Abstract
Current theories of cognitive effort provide either resource-based or motivation-based accounts of its cost. Despite the usefulness of these proposals, it remains unclear how to exactly quantify effort costs - or why certain tasks are more effortful than others. Here, we provide a novel perspective, based on the assumption that the brain constructs a probabilistic internal model of the world under efficient coding principles. We propose that effort cost is a function of the amount of information required to update the internal model to effectively solve a task. This novel theory naturally explains why some tasks - for example, unfamiliar or dual tasks - are costly and permits to precisely quantify these costs using information-theoretic measures. Finally, we argue that information costs translate into local metabolic costs - which sheds light on the adaptive value of cost-avoidance mechanisms (cognitive effort) in preventing the accumulation of local metabolic alterations over time.
1. Introduction
Demanding cognitive tasks, such as mental arithmetic, are strongly aversive: we tend to avoid partaking in such tasks and they lead to unpleasant subjective feeling of mental exertion (Inzlicht et al., 2015). Various studies have revealed that we take into consideration a measure of cognitive cost or cognitive effort when deciding whether or not to engage in a task (Kool et al., 2010; Manohar et al., 2015; Schmidt et al., 2012; Westbrook et al., 2013; Westbrook and Braver, 2015). Furthermore, prolonged performance of demanding tasks leads to cognitive fatigue, which is characterized by a subjective dimension - i.e. feeling of exhaustion, impression of worsened ability and decreased willingness to engage in mental activities (Hockey, 2011; van der Linden et al., 2003) - and an objective dimension, with an actual decrease of task performance (Bailey et al., 2007; Tanaka, 2015; van der Linden et al., 2003). However, it is still unclear what is the origin of cognitive costs (i.e., what is costly about cognitive processing?), how to specify them quantitatively, and whether cognitive costs and cognitive fatigue have some adaptive value.
Previous characterizations of cognitive effort can be classified into two broad categories. First, effort can be framed as a consequence of resource limitations such as depletable metabolic precursors or interferences arising from shared uses of cognitive substrates (reviewed in Shenhav et al., 2017). Second, cognitive effort can be described as the phenomenological manifestation of the opportunity cost of engaging limited cognitive resources in demanding cognitive tasks (Kurzban et al., 2013). Here we advance a novel theoretical proposal that casts cognitive costs in terms of information-theoretic principles, which allows us to provide quantitative predictions of task-specific cognitive costs and to bridge resource depletion and opportunity cost accounts of effort. The present framework highlights the relations between cognitive costs, the informational costs required to code a novel task or a policy to face it, and the ensuing metabolic costs of brain information processing. In this perspective, the brain is seen as a statistical machine that builds generative models of its environment and of the tasks it has to solve (Friston, 2010). To do this, it uses efficient coding mechanisms that try to minimize the information it needs to encode, given its current models, to perform accurately in a given task (Collell and Fauquet, 2015; Harremoës and Tishby, 2007; Laughlin, 2001; Sims, 2016; Wei and Stocker, 2015). By casting cognitive costs in terms of efficient information coding, this framework predicts that certain tasks - e.g., unfamiliar tasks or those that require counteracting natural biases (or default policies) - would be particularly costly, as they would require larger amounts of information to be coded. Importantly, these informational and cognitive costs have direct metabolic equivalents - in the sense that inefficient coding and large informational demands imply higher local metabolic costs, and accumulation of local metabolic alterations in the brain. Hence, ultimately, the avoidance of cognitive costs is an adaptive mechanism that prevents us from engaging in tasks that would imply high metabolic demands in the long run. The phenomenology associated to the costs of cognition - such as the fact that cognitively costly tasks have an associated subjective feeling of cognitive effort, and can lead to cognitive fatigue in the long run - can be understood within this adaptive framework that aims to minimize metabolic demands.
2. Efficient coding and cognitive costs: an example
Efficient coding was initially described as a theory of redundancy reduction, according to which biological systems decorrelate sensory signals to avoid redundancy (Attneave, 1954; Barlow, 1961; Simoncelli and Olshausen, 2001). The theory has been successively extended to include other mechanisms through which neural coding adapts to the statistical structure of its environment (Simoncelli, 2003; Smith and Lewicki, 2006). One crucial aspect of efficient coding is the usage of an adaptive code, in which the cost for encoding each symbol is inversely proportional to its frequency in the environment - given the agent’s model of the environment (Collell and Fauquet, 2015; Fairhall et al., 2001). As highlighted by Shannon’s pioneering work, the minimal quantity of information necessary to encode a symbol in a message is equal to its negative log probability, or surprisal - which implies that under optimal encoding strategy, less likely, or less predictable events require more information (e.g. more bits in a computer memory) to be encoded. Clearly, for biological organisms, surprisal is a function of prior knowledge - as encoded in the organisms’ internal model (Friston, 2010). Here we argue that the information cost associated with a task corresponds to how much an agent should update its prior knowledge in the light of novel evidence (which, in Bayesian terms would correspond to updating a prior distribution to form a posterior distribution); and this, in turn, depends on both the structure of the task (e.g., how many contingencies exist) and the agent’s prior knowledge (e.g., what the agent already knows about the task).
