Understanding the structure of a problem, such as the relationships between stimuli, supports fast learning and flexible reasoning. Rodent work has suggested that the abstraction of structure away from sensory details occurs over the course of multiple days in the cortex. However, direct evidence of such explicit relational representations in humans is scarce, and it is unclear whether they emerge on similar timescales. Here, we combine a graph-learning paradigm with functional magnetic resonance imaging (fMRI) to look for such a relational map in the human brain. We first trained participants on two associative graphs with the same structure. We then scanned participants twice while they used this knowledge, with several days between scanning sessions. Using fMRI repetition suppression, we found an abstract relational representation in the medial prefrontal cortex (mPFC) that emerged across the two scanning sessions. This finding was also replicated using representational similarity analysis (RSA). These results shed new light on how neural representations organizing relational knowledge change with time.

Planning is critical for adaptive behaviour in a changing world, because it lets us anticipate the future and adjust our actions accordingly. While prefrontal cortex is crucial for this process, it remains unknown how planning is implemented in neural circuits. Prefrontal representations were recently discovered in simpler sequence memory tasks, where different populations of neurons represent different future time points. We demonstrate that combining such representations with the ubiquitous principle of neural attractor dynamics allows circuits to solve much richer problems including planning. This is achieved by embedding the environment structure directly in synaptic connections to implement an attractor network that infers desirable futures. The resulting 'spacetime attractor' excels at planning in challenging tasks known to depend on prefrontal cortex. Recurrent neural networks trained by gradient descent on such tasks learn a solution that precisely recapitulates the spacetime attractor – in representation, in dynamics, and in connectivity. Analyses of networks trained across different environment structures reveal a generalisation mechanism that rapidly reconfigures the world model used for planning, without the need for synaptic plasticity. The spacetime attractor is a testable mechanistic theory of planning. If true, it would provide a path towards detailed mechanistic understanding of how prefrontal cortex structures adaptive behaviour.

The entorhinal cortex (EC) supports a coordinate system for spatial memories, organised in a hierarchy along the EC dorso-ventral axis. Recent theories suggest that a similar coordinate system could scaffold non-spatial memories. Here we show that an abstract hierarchical coordinate system supports arbitrary sequence memories in the human medial temporal lobe (MTL). In single-unit recordings from MTL, we find abstract, coordinate-like coding in a simple sequential memory task. In fMRI we find that abstract coordinate representations are arranged hierarchically along the entorhinal cortex, mirroring the anatomical gradient of grid cells in the rodent EC but now for non-spatial sequences. We replicate this finding in an independent cohort of participants. These data suggest that memories are scaffolded on a hierarchical coordinate system aligned to preserved anatomy across domains and species.

Animals integrate knowledge about how the state of the environment evolves to choose actions that maximise reward. Such goal-directed behaviour - or model-based (MB) reinforcement learning (RL) - can flexibly adapt choice to changes, being thus distinct from simpler habitual - or model-free (MF) RL - strategies. Previous inactivation and neuroimaging work implicates prefrontal cortex (PFC) and the caudate striatal region in MB-RL; however, details are scarce about its implementation at the single-neuron level. Here, we recorded from two PFC regions - the dorsal anterior cingulate cortex (ACC) and dorsolateral PFC (DLPFC), and two striatal regions, caudate and putamen - while two rhesus macaques performed a sequential decision-making (two-step) task in which MB-RL involves knowledge about the statistics of reward and state transitions. All four regions, but particularly the ACC, encoded the rewards received and tracked the probabilistic state transitions that occurred. However, ACC (and to a lesser extent caudate) encoded the key variables of the task - namely the interaction between reward, transition, and choice - which underlies MB decision-making. ACC and caudate neurons also encoded MB-derived estimates of choice values. Moreover, caudate value estimates of the choice options flipped when a rare transition occurred, demonstrating value update based on structural knowledge of the task. The striatal regions were unique (relative to PFC) in encoding the current and previous rewards with opposing polarities, reminiscent of dopaminergic neurons, and indicative of an MF prediction error. Our findings provide a deeper understanding of selective and temporally dissociable neural mechanisms underlying goal-directed behaviour.

