CAJAL 2024

Author and instructor: steeve.laquitaine@epfl.ch; laquitainesteeve@gmail.com
For the Cajal advanced training course, 2024, Bordeaux

Abstract

Project: "Computational analytical methods to link high-dimensional neuronal population and behavioral data"

Instructor: Steeve Laquitaine, PhD (Swiss Federal Institute of Technology, Switzerland)

Modern technical innovations now allow experimentalists to measure and manipulate the dynamic distributed activity of large populations of neurons in behaving animals. With recent progress in machine learning, they now also have the capability to link neural population activity with behavior in real-time, across days, across a wide range of tasks and animals. The massive datasets generated have stimulated the rise of an Open Science framework to store, share and accelerate data and analyses within the Neuroscience community, in a standardized and reproducible manner. At the end of the course students will be able to locate, retrieve datasets made available by the research community and to share their own with the community. They will know how to use state-of-the-art modeling and visualisation techniques, via discovery-driven and hypothesis-driven approaches, to identify factors that explain joint changes in neural activity and behavior in 2P ca-imaging, extracellular electrophysiological recording experiments, across species. They will learn to identify the neurons that contribute to these variations. They will understand the advantages and limitations of traditional and popular modern techniques and know how to use them to arbitrate between techniques.

Main outcomes:

• Know how to use the Allen Institute SDK, browse the Dandi archive, FigShare, dataryad to retrieve and share standardized, repropducible datasets and code
• How to analyze (approaches) and characterize (metrics) high-dimensional neural data
• Understand the advantages and limitations of the most popular analytical techniques
• Know how to implement and rule out models that link neuronal activity to behavior (model selection via decoding, goodness-of-fit, consistency, robustness).

Methodology:

• Analysis of neuropixels recordings and ca-imaging of cortical activity in mice viewing natural scenes (de Vries et al., 2020, Allen Institute dataset),
• Analysis of tetrode recordings of Hippocampus activity in mice during virtual navigation (Grossmark, Buzsaki, Science, 2016),
• Analysis of DREAD manipulation and ca-imaging of cortical activity in mice during reward-based navigation (Krishnan et al., Nat Commun, 2022)
• Analysis of 100-electrode array recording of monkeys' motor cortical activity during motor reaching (Chowdhury et al., elife, 2020).
• Traditional and state-of-the art machine learning-based dimensionality reduction techniques, topological data analysis of neural manifolds
• Programming in Python, low-code for beginners, full code available for tuning
• Programming in Google Colab, on Laptop

0. Prerequisites (DAY 1)

Notebooks: .

1. Theory: From neural tuning to manifolds

Learning outcomes:

• Know what is a manifold and what it is not.
• Know what is an entangled manifold and how to disentangle it.
• Know how to link individual neurons' tuning functions and population manifolds in the absence of noise (simplification).
• Recognize the different types of underlying neural codes ("splitter", "lumper")

Readings: Kriegeskorte, N., & Wei, X. X. (2021). Neural tuning and representational geometry. Nature Reviews Neuroscience, 22(11), 703-718.

Python prerequisites

• installing and importing libraries
• using functions
• plotting with matplotlib library

Notebooks: .

2. Theory: Manifold dimensionality

Learning outcome:

• Know what manifold dimensionality is and why it matters.
• Know the factors that determine the manifold's dimensionality and how.

Readings:

• Wärnberg and Kumar, “Perturbing Low Dimensional Activity Manifolds in Spiking Neuronal Networks.”
• Rigotti, M., Barak, O., Warden, M. R., Wang, X. J., Daw, N. D., Miller, E. K., & Fusi, S. (2013). The importance of mixed selectivity in complex cognitive tasks. Nature, 497(7451), 585-590.
• Cunningham, J. P., & Yu, B. M. (2014). Dimensionality reduction for large-scale neural recordings. Nature neuroscience, 17(11), 1500-1509.

Notebooks: .

3. Hands-on: PCA-based manifolds

Learning outcomes:

• Know how to compute manifolds for large populations of neurons, using a simple machine learning technique, PCA.
• Know what is the representational geometry framework.
• Know how the manifold geometry depends on its individual neurons' tuning functions.
• Know how to measure the dimensionality of neural manifolds, with PCA.

Readings: Kriegeskorte, N., & Wei, X. X. (2021). Neural tuning and representational geometry. Nature Reviews Neuroscience, 22(11), 703-718.

Python prerequisites

• installing and importing libraries
• using functions
• plotting with matplotlib library

Notebook: .

4. Hands-on: Cebra beats them all

Learning outcomes:

• Know how to compute manifolds from large neuron populations with state-of-the-art (SOTA) machine learning techniques.
• Know what latent variable models are.
• Know what identifiability is and why it matters.
• Know how to benchmark SOTA machine learning techniques on a synthetic dataset, using a linear reconstruction R-squared.

