{"id":{"repo_id":"edinburgh","oai_identifier":"oai:era.ed.ac.uk:1842/42924"},"canonical_url":"https://search.dev.ndltd.org/etd/edinburgh/oai:era.ed.ac.uk:1842/42924","repository":{"repo_id":"edinburgh","name":"University of Edinburgh","base_url":"https://era.ed.ac.uk/server/oai/request"},"display":{"title":"Mechanisms underlying spatial navigation","abstract":"How do our brains learn & remember locations and navigate towards them? Here I present three strands of work that address this general question. First, I investigate the information conveyed by grid cells, whose firing fields tile the environment in a hexagonal grid. In doing so, they are thought to provide a static map of space. Current models of navigation propose that this static grid cell map is used to support navigation behaviours. However, recent work shows that this grid map also conveys information about rewards and is deformed by environmental geometry, suggesting that grid cells provide more than just a static map of space. What other information do grid cells convey? Answering this is important for informing the development of models for spatial navigation. Recently, our experimental results suggest that firing fields of a grid cell appear to be influenced by head direction, and that each firing field has its own head direction preference. This surprising ‘local’ influence of head direction could be used by downstream networks to disambiguate points of view at various locations to aid in navigation. However, it was unclear if (1) existing models accounted for this field-level head direction influence, and (2) to what extent trajectory biases could cause spurious findings of head direction influence. I set out to address these questions by simulating existing grid cell models on experimentally recorded rodent trajectories. I found that existing models did not generate the experimentally observed head direction influence, suggesting that this property of grid cells was signal rather than noise, and that previous models could not account for it. Altogether, this informs the development of new grid cell readout models that can incorporate this newly found dynamic property of grid cells. Second, I focus on understanding how neural codes may support navigation towards goal locations. By recording from the brains of mice while they navigated to rewards in a virtual reality task, we discovered ramp-like neural codes. These codes increase or decrease their firing in a ramp-like manner towards or away from the reward location. These continuous codes were a surprising finding and not predicted by existing models of spatial navigation. To gain a foothold in understanding these neurons, I developed an artificial version of the virtual reality task, posed it as a reinforcement learning problem, and trained artificial recurrent neural networks (RNNs) to solve it. Surprisingly, I also found that ramp-like neural activity emerged in the RNNs, suggesting similar underlying mechanisms and providing a testbed for testing hypotheses about the ramp cells. One hypothesis is that ramp cells are an epiphenomenon or a holdover from learning and not used during task execution. To address this, I perturbed populations of ramp and non-ramp cells, finding that ramp cells were in fact important for performing the behaviour. A further hypothesis is that ramp cells provide an easily decodable representation for downstream areas to ‘read out’. I tested this by performing perturbations of RNN readout, finding that ramp cells were important for location decoding, whereas non-ramp cells were not important. Overall these characterise the functional roles of ramp cells, providing avenues for experiments and also adds to the literature showing convergence between artificial and biological networks in goal-directed navigation. Third, having developed RNNs that solve the task with biologically plausible activity, I set out to understand how these networks solve the task. There is no clear roadmap for understanding how artificial (or even biological) brains carry out computations, so an additional outcome of this work is a case study demonstrating how such a circuit can be dissected. By using a combination of neuroscience inspired methods, such as artificial optogenetics, artificial electrophysiology, and task learning/generalisation, combined with artificial-exclusive methods such as fixed point analysis and machine learning attribution methods, I extract a set of computational principles that are used to solve the task. First I found that the population activity evolved across a low-dimensional manifold that represented the virtual track. Noisy velocity inputs pushed the trajectory along the manifold, enabling the tracking of location. Using fixed-point analysis I found that the manifold was segmented by input-dependent fixed points, which allowed path integration error to be reset by anchoring. An input-dependent continuous attractor was also present, allowing the current location to be remembered while the agent stopped. These dynamical elements allowed the current location on the track to be represented on the manifold. A downstream decoder region was then able to decode when the trajectory was in the ‘reward’ region, causing the agent to stop in the correct location, enabling goal-directed navigation. Next I sought to understand how and if such dynamics could support generalisation by training these networks on additional reward zones. I found that networks were able to rapidly learn additional reward zones, demonstrating generalisation abilities also found in humans. To understand this, I examined the population activity and found that surprisingly the same manifolds were used across reward zones, but instead the traversal rate across it had been altered to match the new reward zones. Such a mechanism was implemented by influencing RNN neurons in a