Humans and animals plan actions to achieve goals in worlds that are complex and continually changing. While planning is critically dependent on the prefrontal cortex in humans, little is known about its cellular underpinnings. Mechanistic understanding has been limited by a scarcity of controlled animal experiments in which subjects must flexibly plan novel behaviours on every trial. Here we characterise the neural representations and dynamics of mouse medial frontal cortex (mFC) during flexible navigation in structured environments. We trained mice to navigate complex mazes, to goals that changed location on every trial. Optogenetic silencing established that mFC was necessary for efficient navigation. mFC activity was dominated by two factorised components: (i) a structured representation of subjects' position within the maze that formed an efficient code for behavioural trajectories, and (ii) a flexible representation of the shortest path-distance to the current goal. Both representations oscillated within local field potential (LFP) theta cycles, processing from further to closer to the goal at a systematic offset. These data suggest a computation in which mFC evaluates possible futures by their distance-to-goal to update a structured behavioural policy.

Why do biological and artificial neurons sometimes modularise, each encoding a single meaningful variable, and sometimes entangle their representation of many variables? In this work, we develop a theory of when biologically inspired networks---those that are nonnegative and energy efficient---modularise their representation of source variables (sources). We derive necessary and sufficient conditions on a sample of sources that determine whether the neurons in an optimal biologically-inspired linear autoencoder modularise. Our theory applies to any dataset, extending far beyond the case of statistical independence studied in previous work. Rather we show that sources modularise if their support is ``sufficiently spread''. From this theory, we extract and validate predictions in a variety of empirical studies on how data distribution affects modularisation in nonlinear feedforward and recurrent neural networks trained on supervised and unsupervised tasks. Furthermore, we apply these ideas to neuroscience data, showing that range independence can be used to understand the mixing or modularising of spatial and reward information in entorhinal recordings in seemingly conflicting experiments. Further, we use these results to suggest alternate origins of mixed-selectivity, beyond the predominant theory of flexible nonlinear classification. In sum, our theory prescribes precise conditions on when neural activities modularise, providing tools for inducing and elucidating modular representations in brains and machines.

The hippocampus is critical for memory, imagination and constructive reasoning. Recent models have suggested that its neuronal responses can be well explained by state spaces that model the transitions between experiences. Here we use simulations and hippocampal recordings to reconcile these views. We show that if state spaces are constructed compositionally from existing building blocks, or primitives, hippocampal responses can be interpreted as compositional memories, binding these primitives together. Critically, this enables agents to behave optimally in new environments with no new learning, inferring behavior directly from the composition. We predict a role for hippocampal replay in building and consolidating these compositional memories. We test these predictions in two datasets by showing that replay events from newly discovered landmarks induce and strengthen new remote firing fields. When the landmark is moved, replay builds a new firing field at the same vector to the new location. Together, these findings provide a framework for reasoning about compositional memories and demonstrate that such memories are formed in hippocampal replay.

The prefrontal cortex (PFC) is crucial for economic decision-making. However, how PFC value representations facilitate flexible decisions remains unknown. We reframe economic decision-making as a navigation process through a cognitive map of choice values. We found rhesus macaques represented choices as navigation trajectories in a value space using a grid-like code. This occurred in ventromedial PFC (vmPFC) local field potential theta frequency across two datasets. vmPFC neurons deployed the same grid-like code and encoded chosen value. However, both signals depended on theta phase: occurring on theta troughs but on separate theta cycles. Finally, we found sharp-wave ripples-a key signature of planning and flexible behavior-in vmPFC. Thus, vmPFC utilizes cognitive map-based computations to organize and compare values, suggesting an alternative architecture for economic choice in PFC.

Humans form cognitive maps that enable inferences beyond direct experience, relying on hexagonal grid-cell-like neural codes as a schema for two-dimensional (2D) spaces. However, how new experiences align with this schema remains unknown. We recorded intracranial activity from 42 epilepsy patients while they learned rank relations among feature objects, then combined these features into compounds occupying a 2D conceptual space. Hippocampal ripples during brief pauses between learning trials increased with experience, signaling integration of the learned ranks. Crucially, ripple activity during post-learning rest predicted the later appearance of grid-like codes in the entorhinal and medial prefrontal cortex (mPFC) when participants inferred unseen relations among compounds. Ripples synchronized with mPFC during rest were specifically associated with later schema-based inference rather than direct memory retrieval. These findings show that hippocampal ripples align new experiences with an existing grid-like schema, transforming discrete events into structured knowledge that supports flexible reasoning in human cognition.

