Publications
all Publications
Praturu, A., Sharpee, T.O. Adaptive data embedding for curved spaces. (2024) iScience. 27(12):111266. DOI: 10.1016/j.isci.2024.111266
+ expand abstract
Recent studies have demonstrated the significance of hyperbolic geometry in uncovering low-dimensional structure within complex hierarchical systems. We developed a Bayesian formulation of multi-dimensional scaling (MDS) for embedding data in hyperbolic spaces that allows for a principled determination of manifold parameters such as curvature and dimension. We show that only a small amount of data are needed to constrain the manifold, the optimization is robust against false minima, and the model is able to correctly discern between Hyperbolic and Euclidean data. Application of the method to COVID sequences revealed that viral evolution leaves the dimensionality of the space unchanged but produces a logarithmic increase in curvature, indicating a constant rate of information acquisition optimized under selective pressures. The algorithm also detected a contraction in curvature after the introduction of vaccines. The ability to discern subtle changes and structural shifts showcases the utility of this approach in understanding complex data dynamics.
Alvarez-Kuglen, M., Ninomiya, K., Qin, H., Rodriguez, D., Fiengo, L., Farhy, C., Hsu, W.M., Kirk, B., Havas, A., Feng, G.S., Roberts, A.J., Anderson, R.M., Serrano, M., Adams, P.D., Sharpee, T.O., Terskikh, A.V. ImAge quantitates aging and rejuvenation. (2024) Nat Aging. DOI: 10.1038/s43587-024-00685-1
+ expand abstract
For efficient, cost-effective and personalized healthcare, biomarkers that capture aspects of functional, biological aging, thus predicting disease risk and lifespan more accurately and reliably than chronological age, are essential. We developed an imaging-based chromatin and epigenetic age (ImAge) that captures intrinsic age-related trajectories of the spatial organization of chromatin and epigenetic marks in single nuclei, in mice. We show that such trajectories readily emerge as principal changes in each individual dataset without regression on chronological age, and that ImAge can be computed using several epigenetic marks and DNA labeling. We find that interventions known to affect biological aging induce corresponding effects on ImAge, including increased ImAge upon chemotherapy treatment and decreased ImAge upon caloric restriction and partial reprogramming by transient OSKM expression in liver and skeletal muscle. Further, ImAge readouts from chronologically identical mice inversely correlated with their locomotor activity, suggesting that ImAge may capture elements of biological and functional age. In sum, we developed ImAge, an imaging-based biomarker of aging with single-cell resolution rooted in the analysis of spatial organization of epigenetic marks.
Alvarez-Kuglen, M., Rodriguez, D., Qin, H., Ninomiya, K., Fiengo, L., Farhy, C., Hsu, W.M., Havas, A., Feng, G.S., Roberts, A.J., Anderson, R.M., Serrano, M., Adams, P.D., Sharpee, T.O., Terskikh, A.V. Imaging-based chromatin and epigenetic age, ImAge, quantitates aging and rejuvenation. (2023) Res Sq. DOI: 10.21203/rs.3.rs-3479973/v1
+ expand abstract
Biomarkers of biological age that predict the risk of disease and expected lifespan better than chronological age are key to efficient and cost-effective healthcare. To advance a personalized approach to healthcare, such biomarkers must reliably and accurately capture individual biology, predict biological age, and provide scalable and cost-effective measurements. We developed a novel approach – image-based chromatin and epigenetic age (ImAge) that captures intrinsic progressions of biological age, which readily emerge as principal changes in the spatial organization of chromatin and epigenetic marks in single nuclei without regression on chronological age. ImAge captured the expected acceleration or deceleration of biological age in mice treated with chemotherapy or following a caloric restriction regimen, respectively. ImAge from chronologically identical mice inversely correlated with their locomotor activity (greater activity for younger ImAge), consistent with the widely accepted role of locomotion as an aging biomarker across species. Finally, we demonstrated that ImAge is reduced following transient expression of OSKM cassette in the liver and skeletal muscles and reveals heterogeneity of in vivo reprogramming. We propose that ImAge represents the first-in-class imaging-based biomarker of aging with single-cell resolution.
Little, J.C., Kaaronen, R.O., Hukkinen, J.I., Xiao, S., Sharpee, T., Farid, A.M., Nilchiani, R., Barton, C.M. Earth Systems to Anthropocene Systems: An Evolutionary, System-of-Systems, Convergence Paradigm for Interdependent Societal Challenges. (2023) Environ Sci Technol. DOI: 10.1021/acs.est.2c06203
+ expand abstract
Humans have made profound changes to the Earth. The resulting societal challenges of the Anthropocene (e.g., climate change and impacts, renewable energy, adaptive infrastructure, disasters, pandemics, food insecurity, and biodiversity loss) are complex and systemic, with causes, interactions, and consequences that cascade across a globally connected system of systems. In this Critical Review, we turn to our “origin story” for insight, briefly tracing the formation of the Universe and the Earth, the emergence of life, the evolution of multicellular organisms, mammals, primates, and humans, as well as the more recent societal transitions involving agriculture, urbanization, industrialization, and computerization. Focusing on the evolution of the Earth, genetic evolution, the evolution of the brain, and cultural evolution, which includes technological evolution, we identify a nested evolutionary sequence of geophysical, biophysical, sociocultural, and sociotechnical systems, emphasizing the causal mechanisms that first formed, and then transformed, Earth systems into Anthropocene systems. Describing how the Anthropocene systems coevolved, and briefly illustrating how the ensuing societal challenges became tightly integrated across multiple spatial, temporal, and organizational scales, we conclude by proposing an evolutionary, system-of-systems, convergence paradigm for the entire family of interdependent societal challenges of the Anthropocene.
Yang, J.Y., O’Connell, T.F., Hsu, W.M., Bauer, M.S., Dylla, K.V., Sharpee, T.O., Hong, E.J. Restructuring of olfactory representations in the fly brain around odor relationships in natural sources. (2023) bioRxiv. DOI: 10.1101/2023.02.15.528627
+ expand abstract
A core challenge of olfactory neuroscience is to understand how neural representations of odor are generated and progressively transformed across different layers of the olfactory circuit into formats that support perception and behavior. The encoding of odor by odorant receptors in the input layer of the olfactory system reflects, at least in part, the chemical relationships between odor compounds. Neural representations of odor in higher order associative olfactory areas, generated by random feedforward networks, are expected to largely preserve these input odor relationships. We evaluated these ideas by examining how odors are represented at different stages of processing in the olfactory circuit of the vinegar fly . We found that representations of odor in the mushroom body (MB), a third-order associative olfactory area in the fly brain, are indeed structured and invariant across flies. However, the structure of MB representational space diverged significantly from what is expected in a randomly connected network. In addition, odor relationships encoded in the MB were better correlated with a metric of the similarity of their distribution across natural sources compared to their similarity with respect to chemical features, and the converse was true for odor relationships encoded in primary olfactory receptor neurons (ORNs). Comparison of odor coding at primary, secondary, and tertiary layers of the circuit revealed that odors were significantly regrouped with respect to their representational similarity across successive stages of olfactory processing, with the largest changes occurring in the MB. The non-linear reorganization of odor relationships in the MB indicates that unappreciated structure exists in the fly olfactory circuit, and this structure may facilitate the generalization of odors with respect to their co-occurence in natural sources.
Zhang, H., Rich, P.D., Lee, A.K., Sharpee, T.O. Hippocampal spatial representations exhibit a hyperbolic geometry that expands with experience. (2022) Nature Neuroscience. DOI: 10.1038/s41593-022-01212-4
+ expand abstract
Daily experience suggests that we perceive distances near us linearly. However, the actual geometry of spatial representation in the brain is unknown. Here we report that neurons in the CA1 region of rat hippocampus that mediate spatial perception represent space according to a non-linear hyperbolic geometry. This geometry uses an exponential scale and yields greater positional information than a linear scale. We found that the size of the representation matches the optimal predictions for the number of CA1 neurons. The representations also dynamically expanded proportional to the logarithm of time that the animal spent exploring the environment, in correspondence with the maximal mutual information that can be received. The dynamic changes tracked even small variations due to changes in the running speed of the animal. These results demonstrate how neural circuits achieve efficient representations using dynamic hyperbolic geometry.
Ghaninia, M., Zhou, Y., Knauer, A.C., Schiestl, F.P., Sharpee, T.O., Smith, B.H. Hyperbolic odorant mixtures as a basis for more efficient signaling between flowering plants and bees. (2022) PLOS One. 17(7):e0270358. DOI: 10.1371/journal.pone.0270358
+ expand abstract
Animals use odors in many natural contexts, for example, for finding mates or food, or signaling danger. Most analyses of natural odors search for either the most meaningful components of a natural odor mixture, or they use linear metrics to analyze the mixture compositions. However, we have recently shown that the physical space for complex mixtures is ‘hyperbolic’, meaning that there are certain combinations of variables that have a disproportionately large impact on perception and that these variables have specific interpretations in terms of metabolic processes taking place inside the flower and fruit that produce the odors. Here we show that the statistics of odorants and odorant mixtures produced by inflorescences (Brassica rapa) are also better described with a hyperbolic rather than a linear metric, and that combinations of odorants in the hyperbolic space are better predictors of the nectar and pollen resources sought by bee pollinators than the standard Euclidian combinations. We also show that honey bee and bumble bee antennae can detect most components of the B. rapa odor space that we tested, and the strength of responses correlates with positions of odorants in the hyperbolic space. In sum, a hyperbolic representation can be used to guide investigation of how information is represented at different levels of processing in the CNS.
