Variance as a signature of neural computations during decision making

“during Decision Making”

“during Decision Making”

“Lastly, we consider a recurrent neural network that is exemplary of a class of dynamical ‘‘attractor’’ models of decision making (e.g., Albantakis and Deco, 2009; Bogacz et al., 2006; Machens et al., 2005; Usher and McClelland, 2001; Wang, 2002).”

“during Decision Making”

“This is the same as drift diffusion with an upper and lower stopping bound (Bogacz et al., 2006; Ratcliff and Rouder, 1998), so long as the evidence for one alternative is evidence against the other (Gold and Shadlen, 2007).”

“For example, the irregular discharge of neurons bears on theories of coding, synaptic integration and circuit function (Shadlen and Newsome, 1998; Softky and Koch, 1993).”

“Together, the mean and variance of neural responses furnish rich insight into the limits of perception, motor control and decision making (Faisal et al., 2008; Glimcher, 2005; Parker and Newsome, 1998; Shadlen and Newsome, 1998).”

“Lastly, we consider a recurrent neural network that is exemplary of a class of dynamical ‘‘attractor’’ models of decision making (e.g., Albantakis and Deco, 2009; Bogacz et al., 2006; Machens et al., 2005; Usher and McClelland, 2001; Wang, 2002).”

“For example, the rise of mean firing rates to a threshold value could imply preparation for a saccadic eye movement (Hanes and Schall, 1996).”

“during Decision Making”

“An extension to the cross correlation of firing rates (or spike cross-correlogram) is another potentially useful extension, especially when the rate is changing in time and from trial to trial (Aertsen et al., 1989; Vaadia et al., 1995).”

“during Decision Making”

“These values approximate the average firing rate of a population of weakly correlated MT neurons to 0% coherent motion in a 10 ms sample (Britten et al., 1996).”

“All models were parameterized to approximate the firing rates of LIP neurons in Churchland et al. (2008).”

“…near independence from conditions affecting the mean firing rate, such as motion strength, contrast, and attentional state (Britten et al., 1993; Geisler et al., 2001; McAdams and Maunsell, 1999; Tolhurst et al., 1983), imply that f is unlikely to vary systematically as a function of firing rate.”

“The monkeys’ choices and RTs on this and similar tasks suggest that the decision is based on the accumulation of noisy samples of evidence (Bogacz et al., 2006; Gold and Shadlen, 2007; Ratcliff and Rouder, 1998).”

“An extension to the cross correlation of firing rates (or spike cross-correlogram) is another potentially useful extension, especially when the rate is changing in time and from trial to trial (Aertsen et al., 1989; Vaadia et al., 1995).”

“Together, the mean and variance of neural responses furnish rich insight into the limits of perception, motor control and decision making (Faisal et al., 2008; Glimcher, 2005; Parker and Newsome, 1998; Shadlen and Newsome, 1998).”

“Some features of the PPC are very similar to the DDM: firing rates of LIP neurons are produced by a mixture of deterministic and stochastic components, and independent samples of evidence from noisy, direction selective neurons are effectively summed at each time step.”

“…mean spike count and its near independence from conditions affecting the mean firing rate, such as motion strength, contrast, and attentional state (Britten et al., 1993; Geisler et al., 2001; McAdams and Maunsell, 1999; Tolhurst et al., 1983), imply that f is unlikely to vary systematically as a…”

“By perturbing the background of random dot motion displays, Huk and Shadlen (2005) demonstrated that LIP neurons represent the integral of motion evidence in the display, but thesemeasurements did not demonstrate that spike trains from individual trials represent realizations of random walk or…”

“Lastly, we consider a recurrent neural network that is exemplary of a class of dynamical ‘‘attractor’’ models of decision making (e.g., Albantakis and Deco, 2009; Bogacz et al., 2006; Machens et al., 2005; Usher and McClelland, 2001; Wang, 2002).”

“All motion strengths are included (7008 trials). representation of noisy momentary evidence, without appreciable integration (Cisek et al., 2009), possibly related to agradual shift of attention to a choice target (Gottlieb and Balan, 2010).”

“For example, in dorsal premotor cortex, neural variability decreases gradually until the monkey’s movement, sometimes over a period as long as 400 ms (Churchland et al., 2006).”

“The lower average rate is probably not explained by amechanism that invokes less excitation or greater suppression on all trials, owing perhaps to greater uncertainty (Basso and Wurtz, 1998), or normalization (Tolhurst and Heeger, 1997), or surround inhibition (Balan et al., 2008).”

