No cause for pause: new analyses of ramping and stepping dynamics in LIP (Rebuttal to Response to Reply to Comment on Latimer et al 2015)

Abstract

We recently presented a statistical comparison between two models of latent dynamics in macaque lateral intraparietal (LIP) area spike trains-a continuous 'ramping' (diffusion-to-bound) model, and a discrete 'stepping' model-and found that a substantial fraction of neurons (recorded in two different studies) were better supported by the stepping model . Here, we respond to a recent challenge to the validity of these findings that focuses primarily on the possibility of a lower bound on LIP firing rates . The paper in question proposed alternate formulations of the ramping model, and argued (via indirect analyses) that half the neurons in the population were better explained by the new model; if correct, this would lead to an even split in the number of neurons better explained by each model. These analyses, while interesting, do not alter the conclusions of our original paper. Here, we review the criticisms raised by Zylberberg & Shadlen and report several new analyses using models with lower bounds. First, we show that the stepping model continued to provide a better description of LIP spike trains when fit using only an early period of each trial. Second, we performed a direct model comparison between our stepping model and a ramping-with-baseline model proposed by Zylberberg & Shadlen; we found that (in a pleasing moment of agreement) roughly half the neurons were better explained by each model. Interestingly, inspection of the cells that switched classifications revealed that many did not strictly exhibit the classical ramping PSTHs that motivated these analyses in the first place. We also examined two other issues raised in recent discussions of LIP: (1) We show that a non-integrating model is consistent with some core aspects of behavioral data previously offered as evidence for continuous integration; and (2) We examine analyses based on the response covariance ("CorCE"), and show that it does not reliably distinguish ramping and stepping dynamics for our dataset. Taken together, these discussions highlight the value of data-driven characterizations of both neural and behavioral dynamics with appropriate statistical tools.

Brittleness in model selection analysis of single neuron firing rates

“…In this viewpoint, we highlight a deeper, conceptual, challenge to the application and interpretation of model selection; one that emerges from a common lack of robustness, which we term “brittleness,” of selection results in the face of small and apparently tangential deviations between models and data. We encountered this brittleness as we sought to expand on recent results using model selection (Latimer et al, 2015b, 2017) and so present our findings in the context of that study, but note that qualitatively similar issues have arisen in other fields (e.g., ecology; Anderson and Burnham, 2002) and so the issue is very likely to be pervasive, although it appears to be still underappreciated in neuroscience and allied fields.…”

“…This family of approaches, which includes cross-validation (Gelman et al, 2014), a variety of information criteria (Akaike, 1974; Hannan and Quinn, 1979; Akaike, 1998; Aho et al, 2014; Gelman et al, 2014; Spiegelhalter et al, 2002, 2014), and Bayesian model evidence or Bayes factors (Gelman et al, 2014; Kass and Raftery, 1995), compares two or more different models—representative of two or more working hypotheses—to select the model that provides a better account for a set of observations. Recent years have seen burgeoning interest in applying model selection in neuroscience, both for the firing patterns of single neurons (Bollimunta et al, 2012; Latimer et al, 2015b,a, 2016, 2017; Rossant et al, 2011), as well as for functional imaging and encephalographic signals (Durstewitz et al, 2016; Linderman and Gershman, 2017; Marreiros et al, 2010a,b; Mars et al, 2012). While broadly supportive, previous authors have highlighted potential pitfalls and challenges to the proper application of model selection approaches in neuroscience and other fields (Aho et al, 2014; Anderson and Burnham, 2002; Churchland and Kiani, 2016; Mars et al, 2012).…”

Internal Clocks, mGluR7 and Microtubules: A Primer for the Molecular Encoding of Target Durations in Cerebellar Purkinje Cells and Striatal Medium Spiny Neurons

“…Furthermore, performance in predictive timing tasks synchronizes ramping activity and theta-frequency oscillations in the frontal cortex and cerebellum (Parker, 2016). It is important to note, however, that although ''ramping'' may provide a useful description of the neural activity observed during temporal processing, it is likely that computational models incorporating stepping dynamics offer a more complete account of the underlying timing mechanism(s) than models utilizing ramping dynamics (e.g., Latimer et al, 2015Latimer et al, , 2017. Moreover, as cautioned by Kononowicz et al (2018) and Paton and Buonomano (2018), ramping activity (in contrast to population clocks) is often best described as representing activity in a brain area that is monitoring some unknown time signal occurring elsewhere in the brain, rather than the locus of a clock, i.e., generator of the time base.…”

Discrete Stepping and Nonlinear Ramping Dynamics Underlie Spiking Responses of LIP Neurons during Decision-Making

“…Although the ramping model formulated in Latimer et al ( , 2017 was motivated to capture the hypothesized linear relationship between a biased diffusion-to-bound process and singleneuron firing rates, neurons might exhibit nonlinear relationships between a putative latent diffusion process and their firing rates. To investigate this possibility, we fit nonlinear ramping models with a variety of different nonlinearities: a soft-rectified square root function (''sqrt''), a soft-rectified quadratic function (''quad''), or an exponential function (''exp'') (STAR Methods).…”

“…They found that the majority of LIP cells were better explained by the stepping model. However, subsequent literature has sparked debate over the interpretation of these results (Shadlen et al, 2016;Zylberberg and Shadlen, 2016;Chandrasekaran et al, 2018;Latimer et al, 2017;Zhao and Kording, 2018).…”