@article {Sch{\o}yen2022.08.18.504379,
	title = {Coherently Remapping Toroidal Cells But Not Grid Cells are Responsible for Path Integration in Virtual Agents},
	journal = {BioRxiv},
	year = {2022},
	publisher = {Cold Spring Harbor Laboratory},
	abstract = {Animals employ a neural system to map physical environmental position to neural activity and encode allocentric location. Grid cells, proposedly a vital component of this system, form a population code of space by firing in characteristic tessellated triangles of locations. This population code remaps across environments and behavioural states, independently of specific sensory inputs, pointing to a substrate of standard computation across environments, which many speculate to be path integration. However, testing whether these cells are crucial for path integration is outside the scope of current experiments and calls for complementary methods, possibly given by computational models. Recently, normative artificial neural network models have shown that path integration and grid-cell-like activity can be found in recurrent neural networks (RNNs) trained to navigate in a simulated two-dimensional environment. Remarkably, the emergent spatial profile of these grid-like cells is similar to biological cell responses in that they set up a toroidal structure. Here, we extend the RNN normative model to multiple environments and show that cells that form the toroidal structure are crucial for path integration. However, cells selected through the grid cell score, a common defining property of grid cells, are much less important and comparable to randomly selected cells. Moreover, we show that the model can navigate multiple environments and that toroidal cells remap across environments in a biologically plausible way. Results demonstrate a causal relation between toroidal cells and path integration in virtual agents and propose a mechanism of remapping in grid cells based on remapping in place cells. The work is anticipated to impact both experimental and computational neuroscience and machine learning due to the methods employed and the evaluation of results. For example, we propose explicit experiments that can evaluate both the model{\textquoteright}s validity and the role of grid cells in navigation. Moreover, the model may elucidate how high-dimensional data is mapped to low-dimensional structures, possibly providing a substrate for interpolation.Competing Interest StatementThe authors have declared no competing interest.},
	doi = {10.1101/2022.08.18.504379},
	url = {https://www.biorxiv.org/content/early/2022/09/16/2022.08.18.504379},
	author = {Sch{\o}yen, Vemund and Markus Borud {Pettersen} and Holzhausen, Konstantin and Fyhn, Marianne and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@misc {43003,
	title = {Emergent Place Cells and Remapping in a Recurrent Neural Network Model},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Markus Borud {Pettersen} and Sch{\o}yen, Vemund and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@article {28486,
	title = {Inferring causal connectivity from pairwise recordings and optogenetics},
	journal = {BioRxiv},
	year = {2022},
	publisher = {Cold Spring Harbor Laboratory},
	abstract = {To study how the brain works mechanistically, neuroscientists want to quantify causal interactions between neurons, typically requiring perturbations. When using optogenetic interventions, multiple neurons are usually perturbed which produces a confound {\textendash} any of the stimulated neurons can have affected the postsynaptic neuron making it challenging to discern which of the neurons produced the causal effect. Here we show how such confounds produce large biases, and we explain how they can be reduced by combining instrumental variable (IV) and difference in differences (DiD) techniques from econometrics. The interaction between stimulation and the absolute refractory period of the neuron produces a weak, approximately random signal which can be exploited to estimate causal transmission probability. On simulated neural networks, we find that estimates using ideas from IV and DiD outperform na{\"\i}ve techniques suggesting that methods from causal inference can be useful when studying neural interactions.},
	keywords = {causal inference, connectivity, Neuroscience},
	author = {Lepper{\o}d, Mikkel and St{\"o}ber, Tristan and Hafting, Torkel and Fyhn, Marianne and Kording, Konrad}
}
@article {https://doi.org/10.48550/arxiv.2211.01236,
	title = {Isometric Representations in Neural Networks Improve Robustness},
	journal = {arxiv},
	year = {2022},
	publisher = {arXiv},
	keywords = {Cryptography and Security (cs.CR), FOS: Biological sciences, FOS: Computer and information sciences, Machine Learning (cs.LG), Neurons and Cognition (q-bio.NC)},
	doi = {10.48550/ARXIV.2211.01236},
	url = {https://arxiv.org/abs/2211.01236},
	author = {Beshkov, Kosio and Verhellen, Jonas and Lepper{\o}d, Mikkel}
}
@misc {43015,
	title = {Learning Flexibility in Parahippocampal Networks},
	year = {2022},
	address = {Federation of European Neuroscience Societies},
	author = {Nymoen, Ingeborg and Rogge, Frederik and Lepper{\o}d, Mikkel and Hafting, Torkel and Kristian Kinden {Lensj{\o}} and Fyhn, Marianne}
}
@misc {43002,
	title = {Manifold Propagation Through Neural Networks},
	year = {2022},
	address = {Federation of European Neuroscience Societies},
	author = {Bechkov, Constantin and Verhellen, Jonas and Lepper{\o}d, Mikkel}
}
@misc {43005,
	title = {Manifold propagation through recurrent neural networks},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Bechkov, Constantin and Verhellen, Jonas and Lepper{\o}d, Mikkel}
}
@misc {43001,
	title = {Model-based meta reinforcement learning for alchemy},
	year = {2022},
	address = {Federation of European Neuroscience Societies},
	author = {Homa Priya {Targopula} and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@misc {43007,
	title = {Navigating Multiple Environments with Emergent Grid Cell Remapping},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Sch{\o}yen, Vemund and Markus Borud {Pettersen} and Holzhausen, Konstantin and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@article {43000,
	title = {NeuroAI - A strategic opportunity for Norway and Europe},
	journal = {Nordic Machine Intelligence},
	volume = {2},
	year = {2022},
	month = {Mar-06-2022},
	publisher = {Nordic Machine Intelligence },
	doi = {10.5617/nmi.9950},
	url = {https://journals.uio.no/NMI/article/view/9950https://journals.uio.no/NMI/article/download/9950/8366https://journals.uio.no/NMI/article/download/9950/8366},
	author = {Nichele, Stefano and S{\ae}b{\o}, Solve and Pettersen, Klas and Lepper{\o}d, Mikkel}
}
@misc {43006,
	title = {Place and grid cell navigation in multiple environments},
	year = {2022},
	address = {Federation of European Neuroscience Societies},
	author = {Sch{\o}yen, Vemund and Markus Borud {Pettersen} and Holzhausen, Konstantin and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@misc {43008,
	title = {Robustness of neural networks trained with biologically inspired local learning rules},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Holzhausen, Konstantin and Lepper{\o}d, Mikkel and Malthe-S{\o}renssen, Anders}
}
@misc {43004,
	title = {On the Structural Sensitivity of the Successor Representation},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Rogge, Frederik and Malthe-S{\o}renssen, Anders and Fyhn, Marianne and Lepper{\o}d, Mikkel}
}