Humans create internal cognitive maps that allow us to make inferences beyond direct experience. These maps often rely on hexagonal grid-cell-like neural codes, serving as a schema for two-dimensional (2D) spaces. Yet it remains unclear how new experiences become aligned with this schema, especially in non-spatial contexts. Here, we show that hippocampal ripples - brief bursts of neuronal activity during rest - predict the emergence of grid-like codes in a novel 2D inference task. We recorded intracranial neuronal activity in 42 epilepsy patients as they learned rank relationships among feature objects (for example, objects differing in 'magic' or 'speed'). After learning, these objects were combined to form 'compounds' occupying a 2D conceptual space defined by two feature dimensions. During learning, hippocampal ripple activity increased during pauses between trials, suggesting that ripples integrated newly acquired information offline. Subsequently, ripple activity during post-learning rest predicted the later emergence of grid-like codes in the entorhinal cortex (EC) and medial prefrontal cortex (mPFC), a core region of the default mode network (DMN), when participants inferred unseen relationships among the compounds. Critically, coordination during rest between hippocampal ripples and DMN activity in the mPFC predicted participants' ability to infer complex relationships beyond direct memory retrieval. These findings provide the first direct evidence that hippocampal ripples, working with the DMN, align new experiences with a grid-like schema offline, transforming discrete learning events into structured knowledge that supports flexible and adaptive reasoning in human cognition. ### Competing Interest Statement The authors have declared no competing interest.

How do humans integrate fragmented experiences into a coherent structure for novel inferences? Although offline replay is proposed to reorganize memories, whether it constructs an integrated cognitive map remains unclear. Using magnetoencephalography, we tracked neural activity as participants learned one-dimensional, pairwise rank relationships that together formed a two-dimensional (2D) conceptual map, and then inferred unobserved relationships. Offline replay during rest integrated piecemeal memories into a 2D representation, predicting future inference accuracy. This offline replay and fast on-task replay during inference correlated with grid-cell-like code, representing a generalizable schema that minimized effortful online computations. In contrast, slow on-task replay focusing on trial-specific details, negatively correlated with grid-like codes and inference performance. Together, replay builds an efficient cognitive map offline, reducing reliance on deliberate computations online. ### Competing Interest Statement The authors have declared no competing interest.

Adaptive behavior in complex environments critically relies on the ability to appropriately link specific choices or actions to their outcomes. However, the neural mechanisms that support the ability to credit only those past choices believed to have caused the observed outcomes remain unclear. Here, we leverage multivariate pattern analyses of functional magnetic resonance imaging (fMRI) data and an adaptive learning task to shed light on the underlying neural mechanisms of such specific credit assignment. We find that the lateral orbitofrontal cortex (lOFC) and hippocampus (HC) code for the causal choice identity when credit needs to be assigned for choices that are separated from outcomes by a long delay, even when this delayed transition is punctuated by interim decisions. Further, we show when interim decisions must be made, learning is additionally supported by lateral frontopolar cortex (lFPC). Our results indicate that lFPC holds previous causal choices in a "pending" state until a relevant outcome is observed, and the fidelity of these representations predicts the fidelity of subsequent causal choice representations in lOFC and HC during credit assignment. Together, these results highlight the importance of the timely reinstatement of specific causes in lOFC and HC in learning choice-outcome relationships when delays and choices intervene, a critical component of real-world learning and decision making.

Piaget's theory emphasizes children develop structured knowledge schemas for assimilating new concepts, yet the neural mechanisms and their link to intelligence remain unclear. In 203 participants aged 8-25 years, we investigated how maturation of neural representations of a two-dimensional knowledge map supports inferential reasoning and assimilation. We found that grid-cell-like neural codes in the entorhinal cortex (EC) strengthen with age, forming structured representations in non-spatial conceptual spaces. This maturation is directly linked to improved inferential reasoning. These grid-like codes support the medial prefrontal cortex (mPFC) in encoding distance relationships between concepts. As participants assimilated new information, they integrated it into existing grid patterns in the EC. Furthermore, maturation of these neural codes predicts real-world intelligence measures, particularly in abstract reasoning. Our findings show that the development of non-spatial grid-like neural codes underpins inference and knowledge assimilation, providing a neural basis for cognitive development and linking cellular neuroscience with intelligence. ### Competing Interest Statement The authors have declared no competing interest.

