As sensory information about the world is often noisy and/or ambiguous, an evidence accumulation process for increasing signal-to-noise ratio is thought to be fundamental to perceptual decision-making. Neural circuits that perform this are incompletely known, but canonically hypothesized to involve multiple stages starting from the detection of momentary sensory signals, which are then accumulated through time and later categorized into an appropriate behavioral action (Gold and Shadlen, 2007; Brody and Hanks, 2016; Caballero et al., 2018). In this picture, the sensory detection stage has a predominantly feedforward role, that is, providing input to but not otherwise involved in accumulation and decision formation. However, another large body of literature has demonstrated that sensory processing in even the earliest sensory cortices can be modified by various external and internal contexts, including motor feedback, temporal statistics, learned associations, and attentional control (Roelfsema and de Lange, 2016; Gilbert and Sigman, 2007; Kimura, 2012; Gavornik and Bear, 2014; Glickfeld and Olsen, 2017; Niell and Stryker, 2010; Saleem et al., 2013; Shuler and Bear, 2006; Fiser et al., 2016; Haefner et al., 2016; Lee and Mumford, 2003; Zhang et al., 2014; Saleem et al., 2018; Makino and Komiyama, 2015; Keller et al., 2012; Poort et al., 2015; Li et al., 2004; Stănişor et al., 2013; Petreanu et al., 2012; Romo et al., 2002; Luna et al., 2005; Nienborg et al., 2012; Yang et al., 2016; Britten et al., 1996; Froudarakis et al., 2019; Keller and Mrsic-Flogel, 2018). For example, feedback-based gain control of sensory responses has been suggested as an important mechanism for enhancing behaviorally relevant signals, while suppressing irrelevant signals (Manita et al., 2015; Hillyard et al., 1998; Harris and Thiele, 2011; Azim and Seki, 2019; Douglas and Martin, 2007; Ahissar and Kleinfeld, 2003).

The above two ideas—evidence accumulation and context-specific modulations—make two different but both compelling points about how sensory signals should be processed to support behavior. The two ideas are not mutually incompatible, and insight into the brain’s specific implementation may be gained from a systematic investigation of sensory representations in the brain. To observe how each sensory increment influences neural dynamics, we utilized a behavioral paradigm with precisely initiated timings of sensory inputs that should drive an evidence accumulation process (Brunton et al., 2013). Specifically, we recorded from posterior cortical areas during a navigational decision-making task (Pinto et al., 2018; BRAIN CoGS Collaboration, 2017) where as mice ran down the central corridor of a virtual T-maze, pulses of visual evidence (‘cues’) randomly appeared along both left and right sides of the corridor. To obtain rewards, mice should accumulate the numerosities of cues, then turn down the maze arm corresponding to the side with more cues. The well-separated and randomized timing of cues allowed us to clearly identify putative sensory responses that were time-locked to each pulse, whereas the seconds-long periods over which cues were delivered allowed us to observe the timecourse of neural responses throughout a gradually unfolding decision.

Across posterior cortices, the bulk of neural activity was sequentially active vs. time in the trial, in a manner that did not depend directly on the sensory cues, as we describe in detail in another article (Koay et al., 2019). Even in the primary (V1) and secondary visual areas, only 5–15% of neurons active during the task had responses that were time-locked to sensory cues (‘cue-locked cells’). Still, it is known that remarkably small signals on the order of a few cortical neurons can influence behavior (Doron and Brecht, 2015; Buchan and Rowland, 2018; Tanke et al., 2018; Lerman et al., 2019; Carrillo-Reid et al., 2019; Marshel et al., 2019). Here, we focused on the cue-locked cells, as candidates for momentary sensory inputs that may drive an accumulation and decision-making process. The responses of these cells to cues were well-described by a single impulse response function per neuron, but with amplitudes that varied across the many cue presentations. The cue-response amplitudes of most cells varied systematically across time in the trial, as well as across trials depending on behavioral context, thus suggesting gain modulation effects potentially related to decision-making dynamics. Across posterior cortices and including as early as in V1, these variations in cue-response amplitudes contained information about multiple visual, motor, cognitive, and memory-related contextual variables. Notably, in all areas about 50% of cue-locked cells had response amplitudes that depended on the choice reported by the animal at the end of the trial, or depended on the value of the gradually accumulating evidence. Top-down feedback, potentially from non-sensory regions in which the choice is formed, has been proposed to explain choice-related effects in sensory responses (Britten et al., 1996; Romo et al., 2003; Nienborg and Cumming, 2009; Yang et al., 2016; Bondy et al., 2018; Wimmer et al., 2015; Haefner et al., 2016). The dependence on accumulating evidence that we observed supports the hypothesis that this feedback may originate from an accumulator that itself eventually drives choice.