systematic way that varied across a low-dimensional subspace. These results show that low-dimensional manifolds can act as schemas representing a spatial environment, and that these schemas can support generalisation by altering the rate of velocity integration along them. Such a mechanism could be implemented by neuromodulatory activity in the retrohippocampal cortices where we discovered ramp cells. Together these results contribute to our understanding of goal-directed navigation and spatial memory. First by contributing to showing that grid cell representations are much richer than originally thought, and by contributing to establishing a biophysical basis for this. Second, I find that discrete neural codes are not the only way to solve spatial navigation tasks in RNNs, and that RNNs generate similar neural activity to biological brains during spatial navigation. Finally I show how spatial memory and generalisation can be implemented, showing how population dynamics can support spatial cognition and implement schemas.","abstract_html":"How do our brains learn & remember locations and navigate towards them? Here I present three strands of work that address this general question. First, I investigate the information conveyed by grid cells, whose firing fields tile the environment in a hexagonal grid. In doing so, they are thought to provide a static map of space. Current models of navigation propose that this static grid cell map is used to support navigation behaviours. However, recent work shows that this grid map also conveys information about rewards and is deformed by environmental geometry, suggesting that grid cells provide more than just a static map of space. What other information do grid cells convey? Answering this is important for informing the development of models for spatial navigation. Recently, our experimental results suggest that firing fields of a grid cell appear to be influenced by head direction, and that each firing field has its own head direction preference. This surprising ‘local’ influence of head direction could be used by downstream networks to disambiguate points of view at various locations to aid in navigation. However, it was unclear if (1) existing models accounted for this field-level head direction influence, and (2) to what extent trajectory biases could cause spurious findings of head direction influence. I set out to address these questions by simulating existing grid cell models on experimentally recorded rodent trajectories. I found that existing models did not generate the experimentally observed head direction influence, suggesting that this property of grid cells was signal rather than noise, and that previous models could not account for it. Altogether, this informs the development of new grid cell readout models that can incorporate this newly found dynamic property of grid cells. Second, I focus on understanding how neural codes may support navigation towards goal locations. By recording from the brains of mice while they navigated to rewards in a virtual reality task, we discovered ramp-like neural codes. These codes increase or decrease their firing in a ramp-like manner towards or away from the reward location. These continuous codes were a surprising finding and not predicted by existing models of spatial navigation. To gain a foothold in understanding these neurons, I developed an artificial version of the virtual reality task, posed it as a reinforcement learning problem, and trained artificial recurrent neural networks (RNNs) to solve it. Surprisingly, I also found that ramp-like neural activity emerged in the RNNs, suggesting similar underlying mechanisms and providing a testbed for testing hypotheses about the ramp cells. One hypothesis is that ramp cells are an epiphenomenon or a holdover from learning and not used during task execution. To address this, I perturbed populations of ramp and non-ramp cells, finding that ramp cells were in fact important for performing the behaviour. A further hypothesis is that ramp cells provide an easily decodable representation for downstream areas to ‘read out’. I tested this by performing perturbations of RNN readout, finding that ramp cells were important for location decoding, whereas non-ramp cells were not important. Overall these characterise the functional roles of ramp cells, providing avenues for experiments and also adds to the literature showing convergence between artificial and biological networks in goal-directed navigation. Third, having developed RNNs that solve the task with biologically plausible activity, I set out to understand how these networks solve the task. There is no clear roadmap for understanding how artificial (or even biological) brains carry out computations, so an additional outcome of this work is a case study demonstrating how such a circuit can be dissected. By using a combination of neuroscience inspired methods, such as artificial optogenetics, artificial electrophysiology, and task learning/generalisation, combined with artificial-exclusive methods such as fixed point analysis and machine learning attribution methods, I extract a set of computational principles that are used to solve the task. First I found that the population activity evolved across a low-dimensional manifold that represented the virtual track. Noisy velocity inputs pushed the trajectory along the manifold, enabling the tracking of location. Using fixed-point analysis I found that the manifold was segmented by input-dependent fixed points, which allowed path integration error to be reset by anchoring. An input-dependent continuous attractor was also present, allowing the current location to be remembered while the agent stopped. These dynamical elements allowed the current location on the track to be represented on the manifold. A downstream decoder region was then able to decode when