Many will agree that algebra is difficult to learn – it involves planning, problem-solving, the manipulation of symbols, and the application of abstract rules. Although it’s tempting to imagine a specialized region of the brain for each of these processes, they may actually recruit roughly the same widely-distributed and general-purpose “task network” of brain regions. The individual contribution of each region has been, and continues to be, a matter of much debate.
However, the functional specialization of each brain region may be best understood as fulfilling a particular balance between the computational tradeoffs that arise in connectionist networks. Prefrontal, posterior and subcortical regions may interact in a complementary fashion to satisfy these opposing requirements, as described below in a sample domain of high-level cognition: planning.
Efficient planning requires a balance between at least three opposing characteristics: 1) a plan must by definition relate to a distant goal, and yet to be effective should be grounded in the here-and-now; 2) current “sub”goals must be flexibly updated as they are accomplished, but the ultimate goal must be stably maintained; and 3) planning must involve the recombination of old behaviors for novel purposes, but should do so without causing catastrophic interference on older plans (which may themselves involve a different recombination of similar behaviors for alternate purposes).
It seems unlikely that a single brain region could satisfy all of these differing requirements – indeed, planning and problem-solving are associated with very widespread neuronal activation. But closer examination reveals that these regions can be functionally partitioned according to how they each satisfy these opposing requirements.
For example, prefrontal cortex (PFC) may be particularly well-suited to the stable representation of high-level goals and their constituent subgoals. First, the distance of PFC from sensory cortex makes it an ideal candidate for the representation of abstract goal states that may differ substantially from the current environmental context. Second, the striped anatomy of PFC could allow for the stable representation of multiple competing or inter-related goals. Third, PFC’s hierarchical organization may allow for goals to be organized in a “nesting cascade” from the more temporally distant to the more immediate, an idea already supported by some neuroimaging evidence.
While PFC is a good candidate for goal maintenance, it lacks a mechanism for flexibly updating representations as goals are accomplished. Computational models suggest that this “flexibility-stability” dilemma may be circumvented by subcortical functioning – in particular that of the basal ganglia – which can selectively update PFC with task-relevant representations via an “adaptive gating” signal. Consistent with these accounts, a variety of subcortical regions – including the basal ganglia – are reliably coactivated with prefrontal regions in planning tasks. Similarly, basal ganglia regions might be involved in the selection of the most advantageous plan from among multiple competing plans or motor actions and in reversal learning – useful if a plan “backfires” or otherwise fails to achieve the expected reward.
Traditional views of the basal ganglia emphasize its role in the initiation of habitual actions, but planning is particularly important in novel circumstances – habit will often suffice in more familiar scenarios. However, new plans should not completely “overwrite” older plans or habits that might later useful. This computational tradeoff between stability and plasticity may be mitigated by the hippocampus, in which highly-plastic and extremely sparse conjunctive representations can be used to rapidly form new associations without disrupting older associations. Such a system could be particularly important in planning, where stimuli must be “remapped” to different responses in order to accomplish a novel plan without also destroying older habits or plans.
Supporting evidence for the role of hippocampus in planning comes from computational models of prospective memory as well as electrophysiological work demonstrating hippocampal sensitivity to goals. Hippocampus may also interact directly with the ventral striatum, perhaps facilitating its role in the acquisition of new skills.
In summary, the opposing computational requirements of planning may be balanced by a specific division of labor between prefrontal, posterior, and subcortical regions. The architecture of prefrontal cortex may be particularly suited for maintaining temporally nested goals and subgoals, spanning the temporal spectrum from immediate (in premotor areas) to ultimate (in frontopolar areas). These goal representations can be selectively updated as they are accomplished through an adaptive gating signal originating from the basal ganglia. Finally, novel plans can be rapidly formed without catastrophic interference on previous plans or habits by rich interactions between hippocampus and the ventral striatum. Thus cooperation among a variety of brain regions, each of which fills a particular computational or functional niche, may underlie the characteristic flexibility of human planning.