In sum, the amplitude modulations of cue-locked responses in this report can be thought of as due to multiplicative effects (or equivalently, changes in gain) on the brain’s internal representation of individual sensory pulses. These multiplicative effects were moreover not entirely random from one cue to the next, but rather depended on task-specific factors including those that the brain presumably keeps track of using internal neural dynamics, such as the accumulated evidence. We thus suggest that psychophysical studies of pulsatile-evidence accumulation may benefit from considering that even at the earliest, sensory input stage, neural variability can have a component that is correlated across responses to multiple cues in a trial, as opposed to the independent noise often assumed under lack of knowledge otherwise. Our findings in this article point to candidate neural bases for temporally correlated noise that has been deduced from behavioral data to limit perceptual accuracy, for example in odor discrimination tasks for rats where the subject was free to continue acquiring sensory samples (Zariwala et al., 2013).

We used cellular-resolution two-photon imaging to record from six posterior cortical regions of 11 mice trained in the Accumulating-Towers task (Figure 1a–c). These mice were from transgenic lines that express the calcium-sensitive fluorescent indicator GCaMP6f in cortical excitatory neurons (Materials and methods), and prior to behavioral training underwent surgical implantation of an optical cranial window centered over either the right or left parietal cortex. The mice then participated in previously detailed behavioral shaping (Pinto et al., 2018) and neural imaging procedures as summarized below.

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Mice were trained in a head-fixed virtual reality system (Dombeck et al., 2010) to navigate in a T-maze. As they ran down the stem of the maze, a series of transient, randomly located tower-shaped cues (Figure 1b,c) appeared along the right and left walls of the cue region corridor (length $L_{cue}\approx 200$ cm, average running speed in cue region $\approx 60cm/s$; see Materials and methods), followed by a delay region where no cues appeared. The locations of cues were drawn randomly per trial, with Poisson-distributed mean counts of 7.7 on the majority and 2.3 on the minority side, and mice were rewarded for turning down the arm corresponding to the side with more cues. In agreement with previous work (Pinto et al., 2018), all mice in this study exhibited characteristic psychometric curves (Figure 1d) and utilized multiple pieces of evidence to make decisions, with a small primacy effect (Figure 1e).

As the timing and visual location of the tower-shaped cues are important information about the behavior that we wished to relate to the neural activity, we programmed the virtual reality software to make a given cue visible to the mouse exactly when it reached a distance of 10 cm before the cue’s location along the T-maze stem (i.e. in the y coordinate, see Figure 1c). We refer to this instant at which a cue becomes visible as the ‘onset time’ for that cue, and used it to define the behavioral timings of visual pulses in all neural data analyses. Cues were made to vanish from view after 200 ms, although 1/11 mice ran so quickly that cues occasionally fell outside of the display range of the virtual reality system before that period (cue duration was ~190 ms for that mouse, see Materials and methods and Figure 1—figure supplement 1 for details on timing precision). Lastly, as mice controlled the virtual viewing angle θ, cues could appear at a variety of visual angles ${\varphi }_{cue}$ (Figure 1c). We accounted for this in all relevant data analyses, as well as conducted control experiments in which θ was restricted to be exactly zero from the beginning of the trial up to midway in the delay period (referred to as θ-controlled experiments; see Materials and methods).

For each mouse, we first identified the locations of the visual areas (Figure 1f; Materials and methods) using one-photon widefield imaging and a retinotopic visual stimulation protocol (Zhuang et al., 2017). Then, while the mice performed the task, we used two-photon imaging to record from $500\mu m\times 500\mu m$ fields of view in either layers 2/3 or 5 from one of six areas (Supplementary file 1, Supplementary file 2): the primary visual cortex (V1), secondary visual areas (V2 including anteromedial area [AM], posteromedial area [PM], medial-to-AM area [MMA], medial-to-PM area [MMP] [Zhuang et al., 2017]), and retrosplenial cortex (RSC). These fields of view were selected only to have good imaging quality (high apparent density of cells as unobscured as possible by brain vasculature), that is, prior to the start of the behavioral session and without any criteria based on neural responses. After correction for rigid brain motion, regions of interest representing putative single neurons were extracted using a semi-customized (Materials and methods) demixing and deconvolution procedure (Pnevmatikakis et al., 2016). The fluorescence-to-baseline ratio $\Delta F/F$ was used as an estimator of neural activity, and only cells with $\ge 0.1$ transients per trial were selected for analysis. In total, we analyzed 10,113 cells from 143 imaging sessions, focusing on 891 neurons identified as time-locked to the visual cues as explained in the next sections.

