Research Overview

We develop statistical models and open-source computational tools to extract insights from neural data. We are particularly interested in characterizing flexibility and variability in neural circuits—e.g., how do the dynamics of large neural ensembles change over the course of learning a new skill, during periods of high attention or task engagement, or during development and aging. Summarizing these processes even on an descriptive level is a difficult and unsolved challenge.

Past projects have explored the use of tensor decomposition as a model of trial-by-trial gain modulation, time warping models to account for trial-by-trial timing variability, spontaneous remapping of spatial coding in entorhinal cortex, and neural sequence detection methods through convolutional matrix factorizations and Bayesian nonparametric mixture models.

Alex Williams (PI)

Assistant Professor @ NYU
Associate Research Scientist @ Flatiron Institute


Alex is jointly appointed as an assistant professor in the Center for Neural Science at NYU and an associate research scientist + project leader in the Center for Computational Neuroscience at the Flatiron Institute. Alex performed his postdoctoral and graduate work at Stanford University, respectively with Scott Linderman and Surya Ganguli. Before that, he worked one year at the Salk Institute with Terry Sejnowski and two years at Brandeis University with Eve Marder and Tim O'Leary. He began studying neuroscience at Bowdoin College, where he was advised by Patsy Dickinson.

Join the Lab!

We are currently hiring researchers at all levels including undergraduates, PhD students, and postdocs. Prospective grad students must first apply to a PhD or Masters program at NYU before joining. Check out PhD programs in neuroscience, data science, or applied mathematics, for example. Postdoc applicants should email Alex to set up a meeting. Please include a CV and contact information for 2-3 references in your initial email. We are committed to building a diverse research group at the intersection of neuroscience, statistics, and machine learning—we encourage applicants from all backgrounds and levels of experience to apply.

Publications & Preprints

  • Generalized Shape Metrics on Neural Representations.
  • Williams AH, Kunz E, Kornblith S, Linderman SW (2021). Neural Information Processing Systems. Virtual conference.
  • Dynamic and reversible remapping of network representations in an unchanging environment.
  • Low IIC, Williams AH, Campbell MG, Linderman SW, Giocomo LM (2021). Neuron. 109(18):2967-2980.e11
  • Statistical Neuroscience in the Single Trial Limit.
  • Williams AH, Linderman SW (2021, in press). Current Opinion in Neurobiology.
  • Point process models for sequence detection in high-dimensional neural spike trains.
  • Williams AH, Degleris A, Wang Y, Linderman SW (2020). Neural Information Processing Systems. Virtual Conference.
  • Combining tensor decomposition and time warping models for multi-neuronal spike train analysis.
  • Williams AH (2020). bioRxiv preprint.
  • Discovering precise temporal patterns in large-scale neural recordings through robust and interpretable time warping.
  • Williams AH, Poole B, Maheswaranathan N, Dhawale AK, Fisher T, Wilson CD, Brann DH, Trautmann E, Ryu S, Shusterman R, Rinberg D, Ölveczky BP, Shenoy KV, Ganguli S (2020). Neuron. 105(2):246-259.e8
  • Universality and individuality in neural dynamics across large populations of recurrent networks.
  • Maheswaranathan N*, Williams AH*, Golub MD, Ganguli S, Sussillo D (2019). Neural Information Processing Systems. Vancouver, CA.
  • Reverse engineering recurrent networks for sentiment classification reveals line attractor dynamics.
  • Maheswaranathan N*, Williams AH*, Golub MD, Ganguli S, Sussillo D (2019). Neural Information Processing Systems. Vancouver, CA
  • Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updates.
  • Degleris A, Antin B, Ganguli S, Williams AH (2019). arXiv preprint. 1907.00139
  • Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.
  • Mackevicius EL*, Bahle AH*, Williams AH, Gu S, Denissenko NI, Goldman MS, Fee MS (2019). eLife. 8:e38471
  • Unsupervised discovery of demixed, low-dimensional neural dynamics across multiple timescales through tensor components analysis.
  • Williams AH, Kim TH, Wang F, Vyas S, Ryu SI, Shenoy KV, Schnitzer M, Kolda TG, Ganguli S (2018). Neuron. 98(6):1099–1115.e8
  • Dendritic trafficking faces physiologically critical speed-precision tradeoffs.
  • Williams AH, O’Donnell C, Sejnowski T, O’Leary T (2016). eLife. 5:e20556
  • Distinct or shared actions of peptide family isoforms: II. Multiple pyrokinins exert similar effects in the lobster stomatogastric nervous system.
  • Dickinson PS, Kurland SC, Qu X, Parker BO, Sreekrishnan A, Kwiatkowski MA, Williams AH, Ysasi AB, Christie AE (2015). J Exp Biol. 218:2905-17
  • Summary of the DREAM8 parameter estimation challenge: Toward parameter identification for whole-cell models.
  • Karr JR, Williams AH, Zucker JD, Raue A, Steiert B, Timmer J, Kreutz C, DREAM8 Parameter Estimation Challenge Consortium, Wilkinson S, Allgood BA, Bot BM, Hoff BR, Kellen MR, Covert MW, Stolovitzky GA, Meyer P (2015). PLoS Comput Biol. 11(5):e1004096
  • Cell types, network homeostasis and pathological compensation from a biologically plausible ion channel expression model.
  • O’Leary T, Williams AH, Franci A, Marder E (2014). Neuron. 82(4):809-21
  • Many parameter sets in a multicompartment model oscillator are robust to temperature perturbations.
  • Caplan JS, Williams AH, Marder E (2014). J Neurosci. 34(14):4963-75
  • The neuromuscular transform of the lobster cardiac system explains the opposing effects of a neuromodulator on muscle output.
  • Williams AH, Calkins A, O’Leary T, Symonds R, Marder E, Dickinson PS (2013). J Neurosci. 33(42):16565-75
  • Correlations in ion channel expression emerge from homeostatic regulation mechanisms.
  • O’Leary T, Williams AH, Caplan JS, Marder E (2013). Proc Natl Acad Sci USA. 110(28):E2645-54
  • Animal-to-animal variability in the phasing of the crustacean cardiac motor pattern: an experimental and computational analysis.
  • Williams AH, Kwiatkoswki MA, Mortimer AL, Marder E, Zeeman ML, Dickinson PS (2013). (2013). J Neurophysiol. 109:2451-65.