In tasks that have clear stimulus-response association rules, determining such information costs is quite straightforward. Let’s consider for example a digit-key association task, in which participants have to press the key that corresponds to the digit they see on the screen. If there are 4 possible digits and their probability distribution is uniform, the joint probability distribution prior to seeing the digit is the one shown in Figure 1 (left).
When participants see a digit on the screen, they have to update their prior distribution to a posterior distribution in which all the probability mass is in one stimulus-response association (i.e., one cell becomes 1 and all the other cells become zero, see Figure 1, right). This operation requires summing up the log probability of each possible stimulus-response combination (see below for a formal specification) - which, in this case, results in an information cost of −log(4). This approach has been used more than 60 years ago in a series of studies that resulted in the well-known Hick-Hyman law (Hick, 1952). In their seminal work, Hick and Hyman used various tasks in which the number of possible stimulus-response associations varied between 2 and 10. Their striking finding, replicated many times since, was that the reaction time in this task varies in linear proportion to the information cost. More recently, the metabolic activity (indexed by the BOLD signal) of brain regions that guided the decision was shown to vary also in proportion to information cost (Wu et al., 2017) - although the study did not systematically assess the quantitative relationships between information and metabolic costs.
This example suggests that in tasks like the digit-key association shown in Figure 1, which have a clear stimulus-response association matrix and in which the statistical structure is known, cognitive costs (CC) would be proportional to information costs (IC), or entropy of the stimulus-response matrix. In more formal terms:
When the statistical structure of the task is unknown and has to be learned, determining information cost requires considering an additional element: a measure of (Kullback-Leibler) divergence D between the real task structure and the agent’s current belief (or estimate) of such structure Q1: with
Intuitively, this formula implies that there would be an additional cost for performing a task whose statistical structure is still unknown. This information penalty is equal to the cost of learning the novel task contingency.
Understanding the mathematical details of these equations is not important. It is sufficient to consider that, first, we cast cognitive costs in terms of information costs required to engage in a task (e.g., encoding its contingencies and/or its structure); and second, that it is possible to use efficient coding principles to specify these information costs. In the next Section, we use these arguments to discuss what characteristics make cognitive tasks costly.
3. Predictions of the framework
We proposed an information-theoretic perspective that directly links cognitive costs to information costs (and metabolic costs, see below) that a participant incurs when engaging in a task. This framework predicts that certain kinds of tasks - those that have many degrees of freedom, are unfamiliar, necessitate to go against natural biases, have variable statistical structure or low signal to noise ratios - will lead to large subjective cognitive effort and will be perceived as aversive in virtue of the fact that they are demanding from an informational (efficient coding) perspective.
3.1 The costs of tasks that have many degrees of freedom
Tasks that have many degrees of freedom, or equivalently, a wide probability distribution of state-action combinations, are expected to be cognitively costly under our framework, as they imply low, widely spread prior probabilities - and thus significant information costs to update the priors (see Figure 2A). Arithmetic tasks, the N-back task, but also chess games or creative writing, which are well known for being cognitively demanding (Hess and Polt, 1964; Kellogg, 1987; Marshall, 2002; Westbrook and Braver, 2015) all assign a small prior probability mass for each possible decision and hence, lead to large divergence with the final posterior obtained when the choice has been made. Intuitively, this would be equivalent to having a very large matrix in Figure 1 (left), with the same, small probability in each cell - and an equally large matrix in Figure 1 (right) with only one cell encoding 1 and all the other cells encoding zero. Similarly, tasks that demand a deep contextualisation of the stimulus-response associations (e.g. learning to navigate in a complex maze) will lead to multidimensional prior distributions whose space can inflate very fast, leading also to fast increase in complexity.