Zhou, Y., Sharpee, T.O. Using Global t-SNE to Preserve Intercluster Data Structure. (2022) Neural Computation.:1-15 DOI: 10.1162/neco_a_01504
+ expand abstract
The t-distributed stochastic neighbor embedding (t-SNE) method is one of the leading techniques for data visualization and clustering. This method finds lower-dimensional embedding of data points while minimizing distortions in distances between neighboring data points. By construction, t-SNE discards information about large-scale structure of the data. We show that adding a global cost function to the t-SNE cost function makes it possible to cluster the data while preserving global intercluster data structure. We test the new global t-SNE (g-SNE) method on one synthetic and two real data sets on flower shapes and human brain cells. We find that significant and meaningful global structure exists in both the plant and human brain data sets. In all cases, g-SNE outperforms t-SNE and UMAP in preserving the global structure. Topological analysis of the clustering result makes it possible to find an appropriate trade-off of data distribution across scales. We find differences in how data are distributed across scales between the two subjects that were part of the human brain data set. Thus, by striving to produce both accurate clustering and positioning between clusters, the g-SNE method can identify new aspects of data organization across scales.
Nowotny, T., van Albada, S.J., Fellous, J.M., Haas, J.S., Jolivet, R.B., Metzner, C., Sharpee, T. Editorial: Advances in Computational Neuroscience. (2022) Frontiers in Computational Neuroscience. 15:824899. DOI: 10.3389/fncom.2021.824899
Shadel, G.S., Adams, P.D., Berggren, W.T., Diedrich, J.K., Diffenderfer, K.E., Gage, F.H., Hah, N., Hansen, M., Hetzer, M.W., Molina, A.J.A., Manor, U., Marek, K., O’Keefe, D.D., Pinto, A.F.M., Sacco, A., Sharpee, T.O., Shokriev, M.N., Zambetti, S. The San Diego Nathan Shock Center: tackling the heterogeneity of aging. (2021) Geroscience. DOI: 10.1007/s11357-021-00426-x
+ expand abstract
Understanding basic mechanisms of aging holds great promise for developing interventions that prevent or delay many age-related declines and diseases simultaneously to increase human healthspan. However, a major confounding factor in aging research is the heterogeneity of the aging process itself. At the organismal level, it is clear that chronological age does not always predict biological age or susceptibility to frailty or pathology. While genetics and environment are major factors driving variable rates of aging, additional complexity arises because different organs, tissues, and cell types are intrinsically heterogeneous and exhibit different aging trajectories normally or in response to the stresses of the aging process (e.g., damage accumulation). Tackling the heterogeneity of aging requires new and specialized tools (e.g., single-cell analyses, mass spectrometry-based approaches, and advanced imaging) to identify novel signatures of aging across scales. Cutting-edge computational approaches are then needed to integrate these disparate datasets and elucidate network interactions between known aging hallmarks. There is also a need for improved, human cell-based models of aging to ensure that basic research findings are relevant to human aging and healthspan interventions. The San Diego Nathan Shock Center (SD-NSC) provides access to cutting-edge scientific resources to facilitate the study of the heterogeneity of aging in general and to promote the use of novel human cell models of aging. The center also has a robust Research Development Core that funds pilot projects on the heterogeneity of aging and organizes innovative training activities, including workshops and a personalized mentoring program, to help investigators new to the aging field succeed. Finally, the SD-NSC participates in outreach activities to educate the general community about the importance of aging research and promote the need for basic biology of aging research in particular.
Hsu, W.M., Kastner, D.B., Baccus, S.A., Sharpee, T.O. How inhibitory neurons increase information transmission under threshold modulation. (2021) Cell Reports. 35(8):109158. DOI: 10.1016/j.celrep.2021.109158
+ expand abstract
Modulation of neuronal thresholds is ubiquitous in the brain. Phenomena such as figure-ground segmentation, motion detection, stimulus anticipation, and shifts in attention all involve changes in a neuron’s threshold based on signals from larger scales than its primary inputs. However, this modulation reduces the accuracy with which neurons can represent their primary inputs, creating a mystery as to why threshold modulation is so widespread in the brain. We find that modulation is less detrimental than other forms of neuronal variability and that its negative effects can be nearly completely eliminated if modulation is applied selectively to sparsely responding neurons in a circuit by inhibitory neurons. We verify these predictions in the retina where we find that inhibitory amacrine cells selectively deliver modulation signals to sparsely responding ganglion cell types. Our findings elucidate the central role that inhibitory neurons play in maximizing information transmission under modulation.
Zhou, Y., Sharpee, T.O. Hyperbolic geometry of gene expression. (2021) iScience. 24(3):102225. DOI: 10.1016/j.isci.2021.102225
+ expand abstract
Patterns of gene expressions play a key role in determining cell state. Although correlations in gene expressions have been well documented, most of the current methods treat them as independent variables. One way to take into account gene correlations is to find a low-dimensional curved geometry that describes variation in the data. Here we develop such a method and find that gene expression across multiple cell types exhibits a low-dimensional hyperbolic structure. When more genes are taken into account, hyperbolic effects become stronger but representation remains low dimensional. The size of the hyperbolic map, which indicates the hierarchical depth of the data, was the largest for human cells, the smallest for mouse embryonic cells, and intermediate in differentiated cells from different mouse organs. We also describe how hyperbolic metric can be incorporated into the t-SNE method to improve visualizations compared with leading methods.
Sharpee, T.O., Berkowitz, J.A. Linking neural responses to behavior with information-preserving population vectors (2019) Current Opinion in Behavioral Sciences. 29:37-44. DOI: https://doi.org/10.1016/j.cobeha.2019.03.004
+ expand abstract
All systems for processing signals, both artificial and within animals, must obey fundamental statistical laws for how information can be processed. We discuss here recent results using information theory that provide a blueprint for building circuits where signals can be read-out without information loss. Many properties that are necessary to build information-preserving circuits are actually observed in real neurons, at least approximately. One such property is the use of logistic nonlinearity for relating inputs to neural response probability. Such nonlinearities are common in neural and intracellular networks. With this nonlinearity type, there is a linear combination of neural responses that is guaranteed to preserve Shannon information contained in the response of a neural population, no matter how many neurons it contains. This read-out measure is related to a classic quantity known as the population vector that has been quite successful in relating neural responses to animal behavior in a wide variety of cases. Nevertheless, the population vector did not withstand the scrutiny of detailed information-theoretical analyses that showed that it discards substantial amounts of information contained in the responses of a neural population. We discuss recent theoretical results showing how to modify the population vector expression to make it ‘information-preserving’, and what is necessary in terms of neural circuit organization to allow for lossless information transfer. Implementing these strategies within artificial systems is likely to increase their efficiency, especially for brain–machine interfaces.
Amatya, D.N., Linker, S.B., Mendes, A.P.D., Santos, R., Erikson, G., Shokhirev, M.N., Zhou, Y., Sharpee, T., Gage, F.H., Marchetto, M.C., Kim, Y. Dynamical Electrical Complexity Is Reduced during Neuronal Differentiation in Autism Spectrum Disorder. (2019) Stem Cell Reports. DOI: 10.1016/j.stemcr.2019.08.001
+ expand abstract
Neuronal activity can be modeled as a nonlinear dynamical system to yield measures of neuronal state and dysfunction. The electrical recordings of stem cell-derived neurons from individuals with autism spectrum disorder (ASD) and controls were analyzed using minimum embedding dimension (MED) analysis to characterize their dynamical complexity. MED analysis revealed a significant reduction in dynamical complexity in ASD neurons during differentiation, which was correlated to bursting and spike interval measures. MED was associated with clinical endpoints, such as nonverbal intelligence, and was correlated with 53 differentially expressed genes, which were overrepresented with ASD risk genes related to neurodevelopment, cell morphology, and cell migration. Spatiotemporal analysis also showed a prenatal temporal enrichment in cortical and deep brain structures. Together, we present dynamical analysis as a paradigm that can be used to distinguish disease-associated cellular electrophysiological and transcriptional signatures, while taking into account patient variability in neuropsychiatric disorders.
Sharpee, T.O. An argument for hyperbolic geometry in neural circuits. (2019) Current Opinion in Neurobiology. 58:101-104. DOI: 10.1016/j.conb.2019.07.008
+ expand abstract
This review connects several lines of research to argue that hyperbolic geometry should be broadly applicable to neural circuits as well as other biological circuits. The reason for this is that networks that conform to hyperbolic geometry are maximally responsive to external and internal perturbations. These networks also allow for efficient communication under conditions where nodes are added or removed. We will argue that one of the signatures of hyperbolic geometry is the celebrated Zipf’s law (also sometimes known as the Pareto distribution) that states that the probability to observe a given pattern is inversely related to its rank. Zipf’s law is observed in a variety of biological systems – from protein sequences, neural networks to economics. These observations provide further evidence for the ubiquity of networks with an underlying hyperbolic metric structure. Recent studies in neuroscience specifically point to the relevance of a three-dimensional hyperbolic space for neural signaling. The three-dimensional hyperbolic space may confer additional robustness compared to other dimensions. We illustrate how the use of hyperbolic coordinates revealed a novel topographic organization within the olfactory system. The use of such coordinates may facilitate representation of relevant signals elsewhere in the brain.
Berkowitz, J.A., Sharpee, T.O. Quantifying Information Conveyed by Large Neuronal Populations. (2019) Neural Computation.:1-33 DOI: 10.1162/neco_a_01193
+ expand abstract
Quantifying mutual information between inputs and outputs of a large neural circuit is an important open problem in both machine learning and neuroscience. However, evaluation of the mutual information is known to be generally intractable for large systems due to the exponential growth in the number of terms that need to be evaluated. Here we show how information contained in the responses of large neural populations can be effectively computed provided the input-output functions of individual neurons can be measured and approximated by a logistic function applied to a potentially nonlinear function of the stimulus. Neural responses in this model can remain sensitive to multiple stimulus components. We show that the mutual information in this model can be effectively approximated as a sum of lower-dimensional conditional mutual information terms. The approximations become exact in the limit of large neural populations and for certain conditions on the distribution of receptive fields across the neural population. We empirically find that these approximations continue to work well even when the conditions on the receptive field distributions are not fulfilled. The computing cost for the proposed methods grows linearly in the dimension of the input and compares favorably with other approximations.
Zhou, Y., Smith, B.H., Sharpee, T.O. Hyperbolic geometry of the olfactory space. (2018) Science Advances. 4(8):eaaq1458. DOI: 10.1126/sciadv.aaq1458
+ expand abstract
In the natural environment, the sense of smell, or olfaction, serves to detect toxins and judge nutritional content by taking advantage of the associations between compounds as they are created in biochemical reactions. This suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate the distance between species computed along dendrograms and, more generally, between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception.
