Trial-to-trial variability of neural signals

Neurons generate action potentials (spikes) during spontaneous activity and increase or decrease their firing rate in response to synaptic inputs. One of the simplest models of neuronal spiking is a Poisson process, characterized by individual spikes occurring independently of each other, which results in the variance of spike counts being approximately equal to the average number of spikes. Neural variability is frequently measured as the Fano factor, the ratio between the variance and the mean of spike counts across repeated presentations of the same stimulus. In cortical neurons, the Fano factor is typically greater than one, indicating that cortical responses are highly variable. This additional variance is largely correlated between neurons (Cohen and Kohn, 2011) and substantially decreases with external stimulus input, an effect referred to as variability quenching (Churchland et al., 2010). Commonly accepted models of brain function propose that sensory information is encoded in the neurons firing rate, which can be accurately inferred at the population level (Shadlen and Newsome, 1998), but it is still unclear whether second-order statistics such as neural variability and the exact temporal patterns of spiking activity constitute mere noise or may themselves contain information. The following sections examine neural variability, its potential sources, its stimulus-induced decline and its relation to visual attention and perception in more detail.

1.4.1 Sources and stimulus-induced changes of neural variability

Repeated presentations of identical stimuli generate variable numbers of spikes in the same cortical neurons (Tolhurst et al., 1983; Snowden et al., 1992; Britten et al., 1993; Gur et al., 1997) and the time between individual spikes, the inter-spike interval (ISI), is similarly highly variable (Softky and Koch, 1993). Both types of variability appear to be present throughout cortical areas to approximately the same degree, with the variance of spike counts typically around the order of 1.5 times the mean spike count (Lee et al., 1998; Shadlen and Newsome, 1998). This homogeneity does however not seem to generalize to subcortical structures as studies comparing spiking variability in the lateral geniculated nucleus (LGN), a structure of the thalamus transmitting retinal signals to the primary visual cortex V1, with that in visual cortex areas have consistently found variability in the LGN to be lower (Kara et al.,

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2000; Goris et al., 2014; Schölvinck et al., 2015). Spiking variability in cortex has further been shown to be highly correlated between neurons (Cohen and Kohn, 2011; Schölvinck et al., 2015).

What are the sources of neural variability in cortical neurons? Theoretically, there are a number of potential contributing factors, including variable physical stimulus information as well as variability inherited from thalamic inputs, variability in the spike generation of individual neurons, and variability in the ongoing cortical activity that may exert a modulatory influence on neural responses. In vitro experiments have shown that cortical neurons produce highly reliable spike trains (Mainen and Sejnowski, 1995), suggesting that the variability inherent in spike generation contributes only minimally to the variability observed in cortical responses. It is thus likely that synaptic inputs to a given neuron account for a large portion of the observed variability (Shadlen and Newsome, 1998; Carandini, 2004).

While variations in physical stimulus input may be considered negligible under highly controlled experimental conditions, it can be argued that the variability in cortical responses stems from its thalamic inputs rather than from the cortical circuitry (Priebe and Ferster, 2012). This hypothesis is supported by experiments by Sadagopan and Ferster who could show that silencing cortical inputs by local inactivation of the surrounding cortex had little effect on the response variability of V1 neurons (Sadagopan and Ferster, 2012). However, a number of studies examining the relationship between ongoing cortical activity and the response variability of individual neurons arrived at the opposite conclusion. Arieli and colleagues showed that the variability of responses in V1 can be attributed to the magnitude of ongoing activity and that single trial responses can be predicted by the summation of the preceding ongoing activity and a deterministic evoked response (Arieli et al., 1996). Similarly, Schölvinck and colleagues who investigated neural variability in LGN and primary visual cortex V1 found that the additional variability observed in cortical responses was predicted by the sum activity of other neurons in the population, suggesting that neural variability reflects global fluctuations of activity affecting the majority of neurons (Schölvinck et al., 2015). The authors further showed that their magnitude is dependent on cortical state with activity fluctuations being largest during synchronized states (Schölvinck et al., 2015). Goris and colleagues demonstrated that neural response variability arises from fluctuations in cortical excitability that are highly correlated between neurons and increase in strength along the visual pathway (Goris et al., 2014).

