Testing geometric representation hypotheses from simulated place cell
recordings
- URL: http://arxiv.org/abs/2211.09096v1
- Date: Wed, 16 Nov 2022 18:29:17 GMT
- Title: Testing geometric representation hypotheses from simulated place cell
recordings
- Authors: Thibault Niederhauser, Adam Lester, Nina Miolane, Khanh Dao Duc, Manu
S. Madhav
- Abstract summary: Hippocampal place cells can encode spatial locations of an animal in physical or task-relevant spaces.
We simulated place cell populations that encoded either Euclidean- or graph-based positions of a rat navigating to goal nodes in a maze with a graph topology.
- Score: 3.1498833540989413
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: Hippocampal place cells can encode spatial locations of an animal in physical
or task-relevant spaces. We simulated place cell populations that encoded
either Euclidean- or graph-based positions of a rat navigating to goal nodes in
a maze with a graph topology, and used manifold learning methods such as UMAP
and Autoencoders (AE) to analyze these neural population activities. The
structure of the latent spaces learned by the AE reflects their true geometric
structure, while PCA fails to do so and UMAP is less robust to noise. Our
results support future applications of AE architectures to decipher the
geometry of spatial encoding in the brain.
Related papers
- Riemannian Geometry for the classification of brain states with intracortical brain-computer interfaces [3.0026377736031846]
We propose a new method for brain decoding using invasive electrophysiological recordings.
The method achieves a superior mean F1 macro-averaged score across different channel configurations.
The geometric framework reveals distinct spatial contributions of brain regions across varying brain states.
arXiv Detail & Related papers (2025-04-07T22:11:59Z) - A Grid Cell-Inspired Structured Vector Algebra for Cognitive Maps [4.498459787490856]
The entorhinal-hippocampal formation is the mammalian brain's navigation system, encoding both physical and abstract spaces via grid cells.
Here, we propose a mechanistic model for versatile information processing in the entorhinal-hippocampal formation inspired by CANs and Vector Architectures (VSAs)
The novel grid-cell VSA model employs a spatially structured encoding scheme with 3D modules mimicking the discrete scales and orientations of grid cell modules.
arXiv Detail & Related papers (2025-03-11T16:45:52Z) - Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds [18.156807299614503]
We introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines manifold learning with generative modeling.
GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.
arXiv Detail & Related papers (2024-10-16T17:53:26Z) - Geometric Inductive Biases of Deep Networks: The Role of Data and Architecture [22.225213114532533]
We argue that when training a neural network, the input space curvature remains invariant under transformation determined by its architecture.
We show that in cases where the average geometry is low-rank (such as in a ResNet), the geometry only changes in a subset of the input space.
arXiv Detail & Related papers (2024-10-15T19:46:09Z) - Enforcing 3D Topological Constraints in Composite Objects via Implicit Functions [60.56741715207466]
Medical applications often require accurate 3D representations of complex organs with multiple parts, such as the heart and spine.
This paper introduces a novel approach to enforce topological constraints in 3D object reconstruction using deep implicit signed distance functions.
We propose a sampling-based technique that effectively checks and enforces topological constraints between 3D shapes by evaluating signed distances at randomly sampled points throughout the volume.
arXiv Detail & Related papers (2023-07-16T10:07:15Z) - Evaluating the Effectiveness of Large Language Models in Representing
Textual Descriptions of Geometry and Spatial Relations [2.8935588665357086]
This research focuses on assessing the ability of large language models (LLMs) in representing geometries and their spatial relations.
We utilize LLMs including GPT-2 and BERT to encode the well-known text (WKT) format of geometries and then feed their embeddings into classifiers and regressors.
Experiments demonstrate that while the LLMs-generated embeddings can preserve geometry types and capture some spatial relations (up to 73% accuracy), challenges remain in estimating numeric values and retrieving spatially related objects.
arXiv Detail & Related papers (2023-07-05T03:50:08Z) - Fast Marching Energy CNN [5.392025723672817]
We introduce a new method by generating isotropic Riemannian metrics adapted to a problem using CNN.
We then apply this idea to the segmentation of brain tumours as unit balls for the geodesic distance computed with the metric potential output by a CNN.
We show that geodesic distance modules can be used to achieve state-of-the-art performances while ensuring geometrical and/or topological properties.
arXiv Detail & Related papers (2023-06-28T11:24:51Z) - Exploring Data Geometry for Continual Learning [64.4358878435983]
We study continual learning from a novel perspective by exploring data geometry for the non-stationary stream of data.
Our method dynamically expands the geometry of the underlying space to match growing geometric structures induced by new data.
Experiments show that our method achieves better performance than baseline methods designed in Euclidean space.
arXiv Detail & Related papers (2023-04-08T06:35:25Z) - GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided
Distance Representation [73.77505964222632]
We present a learning-based method, namely GeoUDF, to tackle the problem of reconstructing a discrete surface from a sparse point cloud.
To be specific, we propose a geometry-guided learning method for UDF and its gradient estimation.
To extract triangle meshes from the predicted UDF, we propose a customized edge-based marching cube module.
arXiv Detail & Related papers (2022-11-30T06:02:01Z) - Conformal Isometry of Lie Group Representation in Recurrent Network of
Grid Cells [52.425628028229156]
We study the properties of grid cells using recurrent network models.
We focus on a simple non-linear recurrent model that underlies the continuous attractor neural networks of grid cells.
arXiv Detail & Related papers (2022-10-06T05:26:49Z) - Intrinsic dimension estimation for discrete metrics [65.5438227932088]
In this letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces.
We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting.
This suggests that evolutive pressure acts on a low-dimensional manifold despite the high-dimensionality of sequences' space.
arXiv Detail & Related papers (2022-07-20T06:38:36Z) - A singular Riemannian geometry approach to Deep Neural Networks II.
Reconstruction of 1-D equivalence classes [78.120734120667]
We build the preimage of a point in the output manifold in the input space.
We focus for simplicity on the case of neural networks maps from n-dimensional real spaces to (n - 1)-dimensional real spaces.
arXiv Detail & Related papers (2021-12-17T11:47:45Z) - Neural Topological SLAM for Visual Navigation [112.73876869904]
We design topological representations for space that leverage semantics and afford approximate geometric reasoning.
We describe supervised learning-based algorithms that can build, maintain and use such representations under noisy actuation.
arXiv Detail & Related papers (2020-05-25T17:56:29Z) - Cortical surface registration using unsupervised learning [8.57142014602892]
Non-rigid cortical registration is an important and challenging task due to the geometric complexity of the human cortex.
Recent learning-based methods to surfaces yields poor results due to distortions introduced by projecting a sphere to a 2D plane.
We present SphereMorph, a diffeomorphic registration framework for cortical surfaces using deep networks that addresses these issues.
arXiv Detail & Related papers (2020-04-09T15:59:13Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.