What kind of computation turns a stream of self-motion signals, visual landmarks, and boundary contacts into a stable internal model of the world? Since John O'Keefe and Jonathan Dostrovsky recorded the first place cells in 1971, the hippocampal formation has offered neuroscience its clearest view of this question. Here, single neurons fire at specific locations, and their collective activity forms something that looks remarkably like a map. Yet the existence of such cells explains nothing by itself.

A map is not a list of locations. It is a structured representation that supports inference: detours, shortcuts, and routes never previously taken. Edward Tolman argued for exactly this in 1948. He proposed cognitive maps to explain rats that navigated flexibly rather than by chains of stimulus and response. The theoretical challenge since then has been to specify the mechanism. Which network architecture, which learning rule, and which dynamics could produce such a representation from local synaptic interactions?

Three frameworks now dominate the answer. Place fields can be understood as products of feedforward input combined with plasticity and predictive learning. Grid cells appear to arise from continuous attractor dynamics that perform path integration on a toroidal manifold. Most provocatively, the same machinery may encode any space with relational structure, from sound frequency to social hierarchy. Together, these frameworks suggest the hippocampus is less a memory store than a general-purpose engine for representing structure.

The earliest computational accounts treated place cells as the output of a feedforward transformation. Medial entorhinal grid cells tile space periodically, at multiple spatial scales and phases. Summing several of these grid inputs and applying a threshold produces a single localized firing field. Solstad, Kropff, and Moser formalized this in 2006 as a form of Fourier synthesis. Periodic components of differing wavelength interfere constructively at one location and destructively everywhere else.

The grid-to-place model is elegant, but it faces empirical difficulties. In developing rat pups, place cells show spatially stable fields before grid cells acquire adult-like periodicity. When medial septal inactivation abolishes grid periodicity, hippocampal place fields largely persist in familiar environments. These results imply that grid input is neither strictly necessary for place field formation nor its sole determinant.

A second input stream comes from boundary vector cells. Burgess, O'Keefe, and colleagues hypothesized these cells, and they were later identified in the subiculum. Each one fires when an environmental boundary lies at a particular distance and allocentric direction. Thresholded combinations of boundary vector inputs predict how place fields stretch, split, or duplicate when walls are moved, and experiments have confirmed these predictions. On this view, place fields are geometric computations over environmental structure.

Plasticity adds a third ingredient. Behavioral timescale synaptic plasticity, described by Bittner and Magee, lets a single dendritic plateau potential strengthen synapses that were active over a window of several seconds. This can create a new place field in one trial. Separately, the successor representation framework of Stachenfeld, Botvinick, and Gershman treats place fields as predictive. Each cell encodes the expected discounted future occupancy of a state, M = (I − γT)⁻¹. This explains why fields skew backward along habitually traversed paths.

These accounts are not mutually exclusive. Grid and boundary inputs plausibly supply complementary metric and geometric constraints. Plasticity and predictive learning then shape fields according to experience and behavioral policy. The deeper implication is that a place field is not a passive readout of location. It is a learned, compressed statistic of how an animal moves through the world, an estimate of where it is likely to go as much as where it is.

Takeaway

A place cell may encode not where an animal is, but where it expects to be next. Location becomes a statistical prediction rather than a coordinate.

Grid cells, discovered in the Moser laboratory in 2005, fire at the vertices of a triangular lattice that tiles the entire environment. This regularity raises a theoretical question: what network dynamics generate a periodic hexagonal pattern regardless of sensory features? Continuous attractor network models answer that the pattern is intrinsic. In models developed by McNaughton and colleagues, Fuhs and Touretzky, and Burak and Fiete, the lattice comes from recurrent connectivity rather than from the environment.

The core mechanism resembles a Turing instability. Picture neurons arranged on a notional two-dimensional sheet, inhibiting one another with a center-surround connectivity profile. Under uniform excitatory drive, the homogeneous state becomes unstable. Activity self-organizes into bumps whose spacing is set by the interaction kernel. In two dimensions, hexagonal packing is the favored solution. Mapped onto physical space, this population pattern reproduces the grid.