“during Decision Making”

“A constant VarCE is still evident when the firing rate is perturbed by additive noise, as in a doubly stochastic Poisson process (Figure 2D and magenta lines in Figure 2F), also known as a Cox process (Cox and Isham, 1980).”

“A Poisson process with refractoriness ensures f < 1 (Berry and Meister, 1998; Keat et al., 2001).”

“…near independence from conditions affecting the mean firing rate, such as motion strength, contrast, and attentional state (Britten et al., 1993; Geisler et al., 2001; McAdams and Maunsell, 1999; Tolhurst et al., 1983), imply that f is unlikely to vary systematically as a function of firing rate.”

“For example, responses of neurons in primary somatosensory cortex lay the foundation for understanding vibrotactile sensation because mean firing rates are significantly higher for more intense tactile stimuli (Romo and Salinas, 2001).”

“These are conditions in which we would expect the VarCE to be minimal, and the same holds for LIP neurons when rates are relatively stationary, as in the delay period preceding a saccade to one target or during the late predecision period (cf. Maimon and Assad, 2009).”

“This model would also explain decisions using competing mechanisms (Reddi et al., 2003), although we did not implement this.”

“Other violations of the renewallike assumption are characterized in Teich et al. (1997), although we suspect some are simply manifestations of VarCE and less exotic than these authors propose.”

“Together, the mean and variance of neural responses furnish rich insight into the limits of perception, motor control and decision making (Faisal et al., 2008; Glimcher, 2005; Parker and Newsome, 1998; Shadlen and Newsome, 1998).”

“Here, we used a simplified firing-rate version of such a model (Wong et al., 2007).”

“Other violations of the renewallike assumption are characterized in Teich et al. (1997), although we suspect some are simply manifestations of VarCE and less exotic than these authors propose.”

“…near independence from conditions affecting the mean firing rate, such as motion strength, contrast, and attentional state (Britten et al., 1993; Geisler et al., 2001; McAdams and Maunsell, 1999; Tolhurst et al., 1983), imply that f is unlikely to vary systematically as a function of firing…”

“All motion strengths are included (7008 trials). representation of noisy momentary evidence, without appreciable integration (Cisek et al., 2009), possibly related to agradual shift of attention to a choice target (Gottlieb and Balan, 2010).”

“There is an approximately linear relationship between the mean and variance of the spike counts for neurons in several cortical areas for repetitions of identical stimuli (Britten et al., 1993; Churchland et al., 2006; Geisler and Albrecht, 1995;McAdams andMaunsell, 1999).”

“The lower average rate is probably not explained by amechanism that invokes less excitation or greater suppression on all trials, owing perhaps to greater uncertainty (Basso and Wurtz, 1998), or normalization (Tolhurst and Heeger, 1997), or surround inhibition (Balan et al., 2008).”

“The lower average rate is probably not explained by amechanism that invokes less excitation or greater suppression on all trials, owing perhaps to greater uncertainty (Basso and Wurtz, 1998), or normalization (Tolhurst and Heeger, 1997), or surround inhibition (Balan et al., 2008).”

“It follows that the variability of firing rate across repetitions might bear on the fidelity of these neural signals (Barlow, 1956; Bulmer et al., 1957; Tolhurst et al., 1983).”

“Lastly, we consider a recurrent neural network that is exemplary of a class of dynamical ‘‘attractor’’ models of decision making (e.g., Albantakis and Deco, 2009; Bogacz et al., 2006; Machens et al., 2005; Usher and McClelland, 2001; Wang, 2002).”

“Many studies have assumed that the decision system accumulates the noisy output of a motion discrimination system, in which the noise arises from variability in the stimulus sequence (following [88,99]).”

“The statistical variance of neuronal activity in LIP increases gradually and declines earlier for one option compared with the other option immediately before the action (96).”

“This is consistent with the responses of neurons in areas such as lateral intraparietal cortex when they are accumulating information about direction of motion 27,57 .”

“Neuronal responses in LIP, an area associated with spatial attention, are lower to the onset of four than to that of two choice targets (37).”

“Thesolutionstohid- denfictivestatesinthisdynamiccontextwouldbemorecom-plicatedbutnotcomputationallyintractable denfictivestatesinthisdynamiccontextwouldbemorecom-plicatedbutnotcomputationallyintractable.”

“However, Churchland et al. (2011) recently suggested a method for distinguishing such models at the neural level using analyses of high-frequency noise in neural spike trains.”

“Further, variability increase might carry different information from variability reduction (Briggman et al., 2005; Churchland et al., 2011).”

“Trials of the same type therefore had distinguishable trajectories of activity patterns and did not converge to similar paths through a small set of clusters, which is consistent with previous studies of variability in the activity of cortical neurons 21,22,27-29 .”