3.2 The costs of novel or unfamiliar tasks
A similar issue arises with unfamiliar tasks, that is, tasks in which the statistical structure of the sensory states, state transition probabilities (conditional on the performed actions) or action policies (e.g. sequences of motor actions) are poorly known (see Figure 2B). This lack of knowledge of statistical properties of the task leads to non-optimal encoding and large information costs. As shortly discussed above, the extra cost to learn task structure can be formalized as the Kullback-Leibler divergence between the real probability distribution and the one assumed by the subject (given its imperfect knowledge). While the effect of novelty on cognitive effort seems intuitive, relatively little evidence exists on this relation. Yet, a few studies have showed that task effort decreases with training by measuring pupil size - which has been consistently found to index effort (Hyönä et al., 1995; Mykityshyn et al., 2002; Recarte and Nunes, 2000; Solopchuk et al., 2016). It is also interesting to note that training typically leads to decreased (not increased) brain activation (Solopchuk et al., 2017; Wiestler and Diedrichsen, 2013) - plausibly, by increased knowledge of task contingencies and the ensuing decrease of the metabolic costs to maintain the internal generative model.
3.3 The costs of counteracting priors or default policies
Our framework predicts also that tasks that require counteracting deep priors or default policies (e.g., self-control) would be particularly demanding (see Figure 2C). To understand why this is the case, it is necessary to extend our info-theoretic perspective beyond representational (internal coding) issues to also cover action selection - by appealing to the notion of active inference (Friston, 2010). Under the active inference framework, agents are equipped with hierarchical generative models and perform the kind of Bayesian inference described above; and have the general objective to minimize their free energy or, with some simplifications, their surprise - or the discrepancy between what they expect, based on their beliefs, and what they sense. Importantly, they can minimize their surprise in two ways: by changing their beliefs to make them more similar to what they sense about the world (i.e. perceptual processing) or by changing the world to make it more similar to their prior beliefs (i.e. using actions to fulfil one’s own expectations). This duality is possible if one considers that active inference agents are hierarchically organized. While hierarchically lower prior beliefs might faithfully adapt to the external world, hierarchically deeper priors would prescribe what states an agent should achieve by acting (Friston et al., 2012a; Pezzulo et al., 2015). These latter, deeper priors hence play the role of goals and motivational factors that are relatively less permeable to learning (i.e., in Bayesian terms, they have very high precision or inverse uncertainty) because they are key to survival. Indeed, a key statement of active inference is that biological agents need to minimize their long-term surprise in order to survive; if one thinks of these deep priors as describing the “good” states in an agent’s ecological niche, minimizing surprise means that the agent should attempt to remain always close to these states. One example of deep (and perhaps hard-coded) prior is a homeostatic drive, such as the prior probability of body nutrients being within an acceptable physiological range. A discrepancy (prediction error) between such deep prior (e.g., be satiated) and the current interoceptive sensations (e.g., feeling hungry) would not lead to the revision of the prior - since the prior is largely impermeable in virtue of having high precision. Instead, the prediction error would steer a cascade of predictions about the conditions that might restore body nutrients (e.g., consuming food), which in turn would steer an adaptive policy or action sequence to fulfil these predictions (e.g., open the fridge and take some food). This formulation makes it apparent that a hungry active inference agent would assign a high probability to (predicted) states and policies associated to consuming food. Since efficient coding assumes that counteracting such high-probability states (or equivalently, pursuing low-probability states) has high information costs, any task that necessitates counteracting deep priors or their ensuing policies should lead to large information and cognitive costs. This explains the effortful nature of self-control (Kool et al., 2013), which consists precisely in going against natural biases, as investigated in the large, but still very controversial literature on ego depletion (Hagger et al., 2016; Martin S. Hagger et al., 2010; Job et al., 2010; Kurzban et al., 2013; Muraven and Baumeister, 2000).
