To help us navigate, the brain encodes information about the positions of landmarks in space in a series of maps. These maps are housed by two neighbouring brain regions called the hippocampus and entorhinal cortex. These regions also encode information about non-spatial relationships, for example, between two events that often occur close together in time. However, it was not known whether such non-spatial relationships may also be encoded as a map.

To address this question, Garvert et al. showed volunteers a series of objects on a screen. Unbeknown to the volunteers, the order of the objects was not entirely random. Instead, each object could only follow certain others. The objects were thus connected to one another by a network of non-spatial relationships, broadly comparable to the spatial relationships that connect physical locations in the environment. The next day, the volunteers viewed some of the objects again, this time while lying inside a brain scanner. Although the volunteers still believed that the objects had been presented at random, the activity of their hippocampus and entorhinal cortex reflected the non-spatial relationships volunteers had experienced between the objects. The relationships were organised in an abstract map.

This suggests that the brain organises knowledge about abstract non-spatial relationships into maps comparable to those used to represent spatial relationships. The brain can use these maps of non-spatial relationships to guide our behaviour, even though we have no conscious awareness of the information they contain. The maps may also enable us to make new inferences, just as we can use our spatial maps to find short cuts or navigate around obstacles. Future studies should investigate the mechanisms underlying our ability to create maps of non-spatial relationships and how we use them to guide decision making.

Animals efficiently extract abstract relationships between landmarks, events, and other types of conceptual information, often from limited experience. Knowing such regularities can help us act in an environment, because the relationships between items that have never been experienced together can easily be computed and exploited in order to make novel inference. In physical space, spatially tuned cells in the hippocampal–entorhinal system have precise place (O’Keefe and Dostrovsky, 1971) and grid (Hafting et al., 2005) codes that may form the neural basis of a ‘cognitive map’ (O’Keefe and Nadel, 1978). It is likely that the particular form of these representations enables rapid computations of spatial relationships such as distances and vector paths (Bush et al., 2015; Stemmler et al., 2015). The potential for such rapid online computations embedded into neuronal representations may explain how animals can find novel paths through space (McNaughton et al., 2006; Mittelstaedt and Mittelstaedt, 1980) or rapidly reroute when obstacles are introduced (Alvernhe et al., 2011) or removed (Alvernhe et al., 2008). Indeed, in humans, signals that encode distance metrics between landmarks (Howard et al., 2014; Morgan et al., 2011) and directions to goals (Chadwick et al., 2015) can be read out directly from functional magnetic resonance imaging (fMRI) data in the entorhinal cortex.

The hippocampal formation also encodes non-spatial relationships between objects. When these objects can be laid out in a continuous dimension such as time, hippocampal codes extracted from neuronal ensembles (Rubin et al., 2015) or fMRI voxel patterns (Ezzyat and Davachi, 2014) reflect proximity along this dimension. fMRI signals also appear to reflect veridical angles when two-dimensional abstract spaces are formed from continuous dimensions (Constantinescu et al., 2016; Tavares et al., 2015). However, many relationships that are encoded by the hippocampal formation reflect associations or relationships between discrete objects (Horner et al., 2015; Schapiro et al., 2013, 2012; Wimmer and Shohamy, 2012). To be a useful source of knowledge, many associations must be organised within an associative structure, but it is unclear how such structures might be represented in the absence of a continuous organising dimension such as space or time.

Highly complex relational structures are often learnt implicitly i.e. unintentionally and without explicit awareness (Cleeremans et al., 1998; Reber, 1989; Seger and Augart, 1994). Neurally, implicitly acquired relational knowledge can be reflected as increases in neural similarity for pairwise associations in the temporal cortex (Schapiro et al., 2012) or for members of a temporal community structure (Schapiro et al., 2013). However, it is unclear whether map- or graph-like knowledge structures might be encoded non-consciously, i.e. without subjects being aware of relationships between objects.

Here, we explicitly tested this notion using a fMRI adaptation paradigm that allowed us to quantify the relationships between object representations in a neuronal representational space following an implicit learning paradigm. We presented human participants with sequences of objects where stimulus transitions were drawn from random walks along a graph structure. Within the hippocampal-entorhinal system, a map-like organisation of the relationships between object representations could be extracted from fMRI adaptation data acquired on the subsequent day. In this map, associative distance between objects formed a metric that allowed us to extract organising dimensions. This suggests that the brain can automatically organise abstract relational information into map-like structures even if the relationships between objects are non-spatial rather than spatial, discrete rather than continuous, and unavailable to conscious awareness. A signature of map-like encoding was also present behaviourally in a separate group of subjects, demonstrating implicit memory of the structure.

