Psychophysical tasks and performance of human subjects.

A. Illustration of the 2AFC and 3AFC tasks. B. Motion speeds of visual stimuli. The speeds of two stimulus components were plotted versus the log mean speed of each bi-speed stimulus. C. Discriminability of four human subjects performing a standard 2AFC task. Letters are coded symbols for individul subjects. D. In the 3AFC task, the percentage of trials that human subjects reported “no two-speeds”. E. Discriminability of the same subjects performing the 3AFC task. B1-E1. X4 speed separation. B2-E2. X2 speed separation. Each color represents data from one subject. The solid line shows the subject-averaged result. Error bars and error bands represent ±STE.

Monkey psychophysics.

A. Behavioral task and visual stimuli. B. Discriminability of a monkey subject performing a 2AFC task. B1. X4 speed separation. B2. X2 speed separation. Error bars and error bands represent ±STE.

Speed tuning curves of four example neurons to bi-speed stimuli and constituent single-speed components.

A. Illustration of the visual stimuli and the response tuning curves of an example neuron. Green and blue dots in the diagram indicate two overlapping achromatic random-dot patterns moving in the same direction at different speeds. Colors are used for illustration purposes only. The abscissas in green and blue show the speeds of the slower and faster components, respectively. The abscissa in black shows the log mean speed of the two speed components. A-D. Four example neurons are sorted by their preferred speeds (PS) from slow to fast. Error bars represent ±STE. For some data points, error bars were comparable to the symbol size. A1-D1. X4 speed separation. A2-D2. X2 speed separation.

Population-averaged speed tuning curves to bi-speed stimuli and constituent single-speed components.

Speed tuning curves averaged across A. 100 neurons in our dataset. B. 10 neurons that had PS lower than 2.5°/s. C. 61 neurons that had PS between 2.5 and 25°/s. D. 29 neurons that had PS greater than 25°/s. Error bars represent ±STE. For some data points, error bars were comparable to the symbol size. A1-D1. X4 speed separation. A2-D2. X2 speed separation.

Response weight for faster component based on linear regression (N = 100)

Relationship between the responses to the bi-speed stimuli and the constituent stimulus components.

A-E. Each panel shows the responses from 100 neurons. Each dot represents the response from one neuron. The ordinate shows the difference between the responses to a bi-speed stimulus and the slower component (R - Rs). The abscissa shows the difference between the responses to the faster and slower components (Rf - Rs). The regression line is shown in red. F. Response weights for the faster stimulus component obtained from the slope of the linear regression based on the recorded responses of 100 neurons (black symbols), and based on simulated responses to the bi-speed stimuli (gray symbols). Error bars represent 95% confidence intervals. A1-F1. X4 speed separation. A2-F2. X2 speed separation.

Timecourse of MT responses averaged across neurons to bi-speed stimuli.

Peristimulus time histograms (PSTHs) were averaged across 100 neurons. The bin width of PSTH was 10 ms. A1-E1. X4 speed separation. A2-E2. X2 speed separation. In A-C, the left dash line indicates the latency of the response to a bi-speed stimulus, and the right dash line and the arrow indicate when the response to a bi-speed stimulus started to diverge from the response to the faster component.

Comparison of response weights between attention-away and fixation paradigms.

The red and blue curves indicate the response weights for the faster speed component in an attention-away paradigm and a fixation paradigm, respectively, obtained from the same population of 32 neurons. The black curves are the replot of the data in Figure 5F, obtained from 100 neurons in a fixation paradigm. A. X4 speed separation. B. X2 speed separation.

MT responses to bi-speed stimuli moving in different directions and the linear weighted sum (LWS) and normalization model fits.

