Modeling Hierarchical Spatial ReasoningSurabhi Gupta ~ Mount Holyoke College ’11

Research Advisors ~ Prof. Audrey St. John (MHC) & Prof. Dave Touretzky (CMU)

Our understanding of the cognitive map is highly limited. Many animals, such as birds and fish, migrate long distances in search of food, favorable climate and habitat.•How are locations represented in the brain? •How are these locations composed, stored, recalled and decoded? This project seeks to model spatial reasoning using computational neuroscience tools.

Motivation

Concepts in the brain exist in a distributed fashion (Kanerva, 1993). This has many advantages over localist representations: - Robustness against damage - Graceful degradation (“fuzzy” memory)

Background

Figure 1: Spatial locations are represented as a pattern of activity over a network of neurons giving a more biologically realistic description. It

has advantages such as fault-tolerance and automatic generalization compared to a traditional (localist) representation in CS.

vs

Locations exist at many scales -- for instance: a room, a building, a city etc. During pathfinding, the representations corresponding to the most relevant scale are activated. Building on this intuition, we propose a model of hierarchical spatial reasoning using distributed representations.

Model of Pathfinding

Figure 2: The hierarchical properties of space are modeled within a mathematical framework using distributed representations. The

pathfinding process involves search across different scales. This model satisfies the desiderate for reduced representations (Hinton, 1990)

Training Phase: The subjects were allowed to explore the environment. Next, they were trained on different pathfinding tasks that either involved going from one location to another within the same building or from one building to the other.

ERP Experiment

Figure 3: Virtual 3d Spatial environment. a) The neighborhood contains landmarks such as water fountain, a gazebo etc. that are placed strategically to help in orientation. b) Artifacts such as the red star are placed inside the buildings and serve as markers. A

pathfinding task involves going from one marker to another either within the same building or from one building to another.

During the experiment, a pathfinding task appears on the screen followed by three maps (in random order). These maps correspond to the interior of the two buildings and of the neighborhood. For each map, they are asked to indicate whether or not it was useful in solving the task. Event related potentials (ERPs) are recorded using a 32 channel electrode cap. We compare the evoked brain potentials for the six conditions shown in the table below. We hope to find evidence for the hierarchical spatial reasoning paradigm.

Map B1 Map B2 Map N

Path a-b ✔ X X

Path d-e X ✔ X

Path a-d X X ✔

N

B1

a b c

B2

d e f

I would like to thank Profs. Spector, Bowie, Cohen, Dobosh and Anoopum Gupta for their mentorship. Supported by the Interdisciplinary Training Grant in Computational Neuroscience (NIH/NIDA R09 Da023428) at Carnegie Mellon, the PA Tobacco Settlement fund and the Department of Biological Sciences, CS at MHC.

[1] Pentti Kanerva. Sparse distributed memory and related models, pages 50–76. Oxford University Press, Inc., New York, NY, USA, 1993[2] Geoffrey E. Hinton. Mapping part-whole hierarchies into connectionist networks. Artif. Intell., 46:47–75, November 1990.

Procedure

Acknowledgements & References

Figure 4: Locations a-f are located within building 1 and 2, which are located in the

neighborhood N.

Table 1: Checkmark and cross indicate that the map is useful/not

useful in finding the path.