Zhang, Y., Kastner, D.B., Baccus, S.A., Sharpee, T.O. Optimal Information Transmission by Overlapping Retinal Cell Mosaics. (2018) Proc Conf Inf Sci Syst. 2018. DOI: 10.1109/ciss.2018.8362310
+ expand abstract
The retina provides an excellent system for understanding the trade-offs that influence distributed information processing across multiple neuron types. We focus here on the problem faced by the visual system of allocating a limited number neurons to encode different visual features at different spatial locations. The retina needs to solve three competing goals: 1) encode different visual features, 2) maximize spatial resolution for each feature, and 3) maximize accuracy with which each feature is encoded at each location. There is no current understanding of how these goals are optimized together. While information theory provides a platform for theoretically solving these problems, evaluating information provided by the responses of large neuronal arrays is in general challenging. Here we present a solution to this problem in the case where multi-dimensional stimuli can be decomposed into approximately independent components that are subsequently coupled by neural responses. Using this approach we quantify information transmission by multiple overlapping retinal ganglion cell mosaics. In the retina, translation invariance of input signals makes it possible to use Fourier basis as a set of independent components. The results reveal a transition where one high-density mosaic becomes less informative than two or more overlapping lower-density mosaics. The results explain differences in the fractions of multiple cell types, predict the existence of new retinal ganglion cell subtypes, relative distribution of neurons among cell types and differences in their nonlinear and dynamical response properties.
Sharpee, T.O. General Principles for Sensory Coding (2018) Oxford Research Encyclopedias, Neuroscience.:1-23 DOI: doi.org/10.1093/acrefore/9780190264086.013.110
+ expand abstract
Sensory systems exist to provide an organism with information about the state of the environment that can be used to guide future actions and decisions. Remarkably, two conceptually simple yet general theorems from information theory can be used to evaluate the performance of any sensory system. One theorem states that there is a minimal amount of energy that an organism has to spend in order to capture a given amount of information about the environment. The second theorem states that the maximum rate with which the organism can acquire resources from the environment, relative to its competitors, is limited by the information this organism collects about the environment, also relative to its competitors.
These two theorems provide a scaffold for formulating and testing general principles of sensory coding but leave unanswered many important practical questions of implementation in neural circuits. These implementation questions have guided thinking in entire subfields of sensory neuroscience, and include: What features in the sensory environment should be measured? Given that we make decisions on a variety of time scales, how should one solve trade-offs between making simpler measurements to guide minimal decisions vs. more elaborate sensory systems that have to overcome multiple delays between sensation and action. Once we agree on the types of features that are important to represent, how should they be represented? How should resources be allocated between different stages of processing, and where is the impact of noise most damaging? Finally, one should consider trade-offs between implementing a fixed strategy vs. an adaptive scheme that readjusts resources based on current needs. Where adaptation is considered, under what conditions does it become optimal to switch strategies? Research over the past 60 years has provided answers to almost all of these questions but primarily in early sensory systems. Joining these answers into a comprehensive framework is a challenge that will help us understand who we are and how we can make better use of limited natural resources.
Atencio, C.A., Sharpee, T.O. Multidimensional receptive field processing by cat primary auditory cortical neurons. (2017) Neuroscience. 359:130-141. DOI: 10.1016/j.neuroscience.2017.07.003
+ expand abstract
The receptive fields of many auditory cortical neurons are multidimensional and are best represented by more than one stimulus feature. The number of these dimensions, their characteristics, and how they differ with stimulus context have been relatively unexplored. Standard methods that are often used to characterize multidimensional stimulus selectivity, such as spike-triggered covariance (STC) or maximally informative dimensions (MIDs), are either limited to Gaussian stimuli or are only able to recover a small number of stimulus features due to data limitations. An information theoretic extension of STC, the maximum noise entropy (MNE) model, can be used with non-Gaussian stimulus distributions to find an arbitrary number of stimulus dimensions. When we applied the MNE model to auditory cortical neurons, we often found more than two stimulus features that influenced neuronal firing. Excitatory and suppressive features coded different acoustic contexts: excitatory features encoded higher temporal and spectral modulations, while suppressive features had lower modulation frequency preferences. We found that the excitatory and suppressive features themselves were sensitive to stimulus context when we employed two stimuli that differed only in their short-term correlation structure: while the linear features were similar, the secondary features were strongly affected by stimulus statistics. These results show that multidimensional receptive field processing is influenced by feature type and stimulus context.
Sharpee, T.O. On texture, form, and fixational eye movements. (2017) Current Opinion in Neurobiology. 46:228-233. DOI: 10.1016/j.conb.2017.09.002
+ expand abstract
Recent studies show that small movements of the eye that occur during fixation are controlled in the brain by similar neural mechanisms as large eye movements. Information theory has been successful in explaining many properties of large eye movements. Could it also help us understand the smaller eye movements that are much more difficult to study experimentally? Here I describe new predictions for how small amplitude fixational eye movements should be modulated by visual context in order to improve visual perception. In particular, the amplitude of fixational eye movements is predicted to differ when localizing edges defined by changes in texture or luminance.
Kaardal, J.T., Theunissen, F.E., Sharpee, T.O. A Low-Rank Method for Characterizing High-Level Neural Computations. (2017) Frontiers in Computational Neuroscience. 11:68. DOI: 10.3389/fncom.2017.00068
+ expand abstract
The signal transformations that take place in high-level sensory regions of the brain remain enigmatic because of the many nonlinear transformations that separate responses of these neurons from the input stimuli. One would like to have dimensionality reduction methods that can describe responses of such neurons in terms of operations on a large but still manageable set of relevant input features. A number of methods have been developed for this purpose, but often these methods rely on the expansion of the input space to capture as many relevant stimulus components as statistically possible. This expansion leads to a lower effective sampling thereby reducing the accuracy of the estimated components. Alternatively, so-called low-rank methods explicitly search for a small number of components in the hope of achieving higher estimation accuracy. Even with these methods, however, noise in the neural responses can force the models to estimate more components than necessary, again reducing the methods’ accuracy. Here we describe how a flexible regularization procedure, together with an explicit rank constraint, can strongly improve the estimation accuracy compared to previous methods suitable for characterizing neural responses to natural stimuli. Applying the proposed low-rank method to responses of auditory neurons in the songbird brain, we find multiple relevant components making up the receptive field for each neuron and characterize their computations in terms of logical OR and AND computations. The results highlight potential differences in how invariances are constructed in visual and auditory systems.
Sharpee, T.O. Optimizing Neural Information Capacity through Discretization. (2017) Neuron. 94(5):954-960. DOI: 10.1016/j.neuron.2017.04.044
+ expand abstract
Discretization in neural circuits occurs on many levels, from the generation of action potentials and dendritic integration, to neuropeptide signaling and processing of signals from multiple neurons, to behavioral decisions. It is clear that discretization, when implemented properly, can convey many benefits. However, the optimal solutions depend on both the level of noise and how it impacts a particular computation. This Perspective discusses how current physiological data could potentially be integrated into one theoretical framework based on maximizing information. Key experiments for testing that framework are discussed.
Rowekamp, R.J., Sharpee, T.O. Cross-orientation suppression in visual area V2. (2017) Nature Communications. 8:15739. DOI: 10.1038/ncomms15739
+ expand abstract
Object recognition relies on a series of transformations among which only the first cortical stage is relatively well understood. Already at the second stage, the visual area V2, the complexity of the transformation precludes a clear understanding of what specifically this area computes. Previous work has found multiple types of V2 neurons, with neurons of each type selective for multi-edge features. Here we analyse responses of V2 neurons to natural stimuli and find three organizing principles. First, the relevant edges for V2 neurons can be grouped into quadrature pairs, indicating invariance to local translation. Second, the excitatory edges have nearby suppressive edges with orthogonal orientations. Third, the resulting multi-edge patterns are repeated in space to form textures or texture boundaries. The cross-orientation suppression increases the sparseness of responses to natural images based on these complex forms of feature selectivity while allowing for multiple scales of position invariance.
Sharpee, T.O. Plasticity to the Rescue. (2016) Neuron. 92(5):935-936. DOI: 10.1016/j.neuron.2016.11.042
+ expand abstract
The balance between excitatory and inhibitory inputs is critical for the proper functioning of neural circuits. Landau and colleagues show that, in the presence of cell-type-specific connectivity, this balance is difficult to achieve without either synaptic plasticity or spike-frequency adaptation to fine-tune the connection strengths.
Kuczala, A., Sharpee, T.O. Eigenvalue spectra of large correlated random matrices. (2016) Phys Rev E. 94(5-1):050101. DOI: 10.1103/PhysRevE.94.050101
+ expand abstract
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each other. The analytical results are confirmed by numerical simulations. The results have implications for the dynamics of neural and other biological networks where plasticity induces correlations in the connection strengths within the network. We find that the presence of correlations can have a major impact on network stability.
Sharpee, T.O. How Invariant Feature Selectivity Is Achieved in Cortex. (2016) Front Synaptic Neurosci. 8:26. DOI: 10.3389/fnsyn.2016.00026
+ expand abstract
Parsing the visual scene into objects is paramount to survival. Yet, how this is accomplished by the nervous system remains largely unknown, even in the comparatively well understood visual system. It is especially unclear how detailed peripheral signal representations are transformed into the object-oriented representations that are independent of object position and are provided by the final stages of visual processing. This perspective discusses advances in computational algorithms for fitting large-scale models that make it possible to reconstruct the intermediate steps of visual processing based on neural responses to natural stimuli. In particular, it is now possible to characterize how different types of position invariance, such as local (also known as phase invariance) and more global, are interleaved with nonlinear operations to allow for coding of curved contours. Neurons in the mid-level visual area V4 exhibit selectivity to pairs of even- and odd-symmetric profiles along curved contours. Such pairing is reminiscent of the response properties of complex cells in the primary visual cortex (V1) and suggests specific ways in which V1 signals are transformed within subsequent visual cortical areas. These examples illustrate that large-scale models fitted to neural responses to natural stimuli can provide generative models of successive stages of sensory processing.
