Tolman’s Cognitive Map (1948) has long been championed by theorists as a solution to generating flexible adaptive behavior. Cognitive maps can track the relationship between concrete (e.g., position) and abstract dimensions (e.g., likelihood of reaching a goal state). Evidence that hippocampal activity encodes concrete dimensions has long existed. Until recently, it remained unknown whether abstract dimensions are also encoded.

Nieh, Schottdorf, et al. (2021) present evidence that neural activity in hippocampal area CA1 of mice encode both concrete and abstract dimensions. The activity of 400+ neurons was tracked with two-photon calcium imaging as mice performed a spatial evidence accumulation task. The mice were head fixed on a levitating trackball surrounded by a projected view of a computer-rendered hallway. Running on the ball advanced the view down the hall. Pillars appeared at irregular intervals on the left and right sides of the hall. If mice turned toward the side with more pillars at the end of the hall, they were rewarded.

Task state was defined by both concrete and abstract dimensions. The concrete dimension was the position along the virtual hall. The abstract dimension was the net evidence up to that point regarding whether to turn left versus right come the end of the corridor (i.e., net evidence). The authors argue that this is abstracted knowledge because no single percept carries the relevant information and the relevance for obtaining reward must be learned.

There were two remarkable results. First, there were individual neurons that activated for specific combinations of position and net evidence reflecting the existence of an integrated encoding of concrete and abstract dimensions. Second, the activity of the 400+ neuron ensembles evolved in a highly constrained (non-random) way, effectively tracking a five-dimensional manifold. It is provocative to consider this a glimpse of the cognitive map itself. Yet, I will caution that what remains unclear is whether the analysis used injected extrinsic information into the manifold.

Integrating abstract and concrete dimensions

Traditional analyses of neural tuning ask “Can the activity of neuron Y be accounted for by behavioral state X?” Using this approach, Nieh, Schottdorf, et al. (2021) demonstrated that the activity of individual hippocampal neurons was tuned for net evidence, an abstract dimension. This aligns with evidence of abstract tuning from human functional imaging (e.g., Schapiro et al., 2013) and monkey unit recordings (Knudsen & Wallis, 2021).

Going further, however, Nieh, Schottdorf, and colleagues showed that abstract and concrete dimensions were jointly encoded. In other words, different neurons activated at position X depending upon the concurrent net evidence and vice versa. This indicates that the hippocampus goes beyond tracking several state variables separately to encode an integrated task state. Integrated representations enable flexible behavioral policies wherein different actions are taken from the same physical state based on the state of an inferred variable.

The ability to modify action in each physical state of the world based on internal states is the foundation of cognitive processing. Consider, for example, your own behavioral flexibility while sitting at your computer – you generate many distinct actions to the same stimulus (e.g., your email) based on variance in cognitive state (e.g., looking for distraction or needing to reference an old message). The demonstration of integrated tuning of physical and abstract dimensions in the mice affords them such cognitive processing. Indeed, this is consistent with previous work examining what otherwise appeared as instability of spatial tuning in the hippocampus. Johnson et al. (2009) provide an elegant, even if slightly dated, review of related findings.

Unfolding the manifold of the cognitive map

A second finding reported by Nieh, Schottdorf, and colleagues was the observation that the activity of the hundreds of simultaneously recorded neurons evolved as if constrained to a five-dimensional manifold. This is remarkable both because of the methodological advance and what it says about hippocampal function.

Traditional tuning analyses are akin to filtering in that they ask, “How much of the variance in my data is retained when projected onto a behavioral dimension of interest?” Such analyses can blind you to what isn’t permitted through the filter and can inflate the perceived existence of that which matches the filter. The methodological advance in the approach used by Nieh, Schottdorf, and colleagues was to avoid experimenter-defined states and, instead, ask directly “What is the empirical structure of the activation state space?” This data-driven approach follows data-mining traditions and leverages mature tools from mathematics and computer science.

Concretely, Nieh, Schottdorf, and colleagues asked, “How many dimensions (i.e., numbers) are needed to reliably reconstruct the activity state?” using an approach from algebraic topology. They found that, when the mice performed a simple hallway-running task, the states occupied a four-dimensional space and a five-dimensional space when they performed the evidence-accumulation task. When they compressed the ~400 neuron activity states down to five dimensions and reconstructed the full ~400 neuron pattern, ~36% of the variance was preserved (correlation coefficient ~= 0.6). That so few dimensions account for so much variance means that the population code is highly redundant and is evidence of a tightly integrated system. Yet, that the number of dimensions differs across tasks is remarkable as evidence that the level of integration is tunable.

Yet even data-driven approaches can be sensitive to implementational bias. The approach used by Nieh, Schottdorf, and colleagues preserved information regarding which states occurred nearby in time. Their rationale was that states visited one after another in time should be neighbors on the manifold. However, this adds extrinsic information (beyond brain activity) into the solution. The impact on the result remains unclear. The concern is that constraining the manifold by temporal proximity increases how strongly the extracted manifold incidentally aligns with other time-varying states (e.g., position or net evidence). This concern could be addressed by relaxing the constraint and asking, “What, if any, of the reported results change?”

Extracting a low-dimensional manifold that accounts for activity in a neural circuit already hypothesized to form cognitive maps raises the intriguing possibility that the manifold is the cognitive map itself. Nieh, Schottdorf, and colleagues explored this possibility in two ways. First, they asked if information about experimenter-defined task states, which had played no role in defining the manifold, was preserved in the extracted manifold. Indeed, information about task-relevant variables (position and net evidence) was preserved while information about task-irrelevant variables (screen luminance) was not. Second, they asked if the cognitive map extracted from one animal mapped systematically onto the maps extracted from other animals. Indeed, they did, indicating that the maps shared a homologous structure.

These findings are provocative and raise numerous new questions: The manifold accounts for ~36% of the variance, but how are we to think of the remaining variance? Given that position and net evidence align with two of the five dimensions of the manifold, what aligns with the others? During learning, is the low-dimensional manifold distilled from an initially high-dimensional space by collapsing uninformative variance, or is the manifold initially low dimensional and new dimensions are dilated as needed? Is the manifold of one task space systematically related to the manifold for a related task as predicted by a schema representation? Finally, is there a systematic relationship between the CA1 manifold described here and possible upstream or downstream manifolds?

In conclusion, Nieh, Schottdorf, et al. (2021) show convincing evidence of (1) integrated tuning for concrete and abstract task dimensions by hippocampal neurons in mice and (2) that the ensemble activation dynamics evolve in a highly constrained fashion that is well accounted for by a low-dimensional manifold. Further applications and exploration of the manifold extraction procedure will help clarify what, if any, impact the specific approach used here had on the results. These findings have direct relevance for the cognitive map theory and inform our understanding of how brains enable flexible adaptive behavior. They also raise enticing new questions regarding how that map evolves during learning.