Method:

• With the students, we study the paper section on the generation of the synthetic dataset, describe the design and its objectives in class.

Readings:

• Cunningham, J. P., & Yu, B. M. (2014). Dimensionality reduction for large-scale neural recordings. Nature neuroscience, 17(11), 1500-1509.
• Gokcen, E. (2023). Disentangling communication across populations of neurons (Doctoral dissertation, Carnegie Mellon Univers
• Hurwitz, C., Kudryashova, N., Onken, A., & Hennig, M. H. (2021). Building population models for large-scale neural recordings: Opportunities and pitfalls. Current opinion in neurobiology, 70, 64-73.
• Zhou, D., & Wei, X. X. (2020). Learning identifiable and interpretable latent models of high-dimensional neural activity using pi-VAE. Advances in Neural Information Processing Systems, 33, 7234-7247.
• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368.
• Altan, E., Solla, S. A., Miller, L. E., & Perreault, E. J. (2021). Estimating the dimensionality of the manifold underlying multi-electrode neural recordings. PLoS computational biology, 17(11), e1008591.

Python prerequisites

• installing and importing libraries
• using functions
• plotting with matplotlib library
• basics of scikit-learn software for machine learning
• basics of Keras for Deep Learning

Notebook: .

5. Hands-on: movement neural manifold in primate's S1 (InfoNCE loss)

Learning outcomes:

• Know how to use CEBRA to compute neural manifolds from the monkey's primary somatosensory cortex (S1), for variables of a reaching task.
• Know how to train the model with the standard infoNCE loss.

Method:

• Students study the paper section on the task, describe its design and objectives.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. Shown in Fig. 3, Extended Data Fig. 8

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

6. Hands-on: movement neural manifold in primate's S1 (MSE loss)

Learning outcomes:

• Know how to train CEBRA to compute neural manifolds by minimizing the mean squared error (MSE) loss.
• Know why the loss used matters.

Method:

• Students study the paper section on the task, describe its design and objectives.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. Shown in Fig. 3, Extended Data Fig. 8

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

7. Hands-on: navigation neural manifold with discovery analysis in rat's HPC

Learning outcomes:

• know how to perform a discovery-driven analysis to explore the neural manifolds with CEBRA-Time.
• know how to save a trained model for later re-use.

Method:

• Students study the paper section on the task, describe its design and objectives.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368.

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

8. Hands-on: navigation neural manifold with hypothesis testing in rat's HPC

Learning outcomes:

• know how to perform a more targetted hypothesis-driven analyses, with CEBRA-Behavior mode. We will qualitatively test whether both position and direction are encoded in the rat Hippocampus, by using a control manifold.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. see Figure 2 in Schneider, Lee, Mathis.

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

9. Hands-on: navigation manifold model selection in rat's HPC

Learning outcomes:

• Know how to evaluate several hypotheses and select the best. We will test whether position only, direction only and position and direction are encoded in the rat Hippocampus.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. see Figure 2 in Schneider, Lee, Mathis.

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

10. Hands-on: Hybrid approach

Learning outcomes:

• know how to use CEBRA-Hybrid. We will test whether position and direction and time are encoded in the rat Hippocampus.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. see Figure 2 in Schneider, Lee, Mathis.

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

11. Hands-on: Manifold's consistency

Learning outcomes:

• know how to use CEBRA to measure the consistency of manifolds across subjects.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. see Figure 1 in Schneider, Lee, Mathis.

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

12. Hands-on: more data and generalizable encoding

Learning outcomes:

• Know when and how to merge multiple sessions of a subject together
• Practice the use of consistency metrics

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. see Figure 1 in Schneider, Lee, Mathis.

Python prerequisites:

• installing and importing libraries
• using functions
• plotting with matplotlib library

Notebook: .

13. Theory: Topology data analysis

Learning outcomes:

• Know the basic concepts and techniques of topological data analysis (simplexes, N-dimensional holes, Filtration, Persistent diagram, barcodes)
• Know how to use teaspoon to create synthetic ground truth manifolds.
• Know how to use ripser software to run topological analysis techniques to compute the Persistent diagram and a manifold's barcode.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. see Figure 1 in Schneider, Lee, Mathis.
• Curto, C. What can topology tell us about the neural code? Bull. Am. Math. Soc 54, 63–78 (2016).
• Rybakkena, E., Baasa, N., & Dunnb, B. (2017). Decoding of neural data using cohomological learning.
• Gardner, R. J., Hermansen, E., Pachitariu, M., Burak, Y., Baas, N. A., Dunn, B. A., ... & Moser, E. I. (2022). Toroidal topology of population activity in grid cells. Nature, 602(7895), 123-128.
• Damrich, S., Berens, P., & Kobak, D. (2023). Persistent homology for high-dimensional data based on spectral methods. arXiv preprint arXiv:2311.03087. ISO 690