Sharpee, T.O. Taking a close look at electrosensing. (2016) Elife. 5. DOI: 10.7554/eLife.16209
+ expand abstract
The brain of the brown ghost knifefish, which uses electric fields to “see”, processes electrical signals in a way that is similar to how our brains interpret visual and auditory signals.
Zhang, Y., Sharpee, T.O. A Robust Feedforward Model of the Olfactory System. (2016) PLOS Computational Biology. 12(4):e1004850. DOI: 10.1371/journal.pcbi.1004850
+ expand abstract
Most natural odors have sparse molecular composition. This makes the principles of compressed sensing potentially relevant to the structure of the olfactory code. Yet, the largely feedforward organization of the olfactory system precludes reconstruction using standard compressed sensing algorithms. To resolve this problem, recent theoretical work has shown that signal reconstruction could take place as a result of a low dimensional dynamical system converging to one of its attractor states. However, the dynamical aspects of optimization slowed down odor recognition and were also found to be susceptible to noise. Here we describe a feedforward model of the olfactory system that achieves both strong compression and fast reconstruction that is also robust to noise. A key feature of the proposed model is a specific relationship between how odors are represented at the glomeruli stage, which corresponds to a compression, and the connections from glomeruli to third-order neurons (neurons in the olfactory cortex of vertebrates or Kenyon cells in the mushroom body of insects), which in the model corresponds to reconstruction. We show that should this specific relationship hold true, the reconstruction will be both fast and robust to noise, and in particular to the false activation of glomeruli. The predicted connectivity rate from glomeruli to third-order neurons can be tested experimentally.
Aljadeff, J., Renfrew, D., Vegué, M., Sharpee, T.O. Low-dimensional dynamics of structured random networks. (2016) Phys Rev E. 93(2):022302. DOI: 10.1103/PhysRevE.93.022302
+ expand abstract
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, and T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network connectivity structure and its low-dimensional dynamics. Each connection in the network is a random number with mean 0 and variance that depends on pre- and postsynaptic neurons through a sufficiently smooth function g of their identities. We find that these networks undergo a phase transition from a silent to a chaotic state at a critical point we derive as a function of g. Above the critical point, although unit activation levels are chaotic, their autocorrelation functions are restricted to a low-dimensional subspace. This provides a direct link between the network’s structure and some of its functional characteristics. We discuss example applications of the general results to neuroscience where we derive the support of the spectrum of connectivity matrices with heterogeneous and possibly correlated degree distributions, and to ecology where we study the stability of the cascade model for food web structure.
Hinckley, C.A., Alaynick, W.A., Gallarda, B.W., Hayashi, M., Hilde, K.L., Driscoll, S.P., Dekker, J.D., Tucker, H.O., Sharpee, T.O., Pfaff, S.L. Spinal Locomotor Circuits Develop Using Hierarchical Rules Based on Motorneuron Position and Identity. (2015) Neuron. 87(5):1008-21. DOI: 10.1016/j.neuron.2015.08.005
+ expand abstract
The coordination of multi-muscle movements originates in the circuitry that regulates the firing patterns of spinal motorneurons. Sensory neurons rely on the musculotopic organization of motorneurons to establish orderly connections, prompting us to examine whether the intraspinal circuitry that coordinates motor activity likewise uses cell position as an internal wiring reference. We generated a motorneuron-specific GCaMP6f mouse line and employed two-photon imaging to monitor the activity of lumbar motorneurons. We show that the central pattern generator neural network coordinately drives rhythmic columnar-specific motorneuron bursts at distinct phases of the locomotor cycle. Using multiple genetic strategies to perturb the subtype identity and orderly position of motorneurons, we found that neurons retained their rhythmic activity-but cell position was decoupled from the normal phasing pattern underlying flexion and extension. These findings suggest a hierarchical basis of motor circuit formation that relies on increasingly stringent matching of neuronal identity and position.
Calhoun, A.J., Tong, A., Pokala, N., Fitzpatrick, J.A., Sharpee, T.O., Chalasani, S.H. Neural Mechanisms for Evaluating Environmental Variability in Caenorhabditis elegans. (2015) Neuron. 86(2):428-41. DOI: 10.1016/j.neuron.2015.03.026
+ expand abstract
The ability to evaluate variability in the environment is vital for making optimal behavioral decisions. Here we show that Caenorhabditis elegans evaluates variability in its food environment and modifies its future behavior accordingly. We derive a behavioral model that reveals a critical period over which information about the food environment is acquired and predicts future search behavior. We also identify a pair of high-threshold sensory neurons that encode variability in food concentration and the downstream dopamine-dependent circuit that generates appropriate search behavior upon removal from food. Further, we show that CREB is required in a subset of interneurons and determines the timescale over which the variability is integrated. Interestingly, the variability circuit is a subset of a larger circuit driving search behavior, showing that learning directly modifies the very same neurons driving behavior. Our study reveals how a neural circuit decodes environmental variability to generate contextually appropriate decisions.
Aljadeff, J., Stern, M., Sharpee, T. Transition to chaos in random networks with cell-type-specific connectivity. (2015) Phys. Rev. Lett. 114(8):088101. DOI: 10.1103/PhysRevLett.114.088101
+ expand abstract
In neural circuits, statistical connectivity rules strongly depend on cell-type identity. We study dynamics of neural networks with cell-type-specific connectivity by extending the dynamic mean-field method and find that these networks exhibit a phase transition between silent and chaotic activity. By analyzing the locus of this transition, we derive a new result in random matrix theory: the spectral radius of a random connectivity matrix with block-structured variances. We apply our results to show how a small group of hyperexcitable neurons within the network can significantly increase the network’s computational capacity by bringing it into the chaotic regime.
Kastner, D.B., Baccus, S.A., Sharpee, T.O. Critical and maximally informative encoding between neural populations in the retina. (2015) Proceedings of the National Academy of Sciences of the United States of America. 112(8):2533-8. DOI: 10.1073/pnas.1418092112
+ expand abstract
Computation in the brain involves multiple types of neurons, yet the organizing principles for how these neurons work together remain unclear. Information theory has offered explanations for how different types of neurons can maximize the transmitted information by encoding different stimulus features. However, recent experiments indicate that separate neuronal types exist that encode the same filtered version of the stimulus, but then the different cell types signal the presence of that stimulus feature with different thresholds. Here we show that the emergence of these neuronal types can be quantitatively described by the theory of transitions between different phases of matter. The two key parameters that control the separation of neurons into subclasses are the mean and standard deviation (SD) of noise affecting neural responses. The average noise across the neural population plays the role of temperature in the classic theory of phase transitions, whereas the SD is equivalent to pressure or magnetic field, in the case of liquid-gas and magnetic transitions, respectively. Our results account for properties of two recently discovered types of salamander Off retinal ganglion cells, as well as the absence of multiple types of On cells. We further show that, across visual stimulus contrasts, retinal circuits continued to operate near the critical point whose quantitative characteristics matched those expected near a liquid-gas critical point and described by the nearest-neighbor Ising model in three dimensions. By operating near a critical point, neural circuits can maximize information transmission in a given environment while retaining the ability to quickly adapt to a new environment.
Calhoun, A.J., Chalasani, S.H., Sharpee, T.O. Maximally informative foraging by Caenorhabditis elegans. (2014) Elife. 3. DOI: 10.7554/eLife.04220
+ expand abstract
Animals have evolved intricate search strategies to find new sources of food. Here, we analyze a complex food seeking behavior in the nematode Caenorhabditis elegans (C. elegans) to derive a general theory describing different searches. We show that C. elegans, like many other animals, uses a multi-stage search for food, where they initially explore a small area intensively (‘local search’) before switching to explore a much larger area (‘global search’). We demonstrate that these search strategies as well as the transition between them can be quantitatively explained by a maximally informative search strategy, where the searcher seeks to continuously maximize information about the target. Although performing maximally informative search is computationally demanding, we show that a drift-diffusion model can approximate it successfully with just three neurons. Our study reveals how the maximally informative search strategy can be implemented and adopted to different search conditions.
Sharpee, T.O. Toward functional classification of neuronal types. (2014) Neuron. 83(6):1329-34. DOI: 10.1016/j.neuron.2014.08.040
+ expand abstract
How many types of neurons are there in the brain? This basic neuroscience question remains unsettled despite many decades of research. Classification schemes have been proposed based on anatomical, electrophysiological, or molecular properties. However, different schemes do not always agree with each other. This raises the question of whether one can classify neurons based on their function directly. For example, among sensory neurons, can a classification scheme be devised that is based on their role in encoding sensory stimuli? Here, theoretical arguments are outlined for how this can be achieved using information theory by looking at optimal numbers of cell types and paying attention to two key properties: correlations between inputs and noise in neural responses. This theoretical framework could help to map the hierarchical tree relating different neuronal classes within and across species.
Sharpee, T.O. Function determines structure in complex neural networks. (2014) Proceedings of the National Academy of Sciences of the United States of America. 111(23):8327-8. DOI: 10.1073/pnas.1407198111
Sharpee, T.O., Calhoun, A.J., Chalasani, S.H. Information theory of adaptation in neurons, behavior, and mood. (2014) Current Opinion in Neurobiology. 25:47-53. DOI: 10.1016/j.conb.2013.11.007
+ expand abstract
The ability to make accurate predictions of future stimuli and consequences of one’s actions are crucial for the survival and appropriate decision-making. These predictions are constantly being made at different levels of the nervous system. This is evidenced by adaptation to stimulus parameters in sensory coding, and in learning of an up-to-date model of the environment at the behavioral level. This review will discuss recent findings that actions of neurons and animals are selected based on detailed stimulus history in such a way as to maximize information for achieving the task at hand. Information maximization dictates not only how sensory coding should adapt to various statistical aspects of stimuli, but also that reward function should adapt to match the predictive information from past to future.
