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, in an analysis of noise in decision-making, Churchland et al. (2011) considered a model in which spike rates were from a Poisson process and the rate parameter varied from trial to trial.”

“This shortcoming has motivated recent work to determine the single-trial dynamics of LIP responses in direction discrimination tasks (Churchland et al., 2011; Bollimunta et al., 2012; Latimer et al., 2015).”

“Recently developed methods that partition rate variability (Churchland et al., 2011; Goris et al., 2014) address this, aiming to quantify the sources of variability that arise from fluctuations in cell excitability.”

“…sampling by a modified Boltzmann machine (Geman and Geman, 1984; Hoyer and Hyvärinen, 2003; Ma et al., 2006; Sundareswara and Schrater, 2008; Churchland et al., 2011; Gershman et al., 2012) offers a functional rationale as to why competing perceptual representations should operate far from…”

“Based on these models, we generated presynaptic spikes { s tj } with a doubly stochastic process to reproduce high variability typically observed in cortical activity (Churchland et al., 2011; Tsubo et al., 2012).”

“…single-neuron recordings from monkey visual cortex and lateral intraparietal area (LIP) demonstrating spike counts that could be described by doubly stochastic processes (Churchland et al., 2011), which in turn are possible neuronal correlates of behavioral variability (van den Berg et al., 2012).”

“This ‘Bayesian brain hypothesis’ is supported by ample experimental evidence, ranging from psychophysical findings 4–6 to neuronal recordings 7–9 that are in line with Bayesian computation.”

“However, many accumulator models predict that variability increases over time (Churchland et al. 2011; Ratcliff 1978), which appears to be inconsistent with the poststimulus decline in Fano factor (Fig.”

“The activity of these motor structures can then easily be identified in motor related potentials (Leuthold & Jentzsch, 2002; Lang et al.,1991).”

“The within-saccade accumulation is formally related to evidence accumulation as described in models of perceptual discrimination (Gold and Shadlen 2003; Churchland et al. 2011).”

“Most previous studies on sensory decisionmaking examined the activity of neurons in the parietal and frontal cortex (Churchland et al., 2011; Ding and Gold, 2012; Gold and Shadlen, 2000; Kiani and Shadlen, 2009; Kiani et al., 2008; Kim and Shadlen, 1999; Roitman and Shadlen, 2002; Shadlen and…”

“= Var1⁄2λ |fflfflffl{zfflfflffl} firing rate variability + E Var1⁄2Njλ |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} spiking variability , [4]”

“1e, these transitions appear to coexist with variable spike timing of individual neurons, which is a characteristic feature of a doubly stochastic process, as found in experiments 30,31 .”

“Models 3 and 4 are identical to Models 1 and 2 but in addition allow the drift rate variance to vary over angles (Churchland et al., 2011).”

“A shortcoming of single-trial analysis is that stochastic fluctuations in spikes could be interpreted as signal when they are in fact just related to the spike generation process [58,59].”

“…of perceptual decision-making, responses of neurons in the monkey parietal cortex have been investigated during a task in which they had to report the direction of a noisy motion stimulus when presented with either two, or four response options ( Churchland et al., 2008 ; Churchland et al., 2011 ).”

“In addition to its varying modulation by different stimuli ( Arazi et al., 017b ; Churchland et al., 2011 , 2010 ; Hussar and Pasternak, 2010 ; olff et al., 2019c ), previous studies suggest that TTV is also de- endent on the degree of the brain’s variability at stimulus onset. n non-human data,…”

“At the neural level, variable precision might have a parallel in the single (Bays, 2014) or double stochasticity of neural spike counts (Churchland et al., 2011; Goris, Movshon, & Simoncelli, 2014; van den Berg, Yoo, & Ma, 2017).”

“1 (C); Churchland et al., 2011; Nawrot et al., 2008; Smith, 2010, 2015 ).”

“To evaluate whether the neuronal firing rates on individual trials during the decision-making epoch reflect a process of accumulation of noisy evidence, we analyzed the pattern of variance and autocorrelation of the responses (Churchland et al., 2011; de Lafuente et al., 2015).”

“At the neuronal level in the brain, stochasticity in response to stimuli is well documented (Shadlen and Newsome, 1994; Churchland et al., 2011).”

“Since this momentary evidence is variable, the accumulation resembles Brownian motion of a particle, hence the analogy to diffusion and random walks (Churchland et al. 2011).”

“…sensory sampling variability mirrors the previously reported increase in neural variability preceding a decision to act (Steinmetz and Moore, 2010; Churchland et al., 2011), and the trial-to-trial sampling variability associated with voluntary movements significantly exceeds that of the…”

“Furthermore, neural representations based on probabilistic codes (11) as opposed to trial averaged responses have been successful at capturing key aspects of these behaviors (12), and spiking variability is inherent in these cognitive theories.”

“…the reliability of neural responses to photoactivation, we calculated the Fano factor (FF), defined as the variance- to-mean ratio of spike counts ( Churchland et al., 2011 ), to characterize the variability of neuronal responses 6 ms before (FF before) and 6 ms after (FF after) the laser pulses…”

“ual increase of VarCE and temporal correlation (Churchland et al. 2011).”

“It follows that the time course of this variance mimics the highly non-stationary dynamics of the underlying neuronal processes (Churchland et al. 2011, Churchland et al. 2010).”

“11 Neural activity shows significant variation even under conditions in which measurement error can be shown to be near zero (Churchland et al., 2010, 2011; Tolhurst, Movshon, & Dean, 1983).”

“This approximation depends on the stimulus-independent variance being proportional to the mean rate, which will be true for any rate-modulated renewal process (Nawrot et al., 2008; Churchland et al., 2011) and approximately holds in many cortical recordings (Tolhurst et al.”

