Learning temporal relationships between symbols with Laplace Neural Manifolds

Area of Science:

• Neuroscience
• Computational Neuroscience
• Mathematical Biology

Background:

• Mammalian brains utilize neural timelines for temporal memory, recalling past events.
• Humans can mentally navigate past and future via an internal timeline.
• Existing models lack a comprehensive framework for future timeline construction.

Purpose of the Study:

• To present a mathematical framework for constructing a future-oriented neural timeline.
• To model the brain's ability to infer future relationships from past temporal data.
• To integrate neuroscientific findings on temporal processing and associative learning.

Main Methods:

• Inputting time-series symbol data into a continuous-time system.
• Recording pairwise temporal relationships across various timescales.
• Utilizing the real Laplace transform for temporal memory representation.
• Applying Hebbian learning rules with diverse synaptic time scales for associative memory.

Main Results:

• The framework models temporal relationships between past and present symbols.
• It infers present-to-future relationships using learned temporal contingencies.
• The Hebbian associative matrix stores Laplace successor and predecessor representations.
• Synaptic diversity enables learning non-stationary and joint symbol statistics.

Conclusions:

• The proposed framework mathematically models the brain's internal timeline for future prediction.
• It synthesizes findings on temporal memory, Hebbian learning, and dopamine neuron activity.
• This approach offers insights into how neural systems anticipate future events.