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| Home > Publications database > Exploring Neural Manifold Characteristics Using Adapted Normalizing Flows |
| Poster (After Call) | FZJ-2025-02379 |
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2024
Abstract: Despite the large number of active neurons in the cortex, the activity of neural populations fordifferent brain regions is expected to live on a low-dimensional manifold [1]. Variants of principalcomponent analysis (PCA) are frequently employed to estimate this manifold. However, thesemethods are limited by the assumption that the data conforms to a Gaussian distribution, neglectingadditional features such as the curvature of the manifold. Consequently, their performance asgenerative models tends to be subpar.To fully learn the statistics of neural activity and to generate artificial samples, we use NormalizingFlows (NFs) [2, 3]. These neural networks learn a dimension-preserving estimator of the probabilitydistribution of the data. They differ from other generative networks by their simplicity and by theirability to compute the likelihood exactly.Our adaptation of NFs focuses on distinguishing between relevant (in manifold) and noisedimensions (out of manifold). This is achieved by training the NF to represent maximal datavariance representation in minimal dimensions, akin to PCA's linear model but allowing fornonlinear mappings. Our adaptation allows us to estimate the dimensionality of the neural manifold.As every layer is a bijective mapping, the network can describe the manifold without losinginformation – a distinctive advantage of NFs.We validate our adaptation on artificial datasets of varying complexity where the underlyingdimensionality is known. Our approach can reconstruct data using only a few latent variables, and ismore efficient than linear methods, such as PCA.Following this approach, we identify manifolds in electrophysiological recordings from macaqueV1 and V4 [4]. Our approach faithfully represents not only the variance but also higher orderfeatures, such as the skewness and kurtosis of the data, using fewer dimensions than PCA.[1] J. Gallego et al., Neuron, 94, 5, 978-984, 2017.[2] L. Dinh et al., ICLR, 2015.[3] L. Dinh et al., ICLR, 2017.[4] X. Chen et al., Sci. Data, 9, 1, 77, 2022.
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