the trajectory was in the ‘reward’ region, causing the agent to stop in the correct location, enabling goal-directed navigation. Next I sought to understand how and if such dynamics could support generalisation by training these networks on additional reward zones. I found that networks were able to rapidly learn additional reward zones, demonstrating generalisation abilities also found in humans. To understand this, I examined the population activity and found that surprisingly the same manifolds were used across reward zones, but instead the traversal rate across it had been altered to match the new reward zones. Such a mechanism was implemented by influencing RNN neurons in a systematic way that varied across a low-dimensional subspace. These results show that low-dimensional manifolds can act as schemas representing a spatial environment, and that these schemas can support generalisation by altering the rate of velocity integration along them. Such a mechanism could be implemented by neuromodulatory activity in the retrohippocampal cortices where we discovered ramp cells. Together these results contribute to our understanding of goal-directed navigation and spatial memory. First by contributing to showing that grid cell representations are much richer than originally thought, and by contributing to establishing a biophysical basis for this. Second, I find that discrete neural codes are not the only way to solve spatial navigation tasks in RNNs, and that RNNs generate similar neural activity to biological brains during spatial navigation. Finally I show how spatial memory and generalisation can be implemented, showing how population dynamics can support spatial cognition and implement schemas.","abstract_has_math":false,"creators":["Hawes, Ian"],"institution":"The University of Edinburgh","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Nolan, Matthew","Hennig, Matthias","Spires-Jones, Tara","Price, David"],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-12-19","date_published":"2024-12-19","updated_at":"2026-07-24T02:14:15Z","subjects":["spatial navigation","hexagonal gri","environmental geometry","head direction","field-level head direction influence","recurrent neural networks (RNNs)","low-dimensional subspace","low-dimensional manifolds","spatial environment","spatial memory"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://dx.doi.org/10.7488/era/5477"],"render_values":[{"text":"http://dx.doi.org/10.7488/era/5477","href":"http://dx.doi.org/10.7488/era/5477","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/1842/42924","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Nolan, Matthew","Hennig, Matthias","Spires-Jones, Tara","Price, David"]},{"key":"dc:creator","label":"Author","values":["Hawes, Ian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-12-19T15:40:36Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-12-19T15:40:36Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-12-19"]},{"key":"dc:publisher","label":"Institution","values":["The University of Edinburgh"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["spatial navigation","hexagonal gri","environmental geometry","head direction","field-level head direction influence","recurrent neural networks (RNNs)","low-dimensional subspace","low-dimensional manifolds","spatial environment","spatial memory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1842/42924","http://dx.doi.org/10.7488/era/5477"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["How do our brains learn & remember locations and navigate towards them? Here I present three strands of work that address this general question. First, I investigate the information conveyed by grid cells, whose firing fields tile the environment in a hexagonal grid. In doing so, they are thought to provide a static map of space. Current models of navigation propose that this static grid cell map is used to support navigation behaviours. However, recent work shows that this grid map also conveys information about rewards and is deformed by environmental geometry, suggesting that grid cells provide more than just a static map of space. What other information do grid cells convey? Answering this is important for informing the development of models for spatial navigation. Recently, our experimental results suggest that firing fields of a grid cell appear to be influenced by head direction, and that each firing field has its own head direction preference. This surprising ‘local’ influence of head direction could be used by downstream networks to disambiguate points of view at various locations to aid in navigation. However, it was unclear if (1) existing models accounted for this field-level head direction influence, and (2) to what extent trajectory biases could cause spurious findings of head direction influence. I set out to address these questions by simulating existing grid cell models on experimentally recorded rodent trajectories. I found that existing models did not generate the experimentally observed head direction influence, suggesting that this property of grid cells was signal rather than noise, and that previous models could not account for it. Altogether, this informs the development of new grid cell readout models that can incorporate this newly found dynamic property of grid cells. Second, I focus on understanding how neural codes may support navigation towards goal locations. By recording from the brains of mice while they navigated to rewards in a virtual reality task, we discovered ramp-like neural codes. These codes increase or decrease their firing in a ramp-like manner towards or away from the reward location. These continuous codes were a surprising finding and not predicted by existing models of spatial navigation. To gain a foothold in understanding these neurons, I developed an artificial version of the virtual