Pulses of evidence evoke transient, time-locked responses in all recorded areas

We found neurons in all areas/layers that had activities clearly time-locked to the pulsatile cues (examples in Figure 2a–b). In trials with sparse occurrences of preferred-side cues, the activities of these cells tended to return to baseline following a fairly stereotyped impulse response. Individually, they thus represented only momentary information about the visual cues, although as a population they can form a more persistent stimulus memory (Goldman, 2009; Scott et al., 2017; Miri et al., 2011). Interestingly, the amplitudes of these cells’ responses seemed to vary in a structured way, both across time in a trial, as well as across trials where the mouse eventually makes the choice to turn right vs. left (columns of Figure 2a–b). We therefore wished to quantify whether or not these putatively sensory amplitude changes also encoded other task-related information.

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For a given cell, we estimated the amplitude of its response to each cue $i$ by modeling the cell’s activity as a time series of non-negative amplitudes $A_i$ convolved with an impulse response function (Figure 2c). The latter was defined by lag, rise-time and fall-time parameters that were fit to each cell, but were the same for all cue-responses of that cell (deconvolving calcium dynamics; see Materials and methods). For a subset of neurons, this impulse response model resulted in excellent fits when the model included only primary responses to either right- or left-side cues (e.g. Figure 2d). In much rarer instances, adding a secondary response to the opposite-side cues resulted in a significantly better fit (e.g. Figure 2e; discounting for number of parameters by using AIC_C[Hurvich and Tsai, 1989] as a measure of goodness of fit). We defined cells to be cue-locked if the primary-response model yielded a much better fit to the data than a permutation test (data with cue timings shuffled within the cue region, see Materials and methods). For these cells, the trial-averaged activity predicted by the impulse response model (Figure 2f, magenta) was substantially larger than the magnitude of residuals of the fits (Figure 2f, ‘data - model’ prediction in black). For example, if cells had systematic rises or falls in baseline activity levels vs. time/place that could not be explained as transient responses to cues, then the residual would grow/diminish vs. y location in the cue region. Figure 2—figure supplement 1a shows that systematic trends (i.e. slopes) for the residual vs. y was small for most cells (68% C.I. of slopes across cells were within $\left[-0.098,0.062\right]$, where a slope of ±1 corresponds to a change in residuals from the start to the end of the cue region being equal to the average signal predicted by the impulse response model). There were thus no large, unaccounted-for components in the activity of these identified cue-locked cells, in particular no components with long timescales.

Significantly cue-locked cells comprised a small fraction of the overall neural activity, but were nevertheless present in all areas/layers and exhibited some progression of response properties across posterior cortical areas in a roughly lateral-to-medial order (V1, V2, RSC). Cells with the most precisely time-locked responses to cues were found in the visual areas as opposed to RSC (high-significance tail of distributions in Figure 2g; low significance means that the model fit comparably well to data where cue timings were shuffled within the cue region). Reflecting this, about 5–15% of cells in visual areas were significantly cue-locked, compared to ~5% in RSC (Figure 2h). Of these significant cells, only ∼3% had secondary responses that were moreover much less significantly time-locked (Figure 2—figure supplement 1b); most cells responded to only contralateral cues (Figure 2—figure supplement 1c). The onset of the half-maximum response was ∼200 ms after each pulse (Figure 2i), and the response full-width-at-half-max (FWHM) was ∼100 ms but increased from V1 to secondary visual areas to RSC (Figure 2j). The impulse response model thus identified cells that follow what one might expect of purely visual-sensory responses on a cue-by-cue basis, but up to amplitude changes that we next discuss.

Cue-locked response amplitudes contain information about visual, motor, cognitive, and memory-related contextual task variables

Studies of perceptual decision-making have shown that the animal’s upcoming choice affects the activity of stimulus-selective neurons in a variety of areas (Britten et al., 1996; Nienborg and Cumming, 2009). We analogously looked for such effects (and more) while accounting for the highly dynamical nature of our task. As neurons responded predominantly to only one laterality of cues, all our subsequent analyses focus on the primary-response amplitudes of cue-locked cells. Importantly, the impulse response model deconvolves responses to individual cues, so the response amplitude $A_i$ can be conceptualized as a multiplicative gain factor that the cell’s response was subject to at the instant at which the $i^{th}$ cue appeared.

We used a neural-population decoding analysis to quantify how much information the cue-locked response amplitudes contained about various contextual variables. First, for the $i^{th}$ cue in the trial, we defined the neural state as the vector of amplitudes $A_i$ of cells that responded to contralateral cues only. Then using the neural states corresponding to cues that occurred in the first third of the cue period, we trained a support vector machine (SVM) to linearly decode a given task variable from these neural states (cross-validated and corrected for multiple comparisons; see Materials and methods). This procedure was repeated for the other two spatial bins (second third and final third) of the cue period, to observe changes in neural information that may reflect place-/time-related changes in task conditions (illustrated in Figure 3a). Figure 3b shows that across posterior cortex, four task variables were accurately decodable from the cue-response amplitudes: the view angle $\theta$, running speed, the running tally of evidence ($\Delta \equiv \#R-\#L$), and the eventual choice to turn right or left. The reward outcome from the previous trial could also be decoded, albeit less accurately, while in contrast decoding of the past-trial choice was near chance levels.