“Recently, multiple-choice decision tasks have received increasing attention in the context | 609Overview of different models of decision-making of distinctions between models (Churchland et al. 2011, Ditterich 2010, Leite & Ratcliff 2010, Purcell, Heitz, Cohen, Schall, Logan & Palmeri 2010).”

“…of evidence in favor of peripheral choice targets in the RFs of the neurons (Roitman and Shadlen, 2002; Huk and Shadlen, 2005; Kiani et al., 2008; Churchland et al., 2011), and it is supported in the current study by the time of the earliest significant effects of stimulus strength on LIP…”

“…provide challenging constraints for low-level spiking neural models (e.g., Lo, Boucher, Paré, Schall, & Wang, 2009), and more generally that considerations of behavioral variability can yield insights into neural processes (e.g., Churchland et al., 2011; Purcell, Heitz, Cohen, & Schall, 2012).”

“Analyzing higher-order statistical properties of neurophysiological data from their 2-and 4-alternative random dot motion task, Churchland et al. (2008, 2011) were able to distinguish between models categorized by their different sources of variability.”

“For example, in one line of work, single neurons in the monkey lateral intraparietal area (LIP) have been shown to exhibit strongly choice-predictive activity that builds at a rate proportional to physical evidence strength [33,34], linearly grows in variance as more evidence is sampled over time [35], and reaches a s…”

“It has been suggested that, in addition to firing rates, neural variability across trials can provide further insights about the neural computations underlying deliberation, choice commitment, and action execution (Churchland et al., 2006, 2010, 2011).”

“We then combined the residuals and their associated means using Equation 6 from the study by Churchland et al. (2011) to estimate the VarCE, S Ni 2 , in the six time bins under the four conditions (area by effector), given .”

“Bottom: 95% confidence interval (CI) around the post-error minus post-correct VarCE.”

“We speculate that the sharper decrease in the VarCE seen on visual decisions (Figure 5E, blue) may reflect the dual stabilizing influences of visual sensory input and action planning feedback, while the slower and less deep decrease of the VarCE on auditory decisions (Figure 5E, green) may reflect only a single stabil…”

“In addition, it is difficult to disambiguate different possible neural implementations of computation from the average trajectory since they may only differ in their trial-to-trial variability [6, 21].”

“The predominant model of SAT in decision-making is the “drift-diffusion model,” which suggests that decisions involve a slow accumulation of sensory information until a fixed accuracy criterion is reached (Gold and Shadlen, 2007; Ratcliff and McKoon, 2008; Churchland et al., 2011).”

“Possibly, top-down attention constrains the variability in firing rate (Churchland et al., 2010; Cohen and Maunsell, 2010; Churchland et al., 2011), leading to increased encoding precision.”

“Regarding our modeling approach using the LATER model [12, 13], we should note, however, that its simplistic nature is not compatible with the variance of neurons involved in decision making [37].”

“Estimation of Neural Variability To calculate the across-trial variability of the neural response, we follow the method in Churchland et al. (2011) in which the total calculated variance is approximated as the sum of the VarCE and the point process variance (PPV).”

“Recent evidence points in this direction [54–55], although formal model comparison remains to be done.”

“Moreover, the LATER model appears too simple to be consistent with physiological recordings of neurons involved in decision making (Churchland et al., 2011).”

“Variability is not simply detrimental “noise” that interferes with cognition and sensory processing, but instead is intimately connected with behavioral output (M. M. Churchland et al., 2006; A. K. Churchland et al., 2011).”

“nature of the underlying neural computations (Churchland et al., 2011).”

“In contrast, Roitman and Shadlen (2002) and Churchland et al. (2011) have provided indirect arguments for LIP neurons undergoing a gradual firing rate change.”

“Firing-rate fluctuations and irregular spiking are ubiquitous in the neocortex [1, 2].”

“…or extracellular recordings and regardless of whether the animal is performing a task, passively awake, or anesthetized (Monier et al., 2003; Finn et al., 2007; Mitchell et al., 2007; Churchland et al., 2010, 2011; Hussar and Pasternak, 2010; Ledberg et al., 2012; Qi and Constantinidis, 2012).”

“Measurement of inter-trial variability has been extensively used in the analysis of neural data (Averbeck and Lee, 2003; Churchland et al., 2011, 2010, 2006; He, 2013; Saberi-Moghadam et al., 2016; Schurger et al., 2015).”

“Previous studies of NHP cortical neurons reported that decreases in the variability of neural activity can be a meaningful correlate of important behavioral events (Churchland et al. 2011; Mitchell et al. 2009).”