We found no evidence for a mapping of discrete relationships into Euclidian space. Instead, the fMRI adaptation pattern as well as behaviour are more consistent with distance measures reflecting the distribution of future states. These principles are consistent with a predictive representation such as the successor representation (Dayan, 1993). Such a predictive map of state space may facilitate the rapid computation of values in a reinforcement learning world (Momennejad et al., 2016; Russek et al., 2016). It has recently been demonstrated that the successor representation can account for a number of properties of place cell and grid cell activity (Stachenfeld et al., 2016, 2014).

We exposed 23 human participants to object sequences whose stimulus transitions, unbeknownst to them, were determined by a random walk in a graph (Figure 1A). Subjects performed a behavioural cover task, in which they learned to associate a random stimulus orientation with a button press. In the task instructions, any reference to a sequence or an underlying structure was avoided. After the fMRI experiment, subjects were debriefed and none reported any explicit knowledge of structure in the task. To test whether this exposure to object sequences induced implicit knowledge about the graph, we scanned the subjects on a subsequent day using fMRI while exposing them to a subset of the same objects presented in a random order (only a reduced graph was presented to increase statistical power; Figure 1B). In 10% of the fMRI trials, subjects performed an unrelated cover task, reporting whether a grey patch had been present on the preceding object. Neither accuracy nor response time in this task depended on the object on screen or the transition structure (Figure 1—figure supplement 1).

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We exploited fMRI adaptation (Barron et al., 2016; Grill-Spector et al., 2006) to investigate the representational similarity for different objects on the graph. We reasoned that in regions encoding a map-like representation of the overall task structure, the degree of similarity in neural representation, and therefore the fMRI adaptation, should decrease as a function of distance between items on the graph. Based on this reasoning, we first looked for brain regions whose fMRI responses to each object increased as a linear function of the link distance of the preceding item.

This adaptation analysis revealed a cluster bilaterally in the entorhinal cortex (Figure 2A, family-wise error corrected at peak level within a bilateral entorhinal cortex/subiculum mask, left p=0.014, peak t₂₂ = 4.42, [−18, –19, −22] and right p=0.006, peak t₂₂ = 4.75, [24, −25, −22]. A right, but not left peak also survived small volume correction (SVC) for a larger region of interest [ROI] comprising the hippocampus, parahippocampal cortex, and entorhinal cortex, left p=0.058 and right p=0.026, see ROIs in Figure 2—figure supplement 1). This adaptation effect cannot be explained by basic statistics of the object sequence, such as the number of times an object occurred during training, or basic features of the graph structure, such as the number of neighbours an object has on the graph (Figure 2—figure supplement 3).

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To confirm the statistical robustness of the effect, and to test whether the effect reflected a gradual increase with distance, we separated the effect into two orthogonal components. These components comprised the difference between connected links (length 1) and all other transitions (lengths 2 and 3; Figure 2B, green), and the difference between transitions of length 2 and those of length 3 (Figure 2B, red). These two independent contrasts were used to define ROIs bilaterally in overlapping regions of the entorhinal cortex (both thresholded at p<0.01 uncorrected; ROI 1: left peak t₂₂ = 3.85; [−18, –19, −22] and right peak t₂₂ = 3.26; [24, −25, −22], ROI 2: left peak t₂₂ = 4.55, [18, −16, −25] and right peak t₂₂ = 3.38, [−18, –25, −25]). Because of their statistical independence, we could use the ROI from one contrast to extract data for the corollary test (t₂₂ = 2.27, p=0.03 for length 2 vs. length 3 in ROI 1, Figure 2C; and t₂₂ = 2.34, p=0.03 for connected vs. all other links in ROI 2, Figure 2D). This pair of tests suggests that the fMRI adaptation faithfully represents the link distance. These tests obviate questions of multiple comparisons, because in each case the data are selected from one contrast, and an orthogonal contrast was used for the test statistic.

To further demonstrate this within a single test, we required a coordinate that was independent of all the data. We chose a peak location from an independent study investigating a similar relational measure in spatial maps (Chadwick et al., 2015). Extracting data from this coordinate (ROI 3) revealed a linear effect of link distance (Figure 2E, F_2,44 = 10.04, p<0.001), and correspondingly a significant difference between distances of lengths 1 and 3 (t₂₂ = 3.71, p=0.001) and lengths 2 and 3 (t₂₂ = 3.19, p=0.004), but not between distances of lengths 1 and 2 (t₂₂ = 1.67, p=0.11).

