spostrzeżenie - Computational neuroscience - # Learning Grid Cell Representations through Predictive Coding

Predictive Coding Enables Biologically Plausible Learning of Grid Cells in the Medial Entorhinal Cortex

Q: How can the multi-modularity of grid cells, with different spatial scales, be captured by predictive coding networks?

The multi-modularity of grid cells, characterized by their ability to represent different spatial scales, can be effectively captured by predictive coding networks (PCNs) through the incorporation of hierarchical structures and varying degrees of sparsity in the latent representations. In the context of grid cells, multi-modularity refers to the presence of grid cells that exhibit different firing patterns and spatial scales, which are essential for navigating complex environments. To achieve this, PCNs can be designed with multiple layers, where each layer is responsible for capturing different spatial frequencies or scales of the input space. By adjusting the parameters of the loss function, such as the sparsity constraints and the non-negativity conditions, the network can learn to represent a range of grid patterns. For instance, a PCN can be trained with varying levels of input resolution or by using different types of place cell encodings, such as difference-of-softmaxed-Gaussian (DoS) curves, which have been shown to yield hexagonal grid representations. Moreover, the use of Hebbian learning rules within the PCN framework allows for the emergence of grid cells that are sensitive to the spatial context, enabling the network to adaptively learn grid patterns that correspond to the agent's movement and environmental features. This adaptability is crucial for capturing the multi-scale nature of grid cells, as it allows the network to form representations that are not only hexagonal but also modulated by the spatial dynamics of the environment.

Q: What are the potential limitations of predictive coding in modeling other spatial representations, such as place cells, beyond grid cells?

While predictive coding offers a promising framework for modeling grid cells, it may face limitations when applied to other spatial representations, such as place cells. One significant challenge is the inherent nature of place cell firing, which is often more discrete and location-specific compared to the continuous and periodic firing patterns of grid cells. Place cells are known to activate in response to specific locations in the environment, and their representations may not easily emerge from the predictive coding framework, which typically emphasizes continuous representations and error minimization. Additionally, the reliance on local computations and Hebbian plasticity in predictive coding networks may restrict the ability to capture the complex interactions and dynamics observed in place cell networks. Place cells often exhibit a rich set of temporal dynamics, including phase precession and remapping, which may not be adequately modeled by the static or semi-static nature of predictive coding. Furthermore, the generalizability of the predictive coding framework to different types of spatial tasks, such as those requiring rapid updates or integration of multiple sensory modalities, remains uncertain. While predictive coding has shown success in modeling visual representations, its application to the dynamic and multifaceted nature of spatial navigation and memory formation may require further refinement and adaptation of the underlying algorithms.

Q: Could the predictive coding framework provide insights into the interactions between the entorhinal cortex and hippocampus during spatial navigation and memory formation?

Yes, the predictive coding framework can provide valuable insights into the interactions between the entorhinal cortex (EC) and hippocampus during spatial navigation and memory formation. The EC is known to play a crucial role in integrating spatial information and relaying it to the hippocampus, where memory formation occurs. By modeling these interactions through predictive coding, researchers can explore how the EC encodes spatial predictions and how these predictions influence hippocampal activity. In the context of spatial navigation, predictive coding can elucidate how grid cells in the EC generate predictions about an agent's position based on its movement and environmental cues. These predictions can then be compared to the actual sensory inputs received by place cells in the hippocampus, leading to the formation of error signals that drive learning and memory consolidation. This error-driven learning mechanism aligns with the principles of predictive coding, where discrepancies between predicted and actual inputs are minimized to refine the internal model of the environment. Moreover, the framework can help explain the bidirectional connectivity between the EC and hippocampus, as it allows for the exchange of predictive signals and error corrections. This interaction is essential for updating spatial representations and facilitating memory retrieval. By employing predictive coding, researchers can investigate how the EC's grid cell activity influences the firing patterns of place cells and how these interactions contribute to the overall cognitive map used for navigation and memory tasks. In summary, the predictive coding framework not only enhances our understanding of grid cell emergence but also provides a robust model for exploring the intricate dynamics between the entorhinal cortex and hippocampus, shedding light on the neural mechanisms underlying spatial navigation and memory formation.

Główne pojęcia

Predictive coding, a biologically plausible learning rule, can train neural networks to develop hexagonal grid cell representations from spatial inputs, providing a novel and plausible perspective on the learning mechanisms underlying grid cells.

Streszczenie

This paper investigates the ability of predictive coding networks (PCNs) to learn grid cell representations, which are observed in the medial entorhinal cortex (MEC) of the mammalian brain and are thought to support spatial navigation and abstract computations.

The key findings are:

A simple, 2-layer sparse and non-negative PCN can develop hexagonal grid cell-like latent representations when trained on static place cell inputs, similar to the grid cells observed experimentally.
A temporal extension of PCN, called temporal predictive coding network (tPCN), can also develop grid cell-like representations when trained on path integration tasks, comparable to the grid cells learned by recurrent neural networks (RNNs) trained with backpropagation through time (BPTT).
The authors provide an analytical understanding of why tPCN can learn grid cells, by showing that its Hebbian learning rule implicitly approximates truncated BPTT, avoiding the need for full BPTT as in RNNs.
The authors demonstrate the robustness of grid cell learning in tPCN by varying architectural choices, including the place cell encoding, activation functions, environment size, and the presence of velocity inputs. They find that grid cells can emerge even without velocity inputs, suggesting that path integration is not a sufficient condition for grid cell formation.