“On the contrary, this step would introduce temporal correlations (Churchland et al., 2011), in which case, even with ilPPC, a simple sum of the momentary evidence would no longer be optimal (Bogacz et al.”

“…2002; Simen et al., 2011, 2016) as we have used here; (2) diffusion models where the response bound changes to produce different intervals (Churchland et al., 2011); (3) biophysical state-dependent networks, where time is encoded in the current state of recurrent networks (Buonomano,…”

“These transitions appear to coexist with variable spike timing of individual neurons, which is a characteristic feature of a doubly stochastic process (Churchland et al., 2011; Churchland and Abbott, 2012; Litwin-Kumar and Doiron, 2012).”

“Recent physiological studies have reported evidence for doubly stochastic processes in cortex [12,13,14,15].”

“However, how exactly neural variability drives behavioral variability is largely unknown (Britten et al., 1996; Churchland et al., 2011; Brunton et al., 2013; Haefner et al., 2013).”

“Such incoming bounds are also consistent with findings of increased overall activation levels across groups of neurons with different response selectivities (Churchland, Kiani, & Shadlen, 2008; Drugowitsch et al., 2012). One reason why it is important to correctly formulate decision-making models is that they help to…”

“Otherwise, such finer-grained analyses of the statistics of LIP responses may reflect differential dynamics that are in part due to sensory responses, presaccadic activity, or both (see also Churchland et al. 2011).”

“…the signal of interest is dominated by a small subpopulation of neurons with response fields that overlap one of the choice targets, consistent with earlier single neuron studies ( e.g., Shadlen and Newsome, 1996 ; Roitman and Shadlen, 2002 ; Churchland et al., 2011 ; Gold and Shadlen, 2007 )”

“Furthermore, we show in Text S4 that the model is consistent with features of neuronal activity during random-dot motion tasks [1,26,27].”

“In the lateral intraparietal area (LIP), this activity reflects not only the mean (Roitman and Shadlen 2002; Huk and Shadlen 2005; Kiani et al. 2008) but also the variance and autocorrelation (Churchland et al. 2011) of an evolving DV that explains choice and RT.”

“, [5–7]), human magnetoencephalography (e.”

“Activity in LIP in the coherent dot motion perception task is well characterized by accumulator models (Churchland et al., 2011; Gold et al., 2010; Gold and Shadlen, 2007).”

“Conversely, the variance of firing rate was shown to increase in the course of decision making, and as a function of the number of alternative choices [14].”

“Note that certain tasks, such as perceptual decision-making, may generate an increase in neural variability before the decision is made (Churchland et al., 2011).”

“Area LIP also carries spatial cognitive signals related to perceptual and economic decision-making (Churchland et al. 2011; Dorris and Glimcher 2004; Gold and Shadlen 2007; Kiani and Shadlen 2009; Louie and Glimcher 2010; Louie et al. 2011; Platt and Glimcher 1999; Roitman and Shadlen 2002; Seo et…”

“…filter with a short time constant is capable of simulating the effects of early motion signals, even on RT distributions whose means are 1,000 ms. Churchland et al. (2011) suggested that the UGM cannot explain correlations in neural activity, but those authors also did not include the low-pass…”

“The increase in drift rate difference with coherence is consistent with the literature (Churchland et al., 2011; Donkin et al., 2009; Ho et al., 2009; Mulder et al., 2013; Palmer et al., 2005).”

“Certainly, discharge rates of single neurons wax and wane with variable rates; a measure of the variance of spike rates across trials increases over time as expected if the process were similar to Brownian motion [54].”

“Here, there is substantial evidence that decision termination is mediated by application of a threshold to the neural representation of accumulating evidence [8, 46, 47], and this also holds in experiments that do not allow for free responses, as in our controlled-duration experiment [13, 16, 48].”

“…changes in response variability have been observed as a correlate of active behavioral states (M. M. Churchland et al., 2006; Mitchell et al., 2007; Cohen and Maunsell, 2009; Steinmetz and Moore, 2010; A. K. Churchland et al., 2011), suggesting that variability may reflect behavioral engagement.”

“2009) and electrophysiological (Leon and Shadlen 2003; Janssen and Shadlen 2005; Genovesio et al. 2006; Mita et al. 2009; Churchland et al. 2011) evidence—further improves the advantage of the nonlinear system over a perfect integrator.”

“Our analysis of residual dynamics extends previous work that leveraged trial-by-trial variability to understand neural computations 19,20,22,23,41 , by providing a full, quantitative description of the time-varying dynamics of population-level trial-by-trial variability.”