Morris, R., Sancho-Martinez, I., Sharpee, T.O., Izpisua Belmonte, J.C. Mathematical approaches to modeling development and reprogramming. (2014) Proceedings of the National Academy of Sciences of the United States of America. 111(14):5076-82. DOI: 10.1073/pnas.1317150111
+ expand abstract
Induced pluripotent stem cells (iPSCs) are created by the reprogramming of somatic cells via overexpression of certain transcription factors, such as the originally described Yamanaka factors: Oct4, Sox2, Klf4, and c-Myc (OSKM). Here we discuss recent advancements in iPSC reprogramming and introduce mathematical approaches to help map the landscape between cell states during reprogramming. Our modelization indicates that OSKM expression diminishes and/or changes potential barriers between cell states and that epigenetic remodeling facilitate these transitions. From a practical perspective, the modeling approaches outlined here allow us to predict the time necessary to create a given number of iPSC colonies or the number of reprogrammed cells generated in a given time. Additional investigations will help to further refine modeling strategies, rendering them applicable toward the study of the development and stability of cancer cells or even other reprogramming processes such as lineage conversion. Ultimately, a quantitative understanding of cell state transitions might facilitate the establishment of regenerative medicine strategies and enhance the translation of reprogramming technologies into the clinic.
Aljadeff, J., Segev, R., Berry, M.J., Sharpee, T.O. Spike triggered covariance in strongly correlated gaussian stimuli. (2013) PLOS Computational Biology. 9(9):e1003206. DOI: 10.1371/journal.pcbi.1003206
+ expand abstract
Many biological systems perform computations on inputs that have very large dimensionality. Determining the relevant input combinations for a particular computation is often key to understanding its function. A common way to find the relevant input dimensions is to examine the difference in variance between the input distribution and the distribution of inputs associated with certain outputs. In systems neuroscience, the corresponding method is known as spike-triggered covariance (STC). This method has been highly successful in characterizing relevant input dimensions for neurons in a variety of sensory systems. So far, most studies used the STC method with weakly correlated Gaussian inputs. However, it is also important to use this method with inputs that have long range correlations typical of the natural sensory environment. In such cases, the stimulus covariance matrix has one (or more) outstanding eigenvalues that cannot be easily equalized because of sampling variability. Such outstanding modes interfere with analyses of statistical significance of candidate input dimensions that modulate neuronal outputs. In many cases, these modes obscure the significant dimensions. We show that the sensitivity of the STC method in the regime of strongly correlated inputs can be improved by an order of magnitude or more. This can be done by evaluating the significance of dimensions in the subspace orthogonal to the outstanding mode(s). Analyzing the responses of retinal ganglion cells probed with [Formula: see text] Gaussian noise, we find that taking into account outstanding modes is crucial for recovering relevant input dimensions for these neurons.
Sharpee, T.O. Computational identification of receptive fields. (2013) Annual Review of Neuroscience. 36:103-20. DOI: 10.1146/annurev-neuro-062012-170253
+ expand abstract
Natural stimuli elicit robust responses of neurons throughout sensory pathways, and therefore their use provides unique opportunities for understanding sensory coding. This review describes statistical methods that can be used to characterize neural feature selectivity, focusing on the case of natural stimuli. First, we discuss how such classic methods as reverse correlation/spike-triggered average and spike-triggered covariance can be generalized for use with natural stimuli to find the multiple relevant stimulus features that affect the responses of a given neuron. Second, ways to characterize neural feature selectivity while assuming that the neural responses exhibit a certain type of invariance, such as position invariance for visual neurons, are discussed. Finally, we discuss methods that do not require one to make an assumption of invariance and instead can determine the type of invariance by analyzing relationships between the multiple stimulus features that affect the neural responses.
Sharpee, T.O., Kouh, M., Reynolds, J.H. Trade-off between curvature tuning and position invariance in visual area V4. (2013) Proceedings of the National Academy of Sciences of the United States of America. 110(28):11618-23. DOI: 10.1073/pnas.1217479110
+ expand abstract
Humans can rapidly recognize a multitude of objects despite differences in their appearance. The neural mechanisms that endow high-level sensory neurons with both selectivity to complex stimulus features and “tolerance” or invariance to identity-preserving transformations, such as spatial translation, remain poorly understood. Previous studies have demonstrated that both tolerance and selectivity to conjunctions of features are increased at successive stages of the ventral visual stream that mediates visual recognition. Within a given area, such as visual area V4 or the inferotemporal cortex, tolerance has been found to be inversely related to the sparseness of neural responses, which in turn was positively correlated with conjunction selectivity. However, the direct relationship between tolerance and conjunction selectivity has been difficult to establish, with different studies reporting either an inverse or no significant relationship. To resolve this, we measured V4 responses to natural scenes, and using recently developed statistical techniques, we estimated both the relevant stimulus features and the range of translation invariance for each neuron. Focusing the analysis on tuning to curvature, a tractable example of conjunction selectivity, we found that neurons that were tuned to more curved contours had smaller ranges of position invariance and produced sparser responses to natural stimuli. These trade-offs provide empirical support for recent theories of how the visual system estimates 3D shapes from shading and texture flows, as well as the tiling hypothesis of the visual space for different curvature values.
Kaardal, J., Fitzgerald, J.D., Berry, M.J., Sharpee, T.O. Identifying functional bases for multidimensional neural computations. (2013) Neural Computation. 25(7):1870-90. DOI: 10.1162/NECO_a_00465
+ expand abstract
Current dimensionality-reduction methods can identify relevant subspaces for neural computations but do not favor one basis over the other within the relevant subspace. Finding the appropriate basis can simplify the description of the nonlinear computation with respect to the relevant variables, making it easier to elucidate the underlying neural computation and make hypotheses about the neural circuitry, giving rise to the observed responses. Part of the problem is that although some of the dimensionality reduction methods can identify many of the relevant dimensions, it is usually difficult to map out or interpret the nonlinear transformation with respect to more than a few relevant dimensions simultaneously without some simplifying assumptions. While recent approaches make it possible to create predictive models based on many relevant dimensions simultaneously, there still remains the need to relate such predictive models to the mechanistic descriptions of the operation of underlying neural circuitry. Here we demonstrate that transforming to a basis within the relevant subspace where the neural computation is best described by a given nonlinear function often makes it easier to interpret the computation and describe it with a small number of parameters. We refer to the corresponding basis as the functional basis, and illustrate the utility of such transformation in the context of logical OR and logical AND functions. We show that although dimensionality-reduction methods such as spike-triggered covariance are able to find a relevant subspace, they often produce dimensions that are difficult to interpret and do not correspond to a functional basis. The functional features can be found using a maximum likelihood approach. The results are illustrated using simulated neurons and recordings from retinal ganglion cells. The resulting features are uniquely defined and nonorthogonal, and they make it easier to relate computational and mechanistic models to each other.
Nandy, A.S., Sharpee, T.O., Reynolds, J.H., Mitchell, J.F. The fine structure of shape tuning in area V4. (2013) Neuron. 78(6):1102-15. DOI: 10.1016/j.neuron.2013.04.016
+ expand abstract
Previous studies have shown that neurons in area V4 are involved in the processing of shapes of intermediate complexity and are sensitive to curvature. These studies also suggest that curvature-tuned neurons are position invariant. We sought to examine the mechanisms that endow V4 neurons with these properties. Consistent with previous studies, we found that response rank order to the most- and least-preferred stimuli was preserved throughout the receptive field. However, a fine-grained analysis of shape tuning revealed a surprising result: V4 neurons tuned to highly curved shapes exhibit very limited translation invariance. At a fine spatial scale, these neurons exhibit local variation in orientation. In contrast, neurons that prefer straight contours exhibit spatially invariant orientation-tuning and homogenous fine-scale orientation maps. Both of these patterns are consistent with a simple orientation-pooling model, with tuning for straight or curved shapes resulting, respectively, from pooling of homogenous or heterogeneous orientation signals inherited from early visual areas.
Saremi, S., Sejnowski, T.J., Sharpee, T.O. Double-gabor filters are independent components of small translation-invariant image patches. (2013) Neural Computation. 25(4):922-39. DOI: 10.1162/NECO_a_00418
+ expand abstract
The analysis of natural images with independent component analysis (ICA) yields localized bandpass Gabor-type filters similar to receptive fields of simple cells in visual cortex. We applied ICA on a subset of patches called position-centered patches, selected for forming a translation-invariant representation of small patches. The resulting filters were qualitatively different in two respects. One novel feature was the emergence of filters we call double-Gabor filters. In contrast to Gabor functions that are modulated in one direction, double-Gabor filters are sinusoidally modulated in two orthogonal directions. In addition the filters were more extended in space and frequency compared to standard ICA filters and better matched the distribution in experimental recordings from neurons in primary visual cortex. We further found a dual role for double-Gabor filters as edge and texture detectors, which could have engineering applications.
Jeanne, J.M., Sharpee, T.O., Gentner, T.Q. Associative learning enhances population coding by inverting interneuronal correlation patterns. (2013) Neuron. 78(2):352-63. DOI: 10.1016/j.neuron.2013.02.023
+ expand abstract
Learning-dependent cortical encoding has been well described in single neurons. But behaviorally relevant sensory signals drive the coordinated activity of millions of cortical neurons; whether learning produces stimulus-specific changes in population codes is unknown. Because the pattern of firing rate correlations between neurons–an emergent property of neural populations–can significantly impact encoding fidelity, we hypothesize that it is a target for learning. Using an associative learning procedure, we manipulated the behavioral relevance of natural acoustic signals and examined the evoked spiking activity in auditory cortical neurons in songbirds. We show that learning produces stimulus-specific changes in the pattern of interneuronal correlations that enhance the ability of neural populations to recognize signals relevant for behavior. This learning-dependent enhancement increases with population size. The results identify the pattern of interneuronal correlation in neural populations as a target of learning that can selectively enhance the representations of specific sensory signals.