Trial-to-trial variability in neuronal spiking activity as well as in the membrane potential of single cells has been shown to be dramatically reduced following stimulus presentation compared to the more

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variable spontaneous activity in the absence of driving stimulus input (Churchland et al., 2010).

Importantly, physical stimulation thereby strongly reduces correlated variability that is shared between many neurons (Churchland et al., 2010; Oram, 2011). This variability quenching effect can be observed in a wide range of cortical areas and across a wide range of states including anaesthesia, suggesting that the variability decline originates from low-level mechanisms rather than the influence of microsaccades or attention (Churchland et al., 2010). In theoretical work, Deco and Hugues have shown that neural variability quenching can arise from network effects within an attractor network with balanced excitation and inhibition (Deco and Hugues, 2012), suggesting that variability quenching upon stimulus input constitutes a general property of large, recurrent networks, as similarly predicted earlier (Rajan et al., 2010).

1.4.2 Neural trial-to-trial variability in attention and perception

The variability of spiking responses can influence how reliably sensory information is encoded by neuronal signals (Zohary et al., 1994; Shadlen et al., 1996; Parker and Newsome, 1998), in particular when it is highly correlated between neurons and may thus not be cancelled out by pooling across the neuronal population. In electrophysiological experiments recording from macaque visual cortex, trial-to-trial spiking variability during the sustained response has been shown to be modulated by selective attention, being considerably lower for attended compared to unattended visual stimuli (Mitchell et al., 2007, 2009; Cohen and Maunsell, 2009; Herrero et al., 2013). Attentional modulations of trial-to-trial variability have been linked to a reduction of slow correlated fluctuations in rate and are thought to improve the signal-to-noise ratio of neural signals even more effectively than attention-dependent increases in firing rate (Mitchell et al., 2009). Ni and colleagues further demonstrated that both trial-to-trial variability and correlated variability in visual area V4 closely covary with perceptual performance, showing the same relationship for fast changes in performance mediated by attention and for slow changes mediated by perceptual learning over time (Ni et al., 2018). Moreover, the variability of visually evoked potentials (VEP) has been shown to correlate with the level of trial-to-trial variability prior to stimulus onset as well as with response times, suggesting that behavioural performance may be dependent on the reliability of ongoing activity (Ledberg et al., 2012). In humans, stimulus-induced decreases in trial-to-trial variability have been observed in the EEG and therein linked to perceptual performance (Arazi et al., 2017a). What is more, the magnitude of variability quenching with stimulus

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onset measured in parieto-occipital electrodes has been shown to be a remarkably consistent characteristic of individual subjects and to predict lower contrast discrimination thresholds in subjects that showed a stronger variability decrease (Arazi et al., 2017b, 2017a). Greater trial-to-trial variability in stimulus responses as well as ongoing activity compared to healthy controls have also been observed in individuals with neurodevelopmental disorders affecting sensory processing, such as attention deficit hyperactivity disorder (ADHD) (Dinstein et al., 2015; Saville et al., 2015; Gonen-Yaacovi et al., 2016) and autism (Milne, 2011; Dinstein et al., 2012, 2015; Haigh et al., 2015). A greater similarity in neural activation patterns over multiple repetitions has further been observed for words and faces that were remembered compared to forgotten stimuli, suggesting a possible link between trial-to-trial variability and episodic memory encoding (Xue et al., 2010). More recently, reductions in EEG trial-to-trial variability in the human visual system have been associated with spatial attention whereby stronger variability quenching was observed in the hemisphere contralateral to the attended stimulus location (Arazi et al., 2019). Stronger quenching of EEG trial-to-trial variability has further been shown to predict the visual detection of threshold-level stimuli compared to stimuli that were not consciously perceived (Schurger et al., 2015) and reduced trial-to-trial variability of fMRI activation patterns has also been observed for subjectively visible stimuli using dichoptic color masking (Schurger et al., 2010), suggesting that the level of neural variability across trials may be a potential indicator of visual awareness.