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As the six variables were statistically correlated by nature of the task (e.g. the mouse controls θ to execute the navigational choice, Figure 3a), indirect neural information about one variable could be exploited to increase the performance of decoding another correlated variable (Krumin et al., 2018; Koay et al., 2019). To account for this, we repeated the decoding analyses for a modified set of variables that had statistical correlations removed. As explained in the Materials and methods and illustrated in Figure 3c, we solved for uncorrelated modes being linear combinations of the original time-traces that were closest, in the least-squares sense, to the original traces, while constrained to be themselves uncorrelated with each other. As inter-variable correlations were low throughout the cue region, these uncorrelated modes were very similar to the original task variables. Each uncorrelated mode was identified with its closest original variable and labeled as such, and correlation coefficients between individual uncorrelated modes and their corresponding original variables were > 0.85 for all modes (Figure 3—figure supplement 1). Performances for decoding the uncorrelated modes were a little lower than the original task variables (Figure 3d), as expected since contributions from indirect neural information could no longer be present. Nevertheless, the modes that resembled view angle, speed, evidence, choice, and past-trial reward could all be consistently decoded across imaging sessions for all examined areas (Figure 3e). There was also comparably high performance of decoding evidence and choice in the θ-controlled experiments (Figure 3—figure supplement 2), which explicitly shows that neural information about these variables do not originate solely from changes in visual perspective. In a comparable task where choice was highly correlated with view angle (θ) and y spatial location in the maze, it has previously been reported that θ and y explains most of neural responses in parietal posterior cortex, with small gains from including choice as a third factor (Krumin et al., 2018). Interestingly however, our findings indicate that in a task where choice was distinguishable from other behavioral factors (here, at least within the cue region), there was significant neural information in all examined posterior cortical areas about this internally generated variable, choice.

As a population, the amplitudes of cue-locked cells thus reflected a rich set of present- and past-trial contextual information, with some apparent anatomical differences seen in Figure 3b,d. However, instead of the neural representation being different across different cortical regions, an alternative explanation could be that the accuracy of decoding task variable information depended on experimental factors such as the number of recorded neurons (which differed systematically across cortical areas/layers). To address this, we constructed a linear regression model to predict the decoding accuracy for various datasets as a weighted sum of a set of factors: the cortical area, layer, and number of recorded cells. The cortical area and layer regressors are indicator variables (0 or 1) that specify whether a given dataset was a recording from a particular area and layers 2/3 vs. 5. Likely due to the small numbers of recorded cue-locked cells per session (~0–10), the decoding performance for all variables depended most strongly on the number of cells (Figure 3f). Figure 3f also shows that RSC had significantly lower view angle and speed decoding performance than other regions, which we can think of as increased invariance of cue-locked response amplitudes to low-level visual parameters of the stimuli. Layer 5 was also distinguishable from layer 2/3 data in having reduced performance for decoding speed and past-trial reward.

Decision-related changes in cue-locked response amplitudes are compatible with a feedback origin

Interestingly, the response amplitudes of some individual cue-locked cells appeared to systematically depend on time (e.g. Figure 2a–b), as did the population-level decoding performance for variables such as choice (Figure 3b,d). To understand if these neural dynamics may reflect a gradually unfolding decision-making process, we turned to modeling how amplitudes of cue-locked cell responses may depend on choice and place/time, while accounting for other time-varying behavioral factors.

As a null hypothesis based on previous literature, we hypothesized that cue-response amplitudes can depend on a receptive field specified by the visual angle of the cue (${\varphi }_{cue}$, Figure 1c), as well as running speed (Niell and Stryker, 2010; Saleem et al., 2013). Given limited data statistics, we compared this null hypothesis to three other conceptually distinct models (Materials and methods), each of which aims to parsimoniously explain cue-response amplitudes using small sets of behavioral factors. These models predict the observed cue-response amplitudes to be random samples from a Gamma distribution, where the mean of the Gamma distribution is a function of various behavioral factors at the time at which a given cue appeared. The mean functions for all models have the form $\rho \left({\varphi }_{cue}\right) f\left(v\right) g(\cdots )$, where $\rho \left({\varphi }_{cue}\right)$ is an angular receptive field function, $f\left(v\right)$ is a running speed ($v$) dependence function, and $g(\cdots )$ is specific to each of the three models, as follows. First, the ‘SSA’ model parameterizes stimulus-specific adaptation (Ulanovsky et al., 2003; Sobotka and Ringo, 1994) or enhancement (Vinken et al., 2017; Kaneko et al., 2017) with exponential time-recovery in between cues. Second, the ‘choice’ model allows for a flexible change in amplitudes vs. place/time in the cue region, with a potentially different trend for right- vs. left-choice trials. Third, the ‘cue-counts’ model allows the amplitudes to depend on the running tally of $\#R$, $\#L$, or $\Delta =\#R-\#L$. This selection of models allows us to ask if cue-locked responses are sufficiently explained by previously known effects, or if after accounting for such there are still effects related to the accumulation process, such as choice or cue-count dependence.