Eickenberg, M., Rowekamp, R.J., Kouh, M., Sharpee, T.O. Characterizing responses of translation-invariant neurons to natural stimuli: maximally informative invariant dimensions. (2012) Neural Computation. 24(9):2384-421. DOI: 10.1162/NECO_a_00330
+ expand abstract
The human visual system is capable of recognizing complex objects even when their appearances change drastically under various viewing conditions. Especially in the higher cortical areas, the sensory neurons reflect such functional capacity in their selectivity for complex visual features and invariance to certain object transformations, such as image translation. Due to the strong nonlinearities necessary to achieve both the selectivity and invariance, characterizing and predicting the response patterns of these neurons represents a formidable computational challenge. A related problem is that such neurons are poorly driven by randomized inputs, such as white noise, and respond strongly only to stimuli with complex high-order correlations, such as natural stimuli. Here we describe a novel two-step optimization technique that can characterize both the shape selectivity and the range and coarseness of position invariance from neural responses to natural stimuli. One step in the optimization is finding the template as the maximally informative dimension given the estimated spatial location where the response could have been triggered within each image. The estimates of the locations that triggered the response are updated in the next step. Under the assumption of a monotonic relationship between the firing rate and stimulus projections on the template at a given position, the most likely location is the one that has the largest projection on the estimate of the template. The algorithm shows quick convergence during optimization, and the estimation results are reliable even in the regime of small signal-to-noise ratios. When we apply the algorithm to responses of complex cells in the primary visual cortex (V1) to natural movies, we find that responses of the majority of cells were significantly better described by translation-invariant models based on one template compared with position-specific models with several relevant features.
Atencio, C.A., Sharpee, T.O., Schreiner, C.E. Receptive field dimensionality increases from the auditory midbrain to cortex. (2012) Journal of Neurophysiology. 107(10):2594-603. DOI: 10.1152/jn.01025.2011
+ expand abstract
In the primary auditory cortex, spectrotemporal receptive fields (STRFs) are composed of multiple independent components that capture the processing of disparate stimulus aspects by any given neuron. The origin of these multidimensional stimulus filters in the central auditory system is unknown. To determine whether multicomponent STRFs emerge prior to the forebrain, we recorded from single neurons in the main obligatory station of the auditory midbrain, the inferior colliculus. By comparing results of different spike-triggered techniques, we found that the neural responses in the inferior colliculus can be accounted for by a single stimulus filter. This was observed for all temporal response patterns, from strongly phasic to tonic. Our results reveal that spectrotemporal stimulus encoding undergoes a fundamental transformation along the auditory neuraxis, with the emergence of multidimensional receptive fields beyond the auditory midbrain.
Sharpee, T.O. Adaptive switches in midbrain circuits. (2012) Neuron. 73(1):6-7. DOI: 10.1016/j.neuron.2011.12.017
+ expand abstract
In this issue of Neuron, Mysore and Knudsen (2012) describe a simple, anatomically supported circuit that can categorize stimuli into “strongest” and “others,” regardless of their absolute strength. Such flexible categorization cannot be achieved by lateral inhibition alone but also requires that the inhibitory neurons reciprocally inhibit each other.
Fitzgerald, J.D., Rowekamp, R.J., Sincich, L.C., Sharpee, T.O. Second order dimensionality reduction using minimum and maximum mutual information models. (2011) PLOS Computational Biology. 7(10):e1002249. DOI: 10.1371/journal.pcbi.1002249
+ expand abstract
Conventional methods used to characterize multidimensional neural feature selectivity, such as spike-triggered covariance (STC) or maximally informative dimensions (MID), are limited to Gaussian stimuli or are only able to identify a small number of features due to the curse of dimensionality. To overcome these issues, we propose two new dimensionality reduction methods that use minimum and maximum information models. These methods are information theoretic extensions of STC that can be used with non-Gaussian stimulus distributions to find relevant linear subspaces of arbitrary dimensionality. We compare these new methods to the conventional methods in two ways: with biologically-inspired simulated neurons responding to natural images and with recordings from macaque retinal and thalamic cells responding to naturalistic time-varying stimuli. With non-Gaussian stimuli, the minimum and maximum information methods significantly outperform STC in all cases, whereas MID performs best in the regime of low dimensional feature spaces.
Sharpee, T.O., Nagel, K.I., Doupe, A.J. Two-dimensional adaptation in the auditory forebrain. (2011) Journal of Neurophysiology. 106(4):1841-61. DOI: 10.1152/jn.00905.2010
+ expand abstract
Sensory neurons exhibit two universal properties: sensitivity to multiple stimulus dimensions, and adaptation to stimulus statistics. How adaptation affects encoding along primary dimensions is well characterized for most sensory pathways, but if and how it affects secondary dimensions is less clear. We studied these effects for neurons in the avian equivalent of primary auditory cortex, responding to temporally modulated sounds. We showed that the firing rate of single neurons in field L was affected by at least two components of the time-varying sound log-amplitude. When overall sound amplitude was low, neural responses were based on nonlinear combinations of the mean log-amplitude and its rate of change (first time differential). At high mean sound amplitude, the two relevant stimulus features became the first and second time derivatives of the sound log-amplitude. Thus a strikingly systematic relationship between dimensions was conserved across changes in stimulus intensity, whereby one of the relevant dimensions approximated the time differential of the other dimension. In contrast to stimulus mean, increases in stimulus variance did not change relevant dimensions, but selectively increased the contribution of the second dimension to neural firing, illustrating a new adaptive behavior enabled by multidimensional encoding. Finally, we demonstrated theoretically that inclusion of time differentials as additional stimulus features, as seen so prominently in the single-neuron responses studied here, is a useful strategy for encoding naturalistic stimuli, because it can lower the necessary sampling rate while maintaining the robustness of stimulus reconstruction to correlated noise.
Sharpee, T.O., Atencio, C.A., Schreiner, C.E. Hierarchical representations in the auditory cortex. (2011) Current Opinion in Neurobiology. 21(5):761-7. DOI: 10.1016/j.conb.2011.05.027
+ expand abstract
Understanding the neural mechanisms of invariant object recognition remains one of the major unsolved problems in neuroscience. A common solution that is thought to be employed by diverse sensory systems is to create hierarchical representations of increasing complexity and tolerance. However, in the mammalian auditory system many aspects of this hierarchical organization remain undiscovered, including the prominent classes of high-level representations (that would be analogous to face selectivity in the visual system or selectivity to bird’s own song in the bird) and the dominant types of invariant transformations. Here we review the recent progress that begins to probe the hierarchy of auditory representations, and the computational approaches that can be helpful in achieving this feat.
Rowekamp, R.J., Sharpee, T.O. Analyzing multicomponent receptive fields from neural responses to natural stimuli. (2011) Network. 22(1-4):45-73. DOI: 10.3109/0954898X.2011.566303
+ expand abstract
The challenge of building increasingly better models of neural responses to natural stimuli is to accurately estimate the multiple stimulus features that may jointly affect the neural spike probability. The selectivity for combinations of features is thought to be crucial for achieving classical properties of neural responses such as contrast invariance. The joint search for these multiple stimulus features is difficult because estimating spike probability as a multidimensional function of stimulus projections onto candidate relevant dimensions is subject to the curse of dimensionality. An attractive alternative is to search for relevant dimensions sequentially, as in projection pursuit regression. Here we demonstrate using analytic arguments and simulations of model cells that different types of sequential search strategies exhibit systematic biases when used with natural stimuli. Simulations show that joint optimization is feasible for up to three dimensions with current algorithms. When applied to the responses of V1 neurons to natural scenes, models based on three jointly optimized dimensions had better predictive power in a majority of cases compared to dimensions optimized sequentially, with different sequential methods yielding comparable results. Thus, although the curse of dimensionality remains, at least several relevant dimensions can be estimated by joint information maximization.
Fitzgerald, J.D., Sincich, L.C., Sharpee, T.O. Minimal models of multidimensional computations. (2011) PLOS Computational Biology. 7(3):e1001111. DOI: 10.1371/journal.pcbi.1001111
+ expand abstract
The multidimensional computations performed by many biological systems are often characterized with limited information about the correlations between inputs and outputs. Given this limitation, our approach is to construct the maximum noise entropy response function of the system, leading to a closed-form and minimally biased model consistent with a given set of constraints on the input/output moments; the result is equivalent to conditional random field models from machine learning. For systems with binary outputs, such as neurons encoding sensory stimuli, the maximum noise entropy models are logistic functions whose arguments depend on the constraints. A constraint on the average output turns the binary maximum noise entropy models into minimum mutual information models, allowing for the calculation of the information content of the constraints and an information theoretic characterization of the system’s computations. We use this approach to analyze the nonlinear input/output functions in macaque retina and thalamus; although these systems have been previously shown to be responsive to two input dimensions, the functional form of the response function in this reduced space had not been unambiguously identified. A second order model based on the logistic function is found to be both necessary and sufficient to accurately describe the neural responses to naturalistic stimuli, accounting for an average of 93% of the mutual information with a small number of parameters. Thus, despite the fact that the stimulus is highly non-Gaussian, the vast majority of the information in the neural responses is related to first and second order correlations. Our results suggest a principled and unbiased way to model multidimensional computations and determine the statistics of the inputs that are being encoded in the outputs.
Jeanne, J.M., Thompson, J.V., Sharpee, T.O., Gentner, T.Q. Emergence of learned categorical representations within an auditory forebrain circuit. (2011) Journal of Neuroscience. 31(7):2595-606. DOI: 10.1523/JNEUROSCI.3930-10.2011
+ expand abstract
Many learned behaviors are thought to require the activity of high-level neurons that represent categories of complex signals, such as familiar faces or native speech sounds. How these complex, experience-dependent neural responses emerge within the brain’s circuitry is not well understood. The caudomedial mesopallium (CMM), a secondary auditory region in the songbird brain, contains neurons that respond to specific combinations of song components and respond preferentially to the songs that birds have learned to recognize. Here, we examine the transformation of these learned responses across a broader forebrain circuit that includes the caudolateral mesopallium (CLM), an auditory region that provides input to CMM. We recorded extracellular single-unit activity in CLM and CMM in European starlings trained to recognize sets of conspecific songs and compared multiple encoding properties of neurons between these regions. We find that the responses of CMM neurons are more selective between song components, convey more information about song components, and are more variable over repeated components than the responses of CLM neurons. While learning enhances neural encoding of song components in both regions, CMM neurons encode more information about the learned categories associated with songs than do CLM neurons. Collectively, these data suggest that CLM and CMM are part of a functional sensory hierarchy that is modified by learning to yield representations of natural vocal signals that are increasingly informative with respect to behavior.
