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…”

“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).”

“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).”

“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.”

“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).”

“…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).”