inzicht - Computational neuroscience - # Compositional Representations of Working Memory for Stimulus Identity and Time

Representing "What" and "When" in Working Memory: A Computational Neuroscience Approach Using Laplace Neural Manifolds

Q: How might the compositional representation of "what" and "when" be implemented in other brain regions beyond working memory, such as episodic memory or decision-making?

The compositional representation of "what" and "when" as described in the context of working memory can be extended to other cognitive domains, such as episodic memory and decision-making, by leveraging the same principles of conjunctive coding and temporal representation. In episodic memory, the ability to recall specific events involves not only the content of the memory (the "what") but also the context in which it occurred (the "when"). This dual representation can be implemented in brain regions such as the hippocampus, which is known for its role in forming and retrieving episodic memories. In this context, neurons could exhibit conjunctive receptive fields that encode both the identity of the event and the temporal context, allowing for the retrieval of memories based on cues that specify both content and timing. For instance, the hippocampus could utilize a Laplace Neural Manifold to represent the temporal decay of memories, where the decay rate reflects the recency of the event. This would enable the brain to maintain a structured representation of past experiences, facilitating the integration of temporal information with the content of memories. In decision-making, the "what" could represent the options available, while the "when" could encode the timing of those options in relation to the decision process. Brain regions involved in decision-making, such as the prefrontal cortex, could implement similar compositional representations to weigh options based on their relevance over time. By employing a logarithmic tiling of time, decision-making processes could account for the diminishing relevance of options as time progresses, thus influencing the choice based on both the content of the options and their temporal context.

Q: What are the potential limitations or drawbacks of the Laplace Neural Manifold approach, and how might it be extended or refined to better capture the complexity of real-world cognitive processes?

While the Laplace Neural Manifold (LNM) approach provides a robust framework for understanding working memory dynamics, it does have limitations. One potential drawback is the assumption of linearity in the relationship between the "what" and "when" representations. In real-world cognitive processes, the interactions between content and timing may be more complex and nonlinear, influenced by factors such as emotional salience, context, and individual differences in memory encoding and retrieval. To refine the LNM approach, researchers could explore the incorporation of nonlinear dynamics into the model. This could involve using more sophisticated neural network architectures, such as recurrent neural networks (RNNs) with nonlinear activation functions, to better capture the intricate relationships between stimuli and their temporal contexts. Additionally, integrating mechanisms for attention and context-dependent modulation could enhance the model's ability to reflect the variability observed in human cognition. Another extension could involve the exploration of multi-modal representations, where different types of information (e.g., visual, auditory, and emotional) are integrated within the LNM framework. This would allow for a more comprehensive understanding of how various cognitive processes interact and influence memory and decision-making in real-world scenarios.

Q: Could the principles of conjunctive coding and logarithmic temporal representations revealed in this work shed light on the neural basis of our subjective experience of time and the passage of events?

Yes, the principles of conjunctive coding and logarithmic temporal representations have significant implications for understanding the neural basis of our subjective experience of time and the perception of the passage of events. The idea that our brains may represent time logarithmically aligns with psychological theories suggesting that our perception of time is not linear but rather compresses longer durations into shorter subjective experiences. The LNM framework, with its emphasis on how temporal information is encoded alongside content, can provide insights into how we perceive the flow of time. For instance, as events recede into the past, the decay of memory representations could reflect our subjective experience of time passing, where more recent events are more vividly recalled than those further back. This aligns with the notion that our memory for time is influenced by the density of temporal representations, as suggested by the logarithmic tiling of time. Furthermore, the concept of conjunctive coding could explain how we integrate temporal context with the content of our experiences, allowing us to construct a coherent narrative of events over time. This integration is crucial for episodic memory and the formation of a continuous sense of self, as it enables us to relate past experiences to the present and anticipate future events. By studying the neural mechanisms underlying these representations, researchers can gain a deeper understanding of how our brains construct the subjective experience of time and the continuity of our lived experiences.

Belangrijkste concepten

Neurons in working memory must exhibit conjunctive receptive fields for stimulus identity ("What") and elapsed time ("When") in order to maintain a compositional representation of recent events. The dynamics of such a representation depend critically on the choice of temporal basis functions, with logarithmically-spaced basis functions providing a good match to empirical data.

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The paper explores the implications of a compositional neural representation of "what happened when" in working memory. It shows that neurons in such a representation must exhibit conjunctive receptive fields for stimulus identity ("what") and elapsed time ("when"). This allows the covariance matrix of the neural population to be written in a tractable form, enabling the study of population dynamics using linear dimensionality reduction techniques.

The authors consider two specific choices of temporal basis functions - Laplace and Inverse Laplace - which are related by a linear transformation. Despite this close relationship, the low-dimensional dynamics of the neural populations differ qualitatively, with the Laplace population showing stable stimulus-specific subspaces and the Inverse Laplace population exhibiting rotational dynamics.

The dimensionality of the neural trajectories is shown to depend on the density of the temporal basis functions. A logarithmic tiling of time, as proposed by work in cognitive psychology and supported by neuroscience evidence, provides a good match to empirical data on the growth of dimensionality over time.