Imaizumi, K., Priebe, N.J., Sharpee, T.O., Cheung, S.W., Schreiner, C.E. Encoding of temporal information by timing, rate, and place in cat auditory cortex. (2010) PLOS One. 5(7):e11531. DOI: 10.1371/journal.pone.0011531
+ expand abstract
A central goal in auditory neuroscience is to understand the neural coding of species-specific communication and human speech sounds. Low-rate repetitive sounds are elemental features of communication sounds, and core auditory cortical regions have been implicated in processing these information-bearing elements. Repetitive sounds could be encoded by at least three neural response properties: 1) the event-locked spike-timing precision, 2) the mean firing rate, and 3) the interspike interval (ISI). To determine how well these response aspects capture information about the repetition rate stimulus, we measured local group responses of cortical neurons in cat anterior auditory field (AAF) to click trains and calculated their mutual information based on these different codes. ISIs of the multiunit responses carried substantially higher information about low repetition rates than either spike-timing precision or firing rate. Combining firing rate and ISI codes was synergistic and captured modestly more repetition information. Spatial distribution analyses showed distinct local clustering properties for each encoding scheme for repetition information indicative of a place code. Diversity in local processing emphasis and distribution of different repetition rate codes across AAF may give rise to concurrent feed-forward processing streams that contribute differently to higher-order sound analysis.
Gallarda, B.W., Sharpee, T.O., Pfaff, S.L., Alaynick, W.A. Defining rhythmic locomotor burst patterns using a continuous wavelet transform. (2010) Ann. N. Y. Acad. Sci. 1198:133-9. DOI: 10.1111/j.1749-6632.2010.05437.x
+ expand abstract
We review an objective and automated method for analyzing locomotor electrophysiology data with improved speed and accuracy. Manipulating central pattern generator (CPG) organization via mouse genetics has been a critical advance in the study of this circuit. Better quantitative measures of the locomotor data will further enhance our understanding of CPG development and function. Current analysis methods aim to measure locomotor cycle period, rhythmicity, and left-right and flexor-extensor phase; however, these methods have not been optimized to detect or quantify subtle changes in locomotor output. Because multiple experiments suggest that development of the CPG is robust and that the circuit is able to achieve organized behavior by several means, we sought to find a more objective and sensitive method for quantifying locomotor output. Recently, a continuous wavelet transform (CWT) has been applied to spinal cord ventral root recordings with promising results. The CWT provides greater resolution of cycle period, phase, and rhythmicity, and is proving to be a superior technique in assessing subtle changes in locomotion due to genetic perturbations of the underlying circuitry.
Atencio, C.A., Sharpee, T.O., Schreiner, C.E. Hierarchical computation in the canonical auditory cortical circuit. (2009) Proceedings of the National Academy of Sciences of the United States of America. 106(51):21894-9. DOI: 10.1073/pnas.0908383106
+ expand abstract
Sensory cortical anatomy has identified a canonical microcircuit underlying computations between and within layers. This feed-forward circuit processes information serially from granular to supragranular and to infragranular layers. How this substrate correlates with an auditory cortical processing hierarchy is unclear. We recorded simultaneously from all layers in cat primary auditory cortex (AI) and estimated spectrotemporal receptive fields (STRFs) and associated nonlinearities. Spike-triggered averaged STRFs revealed that temporal precision, spectrotemporal separability, and feature selectivity varied with layer according to a hierarchical processing model. STRFs from maximally informative dimension (MID) analysis confirmed hierarchical processing. Of two cooperative MIDs identified for each neuron, the first comprised the majority of stimulus information in granular layers. Second MID contributions and nonlinear cooperativity increased in supragranular and infragranular layers. The AI microcircuit provides a valid template for three independent hierarchical computation principles. Increases in processing complexity, STRF cooperativity, and nonlinearity correlate with the synaptic distance from granular layers.
Fitzgerald, J.D., Sharpee, T.O. Maximally informative pairwise interactions in networks. (2009) Phys Rev E Stat Nonlin Soft Matter Phys. 80(3 Pt 1):031914. DOI: 10.1103/PhysRevE.80.031914
+ expand abstract
Several types of biological networks have recently been shown to be accurately described by a maximum entropy model with pairwise interactions, also known as the Ising model. Here we present an approach for finding the optimal mappings between input signals and network states that allow the network to convey the maximal information about input signals drawn from a given distribution. This mapping also produces a set of linear equations for calculating the optimal Ising-model coupling constants, as well as geometric properties that indicate the applicability of the pairwise Ising model. We show that the optimal pairwise interactions are on average zero for Gaussian and uniformly distributed inputs, whereas they are nonzero for inputs approximating those in natural environments. These nonzero network interactions are predicted to increase in strength as the noise in the response functions of each network node increases. This approach also suggests ways for how interactions with unmeasured parts of the network can be inferred from the parameters of response functions for the measured network nodes.
Liu, Y.S., Stevens, C.F., Sharpee, T.O. Predictable irregularities in retinal receptive fields. (2009) Proceedings of the National Academy of Sciences of the United States of America. 106(38):16499-504. DOI: 10.1073/pnas.0908926106
+ expand abstract
Understanding how the nervous system achieves reliable performance using unreliable components is important for many disciplines of science and engineering, in part because it can suggest ways to lower the energetic cost of computing. In vision, retinal ganglion cells partition visual space into approximately circular regions termed receptive fields (RFs). Average RF shapes are such that they would provide maximal spatial resolution if they were centered on a perfect lattice. However, individual shapes have fine-scale irregularities. Here, we find that irregular RF shapes increase the spatial resolution in the presence of lattice irregularities from approximately 60% to approximately 92% of that possible for a perfect lattice. Optimization of RF boundaries around their fixed center positions reproduced experimental observations neuron-by-neuron. Our results suggest that lattice irregularities determine the shapes of retinal RFs and that similar algorithms can improve the performance of retinal prosthetics where substantial irregularities arise at their interface with neural tissue.
Sincich, L.C., Horton, J.C., Sharpee, T.O. Preserving information in neural transmission. (2009) Journal of Neuroscience. 29(19):6207-16. DOI: 10.1523/JNEUROSCI.3701-08.2009
+ expand abstract
Along most neural pathways, the spike trains transmitted from one neuron to the next are altered. In the process, neurons can either achieve a more efficient stimulus representation, or extract some biologically important stimulus parameter, or succeed at both. We recorded the inputs from single retinal ganglion cells and the outputs from connected lateral geniculate neurons in the macaque to examine how visual signals are relayed from retina to cortex. We found that geniculate neurons re-encoded multiple temporal stimulus features to yield output spikes that carried more information about stimuli than was available in each input spike. The coding transformation of some relay neurons occurred with no decrement in information rate, despite output spike rates that averaged half the input spike rates. This preservation of transmitted information was achieved by the short-term summation of inputs that geniculate neurons require to spike. A reduced model of the retinal and geniculate visual responses, based on two stimulus features and their associated nonlinearities, could account for >85% of the total information available in the spike trains and the preserved information transmission. These results apply to neurons operating on a single time-varying input, suggesting that synaptic temporal integration can alter the temporal receptive field properties to create a more efficient representation of visual signals in the thalamus than the retina.
Sharpee, T.O., Victor, J.D. Contextual modulation of V1 receptive fields depends on their spatial symmetry. (2009) Journal of Computational Neuroscience. 26(2):203-18. DOI: 10.1007/s10827-008-0107-5
+ expand abstract
The apparent receptive field characteristics of sensory neurons depend on the statistics of the stimulus ensemble–a nonlinear phenomenon often called contextual modulation. Since visual cortical receptive fields determined from simple stimuli typically do not predict responses to complex stimuli, understanding contextual modulation is crucial to understanding responses to natural scenes. To analyze contextual modulation, we examined how apparent receptive fields differ for two stimulus ensembles that are matched in first- and second-order statistics, but differ in their feature content: one ensemble is enriched in elongated contours. To identify systematic trends across the neural population, we used a multidimensional scaling method, the Procrustes transformation. We found that contextual modulation of receptive field components increases with their spatial extent. More surprisingly, we also found that odd-symmetric components change systematically, but even-symmetric components do not. This symmetry dependence suggests that contextual modulation is driven by oriented On/Off dyads, i.e., modulation of the strength of intracortically-generated signals.
Kouh, M., Sharpee, T.O. Estimating linear-nonlinear models using Renyi divergences. (2009) Network. 20(2):49-68. DOI: 10.1080/09548980902950891
+ expand abstract
This article compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramer-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data.
Atencio, C.A., Sharpee, T.O., Schreiner, C.E. Cooperative nonlinearities in auditory cortical neurons. (2008) Neuron. 58(6):956-66. DOI: 10.1016/j.neuron.2008.04.026
+ expand abstract
Cortical receptive fields represent the signal preferences of sensory neurons. Receptive fields are thought to provide a representation of sensory experience from which the cerebral cortex may make interpretations. While it is essential to determine a neuron’s receptive field, it remains unclear which features of the acoustic environment are specifically represented by neurons in the primary auditory cortex (AI). We characterized cat AI spectrotemporal receptive fields (STRFs) by finding both the spike-triggered average (STA) and stimulus dimensions that maximized the mutual information between response and stimulus. We derived a nonlinearity relating spiking to stimulus projection onto two maximally informative dimensions (MIDs). The STA was highly correlated with the first MID. Generally, the nonlinearity for the first MID was asymmetric and often monotonic in shape, while the second MID nonlinearity was symmetric and nonmonotonic. The joint nonlinearity for both MIDs revealed that most first and second MIDs were synergistic and thus should be considered conjointly. The difference between the nonlinearities suggests different possible roles for the MIDs in auditory processing.