We constructed the amplitude model prediction as the AIC_C-likelihood-weighted average of the above models, which accounts for when two or more are comparably good (Volinsky et al., 1999). As illustrative examples, Figure 4a shows how the amplitudes of two simultaneously recorded cue-locked cells in area AM depended on behavioral factors and compared to model predictions. There are clear differences in predictions for right- vs. left-choice trials that can also be seen in the raw amplitude data (restricted to a range of ${\varphi }_{cue}$ such that angular receptive field effects are small, 2nd and 3rd columns of Figure 4a). Although both cells responded preferentially to right-side cues, they had oppositely signed choice modulation effects, defined as the difference between amplitude model predictions on contralateral- vs. ipsilateral-choice trials (Materials and methods). Figure 4b shows two more example choice-modulated cells that had near-constant angular receptive fields. We note that except for the parameters of SSA, all findings in this section were qualitatively similar in θ-controlled experiments where there can be no angular receptive field effects (Figure 4—figure supplement 1).

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To summarize the prevalence and composition of amplitude-modulation effects, we selected the best model per cell using AIC_C, defaulting in ambiguous cases (relative likelihood <0.05) to the null hypothesis. Figure 4—figure supplement 2a shows that there were large fractions of cells with very high AIC_C likelihoods for all three alternative models compared to the null hypothesis. Cells that favored the cue-counts model could also be clearly distinguished from those that favored the SSA model (Figure 4—figure supplement 2b); in fact, exclusion of cells that exhibited SSA had little effect on how well evidence and other variables could be decoded from the neural population (Figure 3—figure supplement 3). In all areas and layers, >85% of cue-locked cells exhibited some form of amplitude modulations beyond angular receptive field and running speed effects (Figure 4c). Overall, ${27}_{-4}^{+4}\%$ of cells were best explained by SSA while ${67}_{-4}^{+4}\%$ favored either choice or cue-counts models. The notable inter-area difference is for layer 5 data, which had a qualitatively smaller proportion of choice-model preferring cells in V1 compared to other areas (p = 0.003, Wilcoxon rank-sum test). Most cells thus exhibited some form of amplitude modulations beyond visuomotor effects, with little difference in composition across areas and layers.

Although SSA, choice, and cue-counts dependencies all predict changes in cue-response amplitudes vs. time in the trial, there were qualitative differences that distinguished SSA from choice and cue-count modulations, as we next discuss. Cells in the two largest categories, SSA and choice, had qualitatively different population statistics for how their cue-response amplitudes depended on place/time in the trial. Most cells (${92}_{-4}^{+3}\%$) that favored the SSA model corresponded to a phenotype with decreased responses to subsequent cues. Adaptation effects were weakest in V1 and stronger other areas (Figure 4d, but see Figure 4—figure supplement 1f–g for θ-controlled experiments), although the ∼0.8 s recovery timescale had no significant inter-area differences (Figure 4—figure supplement 2d). In contrast, cue-locked cells with both choice laterality preferences were intermixed in all areas and layers (Figure 4—figure supplement 2e). Also unlike the decrease in response amplitudes vs. time for cells that favored the SSA model, both subpopulations of positively and negatively choice-modulated cells exhibited gradually increasing effect sizes vs. place/time in the trial (Figure 4e for contralateral cue-locked cells, Figure 4—figure supplement 2g for ipsilateral cue-locked cells). Cells that favored the cue-counts modulated category also had qualitatively different population statistics compared to cells that exhibited SSA. Comparable proportions of cue-counts modulated cells were best explained by dependence on counts on either the contralateral side, ipsilateral side, or the difference of the two sides (Figure 4—figure supplement 2f). For (say) right-cue-locked cells, $\#L$ or $\Delta$ dependencies are not directly explainable by SSA because the modulation is by left-side cues that the cells do not otherwise respond to. The remaining time-independent $\#R$ modulation also cannot be explained by SSA, unless SSA has an infinitely long timescale. Such infinite-timescale SSA would require some additional prescription for ‘resetting’ the adaptation factor, for example at the start of each trial, because otherwise amplitudes would continue to decrease/increase throughout the ~1 hr long session (which we do not observe).

