Fig. 4: Increased stimulation shapes a steadier attractor in neural space.

a Trial-averaged cortex neuron response under increased nucleus stimulation. b Histogram of the post-stimuli response of all neurons. c The post-stimulation response correlation. Inner- and inter-amplitude correlations are shown in the matrix. d Quantification of populational variability changes with the increase of external stimuli amplitude. A linear regression is performed between the stimulation amplitude and the log of trial variance. In model results, each color stands for a random initialization of the connectivity matrix; in empirical results, each color stands for a mouse. e Relationship between the populational variability and the input neuron size. In empirical data, we calculated the significantly tuned (the top and bottom 20% of the z-scored fluorescence change) neuron proportion as the x-axis. Colors have the same meanings as in (d). f Neural space trajectory visualized on the first and second multidimensional scaling (MDS) components of neural populations. The start and end of stimuli are marked by black and red-filled circles, respectively. Stronger input brings a higher trial consistency and longer traverse in neural space. The upper line shows the empirical results, and the bottom line shows the model-simulated result. g The time-dependent correlation change. The start and end of stimulation are marked by black and red dashed lines, respectively. The empirical result (upper) and the model result (down) are shown. The solid line shows the mean value. The shading represents ± SEM, n = 4 mice. h The time-dependent variability of neural population. The start and end of stimulation are shown in the same way as in (g). The solid line shows the mean value. The shading represents ± SEM. n = 4 mice. i Time-dependent variability with finer-grained amplitude change (left). The time constant of attractor formation (middle) and disappearance (right) with randomized network connectivity (box plotted). The box bounds show the upper and lower quartiles of the distribution. The centered line shows the median. The whiskers show the maximum and minimum. Dots are outliers. n = 20 repeated runs with different initialized connections are conducted. j Visualization of the energy landscape of the neural system in 3D space. Neural activities are projected into a 2D space in a monotonic manner. The height of the landscape represents the energy, which is approximated by the dynamic velocity of each point in the neural space. Each dotted black line is a neural trajectory of one experiment trial. A deeper energy well emerges when the amplitude of external input or the number of input neurons increases. Source data are provided as a Source Data file.