Decoding responses from populations of neurons in macaque primary visual cortex
A.B.A.Graf, A. Kohn, M. Jazayeri & J. A. Movshon
Center for Neural Science, New York University

One of the central questions in computational and systems neuroscience is how the responses from a population of neurons are combined to decode sensory signals. To address this question, we recorded from the superficial layers of primary visual cortex of anesthetized, paralyzed macaque monkeys using a 10 x 10 electrode array with 400 microns spacing between adjacent electrodes. We sorted the recorded waveforms offline to isolate between 44 and 86 simultaneously recorded orientation-selective units. We presented sinusoidal gratings large enough to cover the receptive fields of all recorded units, drifting in 72 directions 5 deg apart. Each grating was presented 50 times for 1280 ms in randomly-sequenced blocks, and was followed by a 1280 ms blank screen.

We considered linear decoders that discriminated between the population activity evoked by pairs of stimuli by computing the weighted sum of the neuronal responses (spike counts). First, we used a likelihood ratio (LR) decoder which compared the likelihood of two stimuli from the underlying response distributions. Our LR decoder assumed that these responses were statistically independent, and that Poisson statistics adequately described the spike count distributions. The LR decoder was linear, and its weights were given by the difference of the logarithms of the tuning curves. Second, we used a linear Support Vector Machine (SVM) which estimated a separating hyperplane in a space whose dimensions corresponded to the neural responses. This hyperplane maximized the distance between classes of neural response and minimized misclassified responses. Unlike the LR decoder, the SVM made no a priori assumptions about the data, and could take advantage of all the structure present in the empirical data.

Using the discrimination accuracy of the decoders as a measure of decoding performance, we constructed population neurometric functions to measure how well pools of neurons could discriminate between different stimulus directions. We explored the impact of correlations on decoding by comparing raw with shuffled population responses (interneuronal correlations removed by trial shuffling). The LR decoder performed better on the shuffled data than on the raw, because it assumed independence between neurons. The SVM decoder, however, performed better on the raw data, showing that it could make use of correlations to improve its decoding performance. This effect was present for different population subsamples and integration times. The linearity of the two decoders allowed us to get a mechanistic insight into decoding. For the SVM decoder, the neurons responding most vigorously across all directions were weighted more heavily than the least responsive neurons. For fine discrimination both decoders emphasized units with preferred directions that were further apart than the stimulus direction difference, a behavior predicted from theory and inferred previously in psychophysics. Furthermore, for the SVM decoder, the increase of decoding accuracy in the presence of correlations was accompanied by a sharpening of the shape of the weight vector.

The LR decoder can be constructed directly from neuronal tuning curves and is appealing because of its simplicity and biological feasibility. However, our results provide evidence that more sophisticated linear classifiers such as the SVM, while retaining much of the simplicity of the LR decoder, can take advantage of neural correlations to decode the activity of neuronal populations with greater precision.