(a) Network model composed of a sensory circuit (MT) with two opposite stimulus-selective excitatory populations E1 and E2 that are coupled to two choice-associated populations D1 and D2 in an integration circuit (for example, LIP, FEF). There are feedforward and top-down feedback connections (strength b_FB) between the two circuits as well as lateral excitatory and inhibitory (population I) recurrent connections within each circuit (connections are represented by lines with a width proportional to the synaptic efficacy and connection probability). The stimulus is modelled as time-varying input currents to neurons in E1 and E2 (red and blue traces show two examples, s.d. σ) mimicking temporal variations in the momentary sensory evidence in favour of one or the opposite direction of motion of an RDK. In addition, sensory neurons receive shared external background Poisson inputs (population X) and decision neurons non-shared Poisson inputs (not shown). (b) Response of the network to an example zero-coherence stimulus (σ=1). Bottom traces show the population-averaged stimulus currents into E1 and E2. Rastergrams show the spiking activity of neurons in E1 and E2 (middle, 800+800 neurons) and in D1 and D2 (top, 240+240 neurons), sorted by rate. Traces below the rastergrams show the corresponding instantaneous population rates (count window T=50 ms). Top-down connections were set to zero (b_FB=0).

(a–c) Network without top-down connections receiving non-replicate zero-coherence stimuli that cause bottom-up correlations (see Methods and ; b_FB=0, σ=1). Average population rates for trials yielding the preferred (red) and the non-preferred choice (blue) for the integration and sensory circuits (a). Time-courses of the average CP (b; count window T=100 ms) and average spike count noise correlations (c; T=250 ms) of sensory neurons. Correlations are shown for pairs of excitatory neurons within (EiEi, pink) and across sensory populations (EiEj, cyan), and of all pairs (EE, black). Average CP, obtained when bottom-up correlations are generated by local background inputs and replicate stimuli, is shown for comparison (grey trace in b; see for details). Upper inset: after stimulus onset, the dynamics of the integration circuit is described by a double-well energy landscape where each minimum corresponds to a choice attractor. When approaching one of the attractors, the impact of sensory activity fluctuations on the state of the integration circuit decreases. (d–f) Same as a–c but using a network with top-down connections (b_FB=1, σ=1). We eliminated bottom-up correlations by using replicate stimuli and global background inputs (Methods). The rates and CP obtained without top-down connections are shown for comparison (dotted lines in d and e). Upper inset: the stability of the choice attractor is increased (represented by an increase in well depth) due to the bottom-up/top-down loop dynamics. Shaded areas represent the stimulus interval.

(a) CP obtained in the network with top-down connections receiving non-replicate stimuli (σ=1, b_FB=1; black) is sustained throughout the stimulus interval (shading). Two complementary contributions to CP are revealed by using replicate stimuli, thus removing bottom-up correlations (green) or by removing the top-down connections (b_FB=0; blue). (b) Psychophysical kernel for the three cases illustrated in a. The ‘integration window’ (dark shading) is defined as the interval containing 85% of the kernel’s total area. (c) Same as a, for a network with slower decision dynamics (Methods). Despite the longer integration window (dark shading), the CP of the combined condition remains approximately invariant (black). (d) CP and correlations in a network with top-down connections in which bottom-up correlations are produced by both trial-to-trial stimulus fluctuations and local background inputs (see ). Using replicate stimuli (grey trace) removes part of the bottom-up contribution to CP and correlations. In addition, making the background inputs global isolates the contribution of top-down connections (green). Count windows were T=100 ms.

Left panels show the time-course of the spike count Fano factor (a), spike count correlation (b) and CP (c) obtained from responses to non-replicate and replicate stimuli using adjusted count windows T=250 ms (a,c) and 100 ms (b). The duration of the sliding count window was adjusted to equalize the mean spike count in all time points (Methods). Fano factor and CP are population averages using only zero-coherence trials (replicate: n=41 neurons and 41 different RDKs; non-replicate: n=118 neurons and 7,733 different RDKs). Correlation was obtained for a single neuronal pair (emu035; shows the correlation of a second pair), averaging over coherences (range: 0–51.2%, Methods). Centre panels show time-averages obtained from the entire stimulus interval for the Fano factor and correlations (P<0.001; permutation tests), and separately for early (0-1 s; P=0.02, permutation test) and late epochs (1-2 s; P=0.63, permutation test) for the CP. Right panels show the dependence on the window size, using non-overlapping windows of fixed duration T. Error bars indicate s.e.m. Thick horizontal lines mark periods of significant difference between the non-replicate and the replicate conditions (P<0.05, permutation test).