One can use similar arguments to explain why counteracting habits is so costly, too. Habitual behaviour is characterized by fast, automatic processing, low effort and lack of flexibility (Kahneman, 2011; Moors and De Houwer, 2006; Schneider and Chein, 2003). In hierarchical formulations of active inference, habits manifest themselves after overtraining, when (priors at) lower hierarchical layers acquire sufficient precision to become relatively impermeable to top-down influences from higher hierarchical levels (Pezzulo et al., 2015). Habits thus steer default responses to environmental stimuli and are largely inflexible and impermeable to long-term goals. This is because, with overtraining, the encoding of task-specific information follows so closely the statistical task structure that all the task-irrelevant information would get ignored. The ensuing cognitive processing does not need to engage higher hierarchical levels; hence, task processing would be extremely efficient but also crucially dependent on the particular task contingencies that have been learned. Expected stimuli, transitions and actions would have very large priors, and would therefore be encoded with minimal cost, while unexpected stimuli, transitions or actions would have very low prior probabilities and would therefore be very costly to encode. This would imply that a person following habitual policies would have lower costs to engage in familiar tasks but higher costs to engage in novel tasks. Intuitively, this impact of familiarity on cognitive cost could explain why novel environments (e.g. new places, new languages, new people, etc.) are generally described as being more fatiguing than familiar ones, while natural, familiar environments would have, on the contrary, restoring effects (Kaplan and Berman, 2010). The cognitive costs associated to (for example) the Stroop and the Simon tasks can be explained within the same framework, by considering that a preponderant habitual, but incorrect action interferes with the response instructed by the stimulus. In incongruent conditions in the Stroop and the Simon tasks, the prior of the correct, instructed action remains lower compared to the priors associated to incorrect, habitual responses (Wang et al., 2016), thus implying a high cognitive cost. In other words, situations that systematically require encoding posteriors that differ greatly from the initial prior distributions, such as incongruent conditions in the Stroop or the Simon tasks will have comparatively larger complexity scores than congruent conditions for which posteriors conform nicely to the prior. The same arguments, based on strong (deep / homeostatic or shallow / habitual) priors can help understand the phenomenology associated to some pathological situations, such as Tourette syndrome and obsessive-compulsive disorders. These and other syndromes have been associated to strong priors that are, however, maladaptive and lead to inappropriate behaviour (Adams et al., 2013; Friston et al., 2014). Patients suffering from these disorders typically describe being able to overcome their (habitual) tics (Delorme et al., 2016) or compulsive behaviour but at the price of tremendous cognitive effort (Kawohl et al., 2009).
3.4 The costs of task switching and dual tasks
Another classic cause of cognitive effort is task switching (see Figure 2D). Changing from a task set to another is associated to a significant cost in performance, usually measured as an increased reaction time, is accompanied with a subjective cognitive effort cost and leads to cognitive fatigue (Apps et al., 2015; Borragán et al., 2017; Sohn et al., 2000; Wylie and Allport, 2000). This is explained in our framework by considering that after a switch from task A to task B, the learned statistical structure of task A would be initially used to encode sensory states, state transition probabilities and action contingencies of task B, thus leading to an additional information cost. The same arguments may apply in more mundane situations in which one is required to switch continuously between multiple tasks (multi-tasking); or to dual-task situations, in which one has either to maintain a sophisticated internal model where the probability distribution span the contingencies of both tasks, or to rapidly and repeatedly switch between the tasks to be executed concurrently. Interestingly, our model makes the specific prediction that switching costs should be proportional to the Kullback-Leibler divergence between the probability distributions governing tasks A and B - or, at least, the subjects’ estimates of these distributions. This prediction remains to be tested in future research.
3.5 The costs for controlling the rate of information processing and the role of arousal
Another task feature that is well known to affect cognitive cost is signal to noise ratio (see Figure 3). When the ratio between signal and noise in sensory data is low, performance decreases, pupil size increases and subjective cognitive effort increases (Manohar et al., 2015; Sarampalis et al., 2009; Zekveld et al., 2014). In predictive coding theories, low signal-to-noise ratio would automatically imply low sensory precision and an attenuated sensory sampling (because sensations are unreliable). However, when one is engaged in an important task, one would want to extract and use sensory information even if it is immersed in high noise - hence attempt to raise the signal-to-noise ratio. In turn, doing so would require up-regulating sensory sampling, or information rate, to counteract the default adjustments (down-regulations)2. However, in our framework that links informational and cognitive costs, this compensatory increase in information rate has an associated cognitive cost (and also a metabolic cost, see Section 4). The adjustability of information rate evokes the concept of task engagement and the fact that motivational factors and reward incentives can influence task performance by putting high information rate at a premium (Camerer et al., 1999). This mechanism implies some cost-benefit computation to select the optimal trade-off between the cost of information rate and the value associated with performance (see Figure 3A-D), akin to many earlier models of effort-based decision making (Chong et al., 2017; Christie and Schrater, 2015; Rigoux and Guigon, 2012; Shenhav et al., 2013; Verguts et al., 2015).