Although relationships between sensory responses and choice can arise in a purely feedforward circuit structure, because sensory neurons play a causal role in producing the behavioral choice (Shadlen et al., 1996), others have noted that this should result in similar timecourses of neural and behavioral fluctuations (Nienborg and Cumming, 2009). Instead, we observed contrasting timecourses: as each trial evolved, there was a slow increase in time in choice modulations of cue-locked responses (Figure 4e; Figure 4—figure supplement 2g), which was opposite to the behaviorally-assessed decrease in time in how sensory evidence fluctuations influenced the mice’s choice (green line in Figure 4e, which was replicated from Figure 1e). Additionally, a feedforward structure predicts that positive fluctuations in right- (left)-preferring cue-locked neurons should produce rightwards (leftwards) fluctuations in choice. Instead, we observed that about half of the cue-locked cells were modulated by choice in a manner opposite to their cue-side preference (Figure 4—figure supplement 2e). Both of these observations argue against a purely feedforward structure, and thus support the existence of feedback influences on sensory responses (Wimmer et al., 2015; Nienborg and Cumming, 2009; Haefner et al., 2016).

Psychophysics-motivated evidence accumulation models Ratcliff and McKoon, 2008; Stone, 1960; Bogacz et al., 2006 have long guided research into how such algorithms may map onto neural activity and areas in the brain. A complementary, bottom-up approach starts from data-driven observations and formulates hypotheses based on the structure of the observations (Shadlen et al., 1996; Wimmer et al., 2015). In this direction, we exploited the mouse model system to systematically record from layers 2/3 and 5 of six posterior cortical areas during a task involving temporal accumulation of pulsatile visual evidence. A separate optogenetic perturbation study showed that all of these areas contributed to mice’s performance of the Accumulating-Towers task (Pinto et al., 2019). We reasoned that to understand how cortical areas contribute to evidence accumulation, a necessary first step is to understand the neural representation of sensory inputs to the process. In this work, we therefore focused on cue-locked cells that had sensory-like responses that is, time-locked to individual pulses of evidence, which comprised ~5–15% of active neurons in visual areas and ~5% in the RSC. These cells are candidates for sensory inputs that may feed into an accumulation process that drives behavior, but could also reflect more complex neural dynamics such as from top-down feedback throughout the seconds-long decision formation process. We characterized properties of cue-locked responses across the posterior cortex, which revealed that although we selected cells that had highly stereotypical time-courses of impulse responses to individual cues, the amplitudes of these responses varied across cue presentations in intriguingly task-specific ways.

One long-standing postulated function of the visual cortical hierarchy is to generate invariant visual representations (DiCarlo et al., 2012), for example for the visual cues regardless of viewing perspective or placement in the T-maze. On the other hand, predictive processing theories propose that visual processing intricately incorporates multiple external and internal contextual information, in a continuous loop of hypothesis formation and checking (Rao and Ballard, 1999; Bastos et al., 2012; Keller and Mrsic-Flogel, 2018). Compatible with the latter hypotheses, we observed that across posterior cortices, cue-locked cells had amplitude modulations that reflected not only visual perspective and running speed (Niell and Stryker, 2010; Saleem et al., 2013), but also the accumulated evidence, choice, and reward history (neural population decoding in Figure 3). Inter-area differences were mostly in degree (Minderer et al., 2019), with V1 having significantly lower performance for decoding view angle and choice, whereas RSC had lower decoding performance for speed but higher decoding performance for evidence (Figure 3f). We also observed an anatomical progression from V1 to secondary visual areas to RSC in terms of increasing timescales of cue-locked responses (Figure 2i–j) and increasing strengths of stimulus-specific adaptation (Figure 4d). Our results are compatible with other experimental findings of increasing timescales along a cortical hierarchy (Murray et al., 2014; Runyan et al., 2017; Dotson et al., 2018; Schmolesky et al., 1998), and theoretical proposals that all cortical circuits contribute to accumulation with intrinsic timescales that follow a progression across brain areas (Hasson et al., 2015; Chaudhuri et al., 2015; Christophel et al., 2017; Sreenivasan et al., 2014).

The amplitude modulations of cue-locked cells can be interpreted as multiplicative gain changes on otherwise sensory responses, and could be clearly distinguished from additive effects due to our experimental design with pulsatile stimuli and high signal-to-noise calcium imaging (Figure 2). While a number of other studies have quantified the presence of multiplicative noise correlations in cortical responses (Goris et al., 2014; Arandia-Romero et al., 2016; Lin et al., 2015), we showed that for most cells the amplitude variations were not random, but instead depended systematically on visuomotor and cognitive variables (Figure 4c). Relationships between sensory responses and choice can arise in a purely feedforward circuit structure (Shadlen et al., 1996), where the causal role of sensory neurons in producing the behavioral choice predicts that choice-related neural and behavioral fluctuations should have similar timecourses (Nienborg and Cumming, 2009). Incompatible with a solely feedforward circuit hypothesis, we instead observed that choice modulations of cue-locked responses increased in time (Figure 4e), whereas the behavioral influence of sensory evidence fluctuations on the mice’s choice decreased in time (Figure 1e). Both the choice- and count-modulation observations discussed here were suggestive of signals originating from an accumulator.

