Discussion

The ability to observe brain activity and, with reasonable certainty, know the subject's mental state, is highly sought after. However, the accuracy of a reverse inference is typically low. Given that a single region can be activated by many different cognitive tasks, in general, observing that a single region is engaged provides limited additional evidence for the engagement of a cognitive function \cite{Poldrack_2011}. Moreover, the applications of reverse inference has, so far, been rather limited to practical business applications \cite{Ariely_2010} or outright abused \cite{Kaplan_2007}. While the selectivity of brain regions to particular cognitive processes has been studied \cite{Lieberman_2015}, reverse inference has not been widely applied to progress our understanding of the brain. The inaccuracy of reverse inference and the dearth of fruitful scientific applications are both due to the false assumptions that typically underlie reverse inferences. If the reverse inference is not based on how the brain actually functions, it likely won't be accurate, and its utility certainly cannot progress our understanding of the brain.
While many cognitive processes are certainly localized, there is no simple one-to-one mapping between every cognitive process and a brain region. Many cognitive processes studied in psychology are likely not natural kinds \cite{Quine_1969} and others are highly distributed \cite{28063661}. An emerging idea is that most cognitive processes (besides, for example, edge detection in visual cortex) are the result of the combinatorial interactions of relatively stable functional networks that each have a specific function \cite{26598686,Power_2011,19620724,28222386,Bzdok_2016}. Most notably, previous work termed this idea network co-occurrence, and, similar to the current work, modeled task activity by combinations of canonical brain networks \cite{Bzdok_2016}. The upshot of this work was the ability to model task activity with combinations of networks.
The previous network co-occurance work, however, was focused on modeling the activity differences between two tasks states, relying on traditional group-level task contrasts (e.g., math versus language processing). Here, we presented a reverse inference method that is based on network co-occurance, but we focused on modeling the raw individual frames of individual's brain activity during cognitive tasks. We lend further credence to the network co-occurance model of brain activity--our method fits the data and was an accurate method of detecting which task the subject was engaged in. Thus, a network co-occurance model can accurately capture individual frames of data as well as differences in activity across different cognitive tasks.
The ability to, given a principled model of the brain and method of reverse inference, gain further insight into the brain was also demonstrated. We presented two novel applications. First, we replicated a previous finding at a much higher temporal resolution in individual subjects, rendering more detailed information about which regions of the brain are sensitive to the number of unique cognitive functions engaged. As the previous analysis looked across group-level activation maps, one could only conclude that, in general across tasks, when more cognitive functions are required, activity in the fronto-parietal network is increased. However, we demonstrated here, with increased spatial resolution, that this phenomenon exists on the sub-second temporal resolution. Second, we used the cognitive component probabilities to detect discrete states that occur during cognitive tasks. We found states that were present across tasks, as well as states that were unique to that task and reflected the processes unique to that task. While much research has been done to study the dynamic interactions between brain networks \cite{26231247,28242315,Shine_2016}, the temporal resolution of functional connectivity does not allow for analysis of these interactions at high temporal resolutions (i.e., what happens in each time point and changes from timepoint  to timepoint), and there are many methodological issues \cite{Power_2017}. Our method to detect states found unique interactions between networks that are likely not captured by dynamic functional connectivity methods. Moreover, out method depends on univariate activity, which eludes many of the methodological issues of dynamic functional connectivity. For example, in the Gambling tasks, we observed a state that was unique to the Gambling task, and involved two networks--the fronto-parietal network and the default mode--being active together, despite these networks traditionally exhibiting negative functional connectivity \cite{15976020}. Moreover, each states boundaries (where activity transitions from high to low) overlap highly with functional connectivity networks. This suggests that we observe functional connectivity networks because there is repeated transient activation of each network (or combinations of networks).
In conclusion, we presented a principled model and method for reverse inference. This method was able to accurately capture individual timepoints of data and predict which task the subject was engaged in. Moreover, we demonstrated that this method can be used to process our understanding of the brain.