Acknowledgements: BP is supported by NSF IGERT and SIGF. AHW is supported by DOE CSGF. SG is supported by Simons Foundation, McKnight Foundation, and James S. McDonnell Foundation.

Time-warped PCA: simultaneous alignment and dimensionality reduction of neural dataBen Poole*1, Alex H. Williams*1, Niru Maheswaranathan*1, Byron Yu2, Gopal Santhanam3, Stephen I. Ryu2, Stephen A. Baccus1, Krishna Shenoy1, Surya Ganguli1

*equal contribution, 1Stanford University, 2Carnegie Mellon University, 3Google X

Motivation: aligning neural data across trials can be challenging.● Different trial lengths in self-paced behaviors● Multiple events of interest within each trial● Unobserved differences in cognitive and attentional states leading to different

reaction and processing times

Introduction

Motivation: bad alignment → illusory complexity

Method: Time-warped PCA

Aligning motor cortex recordings and predicting RT

Our work: jointly learn a low-dimensional representation of the data with trial-specific time warpings for alignment.

Aligning olfactory bulb recordings

twPCA recovers alignment on synthetic data

Shift: Scale: Nonlinear:

PCA: same neuron factors and temporal factors for each trial

Time-warped PCA: different temporal factors for each trial

Temporal warping functions can model diverse temporal variations:

Trials aligned toinhalation onset twPCA alignment

Linear warp to inhalation length Trial warping functions

PCA overestimates the dimensionality of unaligned neural data

Similar artifacts appear in a variety of real neural datasets

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Trial-specifictemporal factors:

Figure from Shusterman et al. (2011)

Reaction time of monkey varies from trial to trial.

Learned alignment on motor cortex neurons can be used to accurately predict reaction time.

twPCA alignment

Preprocessing: crop and extract trials from continuous data

Odor onset poorly aligns mitral cell activity due to trial-to-trialvariability in sniffing and behavior.

twPCA outperforms baseline alignment to sniffing cycle.

Tria

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PCA blurs dynamics

twPCA accurately recovers low-dimensional latent dynamics and alignments

Trial-to-trial jitter leads to temporal derivatives in the PCs!

Data from Chris Wilson & Dmitry Rinberg (NYU)

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Identical model for every trial.

Equivalent to PCA ontrial average.

Time-warped PCA aligns neural data with no supervision.Try it out now: github.com/ganguli-lab/twpca

Trial 1 Trial 2 Trial 3

Aligned to GO cue

Predicting RTfrom warps

Reaction time (RT)

Inhalation length