Our findings extend previous reports of relationships between sensory responses and perceptual decisions, termed ‘choice probability (Britten et al., 1996)’ (CP), and may constitute a form of conjunctive coding of cue and contextual information that preserves both the specificity and precise timing of responses to cues. An interesting question arises as to whether such multiplexing of cue and contextual information can cause potential interference between the different multiplexed information. For example, many evidence accumulation studies have reported positive correlations between CP and the stimulus selectivity of cells (Britten et al., 1996; Celebrini and Newsome, 1994; Cohen and Newsome, 2009; Dodd et al., 2001; Law and Gold, 2009; Price and Born, 2010; Kumano et al., 2016; Sasaki and Uka, 2009; Gu et al., 2014; Nienborg and Cumming, 2014) (for a differing view, see Zaidel et al., 2017 for analyses that better separate effects of stimulus vs. choice responses, and Zhao et al., 2020 for a recent re-analysis at the neural-population level). Translated to our task, positively correlated CP vs. stimulus preferences means that neurons that responded selectively to right cues tended to have increased firing rates when the animal will make a choice to the right. In this kind of coding scheme, increased activity in right-cue-locked cells could be due to either more right-side cues being presented or an internally generated right-choice signal, and there is no obvious way to distinguish between these two possibilities from just the activities of these cells. Our data deviates from the abovementioned CP studies in that highly contralateral-cue-selective neurons could be divided into two near-equally sized subpopulations with positive choice modulation (analogous to CP >0.5) and negative choice modulation (CP <0.5) respectively (Figure 4—figure supplement 2e). As two simultaneously recorded cells that respond to the same visual cue can be oppositely modulated (Figure 4a), these phenomena are not expected from canonical accounts of spatial- or feature/object-based attention in visual processing (Cohen and Maunsell, 2014; Treue, 2014), but rather more compatible with mixed choice- and sensory-selectivity reported in other perceptual decision-making experiments (Raposo et al., 2014).

We can conceptualize how our CP-related findings differ from previous literature by considering how choice modifies the neural-population-level representations of the visual cues, as illustrated in Figure 5 for two hypothetical neurons that both respond to right-side cues. We refer to the joint activity levels of these two hypothetical neurons as the neural (population) state. Figure 5a illustrates that when there is no cue both neurons have near-zero activity levels (gray dots), whereas when a right-side cue is present both neurons have high activity levels with some variations due to noise (purple dots). Conversely, the presence or absence of a right-side cue can be better decoded from the neural-population activity than from individual noisy neurons, by summing their activities or equivalently projecting the two-dimensional neural state onto a cue-decoding direction ${\overrightarrow{d}}_{cue}$ as depicted in Figure 5a. If in addition these two neurons both have CP >0.5 (positive choice modulation), this means that the neural responses in the presence of a right-side cue can further be separated into two distinguishable distributions depending on whether the subject will eventually make a right or left behavioral choice (Figure 5b, blue or red dots for the two choices, respectively). The CP >0.5 case corresponds to both neurons having slightly higher (lower) activity levels on right (left) choice trials, which means that we can decode the subject’s behavioral choice by projecting the neural state onto a choice-decoding direction ${\overrightarrow{d}}_{choice}$ that is more or less aligned with the cue-decoding direction ${\overrightarrow{d}}_{cue}$ (arrows in Figure 5b). However as noted above, collinearity of ${\overrightarrow{d}}_{choice}$ with ${\overrightarrow{d}}_{cue}$ means that based on neural activities alone, there can be many cases where we cannot unambiguously decide whether the subject saw more right-side cues or will make a right behavioral choice (overlap between blue and red points in Figure 5b). This is distinct from the case—as observed in our data—where the two neurons have opposite choice modulations, for example neuron 1 has CP <0.5 (negative choice modulation) whereas neuron 2 has CP >0.5. As depicted in Figure 5c, neuron 1 now has lower activity on right-choice than left-choice trials, whereas neuron 2 has higher activity on right-choice than left-choice trials, leading to a choice-decoding direction ${\overrightarrow{d}}_{choice}$ that is orthogonal to ${\overrightarrow{d}}_{cue}$. Intuitively, if comparable proportions of sensory units are positively vs. negatively modulated by choice, the opposite signs of these modulations can cancel out when sensory unit activities are summed (projected onto ${\overrightarrow{d}}_{cue}$), leading to a readout of sensory information that is less confounded by internally generated choice signals. Our results are compatible with findings from areas MSTd and VIP of nonhuman primates that use alternative analyses (to CP) that more rigorously separates stimulus vs. choice effects on neural activity as they are behaviorally interrelated (Zaidel et al., 2017), as well as a recent re-analysis of area MT data in nonhuman primates performing an evidence-accumulation task (Zhao et al., 2020). Similar arguments have been made for how motor preparatory activity and feedback do not interfere with motor output (Kaufman et al., 2014; Stavisky et al., 2017), and how attentional-state signals can be distinguished from visual stimulus information (Snyder et al., 2018). The use of both positive and negative modulations for coding non-sensory information, such as choice here, may hint at a general coding principle that allows non-destructive multiplexing of information in the same neuronal population.