A. Population-averaged direction tuning curves of 21 neurons in response to stimuli moving at two speeds and in two directions separated by 90° (red). The component direction Dir. 1 (blue) moved at 10°/s, and the component direction Dir. 2 (green) moved at 2.5°/s. The faster component Dir. 1 was always on the clockwise side of Dir. 2. The abscissas in blue and green show the directions of stimulus components Dir. 1 and Dir. 2, respectively. The blue and green axes are shifted by 90° relative to each other. The abscissa in black shows the corresponding VA direction of the two direction components. Error bands represent ±STE. The gray curve represents the average of the component responses. The orange and black curves are the LWS and normalization model fits, respectively, of the population-averaged direction-tuning curve to the bi-speed stimuli. B. The direction-tuning curves of an example neuron showing similar peak responses to the slower and faster components. The orange and black curves are nearly identical and are the LWS and normalization model fits of the bi-speed responses. The weights of wf, ws are from the normalization model fit. C. Response weights for the stimulus components obtained using the LWS model fit. Each circle represents one neuron. D. Response weights obtained using the normalization model fit. The dashed lines in C, D indicate where ws and wf sum to one. Although ws and wf are not constrained to sum to one in the model fits, the fitted weights are roughly aligned with the dashed lines. E. Population-averaged speed tuning curves of MT neurons recorded in our data sample in response to single speeds. The red circles indicate responses to 2.5 and 10º/s. Error bars represent ±STE.

Population neural responses elicited by the bi-speed and single-speed stimuli and the performance of a linear classifier.

A population response of 100 recorded neurons was reconstructed by pooling across recordings in different experimental sessions. Each neuron’s response was averaged across experimental trials and normalized by the maximum response of the spline-fitted speed tuning curve to single speeds. Each dot represents the response from one neuron plotted as the neuron’s PS in the natural logarithm scale. The curves represent the spline-fitted population neural responses. Red: response to the bi-speed stimulus; Black: the response to the corresponding single, log-mean speed. A1-F1. X4 speed separation. The speeds of the bi-speed stimuli are 1.25 and 5°/s (A1), 2.5 and 10°/s (B1), 5 and 20°/s (C1), 10 and 40°/s (D1), 20 and 80°/s (E1). A2-F2. X2 speed separation. The speeds of the bi-speed stimuli are 1.25 and 2.5°/s (A2), 2.5 and 5°/s (B2), 5 and 10°/s (C2), 10 and 20°/s (D2), 20 and 40°/s (E2). Two red dots on the X-axis indicate two component speeds; the black dot indicates the log-mean speed. F1, F2. Performance of a linear classifier to discriminate the population neural responses to the bi-speed stimulus and the corresponding single log-mean speed. Error bars represent STE.

Illustration of the decoding procedure and extraction of speed(s) from population responses reconstructed based on the trial-averaged neuronal responses to the bi-speed stimuli. A-E. X4 speed separation. F-J. X2 speed separation.

The neural population contains 100 recorded neurons, as shown in Figure 9. Each red dot represents the trial-averaged response from one neuron plotted versus the PS of the neuron in the natural logarithm scale. The red curve represents the spline-fitted population neural response. The decoder found either one speed or two speeds with different weights (vertical green bars on the X-axis), giving rise to the estimated and spline-fitted population response (blue curve) that best fitted the recorded and spline-fitted population neural response (red curve). Each blue dot represents the estimated response from one neuron, and the blue curve represents the spline-fitted estimated population response. Two red dots on the X-axis indicate the stimulus speeds. The Y-axis on the right side shows the weight of the readout speed (A, F).

Trial-by-trial readout speeds decoded from population neural responses to the bi-speed stimuli.

The neural population contains 100 recorded neurons and the trial-by-trial responses are randomly generated based on a Poisson process. The convention is the same as in Figure 10. A-E. Speeds decoded from population responses to x4 speed separation. The vertical red lines indicate two component speeds, which are 1.25 and 5°/s (A), 2.5 and 10°/s (B), 5 and 20°/s (C), 10 and 40°/s (D), 20 and 80°/s (E). F-J. Speeds decoded from population responses to x2 speed separation. The red vertical line indicates two component speeds, and the black vertical line indicates the log mean speed. The component speeds are 1.25 and 2.5°/s (F), 2.5 and 5°/s (G), 5 and 10°/s (H), 10 and 20°/s (I), 20 and 40°/s (J).

Discrimination between single- and bi-speed stimuli based on decoded speeds.