Although this distance effect is suggestive of a map-like organisation, it might also merely reflect the temporal proximity between two objects during training. When the temporal and distance relationships between pairs of objects were allowed to compete for variance in a multiple linear regression, the number of links (t₂₂ = 3.29, p=0.003), but not time (t₂₂ = 1.27, p=0.22), explained the neural signal extracted from the independently defined ROI 3 (Figure 3A). Furthermore, relationships between items arranged in a map-like structure are non-directional. Our subjects were not constrained to experience each pair of transitions an equal number of times (Figure 3B). Based upon this, we could test whether the fMRI signal was better predicted by the true or symmetrised distance between any two objects. We constructed a measure of the shortest path between each pair of objects according to the actual number of times each transition was experienced by a subject during training (see 'Materials and methods' section). When allowing this measure to compete with its symmetrised, and thereby non-directional, self in a linear model, it was the symmetrised version alone that predicted the fMRI suppression effect (Figure 3C, t₂₂ = 2.78, p=0.01 and t₂₂ = −1.64, p=0.11).

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In order to test whether these map-like features are a consequence of a map-like organisation, we organised the signal into a 7 × 7 matrix, with each matrix element reflecting the mean fMRI response across subjects to transitions between the corresponding pairs of objects (Figure 3D). For example, element [2,7] in this matrix is the response to object 7 when preceded by object 2 on the graph, averaged across all subjects. Because the signal is suppressed for nearby objects, this matrix is analogous to a distance matrix. When we applied multidimensional scaling (MDS) in order to visualise the most faithful two-dimensional representation of distances in this matrix, the graph structure of our experimental map was recovered despite the subjects’ professed ignorance of any such organisation (Figure 3E). Permutation tests confirm that the multidimensional scaling-mapped distances are significantly more correlated with link distances of the original graph structure than with link distances of a null distribution consisting of all other complete graphs with seven links (r = 0.65, p=0.003, Figure 3—figure supplement 2A). Furthermore, no links cross in the graph resulting from the MDS mapping. This is only true for 13.17% of all possible graphs with nodes in the same location, but seven randomly distributed links (Figure 3—figure supplement 2B). Notably, the data were extracted from an independent ROI taken from an experiment investigating maps in allocentric physical space (Chadwick et al., 2015, ROI 3). Results are comparable if parameter estimates are extracted from an anatomically defined ROI comprising the entorhinal cortex and the subiculum (Figure 3—figure supplement 3).

In the reinforcement learning literature, it has been suggested that a cognitive map of the relationship between states may be most useful if the representation of a state is predictive in nature and reflects the distribution of likely future states. This idea has been formalised as the successor representation (Dayan, 1993; Momennejad et al., 2016; Russek et al., 2016), proposed to be encoded by hippocampal place cells (Stachenfeld et al., 2016, 2014). According to this view, hippocampal place cells do not encode an animal’s current location in space, but instead encode a predictive representation of future locations. The successor representation may facilitate reinforcement learning, because the resulting predictive measure of future states could be flexibly combined with reward representations to enable rapid computation of navigational trajectories (Baram et al., 2017; Dayan, 1993; Momennejad et al., 2016; Russek et al., 2016).

Mathematically, the successor representation can be computed from the adjacency matrix $A$ that defines the relationship between states:

with a discount factor $\gamma$<1. Here, entries $a_{ij}$ for each $A^n$ correspond to the number of possible paths of length $n$ between objects $i$ and $j$. The successor representation therefore computes the weighted sum of distant future states, with $A^n$ discounted more heavily for larger $n$ (i.e. for longer paths between pairs of objects).

Notably, this same representation is common in graph theory, where the matrix ${(I-\gamma A)}^{-1}$ is termed the matrix resolvent and is used to measure the proximity or ‘communicability’ between nodes in the graph. Graph theory also proposes a second measure that is closely related, the matrix exponential (Estrada and Hatano, 2008, 2010):

Both measures compute a weighted sum over future states, which easily generalises from continuous to discrete, and from two-dimensional to high-dimensional spaces.

In order to test whether the neural distance effects are consistent with such predictive measures, we tested for areas whose fMRI responses to each object increased as a linear function of communicability, corresponding to the negative of the matrix exponential. Compared to the successor representation, the matrix exponential has the advantage that it does not require the fitting of a free parameter. The matrix exponential is small for nodes that are far away from each other on a graph, such that it scales negatively with distance. Unlike a mapping into Euclidian space, communicability significantly distorts the graph structure by shortening links that form part of many paths around the graph structure and lengthening links that would be less frequently visited by a random navigator (Figure 4A).