Figure 5

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All in all, our neurophysiological observations in a mouse pulsatile evidence-accumulation task bears some similarity to but also notable differences with respect to an extensive body of related work on evidence accumulation tasks in nonhuman primates (NHP). We hypothesize that although a sensory evidence accumulation process may underlie the decision-making behaviors in all of these tasks, there are qualitative differences in both the nature of the tasks as well as our methods of investigation that may shed light on the differences in reported neurophysiological findings. From a methodological standpoint, the use of randomized pulsatile stimuli gives us the power to exploit the unpredictable (but known to the experimenter) timing of sensory pulses to separate stimulus responses from responses to other aspects of the behavior. One downside to this random design, together with the navigational nature of the task that the mouse controls, is that no two trials are literally identical. We thus trade off the richness of the behavior and the ability to directly identify sensory responses, with an inability to directly measure effects that require exactly repeated trials, such as noise correlations. The scope of our study should therefore be understood as being on signal responses across the posterior cortex, and we do not attempt here to report features such as noise correlations that are contingent on having a fully correct model of signal responses in order to interpret the residual as ‘noise’.

Starting from our most basic neurophysiological observation, the small fractions of cue-locked neural activity in even the visual cortices is not unexpected, because the visual inputs of the task were not tuned to elicit maximal responses from the recorded neurons. In fact, the virtual spatial environment that the mice experienced corresponds to a high rate of visual information beyond just the tower-like cues, all of which are highly salient visual inputs for performing the navigation aspect of the task and may therefore be expected to influence much of the activity in visual cortices. Our observation that choice-related variability in cue-locked cell responses were not lateralized according to brain hemisphere Figure 4—figure supplement 2e, is similar to the non-lateralized choice information in the activities of other (non-cue-locked) neurons that we report in an upcoming article (Koay et al., 2019). These findings of cells with intermixed choice preferences within the same brain hemisphere is compatible with several other rodent neurophysiological findings in evidence-accumulation tasks (Erlich et al., 2011; Hanks et al., 2015; Scott et al., 2017), but not, to the best of our knowledge, the NHP choice probability literature discussed above unless via alternative/extended analyses such as in Zaidel et al., 2017; Zhao et al., 2020. Other than analysis methodology and interspecies differences in brain architecture as a plausible cause for different neural representations of choice, we wonder if these differences could arise from choice and stimulus preferences being related in a more abstract way in our task (and other rodent behavioral paradigms) than in the NHP studies. In the Accumulating-Towers task, although the mouse should choose to turn to the side of the T-maze corresponding to the side with more cues, a navigational goal location is qualitatively different in modality from the retinotopic location of the tower-shaped cues. In contrast, in classic NHP evidence-accumulation tasks (Gold and Shadlen, 2007) the subject should saccade in the same direction as they perceive random dot motion stimulus to be along, that is perform a directly visual-direction-based action to indicate their choice. Our overall hypothesis is that if there is additional task-relevant information that have potentially abstract relationships to the visual cues to be accumulated, the brain may need to employ more complex neural representational schemes—including in as early as V1—in order to keep track of not only the momentary sensory information in visual cortices, but also various environmental and memory-based contexts in which they occur.

A condensed set of imaging and behavioral data as well as secondary results from analyses and modeling have been deposited in Dryad with the DOI: https://doi.org/10.5061/dryad.tb2rbnzxv. This dataset contains all of the information required to reproduce the figures in the manuscript. As the full, raw data generated in this study is extremely large, access to these raw data can be arranged upon reasonable request to the authors.

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Author details

1. Sue Ann Koay

   Princeton Neuroscience Institute, Princeton University, Princeton, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Investigation, Methodology, Writing - original draft

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-9648-2475

2. Stephan Thiberge

   Bezos Center for Neural Circuit Dynamics, Princeton University, Princeton, United States

   Contribution

   Resources, Supervision

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6583-6613

3. Carlos D Brody

   1. Princeton Neuroscience Institute, Princeton University, Princeton, United States
   2. Howard Hughes Medical Institute, Princeton University, Princeton, United States

   Contribution

   Conceptualization, Supervision, Writing - review and editing

   For correspondence

   brody@princeton.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-4201-561X

4. David W Tank

   1. Princeton Neuroscience Institute, Princeton University, Princeton, United States
   2. Bezos Center for Neural Circuit Dynamics, Princeton University, Princeton, United States

   Contribution

   Conceptualization, Resources, Supervision, Writing - review and editing

   For correspondence

   dwtank@princeton.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-9423-4267

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