We work on theoretical and computational problems in neuroscience and biophysics. In particular, we are interested in understanding how neural feature selectivity is influenced by, and to what extent is determined by, the statistics of real-world inputs. One of our long-term goals is to understand how invariant feature selectivity is achieved in cortex.
Projects:
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Probing neural feature selectivity with natural stimuli:
In an effort to make the most of available resources, animals have evolved to be very efficient in processing real-world, or "natural" and to take advantage of statistical regularities present in natural stimuli. One of the distinguishing feature of natural stimuli is the presence of structures at multiple length and time scales. Visual real-world inputs contain lines and edges; natural sounds are characterized by up and down frequency sweeps, whereas odors form plumes. Remarkably, natural stimuli, either visual, auditory, or olfactory, share a lot of the common statistical characteristics. Most importantly, natural signals have been to be deviate strongly from a Gaussian distribtion and are often characterized by long, nearly exponential tails.
Understanding how the brain processes information requires probing neural feature selectivity with natural stimuli. However most methods for analyzing neural responses, such as those based on correlation functions, assume that the input signals are Gaussian. Because natural stimuli are not Gaussian, it was necessary to develop a method that would correctly estimate feature selectivity of neurons, even in cases where they are probed with correlated non-Gaussian inputs. Together with Bill Bialek, I developed the method of "maximally informative dimensions", where stimulus features relevant for spikes of a given neuron are estimated as those that allow one to account for the maximall amount of information between the stimuli and neural responses.
- Adaptation and Optimal Coding:
When applied to neural data from the primary visual cortex, this method allowed for the first time to characterize the filtering properties of real neurons probed with natural stimuli without invoking a fully linear approximation of their response probability. A new kind of adaptation was discovered, where neurons could adapt their filtering at certain spatial frequencies to compensate for changes in the stimulus second-order statistics (stimulus mean and variance was maintained the same). This type of adaptation takes longer than most of the previously reported forms of adaptation.
On a theory side, we could hypothesize that a set of neurons has been designed with the goal of maximizing information transmission about the incoming signals, and derive the appropriate neurons' characteristics from this assumption given the constraints of metabolic costs per response. It would be interesting to derive these properties optimal from the view of information transmission given what we know about the statistics of natural signals and compare with those optimal for transmitting white noise signals. These predictions could then be compared with the results of the above-mentioned experiments.
- Formation of invariant neural
responses:
At successive stages of sensory signal processing, neurons become increasingly less responsive to noise ensembles, but continue to respond to natural stimuli. The increasing complexity of features in the stimulus that are most relevant for generating neuron's responses is accompanied by the increasing degree of invariance with respect to certain continuous transformations, such as translation, scaling or rotation in the case of visual neurons. These two factors combined make it difficult to systematically analyze filter characteristics of neurons at the stages beyond the primary visual cortex. In its current implementation, the method of maximally informative dimensions assumes that the number of filters describing the neuron's response is small, and it is difficult to reliably find more than several filters. To analyze responses of a neuron with a substantial degree of tolerance with respect to object position would require finding a large numbers of filters, all of which represent transformed versions of each other. Therefore work is in progress to design a method that would find the main template or filter of the neurons assuming a priori that the neural response is invariant with respect to a known continuous symmetry.
Last Modified: 1 June, 2007