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

14. Hands-on: Topology data analysis

Learning outcomes:

• know how to describe the topological structure of neural manifolds by using persistent homology analysis (N-dimensional holes or co-cycles, barcodes, Betti numbers).
• know how to visualize CEBRA embeddings into circular coordinates.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. see Figure 2.e.-g. of Schneider, Lee, Mathis.
• Curto, C. What can topology tell us about the neural code? Bull. Am. Math. Soc 54, 63-78 (2016).
• Rybakkena, E., Baasa, N., & Dunnb, B. (2017). Decoding of neural data using cohomological learning.
• Gardner, R. J., Hermansen, E., Pachitariu, M., Burak, Y., Baas, N. A., Dunn, B. A., ... & Moser, E. I. (2022). Toroidal topology of population activity in grid cells. Nature, 602(7895), 123-128.

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

15. Hands-on: Model selection with decoding accuracy

Learning outcomes:

• know how to decode labels from a CEBRA manifold with the kNN technique.
• know how to ensure robust decoding with cross-validation.
• know how to evaluate and compare the decoding performances for neural manifolds obtained from different hypotheses with decoding median error and InfoNCE loss.

Readings:

• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368. see Figure 2.d. of Schneider, Lee, Mathis.

Python prerequisites:

• installing and importing libraries
• plotting with matplotlib library

Notebook: .

16. Hands-on: Decoding movies from V1

Learning outcomes:

• Extract neural manifolds for different neural recording modalities (ca-imaging and neuropixels)
• Compare neural manifolds in V1 evoked by movies features (DINO features) for different recording modalities
• Extract neural manifolds that are consistent across neural recording modalities (Joint training)
• Decode movie frames
• Measure the inter and intra-area linear consistencies of the neural manifolds

Readings:

• de Vries, S. E., Lecoq, J. A., Buice, M. A., Groblewski, P. A., Ocker, G. K., Oliver, M., ... & Koch, C. (2020). A large-scale standardized physiological survey reveals functional organization of the mouse visual cortex. Nature neuroscience, 23(1), 138-151.
• Schneider, S., Lee, J. H., & Mathis, M. W. (2023). Learnable latent embeddings for joint behavioural and neural analysis. Nature, 617(7960), 360-368.

Python prerequisites:

• installing and importing libraries
• using functions
• plotting with matplotlib library
• machine learning with scikit-learn and pytorch libraries

Notebook: .

17. Hands-on: Information capacity

Learning outcomes:

• Know how to train a deep learning model for object recognition
• Know how to measure its layers' neural manifold geometry (dimensionality, radius, correlation)
• Know how to measure its information capacity

Readings:

• Stephenson, C., Feather, J., Padhy, S., Elibol, O., Tang, H., McDermott, J., & Chung, S. (2019). Untangling in invariant speech recognition. Advances in neural information processing systems, 32.
• https://github.com/steevelaquitaine/neural_manifolds_replicaMFT_Cajal/blob/master/examples/MFTMA_VGG16_example.ipynb

Python prerequisites:

• installing and importing libraries
• using functions
• plotting with matplotlib library
• machine learning with scikit-learn and pytorch libraries

Notebook: .

18. Hands-on open datasets: Allen Institute SDK

Learning outcomes:

• know how to access experiment metadata and data streams
• know how to download and organize neuropixels and ca-imaging experiment data according to cortical area, imaging depth, and Cre line
• know how to transform and analyze data

Methodology:

• Analysis of neuropixels recordings and ca-imaging of cortical activity in mice viewing natural scenes (de Vries et al., 2020, Allen Institute dataset)

Readings:

• de Vries, S. E., Lecoq, J. A., Buice, M. A., Groblewski, P. A., Ocker, G. K., Oliver, M., ... & Koch, C. (2020). A large-scale standardized physiological survey reveals functional organization of the mouse visual cortex. Nature neuroscience, 23(1), 138-151.
• https://allensdk.readthedocs.io/en/latest/_static/examples/nb/ecephys_session.html

Notebook: .

19. Hands-on open datasets: DANDI Archive

Learning outcomes:

• Know how to retrieve and share standardized, reproducible datasets and code

Requirements

• Github account

Notebook: .

20. Hands-on open datasets: Figshare

Learning outcomes:

• Know how to retrieve and share standardized, reproducible datasets and code

Requirements:

• You don't need an account to download public datasets such as the one used in the case study mice V1 (https://figshare.com/s/60adb075234c2cc51fa3).

Notebook: .

Hands-on: Use dataryad