At the neural level, the dynamical adjustments (up-regulations) of information rate as a function of sensory noise may depend on arousal. Arousal could be defined as a global brain state characterized by the amplitude of synchronized low-frequency oscillations and sensory responsiveness (McGinley et al., 2015) and is controlled by brainstem nuclei and neuromodulators such as noradrenaline and acetylcholine (Reimer et al., 2016). A large body of literature suggests that arousal modulates signal to noise ratio in cortical representations by sharpening tuning curves and increasing neural gain, thus improving the encoding of the most relevant information, at the expense of less salient or important data (Eldar et al., 2013; Mather et al., 2016; Servan-Schreiber et al., 1990). Arousal increases also the weight (or precision) of sensory inputs in updating internal models (Nassar et al., 2012). It increases with surprisal (Friedman et al., 1973; Lavín et al., 2014; O’Reilly et al., 2013; Preuschoff et al., 2011), precision-weighted prediction errors (Ferreira-Santos, 2016), uncertainty (Yu and Dayan, 2003), and large incentives (Kahneman and Peavler, 1969; Manohar and Husain, 2015). This body of evidence is compatible with the idea that in specific conditions, such as high-valued tasks, decreasing signal-to-noise ratio triggers arousal mechanisms that adjust (up-regulate) information rate3, in order to maintain performance. Interestingly, such dynamical adjustments may be indexed by pupil size, which tracks the level of arousal (Reimer et al., 2016). The reliable relations between arousal, cognitive workload and corresponding increases in pupil size (Beatty and Lucero-Wagoner, 2000) may be productively exploited to design experiments that track the dynamical adjustments of information rate.
3.6 Summary so far
To summarize, we have offered a unitary perspective that may explain many experimental findings on cognitive effort and fatigue - by appealing to the fact that specific kinds of tasks that are known to be cognitively costly, such as novel tasks or those that require counteracting habitual policies or switching contingencies, all have high informational costs associated to encoding or revising probability distributions within the generative models that support task performance. Equipped with this formalization of cognitive costs, we can now turn to the question of what are their possible adaptive roles. We propose that cognitive costs are proxies that the brain uses to prevent local metabolic alterations to occur. For example, in order to decide whether or not to engage in a task, the brain might consider its current level of cognitive fatigue and/or the predicted cognitive costs associated to the task - in order to prevent future local metabolic alterations. The idea that cognitive and metabolic costs are associated is not novel (Laughlin et al., 1998). However, our theory indicates that there is a quantitative relation between the informational costs of a task (as defined above) and its associated metabolic demands. Discussing this relation is the topic of the next section.
4. Cognitive costs and metabolic costs: metabolic consequences of neural activity
Information processing requires energy expenditure (Landauer, 1996; Sengupta et al., 2013; Still et al., 2012). The relation between informational and metabolic costs was central in early theories of efficient coding (Atick, 1992; Attneave, 1954; Barlow, 1961; Borst and Theunissen, 1999; Niven and Laughlin, 2008), which assumed that neural responses, carrying large metabolic costs, impose a constraint on brain information processing capacity. Under this framework, the brain attempts to maximize the amount of (mutual) information it processes, given this fixed capacity limit. More recent approaches have relaxed this principle by using different measures of efficiency, and by considering energetic demand as a cost rather than as a fixed constraint (Denève et al., 2017; Ortega and Braun, 2013; Park and Pillow, 2017; Sengupta et al., 2013). This last, subtle modification opens the door to cost-benefit adjustments of the kind exposed above (see Figure 3), which allow metabolic costs to be adjusted as a function of demands in performance (Marzen and DeDeo, 2017; Park and Pillow, 2017; Sims, 2016).
Numerous pieces of evidence exist in favour of brain reliance on efficient coding, even though most are indirect and qualitative. Low-level vision and audition show data filtering properties and neural codes that are closely similar to predictions issued from efficient coding models (Borst and Theunissen, 1999; Gutnisky and Dragoi, 2008; Laughlin, 2001; Olshausen and Field, 2004; Sharpee et al., 2006; Smith and Lewicki, 2006). Predictability leads to diminished brain activation (Auksztulewicz and Friston, 2016; Bell et al., 2016; Carreiras et al., 2009; Garrido et al., 2013; Lieder et al., 2013; Mars et al., 2008; Meyniel et al., 2016; Overath et al., 2007; Wacongne et al., 2012) and pupil responses (Friedman et al., 1973), but increases reliability of encoding (Kok et al., 2012), in agreement with the idea that predictable stimuli, carrying little information, are encoded more economically. Along the same line, decreased brain activation following training (Chen and Wise, 1995; Solopchuk et al., 2017; Toni et al., 1998; Wiestler and Diedrichsen, 2013) suggests that training decreases metabolic cost by allowing learners to leverage task statistics to optimize brain representations, while increasing the quantity of information being processed.
