Research Experience
Past Research
Determining when different neural networks are functionally identical
What is the relationship between the values of the parameters (weights, threholds, etc..) in a neural network and the input-output relationship which is computed by the network? In particular, under what conditions can we continuously modify the parameter values while leaving the input-output relationship unchanged, which implies that there is a continuum of neural networks with identical functional behavior? We address this question for the case of the popular three layer perceptron model, and discover that in general it is only possible for there to be a continuum of functionally equivalent networks in the case that the gain functions are given by power law, exponential or logarithmic forms, possibly having zero sub-threhold regions. Since there is evidence that the gain functions of many biological neurons are well approximated by power law forms, this suggests that in real neural systems disparate values of system parameters may effect the same computation. These results also have implications for applications of neural networks because many of the commonly used gain functions (tanh, sigmoid, etc...) may be approximated over some range of inputs by a log, exponential or power function. If a training set fails to drive a unit into a region of its gain function which is not well approximated by these forms, it will be impossible to uniquely identify the neural network, and bootstrapping with the original training data will reveal a continuum of error function minima lying on a manifold predicted by the theory. (preprint)
Optimal stimuli and invariant stimuli in hierarchical sensory networks: A quadratic analysis
The response properties of a sensory neuron, including its optimal stimulus, are ultimately generated by the structure of the underlying neural network leading to the sensory periphery. The exact relationship between a neural circuit's architecture and stimulus-response properties remains poorly understood. Here we obtain general theoretical results for quadratic analysis on multilayer feedforward neural networks and classify all possible quadratic behaviors in relation to the optimal stimulus and invariant stimuli. The optimal stimulus, or the stimulus that best drives a neuron, describes a neuron's selectivity, wheras stimulus invariance describes the generalization of a neuron's response to a continuum of equivalently effective stimuli. Despite the intuitive notion of the optimal stimulus as a peak in the stimulus-response relationship, diverse quadratic behaviors are possible and can occur in the same network. Our results provide a theoretical basis for suggesting quadratic analysis around putative optimal stimuli in neurophysiological experiments. We also found that invariant stimuli are ubiquitous in hierarchical networks, and have identified two types of invariant stimulus transformations which leave neural responses unchanged. (preprint)
How optimal stimuli for sensory neurons are constrained by network architecture
Neurophysiologists have long been interested in finding the 'optimal stimulus' for sensory neurons, which is defined as the stimulus which produces the maximum firing rate response. However, it is not clear what constraints the architecture of the underlying neural system which actually generates the responses to sensory stimuli may place on the location of the 'optimal stimulus'. In this study, we analyze feed-forward and recurrent neural network models and discover that for convergent networks whose connections between processing layers form a non-degenerate weight matrix that it is impossible for an strict firing rate maximum to exist in the interior of a compact stimulus space which is isomorphic to the peripheral representation. We further demonstrate that the same conditions which guarantee the non-existence of an optimal stimulus also guarantee that the activity in the network can be controlled using sensory inputs only. This result may explain why many sensory neurons at early stages of processing exhibit their strongest responses to stimuli of maximum contrast. Furthermore, it suggests that for neurons which can be shown to have a strict maximum in a space isomorphic to the periphery that one or more of the conditions of the theorem must be violated. This study broaches the rarely addressed question of the relationship between the phenomenological results observed in experiments and the architecture of the underlying neural systems. (pdf reprint)
Virtual vocalization stimuli for investigating neural representations of species-specific vocalizations
Most studies of the neural representation of species-specific vocalizations have made use of pre-recorded token vocalization stimuli. While the results from these studies are interesting and useful, the inability to systematically manipulate these stimuli makes it difficult to determine which of the many acoustical features present in the vocalization are driving the neural responses. Other studies have made use of synthetic vocalizations, but the synthesis of these vocalizations is typically based on a single exemplar and hence does not capture the full range of acoustical variability present in the natural sound. In this study, we utilized a database of thousands of vocalizations obtained from the common marmoset monkey to develop synthetic "Virtual Vocalization" stimuli. These vocalizations can be systematically varied both within and outside of the range of natural acoustical variation along several parameter dimensions and provide a useful tool for the study of vocalization coding in the auditory cortex. (pdf reprint)
GABA(B) and Trk receptor signaling mediates long-lasting inhibitory synaptic depression.
It is known that the inhibitory projection from the MNTB to the LSO nucleus in the auditory brainstem exhibits an age-dependent form of long-lasting depression when activated at a low rate. However, since this synapse releases both Glycine and GABA during maturation, the mechanism of this age-dependent synaptic depresssion is unclear. Using GABA(B) receptor anatoginists, it was found that synaptic depression was blocked, suggesting a role for GABA-ergic transmission for inhibitory synaptic depression. Using bath applied BDNF and TRK receptor agonists it was also found that neurotrophins may play a role in this age-dependent inhibitory synaptic depression. My role for this project was the creation of the SLICE software package used to collect data as well developing algorithms for data analysis. (pdf reprint)
TopCurrent Research
Estimating and comparing sensory processing models using adaptively collected data
In post-hoc analyses, one can often describe sensory neurophysiology data using several different information-processing models. Although standard methods like Baysian model comparison may be employed to discriminate competing models, a more powerful method for comparing sensory processing models is to estimate models and generate critical stimuli to distinguish competing models in on-line adaptive experiments. This study will explore algorithms for actively selecting data during experiments with dual goals of estimating several competing models and adaptively generate stimuli which will best discriminate them. These algorithms will be applied to topical examples from sensory neuroscience. (poster)
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