Remembering events is crucial to intelligent behavior. Flexible memory retrieval requires a cognitive map and is supported by two key brain systems: hippocampal episodic memory (EM) and prefrontal working memory (WM). Although an understanding of EM is emerging, little is understood of WM beyond simple memory retrieval. We develop a mathematical theory relating the algorithms and representations of EM and WM by unveiling a duality between storing memories in synapses versus neural activity. This results in a formalism of prefrontal WM as structured, controllable neural subspaces (activity slots) representing dynamic cognitive maps without synaptic plasticity. Using neural networks, we elucidate differences, similarities, and trade-offs between the hippocampal and prefrontal algorithms. Lastly, we show that prefrontal representations in tasks from list learning to cue-dependent recall are unified as controllable activity slots. Our results unify frontal and temporal representations of memory and offer a new understanding for dynamic prefrontal representations of WM.

The prefrontal cortex is crucial for learning and decision-making. Classic reinforcement learning (RL) theories center on learning the expectation of potential rewarding outcomes and explain a wealth of neural data in the prefrontal cortex. Distributional RL, on the other hand, learns the full distribution of rewarding outcomes and better explains dopamine responses. In the present study, we show that distributional RL also better explains macaque anterior cingulate cortex neuronal responses, suggesting that it is a common mechanism for reward-guided learning.

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ABSTRACT To flexibly adapt to new situations, our brains must understand the regularities in the world, but also in our own patterns of behaviour. A wealth of findings is beginning to reveal the algorithms we use to map the outside world 1–6 . In contrast, the biological algorithms that map the complex structured behaviours we compose to reach our goals remain enigmatic. Here we reveal a neuronal implementation of an algorithm for mapping abstract behavioural structure and transferring it to new scenarios. We trained mice on many tasks which shared a common structure organising a sequence of goals, but differed in the specific goal locations. Animals discovered the underlying task structure, enabling zero-shot inferences on the first trial of new tasks. The activity of most neurons in the medial Frontal cortex tiled progress-to-goal, akin to how place cells map physical space. These “goal-progress cells” generalised, stretching and compressing their tiling to accommodate different goal distances. In contrast, progress along the overall sequence of goals was not encoded explicitly. Instead a subset of goal-progress cells was further tuned such that individual neurons fired with a fixed task-lag from a particular behavioural step. Together these cells implemented an algorithm that instantaneously encoded the entire sequence of future behavioural steps, and whose dynamics automatically retrieved the appropriate action at each step. These dynamics mirrored the abstract task structure both on-task and during offline sleep. Our findings suggest that goal-progress cells in the medial frontal cortex may be elemental building blocks of schemata that can be sculpted to represent complex behavioural structures.

Grid cells in rodent entorhinal cortex (EC) support a coordinate system for space, enabling robust memory and powerful flexibility in spatial behaviour. This coordinate system is abstract - with the same grid cells encoding position across different sensory environments; and hierarchical - with grid modules of increasing spatial scale occupying increasingly ventral locations in the EC. Recent theories suggest that a similar abstract coordinate system could offer the same benefits to general memories that are not sequences drawn from a 2D surface. Here we show that an abstract hierarchical coordinate system supports arbitrary sequences in the human medial temporal lobe (MTL). In single-unit recordings from MTL, we find abstract, coordinate-like coding of a simple sequential memory task. In an fMRI experiment with more complex hierarchical sequences, we discover an abstract hierarchical representation in EC: the coordinate representations at distinct levels in the hierarchy are arranged on an anatomical gradient along the EC's anterior-posterior axis, homologous to the ventro-dorsal axis in rodents. These results therefore mirror the anatomical gradient of grid cells in the rodent EC but now for arbitrary non-spatial sequences. Together they suggest that memories are scaffolded on a hierarchical coordinate system using common neuronal coding principles, aligned to preserved anatomy, across domains and species. ### Competing Interest Statement The authors have declared no competing interest.