(a,b) Individual CP traces of four example cells (a) and CP correlation matrix C(t_i, t_j) (b) obtained from the homogeneous network (same network as used in , , ; CP estimated from 2,000 trials, count window T=250 ms). Top inset: each dot is the individual CP of one neuron computed in two time bins t_i and t_j and C(t_i, t_j) is the rank correlation coefficient across all neurons (Methods). The values shown correspond to the time bins shaded in a and marked with a white square in b. Coloured dots correspond to the four cells shown in a. (b) CP correlation matrix C(t_i, t_j) shows uniformly high values capturing the maintenance of the sorting of individual CPs across time. Right: Time-course of adjacent CP correlations C(t_i, t_i+1) (red diagonal in b) where CPs were estimated from 100 trials to compare with data. The solid line shows a linear fit. Increased number of trials increased the correlation values but did not change the results qualitatively (). (c,d) Same as a,b, for the heterogeneous network (Methods). The individual CP traces are from representative neurons belonging to four different groups depending on whether they receive stimulus and/or top-down inputs (see Methods and ). The matrix C(t_i, t_j) shows an elevated plateau towards stimulus offset reflecting late increased stability in individual CPs. (e,f) Same as a,b, for the MT data (n=143 neurons; variable trial numbers, range: 25–221, median: 59) recorded in the non-replicate condition (see for replicate condition). Error bars indicate the s.e.m. Dotted lines in e indicate windows straddling stimulus onset or offset.

(a–c) Spike count correlations obtained from neuron pairs in the homogeneous network with bottom-up correlations but no top-down inputs (a), with top-down inputs and no bottom-up correlations (b), and in the heterogeneous network with both top-down inputs and bottom-up correlations (c). The matrix entries ρ(t_i, t_j) are correlation coefficients of the spike counts in time bins t_i and t_j (count window T=250 ms) averaged over cell pairs. Insets: correlations ρ(t_i, t_j) versus time lag t_i−t_j from two instants of the stimulus interval (dashed diagonals in a). Bottom-up correlations were generated by non-replicate stimuli. (d,e) Time-course of correlations in the full model (c) shows large amplitude sustained instantaneous correlations (d; main diagonal in c), caused mainly by stimulus fluctuations (see a), and slowly rising lagged correlations (e, blue dashed diagonal in c), caused by top-down inputs (see b). (f,g) MT correlations (n=32 neuron pairs at coherences −3.2, 0, +3.2%) show similar time-courses as the model: instantaneous correlations (f) do not change significantly over time whereas lagged correlations (g) increase significantly (regression line slopes −0.0092, s⁻¹ and 0.018 s⁻¹, with P=0.718 and P=0.046, respectively; permutation tests). The weak non-monotonic trend of the instantaneous correlations (fast-rise + slow-decay) shown in f can be partly due to the similar trend displayed by the evoked rate (not shown). (h) Slopes of lagged correlations ρ_kk'(t_i, t_i+1) for individual MT pairs versus the mean late CP of the two corresponding neurons (correlation R=0.27, P=0.02). (i) Average early and late CP for pairs with positive (red) and negative (black) slopes of lagged correlations (early: 0–1 s, late: 1–2 s; T=1,000 ms). (j) Average CP time-course for cell pairs showing rising (black) and decaying (red) lagged correlations (T=250 ms). Error bars indicate s.e.m. Thick horizontal lines mark periods of significant difference (P<0.05, permutation test).

(a,b) Spike rastergram and population rates of the decision populations D1 and D2 (240+240 neurons) during an example trial for the network without (a) and with (b) top-down connections (b_FB=0 and b_FB=4, respectively). The same zero-coherence stimulus (c) with large temporal modulation (σ=2.7) caused population D1 to initially cross the arbitrary categorical bound in both cases (dotted line). A large fluctuation (arrow) reversed the state in the network without top-down (a, reversal trial) but not in the network with top-down connections (b). (c) Population-averaged stimulus currents into sensory E1 neurons (red) and E2 neurons (blue). (d) Percentage of reversal trials (solid) and no-bound-crossing trials (dotted) versus value of the non-absorbing bound for different top-down strengths (see inset). (e) Distribution of the population rate difference D1−D2 averaged over the second half of the stimulus interval (1-2 s) for trials in which the choice was ‘1’. Stronger top-down inputs increased the differences in rate and led to fewer trials with rate difference close to zero (weak-confidence trials). (f) Psychophysical kernel shows that the integration window (interval containing 85% of the total area under the kernel; triangles) shortens with increasing top-down strength. (g) Percentage of correct choices as a function of stimulus coherence. Simulation data (squares) were fitted using a Weibull function (solid lines). (h) As the top-down strength decreases, the discrimination threshold, defined as the coherence yielding 82% of correct trials, decreases as one over the square root of the integration window length (solid line is a fit of slope of −0.5 in the log-log graph). The network performance is only slightly worse than the perfect integration of evidence during the integration window (dotted line). Different colours represent top-down strengths (b_FB=0, 1.5, 3, 4.5 and 6).