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We find that neural activity bilaterally in the hippocampal–entorhinal system scales with communicability (Figure 4B, C, family-wise error corrected at peak level within a bilateral entorhinal cortex/subiculum mask, left p=0.001, peak t₂₂ = 5.47 [−18, –19, −25] and right p=0.0005, peak t₂₂ = 5.79, [21, −19, −28]). Both clusters also survived SVC (small-volume correction) for a larger ROI comprising the hippocampus, parahippocampal cortex, and entorhinal cortex (left p=0.004 and right p=0.004, see ROIs in Figure 2—figure supplement 1B). Activity in the same areas also scales with the negative of the successor representation if the free parameter $\gamma$ is set to the commonly used value of $\gamma =\frac{0.85}{{\lambda }_{max}}$ (${\lambda }_{max }=$ largest eigenvalue of $A$ in modulus, Aprahamian et al., 2016; Benzi and Klymko, 2013, Figure 4—figure supplement 1).

In the left hippocampal formation, communicability effects are significant even if Euclidian distances are included as an additional regressor (Figure 4D, p=0.006, peak t₂₂ = 4.72, [−15, –13, −19], SVC mask 1 and p=0.027, SVC mask 2). This suggests that the hippocampal–entorhinal system does not map the graph structure into a Euclidian space. Instead, these results are consistent with the view that the distance effect we observe in this system may be a consequence of the hippocampal formation encoding a predictive representation of states within a graph structure (Stachenfeld et al., 2016, 2014).

A map-like representation in the hippocampal–entorhinal system suggests that subjects acquired implicit knowledge about the graph structure, even in the absence of explicit awareness of any regularities in the object sequence. To reveal such implicit learning behaviourally, we asked an independent group of 26 participants, who were trained in the same way as the scanning cohort on the first graph structure (Figure 5A), to repeat the object orientation cover task on day 2. As was the case for scanned subjects, object transitions were now random and only objects from a reduced graph were presented (Figure 5B). We hypothesised that implicit knowledge about the graph structure would influence response times, such that subjects would respond faster if a preceding object in the test sequence was closer on the graph structure underlying the train sequence. Indeed, we found that log-transformed response times were longer the further away the preceding object was on the graph (Figure 5C, D). In line with our imaging results, response times did not scale with link or Euclidian distance between objects, but instead with communicability (communicability: t₂₅ = 2.77, p=0.01; link distance: t₂₅ = −0.40, p=0.69; Euclidian distance: t₂₅ = −0.85, p=0.40, Figure 5C, D).

Figure 5

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The hippocampal–entorhinal system is engaged when an animal navigates within a physical environment and acquires flexible knowledge about spatial relationships. In mammals, the hippocampal–entorhinal system contributes to spatial navigation by mapping relationships in situations where knowledge is physical, continuous, and consciously available (Chadwick et al., 2015; Derdikman and Moser, 2010; Howard et al., 2014; Spiers and Maguire, 2007). Here, we used a statistical learning paradigm to demonstrate that the hippocampal–entorhinal system also efficiently extracts statistical regularities in a non-spatial task where the relationships between items are discrete, and organises this non-spatial relational knowledge in an abstract relational map, suggesting that the hippocampal–entorhinal system creates metric representations of discrete relationships based on associative strengths (Eichenbaum and Cohen, 2014). Notably, there were no continuous dimensions in our discrete stimulus sets. The dimensions had to be extracted from the associations.

These results add to the notion that the hippocampal formation maps experiences across a wide range of different dimensions, thereby supporting flexible behaviour across many domains of life (O’Keefe and Nadel, 1978; Tolman, 1948). Recent studies have focused on the human hippocampal formation for storing the relational knowledge that makes up simple world models in reinforcement learning (Barron et al., 2013; Boorman et al., 2016; Bornstein and Daw, 2013; Wimmer and Shohamy, 2012). Our findings extend these simple associative paradigms to more complex associative maps, and demonstrate that these maps may be learnt implicitly.

Notably, the resulting map is not Euclidian in nature. Instead, we find that the neural data as well as the behaviour are consistent with a measure corresponding to a weighted sum of future states in the graph structure. This is consistent with the idea that reinforcement learning benefits from knowledge about warped geometries in space, which may be represented as predictive maps, or successor representations, in the hippocampal formation (Stachenfeld et al., 2016, 2014). Such predictive representations of the relationships between discrete objects or states of the world may be combined with reward representations to enable flexible goal-directed behaviour (Baram et al., 2017; Dayan, 1993; Momennejad et al., 2016; Russek et al., 2016).