Overall, this work presents predictive coding as a biologically plausible learning rule that can account for the emergence of grid cells in the MEC, extending the predictive coding theory to spatial representations in the hippocampal formation. The findings offer a novel understanding of how a unified learning algorithm can be employed by different brain regions to represent diverse inputs.

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arxiv.org

Statystyki

The root mean square error (RMSE) between the decoded and ground-truth 2D positions in the path integration task.
The grid score, a metric commonly used to quantify the hexagonal firing pattern of grid cells.

Cytaty

"Grid cells in the medial entorhinal cortex (MEC) of the mammalian brain exhibit a strikingly regular hexagonal firing field over space."
"Although various computational models, including those based on artificial neural networks, have been proposed to explain the formation of grid cells, the process through which the MEC circuit learns to develop grid cells remains unclear."
"Our work therefore offers a novel and biologically plausible perspective on the learning mechanisms underlying grid cells. Moreover, it extends the predictive coding theory to the hippocampal formation, suggesting a unified learning algorithm for diverse cortical representations."

Kluczowe wnioski z

Learning grid cells by predictive coding

by Mufeng Tang,... o arxiv.org 10-03-2024

https://arxiv.org/pdf/2410.01022.pdf

Learning grid cells by predictive coding

Głębsze pytania

How can the multi-modularity of grid cells, with different spatial scales, be captured by predictive coding networks?

The multi-modularity of grid cells, characterized by their ability to represent different spatial scales, can be effectively captured by predictive coding networks (PCNs) through the incorporation of hierarchical structures and varying degrees of sparsity in the latent representations. In the context of grid cells, multi-modularity refers to the presence of grid cells that exhibit different firing patterns and spatial scales, which are essential for navigating complex environments.
To achieve this, PCNs can be designed with multiple layers, where each layer is responsible for capturing different spatial frequencies or scales of the input space. By adjusting the parameters of the loss function, such as the sparsity constraints and the non-negativity conditions, the network can learn to represent a range of grid patterns. For instance, a PCN can be trained with varying levels of input resolution or by using different types of place cell encodings, such as difference-of-softmaxed-Gaussian (DoS) curves, which have been shown to yield hexagonal grid representations.
Moreover, the use of Hebbian learning rules within the PCN framework allows for the emergence of grid cells that are sensitive to the spatial context, enabling the network to adaptively learn grid patterns that correspond to the agent's movement and environmental features. This adaptability is crucial for capturing the multi-scale nature of grid cells, as it allows the network to form representations that are not only hexagonal but also modulated by the spatial dynamics of the environment.

What are the potential limitations of predictive coding in modeling other spatial representations, such as place cells, beyond grid cells?

While predictive coding offers a promising framework for modeling grid cells, it may face limitations when applied to other spatial representations, such as place cells. One significant challenge is the inherent nature of place cell firing, which is often more discrete and location-specific compared to the continuous and periodic firing patterns of grid cells. Place cells are known to activate in response to specific locations in the environment, and their representations may not easily emerge from the predictive coding framework, which typically emphasizes continuous representations and error minimization.
Additionally, the reliance on local computations and Hebbian plasticity in predictive coding networks may restrict the ability to capture the complex interactions and dynamics observed in place cell networks. Place cells often exhibit a rich set of temporal dynamics, including phase precession and remapping, which may not be adequately modeled by the static or semi-static nature of predictive coding.
Furthermore, the generalizability of the predictive coding framework to different types of spatial tasks, such as those requiring rapid updates or integration of multiple sensory modalities, remains uncertain. While predictive coding has shown success in modeling visual representations, its application to the dynamic and multifaceted nature of spatial navigation and memory formation may require further refinement and adaptation of the underlying algorithms.

Could the predictive coding framework provide insights into the interactions between the entorhinal cortex and hippocampus during spatial navigation and memory formation?

Yes, the predictive coding framework can provide valuable insights into the interactions between the entorhinal cortex (EC) and hippocampus during spatial navigation and memory formation. The EC is known to play a crucial role in integrating spatial information and relaying it to the hippocampus, where memory formation occurs. By modeling these interactions through predictive coding, researchers can explore how the EC encodes spatial predictions and how these predictions influence hippocampal activity.
In the context of spatial navigation, predictive coding can elucidate how grid cells in the EC generate predictions about an agent's position based on its movement and environmental cues. These predictions can then be compared to the actual sensory inputs received by place cells in the hippocampus, leading to the formation of error signals that drive learning and memory consolidation. This error-driven learning mechanism aligns with the principles of predictive coding, where discrepancies between predicted and actual inputs are minimized to refine the internal model of the environment.
Moreover, the framework can help explain the bidirectional connectivity between the EC and hippocampus, as it allows for the exchange of predictive signals and error corrections. This interaction is essential for updating spatial representations and facilitating memory retrieval. By employing predictive coding, researchers can investigate how the EC's grid cell activity influences the firing patterns of place cells and how these interactions contribute to the overall cognitive map used for navigation and memory tasks.
In summary, the predictive coding framework not only enhances our understanding of grid cell emergence but also provides a robust model for exploring the intricate dynamics between the entorhinal cortex and hippocampus, shedding light on the neural mechanisms underlying spatial navigation and memory formation.