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Latent models of stepping and ramping: an update on (the debate over) single-trial dynamics in LIP Jonathan Pillow Princeton Neuroscience Institute, Princeton University Comp. Neurosci. Workshop: Computation, Cognition and the Brain

  1. Latent models of stepping and ramping: 
 an update on (the debate over) 
 single-trial dynamics in LIP Jonathan Pillow Princeton Neuroscience Institute, Princeton University Comp. Neurosci. Workshop: Computation, Cognition and the Brain Rutgers University May 30, 2018

  2. “random dots” decision-making task fixed duration or RT fixate targets motion saccade RF

  3. “random dots” decision-making task fixed duration or RT fixate targets motion saccade RF Q : what are the latent dynamics of spike trains in LIP during sensory evidence accumulation?

  4. What do we mean by latent dynamics? “direct” sensory 
 encoding model sensory s stimulus spike spike r response response e.g., “LN” cascade: nonlinearity stimulus filter

  5. What do we mean by latent dynamics? latent variable model sensory s stimulus noisy x latent variable spike rate spike spike r response response

  6. What do we mean by latent dynamics? latent variable model sensory s stimulus noisy x latent variable spike rate spike spike r response response

  7. What do we mean by latent dynamics? latent variable model sensory s stimulus noisy x latent variable spike rate spike spike r response response

  8. <latexit sha1_base64="cH5/fGW0IhCKlhGHqyWgWSJVd4=">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</latexit> <latexit sha1_base64="cH5/fGW0IhCKlhGHqyWgWSJVd4=">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</latexit> <latexit sha1_base64="cH5/fGW0IhCKlhGHqyWgWSJVd4=">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</latexit> <latexit sha1_base64="cH5/fGW0IhCKlhGHqyWgWSJVd4=">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</latexit> What do we mean by latent dynamics? latent dynamical model sensory ... ... s t-1 s t s t+1 stimulus latent 
 dynamics noisy x t-1 x t x t+1 ... trajectory ... r t-1 r t r t+1 ... spike spike response response observations dynamics probability of data: dx 1 dx 2 · · · dx T

  9. Classic account: drift-diffusion model (DDM) • neuron integrates motion “evidence” Accumulated evidence [logLR] time [Gold & Shadlen 2007]

  10. Classic account: drift-diffusion model (DDM) • neuron integrates motion “evidence” LIP response ... IN [spikes/sec] Roitman & Shadlen, 2002 Gold & Shadlen, 2002 = Huk & Shadlen, 2005 Yang & Shadlen, 2007 Accumulated Churchland & Shadlen, 2008 evidence OUT ... [logLR] time [sec]

  11. normative modeling approach: what LIP neurons ought to do, based on a theory of “optimal” decision-making examples : • log-probability (Shadlen & Newsome 1996) • expected utility (Platt & Glimcher 1999) • posterior probability (Beck et al 2008) • change in the RL value function (Seo, Barraclough, & Lee 2009) descriptive modeling approach: • find most accurate statistical description of spike responses • agnostic about function (“l et the data speak for themselves”) example : • variance of conditional expectation (varCE) - (Churchland et al 2011)

  12. classical analysis of LIP responses motion on IN motion sp/s OUT motion sp/s [Shadlen & Newsome, 2001]

  13. but what are the dynamics on single trials? motion on IN motion spike train • averaging obscures sp/s single-trial dynamics noisy “ramping” our goal: 
 infer latent dynamics from spike trains discrete stepping

  14. Chapter 1: Formalizing the models [Latimer et al 2015]

  15. ramping (“diffusion-to-bound”) model noise variance bound height slope initial spike rate 200 400 600 time after motion onset (ms) Poisson spikes: latent state: spiking:

  16. ramping (“diffusion-to-bound”) model noise variance bound height initial spike rate 200 400 600 time after motion onset (ms) Poisson spikes: latent state: spiking:

  17. ramping (“diffusion-to-bound”) model noise variance bound height initial spike rate 200 400 600 time after motion onset (ms) Poisson spikes: latent state: , , 8 model parameters: spiking:

  18. stepping (“discrete switching”) model • semi-Markov model probability of “in” step step time distribution 200 400 600 time after motion onset (ms) spikes: spiking: step times latent

  19. stepping (“discrete switching”) model • semi-Markov model probability of “in” step step time distribution 200 400 600 time after motion onset (ms) spikes: spiking: step times latent

  20. stepping (“discrete switching”) model • semi-Markov model probability of “in” step step time distribution 200 400 600 time after motion onset (ms) spikes: spiking: step times 14 parameters: latent

  21. Fitting: difficult for both models coherence parameters likelihood: 60 bound spike rate (Hz) requires summing over all 30 possible latent paths specified by model • Bayesian inference: use MCMC to compute this integral [Latimer et al 2015]

  22. Which model is better? Q: how to compare models with different numbers of parameters? naively, more parameters ⟹ more flexibility to fit the data • but with too many parameters, we will overfit (fit noise in data)!

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