Our data suggest that the map of the relational structure in discrete abstract space may be encoded by the pattern of firing in the entorhinal cortex, which also encodes maps in continuous physical space. The entorhinal cortex is noted for the presence of grid cells (Hafting et al., 2005), which may provide a metric for measuring distances in physical space (Bush et al., 2015; Stemmler et al., 2015), allowing vector navigation. However, recent theoretical treatments suggest that grid-like firing might also be understood as a principal component decomposition of the covariance information between place cells (Dordek et al., 2016) or the transitions between states (Stachenfeld et al., 2016, 2014). Together with the finding of hippocampal cells in humans that encode individual concepts (which may be analogous to place cells), these theories can explain how grid-like firing patterns could extend to discrete spaces (such as the one we have used here), and also make predictions for how grid-like coding might extend to higher-dimensional spaces (Baram et al., 2017).

Our behavioural results are consistent with the observation that the human brain can acquire abstract knowledge unconsciously and automatically by extracting statistical regularities from incidental exposure to events generated according to a set of rules (Berry and Broadbent, 1984; Cleeremans et al., 1998; Reber, 1989, 1967; Seger and Augart, 1994). The resulting implicit knowledge can be used to guide behaviour despite an inability to verbalise the underlying regularities. Neurally, implicit learning of sequences involves medial temporal lobe structures, including the hippocampus, subiculum, and entorhinal cortex (Schendan et al., 2003). The hippocampal–entorhinal system also responds to the violation of learnt sequence structures (Kumaran and Maguire, 2006) and signals the likelihood of events in learnt sequences (Strange et al., 2005). This may be facilitated by an increase in representational similarity as stimuli become embedded into knowledge structures (Schapiro et al., 2013, 2012). Our results add to this literature by proposing a specific way in which implicit knowledge may be organised in maps to facilitate goal-directed behaviour.

It is notable that we did not find clear evidence for the map-like structure outside the hippocampal formation, although areas such as the orbitofrontal cortex have been shown to represent cognitive maps of decision spaces (Schuck et al., 2016). It is possible that this is because our study relies on implicit learning, and because the subjects do not have to use the associative structure for any task. Indeed, we note that neural signals can be recorded in frontal and parietal cortices, reflecting the ‘state-prediction errors’ that ensue when predicted state relationships are breached during behavioural control (Gläscher et al., 2010). Similar prediction errors in the orbitofrontal cortex during active learning predict later changes in hippocampal representations of the stored model (Boorman et al., 2016). These and similar ideas have led to a theoretical account of place and grid activity in the hippocampal formation as state representations in reinforcement learning models (Stachenfeld et al., 2016, 2014).

It has long been known that the hippocampal formation is important for tasks that rely on associative and relational knowledge. It supports the organisation of stimuli across arbitrary stimulus dimensions such as temporal co-occurrence (Schapiro et al., 2013, 2012) or social rank (Kumaran et al., 2012), and organises behaviourally relevant stimulus categories in a hierarchy (McKenzie et al., 2014). These organisational principles facilitate generalising over individual episodes (Komorowski et al., 2013) and enable transitive inference by combining newly formed associations between discrete stimuli (Collin et al., 2015; Heckers et al., 2004; Horner et al., 2015; Preston et al., 2004; Schlichting et al., 2015). Value spreading across associated stimulus representations in the hippocampus can then directly influence behaviour in novel decision-making situations (Wimmer and Shohamy, 2012). We hope that the current findings help to reconcile these results with the spatial functions of the same neural structures. Such an organisation of relational information might be the basis for an animal’s ability to navigate through an abstract concept space and to perform flexible computations without direct experience.

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Author details

1. Mona M Garvert

   1. Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, London, United Kingdom
   2. Oxford Centre for Functional MRI of the Brain, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom

   Contribution

   MMG, Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   mona.garvert.11@ucl.ac.uk

   Competing interests

   No competing interests declared.

   "This ORCID iD identifies the author of this article:" 0000-0002-8678-5536

2. Raymond J Dolan

   1. Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, London, United Kingdom
   2. Max Planck-UCL Centre for Computational Psychiatry and Ageing Research, London, United Kingdom

   Contribution

   RJD, Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Writing—original draft, Project administration, Writing—review and editing

   Competing interests

   No competing interests declared.

3. Timothy EJ Behrens

   1. Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, London, United Kingdom
   2. Oxford Centre for Functional MRI of the Brain, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom

   Contribution

   TEJB, Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Writing—original draft, Project administration, Writing—review and editing

   Competing interests

   TEJB: Senior editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0003-0048-1177

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