Given the fundamental link between information processing and metabolic demands, the observation that global cerebral energy consumption does not vary between resting and active conditions may appear surprising (Sokoloff, 2009; Sokoloff et al., 1955). Blood delivers glucose and oxygen to brain in excess of demand, such that in physiological conditions (i.e. in absence of hypoxia or hypoglycaemia), the availability of energetic precursors is not a limiting factor to cognitive activity (Brown and Ransom, 2014). However, total blood delivery to the brain is a constant that cannot be upregulated in response to cognitive demand (Brown and Ransom, 2014). Therefore, the cost of cognitive activity can hardly be explained by the need to curb total energetic consumption. It is noteworthy, however, that despite this lack of change in global energetic demand of the brain, global glucose intake increases in the brain during cognitive activity (Volkow et al., 2008). This utilization of glucose in excess of oxygen consumption is referred to as aerobic glycolysis (Vaishnavi et al., 2010). It is modulated by arousal (Dienel and Cruz, 2016) and while the function of aerobic glycolysis remains debated, it may be linked to cortical plasticity (Goyal et al., 2014) and the replenishment of glutamate and GABA reserves (Hertz and Chen, 2017a). This increased glucose demand during active behaviour has justified resource depletion theories of cognitive effort, according to which glucose is the main resource that puts a constraint on cognitive activity (Gailliot et al., 2007). This theory, and the experimental evidence on which it is based, have been put under increased criticism recently (Hagger et al., 2016; Martin S Hagger et al., 2010; Kurzban et al., 2013). Here we consider an alternate view on the link between cognitive cost and metabolic activity, based on the idea that metabolic cost should be understood as a local rather than a global phenomenon.
Astrocytes contain important stocks of glycogen (Benarroch, 2010). These glycogen stores are mobilized during sensory stimulation (Dienel and Cruz, 2006), intense physical exercise (Matsui et al., 2017) or encoding in long-term memory (Hertz and Chen, 2017b). The rate of degradation of glycogen, or glycogenolysis, rises 6-50-fold above resting-state values during neural activity (Dienel and Cruz, 2014) and is under the control of arousal (Gibbs, 2015). Blocking the degradation of glycogen leads to dramatic increases in glucose consumption, indicating that in normal conditions, glycogen is an important source of energy supply during neural activity, and that its lack can be compensated by glucose mobilization, but supposedly with an associated loss of efficiency (Dienel and Cruz, 2014). Blocking the production of glycogen-derived lactate has dramatic consequences on memory formation and physical endurance (Gibbs, 2015; Matsui et al., 2017). Also, glycogen levels fall during daytime, or sleep deprivation and are replenished during sleep (Kong et al., 2002). Finally, de novo synthesis of glutamate depends also on glycogenolysis (Hertz and Chen, 2017b). Therefore, it seems plausible that sustained local neural activity could lead to the local depletion of glycogen reserves, which could be responsible for the feeling of cognitive fatigue that follows prolonged mental demands (Christie and Schrater, 2015). It is worth pointing out that glycogenolysis in human primary visual cortex showed no detectable changes after visual stimulation (Öz et al., 2007). This finding appears to contradict the hypothesis of a link between glycogen reserves and fatigue but the interpretation of this negative result remains debated, in part because of the limited sensitivity of the measurement technique used in this study (DiNuzzo et al., 2012).
Another link between metabolic and cognitive (and informational) costs emerges when considering the role of arousal in adjusting information rate, as discussed earlier. This increased informational demand plausibly corresponds to commensurate surges in energy mobilization. Arousal appears to increase the metabolic mobilization orchestrated by astrocytes in response to neural activity (O’Donnell et al., 2012; Paukert et al., 2014), including glycogen reserves (Hertz and Zielke, 2004; O’Donnell et al., 2012), while also restricting glymphatic circulation, thus limiting the capacity of the brain to eliminate potentially harmful metabolites (Xie et al., 2013). Interestingly, although arousal is a global phenomenon, its effect in cortex is believed to be restricted to active regions (Mather et al., 2016). Increased arousal would thus lead to increased metabolic rate in these active regions, while dampening activation in already less active background structures (Mather et al., 2016). This suggests that - even though global energetic brain expenditure may remain constant across task and rest conditions (Sokoloff, 2009) and increased metabolic costs in specific brain regions may entail decreased demands in other regions (Fox and Raichle, 2007) - cognitive effort and fatigue may be the consequence of local rather than global metabolic demands4.