reality task, posed it as a reinforcement learning problem, and trained artificial recurrent neural networks (RNNs) to solve it. Surprisingly, I also found that ramp-like neural activity emerged in the RNNs, suggesting similar underlying mechanisms and providing a testbed for testing hypotheses about the ramp cells. One hypothesis is that ramp cells are an epiphenomenon or a holdover from learning and not used during task execution. To address this, I perturbed populations of ramp and non-ramp cells, finding that ramp cells were in fact important for performing the behaviour. A further hypothesis is that ramp cells provide an easily decodable representation for downstream areas to ‘read out’. I tested this by performing perturbations of RNN readout, finding that ramp cells were important for location decoding, whereas non-ramp cells were not important. Overall these characterise the functional roles of ramp cells, providing avenues for experiments and also adds to the literature showing convergence between artificial and biological networks in goal-directed navigation. Third, having developed RNNs that solve the task with biologically plausible activity, I set out to understand how these networks solve the task. There is no clear roadmap for understanding how artificial (or even biological) brains carry out computations, so an additional outcome of this work is a case study demonstrating how such a circuit can be dissected. By using a combination of neuroscience inspired methods, such as artificial optogenetics, artificial electrophysiology, and task learning/generalisation, combined with artificial-exclusive methods such as fixed point analysis and machine learning attribution methods, I extract a set of computational principles that are used to solve the task. First I found that the population activity evolved across a low-dimensional manifold that represented the virtual track. Noisy velocity inputs pushed the trajectory along the manifold, enabling the tracking of location. Using fixed-point analysis I found that the manifold was segmented by input-dependent fixed points, which allowed path integration error to be reset by anchoring. An input-dependent continuous attractor was also present, allowing the current location to be remembered while the agent stopped. These dynamical elements allowed the current location on the track to be represented on the manifold. A downstream decoder region was then able to decode when the trajectory was in the ‘reward’ region, causing the agent to stop in the correct location, enabling goal-directed navigation. Next I sought to understand how and if such dynamics could support generalisation by training these networks on additional reward zones. I found that networks were able to rapidly learn additional reward zones, demonstrating generalisation abilities also found in humans. To understand this, I examined the population activity and found that surprisingly the same manifolds were used across reward zones, but instead the traversal rate across it had been altered to match the new reward zones. Such a mechanism was implemented by influencing RNN neurons in a systematic way that varied across a low-dimensional subspace. These results show that low-dimensional manifolds can act as schemas representing a spatial environment, and that these schemas can support generalisation by altering the rate of velocity integration along them. Such a mechanism could be implemented by neuromodulatory activity in the retrohippocampal cortices where we discovered ramp cells. Together these results contribute to our understanding of goal-directed navigation and spatial memory. First by contributing to showing that grid cell representations are much richer than originally thought, and by contributing to establishing a biophysical basis for this. Second, I find that discrete neural codes are not the only way to solve spatial navigation tasks in RNNs, and that RNNs generate similar neural activity to biological brains during spatial navigation. Finally I show how spatial memory and generalisation can be implemented, showing how population dynamics can support spatial cognition and implement schemas."]},{"key":"dc:title","label":"Title","values":["Mechanisms underlying spatial navigation"]}]}],"canonical_facts":{"dc:contributor.advisor":["Nolan, Matthew","Hennig, Matthias","Spires-Jones, Tara","Price, David"],"dc:creator":["Hawes, Ian"],"dc:date.accessioned":["2024-12-19T15:40:36Z"],"dc:date.available":["2024-12-19T15:40:36Z"],"dc:date.issued":["2024-12-19"],"dc:description.abstract":["How do our brains learn & remember locations and navigate towards them? Here I present three strands of work that address this general question. First, I investigate the information conveyed by grid cells, whose firing fields tile the environment in a hexagonal grid. In doing so, they are thought to provide a static map of space. Current models of navigation propose that this static grid cell map is used to support navigation behaviours. However, recent work shows that this grid map also conveys information about rewards and is deformed by environmental geometry, suggesting that grid cells provide more than just a static map of space. What other information do grid cells convey? Answering this is important for informing the development of models for spatial navigation. Recently, our experimental results suggest that firing fields of a grid cell appear to be influenced by head direction, and that each firing field has its own head direction preference. This surprising ‘local’ influence of head direction could be used by downstream networks to disambiguate points of view at various locations to aid in navigation. However, it was unclear if (1) existing models accounted for this field-level head direction influence, and (2) to what extent trajectory biases could cause spurious findings of head