Finally, the authors sketch a continuous attractor neural network model that can implement the Laplace Neural Manifold, exhibiting the required conjunctive receptive fields for "what" and "when". This model provides a bridge between abstract cognitive models of working memory and circuit-level implementation.

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"The fact that Time is a form of our stream of experience is expressed in the idea of equality: the empirical content which fills the length of Time AB can in itself be put into any other time without being in any way different from what it is."
"Given a way to describe empirical content—a "what"—it must be possible to describe every possible what at every possible "when.""
"Neurons in m (ˆx, t) have conjunctive receptive fields as a function of what × when."
"The overall covariance Σ can be written as a Kronecker product of the covariance matrices for stimulus (Σwhat) and time (Σwhen)."
"The dimensionality of the neural trajectories grows logarithmically with elapsed time, matching empirical data."

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"The fact that Time is a form of our stream of experience is expressed in the idea of equality: the empirical content which fills the length of Time AB can in itself be put into any other time without being in any way different from what it is."
"Given a way to describe empirical content—a "what"—it must be possible to describe every possible what at every possible "when.""

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"What" x "When" working memory representations using Laplace Neural Manifolds

by Aakash Sarka... om arxiv.org 10-01-2024

https://arxiv.org/pdf/2409.20484.pdf

"What" x "When" working memory representations using Laplace Neural Manifolds

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How might the compositional representation of "what" and "when" be implemented in other brain regions beyond working memory, such as episodic memory or decision-making?

The compositional representation of "what" and "when" as described in the context of working memory can be extended to other cognitive domains, such as episodic memory and decision-making, by leveraging the same principles of conjunctive coding and temporal representation. In episodic memory, the ability to recall specific events involves not only the content of the memory (the "what") but also the context in which it occurred (the "when"). This dual representation can be implemented in brain regions such as the hippocampus, which is known for its role in forming and retrieving episodic memories.
In this context, neurons could exhibit conjunctive receptive fields that encode both the identity of the event and the temporal context, allowing for the retrieval of memories based on cues that specify both content and timing. For instance, the hippocampus could utilize a Laplace Neural Manifold to represent the temporal decay of memories, where the decay rate reflects the recency of the event. This would enable the brain to maintain a structured representation of past experiences, facilitating the integration of temporal information with the content of memories.
In decision-making, the "what" could represent the options available, while the "when" could encode the timing of those options in relation to the decision process. Brain regions involved in decision-making, such as the prefrontal cortex, could implement similar compositional representations to weigh options based on their relevance over time. By employing a logarithmic tiling of time, decision-making processes could account for the diminishing relevance of options as time progresses, thus influencing the choice based on both the content of the options and their temporal context.

What are the potential limitations or drawbacks of the Laplace Neural Manifold approach, and how might it be extended or refined to better capture the complexity of real-world cognitive processes?

While the Laplace Neural Manifold (LNM) approach provides a robust framework for understanding working memory dynamics, it does have limitations. One potential drawback is the assumption of linearity in the relationship between the "what" and "when" representations. In real-world cognitive processes, the interactions between content and timing may be more complex and nonlinear, influenced by factors such as emotional salience, context, and individual differences in memory encoding and retrieval.
To refine the LNM approach, researchers could explore the incorporation of nonlinear dynamics into the model. This could involve using more sophisticated neural network architectures, such as recurrent neural networks (RNNs) with nonlinear activation functions, to better capture the intricate relationships between stimuli and their temporal contexts. Additionally, integrating mechanisms for attention and context-dependent modulation could enhance the model's ability to reflect the variability observed in human cognition.
Another extension could involve the exploration of multi-modal representations, where different types of information (e.g., visual, auditory, and emotional) are integrated within the LNM framework. This would allow for a more comprehensive understanding of how various cognitive processes interact and influence memory and decision-making in real-world scenarios.

Could the principles of conjunctive coding and logarithmic temporal representations revealed in this work shed light on the neural basis of our subjective experience of time and the passage of events?

Yes, the principles of conjunctive coding and logarithmic temporal representations have significant implications for understanding the neural basis of our subjective experience of time and the perception of the passage of events. The idea that our brains may represent time logarithmically aligns with psychological theories suggesting that our perception of time is not linear but rather compresses longer durations into shorter subjective experiences.
The LNM framework, with its emphasis on how temporal information is encoded alongside content, can provide insights into how we perceive the flow of time. For instance, as events recede into the past, the decay of memory representations could reflect our subjective experience of time passing, where more recent events are more vividly recalled than those further back. This aligns with the notion that our memory for time is influenced by the density of temporal representations, as suggested by the logarithmic tiling of time.
Furthermore, the concept of conjunctive coding could explain how we integrate temporal context with the content of our experiences, allowing us to construct a coherent narrative of events over time. This integration is crucial for episodic memory and the formation of a continuous sense of self, as it enables us to relate past experiences to the present and anticipate future events. By studying the neural mechanisms underlying these representations, researchers can gain a deeper understanding of how our brains construct the subjective experience of time and the continuity of our lived experiences.