If engaging in cognitive tasks produces cognitive fatigue and ultimately depletes local metabolic resources, how are these restored? Cerebral housekeeping is assumed to be one of the main functions of sleep (Tononi and Cirelli, 2014; Xie et al., 2013). The necessity to shut down cerebral activity periodically entails that metabolic steady-state cannot be maintained during continuous periods of brain activity (Tononi and Cirelli, 2014). This rest-dependent housekeeping activity may include the replenishment of protein stocks, of presynaptic calcium, of astrocytic glycogen (Kong et al., 2002), the recycling of membranes, the resting of mitochondria (Tononi and Cirelli, 2014), the replenishment of glutamate vesicles (Tani et al., 2014) or the clearance of the extracellular space (Xie et al., 2013). Some authors have proposed that the accumulation of these deviations from metabolic steady-state could lead cortical regions to enter a local sleep mode, characterized by slow-wave synchronization and associated with disturbed processing capacity (Siclari and Tononi, 2017). Going back to the issue of anaerobic glycolysis, the excess utilization of glucose during intense brain activity could lead to the accumulation of intermediate metabolic pools, which would be converted to their final metabolic destination only during periods of rest or sleep (Madsen et al., 1999). These deviations from steady-state, local sleep modes and accumulation of intermediate metabolites could be accelerated locally when engaging in demanding tasks, eventually leading to fatigue.
Finally, the severity of the behavioural effects associated with local metabolic alterations could depend on the affected brain regions. On the one hand, sensory cortices encompass large area, with topographic organization, in which processing of different input features or spatial locations leads to activations of different cortical regions. Prolonged execution of spatially constrained task leads to local neural alterations (Mednick et al., 2005), and decline in performance that remains limited to the stimulated location (Mednick et al., 2002). Such alterations are easy to compensate. On the other hand, the multiple demand system is an ensemble of brain areas engaged in a large variety of tasks (Fedorenko et al., 2013), including in interoceptive processing (Kleckner et al., 2017), i.e. in adapting behaviour to ensure physiological needs, a function essential to survival. Thus, local metabolic depletion within this network may have more adverse behavioural consequences (and presumably more severe effort and fatigue phenomenology), bridging our theory with the opportunity cost view on mental effort (Kurzban et al., 2013).
In sum, we have argued that information processing leads to quantifiable metabolic costs, in the form of glycogen depletion, accumulation of latent metabolic processes, or local sleep modes, whose consequences would remain largely confined to the neural tissue involved during the task. These local metabolic changes are arousal-dependent, and their consequences could vary in severity as a function of the affected brain region. We propose that effort is the phenomenological consequence of an adaptive mechanism that drives us away from behaviours that are anticipated to worsen these local alterations.
5. Conclusions and relations to alternative views
The phenomenology of cognitive cost and cognitive effort - in terms of subjective feeling of exhaustion experienced when performing a cognitive task and its associated task-avoidance - is relatively well known. Yet, several aspects of the problem of the costs of cognition are currently debated, including the specification of what is costly in cognitive processing, how to quantify these costs and what is their adaptive value.
We have defended a view that starts from the idea that, if the brain encodes information in accordance with the principles of efficient coding, then cognitive cost should be a function of the information cost required to encode and perform the task (using generative models). We have used this theory to explain the cognitive costs associated to (for example) novel or complex tasks, showing that it can provide a unitary perspective on several experimental findings in the literature. Furthermore, we have discussed how cognitive effort (i.e., the subjective feeling associated to performing costly tasks) and cognitive fatigue that ensue from long-term engagement in costly tasks can be considered as adaptive mechanisms that prevent individuals from performing activities that may have adverse consequences in the long run, i.e., activities that imply huge local metabolic demands. In this perspective, difficult cognitive tasks are avoided because they entail an expected loss of long-term utility (caused by potential increases of local metabolic demands).
Our perspective is coherent with several recent theories, which proposed that task avoidance stems from the (optimal) choice between potential policies while accounting for their respective cost. In this framework, cognitive effort is assumed to depend on the degree to which the task depends on cognitive control (Shenhav et al., 2017, 2013). The present work is in continuity with these earlier proposals as it relies on optimality principles and describes cognitive effort as a cost, which discounts the expected utility of a given course of actions (Apps et al., 2015; Chong et al., 2017; Manohar et al., 2015; Westbrook and Braver, 2015). However, our proposal departs from these theories as it addresses more directly the question of the causes of cognitive cost - and casts them in terms of information principles. In particular, the present framework attributes costs to general informational aspects of cognitive processing, rather than specifically to cognitive control. What determines cognitive cost is the amount of information to be processed and tasks involving cognitive control may be more costly in general because they typically require large informational loads (Fan, 2014) on the multiple demand system (Wu et al., 2017).
Another related proposal addresses cognitive effort from a normative perspective, in which apparently maladaptive states (cognitive fatigue) constitute the adaptive response of an optimal controller that has (or feels having) low self-efficacy and limited control over one's own environment, similar to learned helplessness in the animal learning literature (Stephan et al., 2016). Although we have not addressed the long-term consequences of being exposed to complex cognitive tasks, our model would be coherent with this proposal in assuming that prolonged expectations of poor outcomes, or poor control, would crystallize task-avoidance behaviour. In other words, an agent whose local metabolic resources are frequently depleted, could develop an adaptive task aversion, manifested, for example, as chronic fatigue syndrome.
