closely matches the expected behaviour from the models when using the noise levels measured in amygdala neurons (black dots).