Sharpee, T.O., Miller, K.D., Stryker, M.P. On the importance of static nonlinearity in estimating spatiotemporal neural filters with natural stimuli. (2008) Journal of Neurophysiology. 99(5):2496-509. DOI: 10.1152/jn.01397.2007
+ expand abstract
Understanding neural responses with natural stimuli has increasingly become an essential part of characterizing neural coding. Neural responses are commonly characterized by a linear-nonlinear (LN) model, in which the output of a linear filter applied to the stimulus is transformed by a static nonlinearity to determine neural response. To estimate the linear filter in the LN model, studies of responses to natural stimuli commonly use methods that are unbiased only for a linear model (in which there is no static nonlinearity): spike-triggered averages with correction for stimulus power spectrum, with or without regularization. Although these methods work well for artificial stimuli, such as Gaussian white noise, we show here that they estimate neural filters of LN models from responses to natural stimuli much more poorly. We studied simple cells in cat primary visual cortex. We demonstrate that the filters computed by directly taking the nonlinearity into account have better predictive power and depend less on the stimulus than those computed under the linear model. With noise stimuli, filters computed using the linear and LN models were similar, as predicted theoretically. With natural stimuli, filters of the two models can differ profoundly. Noise and natural stimulus filters differed significantly in spatial properties, but these differences were exaggerated when filters were computed using the linear rather than the LN model. Although regularization of filters computed under the linear model improved their predictive power, it also led to systematic distortions of their spatial frequency profiles, especially at low spatial and temporal frequencies.
Clifford, C.W., Webster, M.A., Stanley, G.B., Stocker, A.A., Kohn, A., Sharpee, T.O., Schwartz, O. Visual adaptation: neural, psychological and computational aspects. (2007) Vision Research. 47(25):3125-31. DOI: 10.1016/j.visres.2007.08.023
+ expand abstract
The term ‘visual adaptation’ describes the processes by which the visual system alters its operating properties in response to changes in the environment. These continual adjustments in sensory processing are diagnostic as to the computational principles underlying the neural coding of information and can have profound consequences for our perceptual experience. New physiological and psychophysical data, along with emerging statistical and computational models, make this an opportune time to bring together experimental and theoretical perspectives. Here, we discuss functional ideas about adaptation in the light of recent data and identify exciting directions for future research.
Sharpee, T.O. Comparison of information and variance maximization strategies for characterizing neural feature selectivity. (2007) Stat Med. 26(21):4009-31. DOI: 10.1002/sim.2931
+ expand abstract
This paper compares several statistical methods for analyzing neural feature selectivity with natural stimuli. Despite the non-Gaussian character of correlations in natural stimuli, several relevant stimulus dimensions can be found by maximizing either information or, as is demonstrated here, variance. In the case of information, the relevance of each dimension is quantified by a Kullback-Leibler divergence between the full input probability distribution and that across inputs associated with positive neural responses, both projected onto that dimension. We demonstrate that least-square matching of the nonlinear prediction based on several dimensions relevant to the recorded spike trains yields an optimization scheme similar to information maximization. The relevant dimensions are found as those that capture the most variance in neural response. The variance along a stimulus dimension is given by a Rényi divergence of order 2 instead of the Kullback-Leibler divergence used for maximizing information. Statistical errors expected for the two schemes are shown to be similar through both analytical and numerical calculations. However, in the asymptotic limit of large spike numbers, maximizing information results in smaller errors than variance optimization. Numerical simulations for model cells with different noise levels show that this trend persists, and possibly increases, when the number of spikes decreases. This makes the problem of finding relevant dimensions one of the examples where information-theoretic approaches are no more data limited than the variance-based measures. Variance and information optimization also outperform methods based on the spike-triggered average for all numbers of spikes and neural noise levels.
Sharpee, T., Bialek, W. Neural decision boundaries for maximal information transmission. (2007) PLOS One. 2(7):e646. DOI: 10.1371/journal.pone.0000646
+ expand abstract
We consider here how to separate multidimensional signals into two categories, such that the binary decision transmits the maximum possible information about those signals. Our motivation comes from the nervous system, where neurons process multidimensional signals into a binary sequence of responses (spikes). In a small noise limit, we derive a general equation for the decision boundary that locally relates its curvature to the probability distribution of inputs. We show that for Gaussian inputs the optimal boundaries are planar, but for non-Gaussian inputs the curvature is nonzero. As an example, we consider exponentially distributed inputs, which are known to approximate a variety of signals from natural environment.
Sharpee, T.O., Sugihara, H., Kurgansky, A.V., Rebrik, S.P., Stryker, M.P., Miller, K.D. Adaptive filtering enhances information transmission in visual cortex. (2006) Nature. 439(7079):936-42. DOI: 10.1038/nature04519
+ expand abstract
Sensory neuroscience seeks to understand how the brain encodes natural environments. However, neural coding has largely been studied using simplified stimuli. In order to assess whether the brain’s coding strategy depends on the stimulus ensemble, we apply a new information-theoretic method that allows unbiased calculation of neural filters (receptive fields) from responses to natural scenes or other complex signals with strong multipoint correlations. In the cat primary visual cortex we compare responses to natural inputs with those to noise inputs matched for luminance and contrast. We find that neural filters adaptively change with the input ensemble so as to increase the information carried by the neural response about the filtered stimulus. Adaptation affects the spatial frequency composition of the filter, enhancing sensitivity to under-represented frequencies in agreement with optimal encoding arguments. Adaptation occurs over 40 s to many minutes, longer than most previously reported forms of adaptation.
Victor, J.D., Mechler, F., Repucci, M.A., Purpura, K.P., Sharpee, T. Responses of V1 neurons to two-dimensional hermite functions. (2006) Journal of Neurophysiology. 95(1):379-400. DOI: 10.1152/jn.00498.2005
+ expand abstract
Neurons in primary visual cortex are widely considered to be oriented filters or energy detectors that perform one-dimensional feature analysis. The main deviations from this picture are generally thought to include gain controls and modulatory influences. Here we investigate receptive field (RF) properties of single neurons with localized two-dimensional stimuli, the two-dimensional Hermite functions (TDHs). TDHs can be grouped into distinct complete orthonormal bases that are matched in contrast energy, spatial extent, and spatial frequency content but differ in two-dimensional form, and thus can be used to probe spatially specific nonlinearities. Here we use two such bases: Cartesian TDHs, which resemble vignetted gratings and checkerboards, and polar TDHs, which resemble vignetted annuli and dartboards. Of 63 isolated units, 51 responded to TDH stimuli. In 37/51 units, we found significant differences in overall response size (21/51) or apparent RF shape (28/51) that depended on which basis set was used. Because of the properties of the TDH stimuli, these findings are inconsistent with simple feedforward nonlinearities and with many variants of energy models. Rather, they imply the presence of nonlinearities that are not local in either space or spatial frequency. Units showing these differences were present to a similar degree in cat and monkey, in simple and complex cells, and in supragranular, infragranular, and granular layers. We thus find a widely distributed neurophysiological substrate for two-dimensional spatial analysis at the earliest stages of cortical processing. Moreover, the population pattern of tuning to TDH functions suggests that V1 neurons sample not only orientations, but a larger space of two-dimensional form, in an even-handed manner.
Sharpee, T., Sugihara, H., Kurgansky, A.V., Rebrik, S., Stryker, M.P., Miller, K.D. Probing feature selectivity of neurons in primary visual cortex with natural stimuli. (2004) Proc SPIE Int Soc Opt Eng.(5467):212-222
+ expand abstract
One way to characterize neural feature selectivity is to model the response probability as a nonlinear function of the output of a set of linear filters applied to incoming signals. Traditionally these linear filters are measured by probing neurons with correlated Gaussian noise ensembles and calculating correlation functions between incoming signals and neural responses. It is also important to derive these filters in response to natural stimuli, which have been shown to have strongly non-Gaussian spatiotemporal correlations. An information-theoretic method has been proposed recently for reconstructing neural filters using natural stimuli in which one looks for filters whose convolution with the stimulus ensemble accounts for the maximal possible part of the overall information carried the sequence of neural responses. Here we give a first-time demonstration of this method on real neural data, and compare responses of neurons in cat primary visual cortex driven with natural stimuli, noise ensembles, and moving gratings. We show that the information-theoretic method achieves the same quality of filter reconstruction for natural stimuli as that of well-established white-noise methods. Major parameters of neural filters derived from noise ensembles and natural stimuli, as well as from moving gratings are consistent with one another. We find that application of the reverse correlation method to natural stimuli ensembles leads to significant distortions in filters for a majority of studied cells with non-zero reverse-correlation filter.
Sharpee, T., Rust, N.C., Bialek, W. Analyzing neural responses to natural signals: maximally informative dimensions. (2004) Neural Computation. 16(2):223-50. DOI: 10.1162/089976604322742010
+ expand abstract
We propose a method that allows for a rigorous statistical analysis of neural responses to natural stimuli that are nongaussian and exhibit strong correlations. We have in mind a model in which neurons are selective for a small number of stimulus dimensions out of a high-dimensional stimulus space, but within this subspace the responses can be arbitrarily nonlinear. Existing analysis methods are based on correlation functions between stimuli and responses, but these methods are guaranteed to work only in the case of gaussian stimulus ensembles. As an alternative to correlation functions, we maximize the mutual information between the neural responses and projections of the stimulus onto low-dimensional subspaces. The procedure can be done iteratively by increasing the dimensionality of this subspace. Those dimensions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace. If the dimensionality of the relevant subspace indeed is small, it becomes feasible to map the neuron’s input-output function even under fully natural stimulus conditions. These ideas are illustrated in simulations on model visual and auditory neurons responding to natural scenes and sounds, respectively.
Dykman, M.I., Sharpee, T., Platzman, P.M. Enhancement of tunneling from a correlated 2D electron system by a many-electron Mössbauer-type recoil in a magnetic field. (2001) Phys. Rev. Lett. 86(11):2408-11. DOI: 10.1103/PhysRevLett.86.2408
+ expand abstract
We consider the effect of electron correlations on tunneling from a 2D electron layer in a magnetic field parallel to the layer. A tunneling electron can exchange its momentum with other electrons, which leads to an exponential increase of the tunneling rate compared to the single-electron approximation. The effect depends on the interrelation between the dynamics of tunneling and momentum exchange. The results explain and provide a no-parameter fit to the data on electrons on helium. We also discuss tunneling in semiconductor heterostructures.