It is also worth noting that challenging cognitive activity is not always experienced as aversive but may be even sought for (Cacioppo et al., 1984). Idling or engaging in repetitive, monotonous tasks can be also unpleasant (Nakamura and Csikszentmihalyi, 2002). This seeking of effortful activities, in apparent contradiction with our framework, can be explained by the mediating influence of intrinsic motivation. Complex tasks need mastery, and intrinsic motivation appears to depend in large part on the feeling of competence and autonomy, i.e. the feeling of being capable of performing a task, despite its difficulty (Ryan and Deci, 2000) - and in the active inference setting, on the necessity to improve one’s internal models (Friston et al., 2017). Pathologies like depression are characterized by increased task aversion (Salamone et al., 2016), fatigue-induced performance decline can be counteracted by self-affirmation (Job et al., 2010; Schmeichel and Vohs, 2009) and people report enjoying challenging tasks even when controlling for perceived expertise (Abuhamdeh and Csikszentmihalyi, 2012). Intrinsic motivation has been associated to anterior insula (Arsalidou et al., 2017; Lee et al., 2012; Wager and Barrett, 2004), an interoceptive brain area, suggesting that motivation to perform a task stems from our belief that its performance would lead eventually to positive effects on interoceptive states. This connects to the “dark room” problem evoked in the context of active inference, in which minimization of free energy and cognitive effort seem to predict that agents should seek the absence of interaction with the environment in order to suppress information cost altogether. However, because of the aforementioned deep priors of maintaining interoceptive states within ranges compatible with survival (Friston et al., 2012b), this putative preference for null information cost is overtaken by interoceptive needs (in terms of both homeostatic imperatives and intrinsic motivation), which leads naturally to exploratory behaviour, targeted to resolve uncertainty about future states of the world (Friston et al., 2015). In other words, improving one’s internal model to minimize surprise in the future can compensate the short-term costs of investing effort in the present moment. Spontaneous engagement in demanding tasks would therefore depend on the cost-benefit comparison between immediate informational and metabolic costs and future needs, mediated by mechanisms of exploration, model learning or intrinsic motivation that are part and parcel of active inference (or free energy minimization; Friston et al., 2017). We believe that neuroimaging studies on mental fatigue will be particularly helpful to disentangle the contribution of local brain metabolism and intrinsic motivation to task aversiveness.
In sum, we have provided a novel view on cognitive effort costs, based on principles of efficient coding and active inference. While supported by previous experimental evidence, it makes specific quantitative predictions, which will be an exciting venue of future research.
Acknowledgements
This work was supported by Fonds de la Recherche Scientifique (FNRS-FDP), Fondation Médicale Reine Elisabeth (FMRE), the Fondation Louvain and IdEx Bordeaux.
Footnotes
↵1 It is worth noting that the above example implies a massive lossy compression during stimuli perception, since all the information presented on the screen (>106 bits) is compacted into the few bits necessary to encode which of the possible digits is being presented. This sort of perceptual compression is outside the scope of this work; formal treatments of this problem rely on methods like the Blahut-Arimoto algorithm (Grau-Moya and Braun, 2015; Park and Pillow, 2017).
↵2 If information rate really adjusts to noise, it may be implemented as a trade-off between the metabolic cost associated to information rate and the behavioural cost of distortion (Alemi et al., 2017; Marzen and DeDeo, 2017; Still et al., 2012; van den Berg and Ma, 2017) rather than as a variation of information rate to keep distortion constant, since the latter mechanism would lead to prohibitive increase in information rate when noise is high. See also (Gold and Stocker, 2017; Sims, 2016) for a critical discussion of information rate adjustments in the brain.
↵3 In turn, since arousal is associated with diminished processing of less salient data, it also leads to an opportunity cost, with a down-regulation of exploratory or housekeeping processes (Kurzban et al., 2013; Raichle, 2010) - which also connects our framework to the opportunity cost view on cognitive effort (Kurzban, 2016).
↵4 Since effort and fatigue are both global phenomena, they should result from some form of integration of the local alterations. This integration should be nonlinear and convex, such that the marginal cost of increasing metabolic activity increases with metabolic activity. Short of that, the cost of local metabolic activity in one region of the brain could be compensated by decreased activity in other brain regions. Discussing the neural substrate of this integration is outside the scope of the present work but anterior cingulate cortex and anterior insula should be considered as potential hubs for such integration (Engström et al., 2013).