P077 An Intrinsic Dimension Estimator for Neural Manifolds
Jacopo Fadanni*1, Rosalba Pacelli2, Alberto Zucchetta2, Pietro Rotondo3, Michele Allegra1,5
1Physics and Astronomy Department, University of Padova, Padova, Italy
2Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova, Italy
3Department of Mathematical, Physical and Computer Sciences, University of Parma, Parma, Italy
4Padova Neuroscience Center, University of Padova, Padova, Italy
*Email:jacopo.fadanni@unipd.it
Introduction
Recent technical breakthroughs have enabled a rapid surge in the number of neurons that can be simultaneously recorded[1,2] calling for the development of robust methods to investigate neural activity at a population level.
In this context, it is becoming increasingly important to characterize the neural activity manifold, the set of configurations visited by the network within the Euclidean space defined by the instantaneous firing rates of all neurons[3]. A key parameter of the manifold geometry is its intrinsic dimension (ID), the number of coordinates needed to describe the manifold. While several studies suggested that the ID may be typically low, contrasting findings have disputed this statement, leading to a wide debate [1,2,3,4].
Methods
In this study we present a variant of the Full Correlation Integral (FCI), an ID estimator that was shown to be particularly robust under undersampling and high dimensionality, improving over the classical Correlation Dimension estimator[5].Our variant overcomes the limitation of standard FCI in the case of curvature effects doing a local estimation of the true IDas the peak in the distribution of local estimates. Crucially, local estimates are restricted to approximately flat neighborhoods, as determined by a suitable local parameter, which allows us to avoid overestimation. Our procedure yields a robust estimator for typically challenging situations encountered with neural manifolds.
Results
We proved the reliability of our metric by testing it in two significantly challenging cases. First, we used it to characterize neural manifolds of RNNs performing simple tasks[6], where strong curvature effects generally lead to overestimates. Second, we used it on a benchmark dataset including non-linearly embedded high-dimensional neural data, where all other methods yield underestimates[7]. In Figure 1 we show a comparison between our method and other available methods for the RNN and for the high-dimensional neural data. Linear methods overestimate the ID in the case of curved manifolds, while nonlinear methods underestimate the ID in the case of high-dimensional manifolds. In both situations, our method performed well.
Discussion
Proposing a robust estimator for the ID, our work adds a relevant tool in the open debate about the dimensionality of neural manifolds.
The intrinsic properties of the FCI estimator make it robust to undersampling and high dimensionality, avoiding the so-called ‘curse of dimensionality’ effects. Our local variant makes it robust also for curved manifolds where the ID and the embedding dimension strongly differ. Limitations of our method arise only in extremely non-uniformly sampled manifolds, where the conditions for the applicability of the FCI are unfulfilled[5].
Our method is an important step forward in the current research on neural manifolds, and it is thus of interest to the computational neuroscience community at large.
Figure 1. Left, an example of network activity projected onto the first 3 PCs. IDFCI = 2.1; IDPA = 7; MLE = 3.6. IDTwoNN = 7.1 Right: comparison between different ID estimators in the case of high-dimensional manifolds linearly embedded[7]. Our method performs well for all the dimensionality
Acknowledgements
This work was supported by PRIN grant 2022HSKLK9, CUP C53D23000740006, “Unveiling the role of low dimensional activity manifolds in biological and artificial neural networks”
References
● https://doi.org/10.1038/s41586-019-1346-5
● https://doi.org/10.1126/science.aav7893
● https://doi.org/10.1016/j.conb.2021.08.002
● https://doi.org/10.1038/s41593-019-0460-x
● https://doi.org/10.1038/s41598-019-53549-9
● https://doi.org/10.1038/s41593-018-0310-2
● https://doi.org/10.1371/journal.pcbi.1008591