A-J. The distributions of the speed separation between two readout speeds in each trial for the bi-speed stimuli (yellow) and the single, log-mean speed (blue). The bin width is 0.05. The abscissa is shown in the natural logarithm scale. The red dotted line indicates veridical speed separation. A-E. X4 speed separation. The speeds of the bi-speed stimuli are 1.25 and 5°/s (A), 2.5 and 10°/s (B), 5 and 20°/s (C), 10 and 40°/s (D), 20 and 80°/s (E). F-J. X2 speed separation. The speeds of the bi-speed stimuli are 1.25 and 2.5°/s (F), 2.5 and 5°/s (G), 5 and 10°/s (H), 10 and 20°/s (I), 20 and 40°/s (J). K-L. The performance of discriminating a bi-speed stimulus from the corresponding log-mean speed is based on the speed separation of the decoded speeds. K. X4 speed separation; L. X2 speed separation. The black triangles in A-J indicate the speed separation threshold of x1.3 (0.26 on the log scale) used for discriminating bi-speed and single-speed stimuli.

Population-averaged speed tuning curves to bi-speed stimuli and constituent single-speed components recorded in an attention-away and a fixation paradigm.

Speed tuning curves from one monkey (RG) averaged across A1-D1. 5 neurons that had PS ≤ 2.5°/s, A2-D2. 6 neurons that had PS between 2.5 and 25°/s, A3-D3. 21 neurons that had PS > 25°/s. Error bars represent ±STE. A1-A3 and B1-B3. X4 speed separation; C1-C3 and D1-D3. X2 speed separation. A1-A3 and C1-C3. Attention directed away from the RF; B1-B3 and D1-D3. Fixation paradigm.

Trial-by-trial readout speeds decoded from population neural responses to single speeds.

The neural population contained 100 recorded neurons, as shown in Figure 9. The trial-by-trial responses were randomly generated based on a Poisson process, with the mean set to the spike count averaged across the recorded trials. Each row shows the readout speed(s) from one trial, and each dot’s size is proportional to the weight of the readout speed. If only one speed is decoded in a trial, that readout speed is shown in red. In trials with two readout speeds, the slower and faster readout speeds are shown in green and blue, respectively. The white background indicates trials with a weight difference between two readout speeds less than 0.7 and are considered to have two readout speeds. The gray background indicates trials with a weight difference greater than 0.7 and are considered to have only one readout speed. The vertical black line and the speed marked in each panel indicate the stimulus speed. A-G. Speeds decoded from recorded population neural responses to single speeds from 1.25 to 80°/s. Note that, at the stimulus speed of 80°/s (G), in addition to picking up the veridical speed of 80°/s (log speed of 4.382), the decoder often picked up a slower speed at 2.872°/s (log speed of 1.055), which was at the largest speed separation from 80°/s used in our searching algorithm (x27.86, log value 3.327). This border effect can also be seen at the stimulus speed of 1.25°/s (A) as well, in which a weaker and faster speed was sometimes picked up around 34.8°/s (log speed of 3.55). H-L. Speeds decoded from inferred population neural response to single speeds, which are the log-mean speeds of the bi-speed stimuli with x2 speed separation. The responses of these log mean speeds of x2 speed separation were obtained from the splined-fitted, trial-averaged speed-tuning curve of each neuron. M. Comparison of the readout speeds and the stimulus speeds. The diagonal line is the unity line. The ordinate represents the speed at the peak of the readout speed distribution pooled across simulated trials (not shown). At the stimulus speed of 1.77°/s (H), the distribution of the readout speed has two peaks, indicated by a solid circle (at 1.77°/s) and an open circle (at 1.25°/s). At the stimulus speed of 80°/s (G), the distribution of the readout speed also has two peaks; only the readout speed for the higher peak is shown in M.

Analysis of decoding the speeds of the bi-speed stimulus with the fastest speeds of 20 and 80°/s.

A. Evolution of the objective function averaged across all 200 trials as the decoder searched through different speed separations. The red dot on the X-axis indicates the speed separation of the stimulus speeds. B, E. Evolution of the objective functions averaged across trials considered to have two (B) and one (E) readout speed(s). In A, B, and E, the error bands indicate ±STE. The black arrow indicates the speed separation where the objective function reaches its peak. The horizontal dotted line indicates the peak value of the objective function. C, F. Evolution of the readout speeds (darker and thick lines) and their weights (lighter and thin lines) as the decoder searched through different speed separations in trials considered to have two (C) and one (F) readout speed(s). D. Population neural responses averaged across trials that are considered to have two readout speeds (purple) and one readout speed (orange). Each dot represents the trial-averaged response of one neuron. The curves represent the spline-fitted population neural responses. The two red dots on the X-axis indicate stimulus speeds of 20 and 80°/s.