PARAMETRIC MODELING OF THE TEMPORAL DYNAMICS OF NEURONAL RESPONSES USING CONNECTIONIST ARCHITECTURES

1. We describe an exploratory approach to the parametric modeling of dynamical (time-varying) neurophysiological data. The models use stimulus data from a window of time to predict the neuronal firing rate at the end of that window. The most successful models were feedforward three-layered networks of input, hidden, and output ''nodes'' connected by weights that were adjusted during a training phase by the backpropagation algorithm. The memory in these models was represented by delay lines of varying length propagating activation between the layers. Connectionist models with no memory (1 sequential node per layer) as well as zero-memory nonlinear nonconnectionist models were also tested. 2. Models were tested with recordings of neuronal activity from the auditory thalamic nucleus ovoidalis of urethane-anesthetized zebra finches (Taeniopygia guttata). All cells reported here showed phasic/tonic responses. Extensive modeling of one neuron (cell 1) defined a ''canonical'' architecture, which was most successful in modeling this cell. The canonical model had a zero-memory input layer, a hidden layer with 29 bins representing 185.6 ms, and a single output node whose value as a function of sequential bin position represented the output of the neuron as a function of time. The canonical model achieved convergence on the entire data set for cell 1, including responses to single tone bursts and zebra finch songs. The ''frequency'' weights of the canonical model matched well excitatory and inhibitory frequencies for cell 1 as determined by the cell's frequency tuning curve. The ''memory'' weights of the canonical model were dominated by excitation over the first 25 ms followed by inhibition. 3. When trained with only the dynamical responses to tone bursts, the canonical model also accurately predicted the responses to song (average R2 = 0.823). Thus for this neuron the responses to single tone bursts were sufficient to predict most of the responses to six different songs, each presented at three different amplitudes, although a Monte Carlo procedure indicated the residual variance was not just due to noise (P < 0.001). 4. The model's ability to predict the responses to song was further explored by altering the tone burst (training) data. For cell 1, the responses to songs were most strongly related to the phasic/tonic details of the temporal responses to tone bursts. Changes in the characteristic frequency, frequency tuning curves, and rate/intensity function of the neuron had less effect. These experiments would be difficult or impossible to conduct electrophysiologically. The modeling of neuronal temporal dynamics for this cell therefore gave insight into relationships between response properties that would otherwise not have been experimentally tractable. 5. A total of 16 other neurons were tested with the canonical architecture originally derived for cell 1. For nine of these, the canonical architecture converged on the entire stimulus set with good (mean R2 = 0.774) to excellent (mean R2 = 0.924) results. When a match between frequency weights and a cell's frequency tuning curve was explicitly implemented, one of the remaining seven cells converged well and two others partially converged. Presumably, further attempts to adjust the model architecture would have produced better results for more of the cells. 6. A Monte Carlo procedure indicated that for all models, whether trained just with tone bursts or the entire stimulus set available for that cell, the remaining variance between a model's prediction and the corresponding neuronal response could not be explained on the basis of random fluctuations in the neuronal response. It is unclear whether the remaining variance results from higher-order nonlinear interactions (e.g., two-tone interactions) and/or from inadequate model architectures. 7. The ability to model neurons with similar classical properties with a single parametric model demonstrates that connectionist modeling approaches can provide insight into relationships among complex sets of electrophysiological data (e.g., responses to tone bursts and complex stimuli) that would have otherwise proven difficult to obtain. With the techniques reported here, for models that converge, it is possible to apply quantitative and statistical rigor to assertions regarding the predictive power of a stimulus repertoire.