“These models have a thorough grounding in theory and confirmation by experiment (Machens et al., 2005; Uchida et al., 2006; Wang, 2008; Churchland et al., 2011).”

“To this end, we removed the Poisson-like component of the variance associated with spike counts—the variability that would be present even if the rates were identical from trial to trial (termed the point process variance in Churchland et al., 2011).”

“In summary, the dip in VarCE prior to decision onset is probably not a correlate of the resetting of the integrator.”

“, 2013) during different reaching tasks and when a decision is made about future eye movements (Churchland et al., 2011).”

“The noise accounts for both noisiness of the evidence itself (an important aspect in the moving-dot paradigm [9,33,34,40]) and internal noise in the brain.”

“…phase coherence, and pre-poststimulus differences in all these measures (Arazi et al., 2017a, 2017b; Baria et al., 2017; Braun et al., 2022; Churchland et al., 2011, 2010; Deha-ghani et al., 2022; He, 2013; Huang et al., 2015; Northoff and Zilio, 2022b; Schurger et al., 2015;…”

“For instance, it is broadly observed that as neural activity increases, the signal-to-noise ratio of decoded neural quantities also increases (e.g., McAdams andMaunsell 1999, Churchland et al. 2011).”

“Additionally, we examined the relationship between the response magnitude and variability of single neurons by calculating the neurons’ Fano factor (Churchland et al., 2010; Goris et al., 2014; Churchland et al., 2011) in the low and high pre-stimulus trials.”

“Mirroring the findings on firing rates for items in working memory, nonhuman primate electrophysiology studies have shown that average firing rates decrease and firing rate variability increases when the number of response alternatives increases (Churchland and Ditterich 2012; Churchland et al. 2011).”

“…approach based on trial-by-trial variations in firing rate has been used before to characterize Fano factors 1 in hippocampal neurons (Olypher et al., 2002) and recently in LIP itself to differentiate between different models of decision making (Shadlen and Newsome, 1998; Churchland et al., 2011).”

“…model has variance with both linear and quadratic terms, and can capture the relationship of spike count variance to mean response over the extended range [51, 52]: where the constant g governs the transition from the Poisson range (smaller µ ( s )) to the super-Poisson range (larger µ ( s )) (Fig.”

“The Fano factor provides a quantification of the variability in neuronal responses to the stimulus (Churchland et al. 2011).”

“…of intermediate quantities are unbiased; we also derive a nonparametric estimator of φi from spike trains, in contrast to Goris et al. (2014), who assume φi = 1, and Churchland et al. (2011), who use φi like a tuning parameter and choose it such that variances and correlations are well defined.”

“Furthermore, it has been suggested that neuronal variability may itself play a crucial cognitive role during decision-making (Churchland et al., 2011).”

“Overall modulation strength in the population is determined by the modulator variance (var(mt) = σ(2) m - see also [8]).”

“The velocity-to-position neural integrator lies between FTNs and abducens neurons, and integration could accumulate variation as a function of time (Churchland et al. 2011).”

“Several recent studies have acknowledged this objective with a particular emphasis on multiple alternatives (Ditterich, 2010; Leite and Ratcliff, 2010; Purcell et al., 2010; Churchland et al., 2011).”

“Large spike count variability across controlled trials is commonly observed in cortical neurons in evoked conditions (Shadlen and Newsome, 1994; Churchland et al., 2011), and such stochasticity in spike emission is seen in balanced networks that obey Dale’s law (Tsodyks et al.”

“Analogous to the variance of conditional expectation (VarCE) that Churchland and colleagues studied previously in the LIP neurons [21], we calculate the response variability of the units in the hidden layer (Fig 5D).”

“A more common assumption, made to our knowledge in all earlier work on decisions on the direction of motion (Ratcliff & McKoon, 2008; Roitman & Shadlen, 2002), is that evidence sampled at a given time is associated with object motion (e.g., that a dot moves to the left or to the right, see Figure 12d for the evidence…”

“, a linear increase as a function of time) across trials and the autocorrelation of x(t) within trials (a function of both the lag between samples and the time of the first sample) [8, 9].”

“The logic underlying this work (e.g., Churchland et al., 2011; Gold and Shadlen, 2007; Hanks et al., 2015; Mante et al., 2013; Ratcliff et al., 2003; Yartsev et al., 2018) is that behavior is well approximated by gradual evidence accumulation (Ratcliff and McKoon, 2008).”

“A neural signature of this effect can sometimes be seen in the timecourse of residual response variance (that is, response variance that is not due to choice outcome or stimulus strength) 26 .”

“…has shown that different regions exhibit varied timescales of fluctuations in neuronal population activity, that is, magnitude of autocorrelation ( Churchland et al., 2011 ; Murray et al., 2014 ), which varied in the presence of a stimulus or a task ( Nougaret et al., 2021 ; Runyan et al., 2017 ;…”

“In the present study, a higher mean-variance relationship in learning populations may indicate that acoustic encoding is more flexible than in populations that do not track trial-by-trial behavior (75, 77, 78).”

“Neuronal spike patterns are highly variable, and display substantial diversity across neurons, during both maintained activity and evoked responses (Softky & Koch, 1993; Churchland et al. 2011).”

“An excellent example of this joined effort is illustrated by Churchland et al. [103].”

“To dig deeper into the nature of the observed ramping signals, we tested for statistical signatures of a bounded accumulation process 48,49 —(1) increasing variance of the underlying rate (variance of the conditional expectation, VarCE) followed by a collapse near decision termination, and (2) a…”

“It is therefore important to consider response variability in awake brains in addition to magnitude-based metrics when quantifying tuning and discriminability in neurons (Churchland et al., 2011; Mazurek et al., 2014).”