direction influence. I set out to address these questions by simulating existing grid cell models on experimentally recorded rodent trajectories. I found that existing models did not generate the experimentally observed head direction influence, suggesting that this property of grid cells was signal rather than noise, and that previous models could not account for it. Altogether, this informs the development of new grid cell readout models that can incorporate this newly found dynamic property of grid cells. Second, I focus on understanding how neural codes may support navigation towards goal locations. By recording from the brains of mice while they navigated to rewards in a virtual reality task, we discovered ramp-like neural codes. These codes increase or decrease their firing in a ramp-like manner towards or away from the reward location. These continuous codes were a surprising finding and not predicted by existing models of spatial navigation. To gain a foothold in understanding these neurons, I developed an artificial version of the virtual reality task, posed it as a reinforcement learning problem, and trained artificial recurrent neural networks (RNNs) to solve it. Surprisingly, I also found that ramp-like neural activity emerged in the RNNs, suggesting similar underlying mechanisms and providing a testbed for testing hypotheses about the ramp cells. One hypothesis is that ramp cells are an epiphenomenon or a holdover from learning and not used during task execution. To address this, I perturbed populations of ramp and non-ramp cells, finding that ramp cells were in fact important for performing the behaviour. A further hypothesis is that ramp cells provide an easily decodable representation for downstream areas to ‘read out’. I tested this by performing perturbations of RNN readout, finding that ramp cells were important for location decoding, whereas non-ramp cells were not important. Overall these characterise the functional roles of ramp cells, providing avenues for experiments and also adds to the literature showing convergence between artificial and biological networks in goal-directed navigation. Third, having developed RNNs that solve the task with biologically plausible activity, I set out to understand how these networks solve the task. There is no clear roadmap for understanding how artificial (or even biological) brains carry out computations, so an additional outcome of this work is a case study demonstrating how such a circuit can be dissected. By using a combination of neuroscience inspired methods, such as artificial optogenetics, artificial electrophysiology, and task learning/generalisation, combined with artificial-exclusive methods such as fixed point analysis and machine learning attribution methods, I extract a set of computational principles that are used to solve the task. First I found that the population activity evolved across a low-dimensional manifold that represented the virtual track. Noisy velocity inputs pushed the trajectory along the manifold, enabling the tracking of location. Using fixed-point analysis I found that the manifold was segmented by input-dependent fixed points, which allowed path integration error to be reset by anchoring. An input-dependent continuous attractor was also present, allowing the current location to be remembered while the agent stopped. These dynamical elements allowed the current location on the track to be represented on the manifold. A downstream decoder region was then able to decode when the trajectory was in the ‘reward’ region, causing the agent to stop in the correct location, enabling goal-directed navigation. Next I sought to understand how and if such dynamics could support generalisation by training these networks on additional reward zones. I found that networks were able to rapidly learn additional reward zones, demonstrating generalisation abilities also found in humans. To understand this, I examined the population activity and found that surprisingly the same manifolds were used across reward zones, but instead the traversal rate across it had been altered to match the new reward zones. Such a mechanism was implemented by influencing RNN neurons in a systematic way that varied across a low-dimensional subspace. These results show that low-dimensional manifolds can act as schemas representing a spatial environment, and that these schemas can support generalisation by altering the rate of velocity integration along them. Such a mechanism could be implemented by neuromodulatory activity in the retrohippocampal cortices where we discovered ramp cells. Together these results contribute to our understanding of goal-directed navigation and spatial memory. First by contributing to showing that grid cell representations are much richer than originally thought, and by contributing to establishing a biophysical basis for this. Second, I find that discrete neural codes are not the only way to solve spatial navigation tasks in RNNs, and that RNNs generate similar neural activity to biological brains during spatial navigation. Finally I show how spatial memory and generalisation can be implemented, showing how population dynamics can support spatial cognition and implement schemas."],"dc:identifier.uri":["https://hdl.handle.net/1842/42924","http://dx.doi.org/10.7488/era/5477"],"dc:language.iso":["en"],"dc:publisher":["The University of Edinburgh"],"dc:subject":["spatial navigation","hexagonal gri","environmental geometry","head direction","field-level head direction influence","recurrent neural networks (RNNs)","low-dimensional subspace","low-dimensional manifolds","spatial environment","spatial memory"],"dc:title":["Mechanisms underlying spatial navigation"],"dc:type":["Thesis or Dissertation"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD Doctor of Philosophy"]},"updated_at":"2026-07-24T02:14:15Z"}