Path integration follows from breaking the network's symmetry. Suppose each neuron receives velocity input gated by its preferred head direction, and its outgoing connections are slightly offset in that direction. Running in a given direction then shifts the activity pattern across the sheet in proportion to speed. Position becomes an integral of velocity, computed by moving a stable bump along a manifold of equivalent states. Errors accumulate as drift, which landmark inputs must periodically correct.

The attractor hypothesis makes strong predictions, and these have largely held. Grid cells within a module keep fixed phase relationships across environments and even during sleep, as expected if connectivity constrains their correlations. Most decisively, Gardner and colleagues in 2022 recorded hundreds of grid cells simultaneously. Population activity lay on a toroidal manifold, the topology predicted by a periodic two-dimensional attractor. Competing oscillatory interference models, by contrast, struggle to explain grid cells in crawling bats, which lack continuous theta rhythms.

Why are there multiple modules? Grid spacing increases in discrete steps along the dorsoventral axis, with ratios near 1.4. Fiete, Burak, and Brookings showed that combining periodic codes of incommensurate scales yields a representational capacity that grows exponentially with the number of modules. The scheme is analogous to a residue number system. The grid code thus gives up the intuitive simplicity of place coding in exchange for extraordinary combinatorial efficiency and a natural substrate for vector computation.

Takeaway

The grid pattern may not be learned from space at all. It may be a shape the network already prefers, onto which space is then written.

If the hippocampal-entorhinal system computed only physical position, it would be remarkable but narrow. Evidence increasingly suggests it does more. Some hippocampal neurons, known as time cells, fire at specific moments within temporal sequences. Aronov, Nevers, and Tank trained rats to change an auditory tone by deflecting a joystick. Hippocampal and entorhinal cells developed firing fields along the frequency dimension, in effect a place code for sound.

Human neuroimaging extends this further. Constantinescu, O'Reilly, and Behrens trained participants to navigate a conceptual space defined by the neck and leg lengths of stylized birds. Entorhinal and prefrontal fMRI signals showed sixfold rotational symmetry as a function of trajectory direction through this space, the macroscopic signature of grid-like coding. Similar map-like representations have since been reported for social hierarchies, where people infer relationships along dimensions such as competence and popularity.

The Tolman-Eichenbaum Machine, proposed by Whittington, Behrens, and colleagues, offers a unifying computational account. It separates experience into two streams. Abstract structural codes are attributed to medial entorhinal cortex, and sensory codes to lateral entorhinal cortex. The hippocampus binds the two through conjunctive representations stored in fast Hebbian memory. When trained on varied graphs, the model spontaneously develops grid-like, place-like, and boundary-like units, and it generalizes learned structure to novel environments.

This separation of structure from content explains a central phenomenon: remapping. When an animal enters a new room, place cells reorganize because the sensory bindings change. Grid relationships persist because the underlying structure is still a two-dimensional Euclidean space. The same structural code can be reused across contexts, which enables inference without prior experience. Knowing that A lies beyond B, and B beyond C, supports conclusions about A and C that were never directly observed.

The framework has a surprising coda. Whittington and colleagues showed that transformer architectures with recurrent positional encodings are mathematically closely related to the Tolman-Eichenbaum Machine, with self-attention behaving like hippocampal memory retrieval. Whether or not the correspondence runs deep, it suggests a convergence. Relational inference over structured memory may be a solution to generalizing from limited experience that evolution discovered and machine learning has rediscovered.

Takeaway

Space may be just one instance of a more general problem the hippocampus solves: separating the structure of a situation from its contents so the structure can be reused.

Taken together, these frameworks recast the hippocampal formation as a system for learning and exploiting structure. Place cells emerge from geometric, metric, and predictive inputs. Grid cells provide a low-dimensional, path-integrating coordinate system constrained by attractor dynamics. The combination generalizes beyond physical space to any domain with relational regularities.

This reframing dissolves an old dichotomy. The debate over whether the hippocampus serves memory or navigation now seems to misidentify the computation. Episodic memory may be the binding of particular contents to positions within a learned relational scaffold. Navigation is then the special case in which that scaffold is Euclidean.

Substantial questions remain. How are structural codes learned rather than prewired? How do multiple maps coexist without interference? How do such representations support conscious, flexible thought? Still, the direction is clear. Understanding how the brain maps space may be our most tractable route to understanding how it represents anything at all.