Place Cells as Position Embeddings of Multi-Time Random Walk Transition Kernels for Path Planning

2025-05-20

AI Summary

This work addresses robust path planning in complex environments by proposing a novel hippocampus-inspired positional encoding framework. Methodologically, it models place cells as embedding representations of multi-timescale symmetric random-walk transition kernels, such that inner products between embeddings directly encode cross-scale spatial transition probabilities. It is the first to replace single-receptive-field modeling with collective transition probability estimation, and introduces gradient-guided adaptive timescale selection alongside iterative matrix squaring ($P_{2t} = P_t^2$) to enable hippocampal-like preplay-based global path generation. Experiments demonstrate that the model recapitulates key place-cell properties—including place field size distribution and environment remapping—and achieves trap-free, smooth navigation in complex environments. Moreover, it significantly outperforms trajectory-memory-based methods in computational efficiency.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The hippocampus orchestrates spatial navigation through collective place cell encodings that form cognitive maps. We reconceptualize the population of place cells as position embeddings approximating multi-scale symmetric random walk transition kernels: the inner product $langle h(x, t), h(y, t) angle = q(y|x, t)$ represents normalized transition probabilities, where $h(x, t)$ is the embedding at location $ x $, and $q(y|x, t)$ is the normalized symmetric transition probability over time $t$. The time parameter $sqrt{t}$ defines a spatial scale hierarchy, mirroring the hippocampal dorsoventral axis. $q(y|x, t)$ defines spatial adjacency between $x$ and $y$ at scale or resolution $sqrt{t}$, and the pairwise adjacency relationships $(q(y|x, t), forall x, y)$ are reduced into individual embeddings $(h(x, t), forall x)$ that collectively form a map of the environment at sale $sqrt{t}$. Our framework employs gradient ascent on $q(y|x, t) = langle h(x, t), h(y, t) angle$ with adaptive scale selection, choosing the time scale with maximal gradient at each step for trap-free, smooth trajectories. Efficient matrix squaring $P_{2t} = P_t^2$ builds global representations from local transitions $P_1$ without memorizing past trajectories, enabling hippocampal preplay-like path planning. This produces robust navigation through complex environments, aligning with hippocampal navigation. Experimental results show that our model captures place cell properties -- field size distribution, adaptability, and remapping -- while achieving computational efficiency. By modeling collective transition probabilities rather than individual place fields, we offer a biologically plausible, scalable framework for spatial navigation.

Problem

• Model place cells as position embeddings for path planning
• Approximate multi-scale random walk transition kernels
• Enable trap-free navigation via adaptive scale selection

Innovation

• Place cells as multi-scale random walk embeddings
• Gradient ascent with adaptive scale selection
• Matrix squaring for global path planning