Biology subjects

Pettersen, M.

Publications and source records attributed to Pettersen, M..

3 recordsLinked to original sources

bioRxiv2025

Exponential Map Models as an Interpretable Framework for Generating Neural Spatial Representations

AO_SCPLOWBSTRACTC_SCPLOWA fundamental challenge in neuroscience and AI is understanding how physical space is mapped into neural representations. While artificial neural networks can generate brain-like spatial representations, such as place and grid cells, their "black-box" nature makes it difficult to determine if these representations arise as general solutions or as artifacts of a chosen architecture, objective function, or training protocol. Critically, these models offer no guarantee that learned solutions for core navigational tasks, like path integration (updating position from self-motion), will generalize beyond their training data. To address these challenges, we introduce a first-principles framework based on an exponential map model. Instead of using deep networks or gradient optimization, the presented model uses generator matrices to map physical locations into neural representations through the matrix exponential, creating a transparent framework that allows us to identify several exact algebraic conditions underlying key properties of neural maps. We show that path invariance (ensuring location representations are independent of traversal route) is achieved if the generators commute, while translational invariance (maintaining consistent spatial relationships across locations) demands generators producing orthogonal transformations. We also show that preserving the metric of flat space requires the eigenvalues of the generator matrices to form sets of roots of unity. Finally, we demonstrate that the proposed framework constructs diverse biologically relevant spatial tuning, including place cells, grid cells, and context-dependent remapping. The framework we propose thus offers a transparent, theoretically-grounded alternative to "black-box" models, revealing the exact conditions required for a coherent neural map of space.

neuroscience↗

bioRxiv2024

Self-Supervised Grid Cells Without Path Integration

Grid cells, found in the medial Entorhinal Cortex, are known for their regular spatial firing patterns. These cells have been proposed as the neural solution to a range of computational tasks, from performing path integration, to serving as a metric for space. Their exact function, however, remains fiercely debated. In this work, we explore the consequences of demanding distance preservation over small spatial scales in networks subject to a capacity constraint. We consider two distinct self-supervised models, a feedforward network that learns to solve a purely spatial encoding task, and a recurrent network that solves the same problem during path integration. We find that this task leads to the emergence of highly grid cell-like representations in both networks. However, the recurrent network also features units with band-like representations. We subsequently prune velocity inputs to subsets of recurrent units, and find that their grid score is negatively correlated with path integration contribution. Thus, grid cells emerge without path integration in the feedforward network, and they appear substantially less important than band cells for path integration in the recurrent network. Our work provides a minimal model for learning grid-like spatial representations, and questions the role of grid cells as neural path integrators. Instead, it seems that distance preservation and high population capacity is a more likely candidate task for learning grid cells in artificial neural networks.

neuroscience↗

bioRxiv2024

Learning Conjunctive Representations

Hippocampal place cells are known for their spatially selective firing patterns, which has led to the suggestion that they encode an animals location. However, place cells also respond to contextual cues, such as smell. Furthermore, they have the ability to remap, wherein the firing fields and rates of cells change in response to environmental changes. How place cell responses emerge, and how these representations remap is not fully understood. In this work, we propose a similarity-based objective function that translates proximity in space, to proximity in representation. We show that a neural network trained to minimize the proposed objective learns place-like representations. We also show that the proposed objective is trivially extended to include other sources of information, such as context information, in the same way. When trained to encode multiple contexts, networks learn distinct representations, exhibiting remapping behaviors between contexts. The proposed objective is invariant to orthogonal transformations. Such transformations of the original trained representation (e.g. rotations), therefore yield new representations distinct from the original, without explicit relearning, akin to remapping. Our findings shed new light on the formation and encoding properties of place cells, and also demonstrate an interesting case of representational reuse.

neuroscience↗