Clustering for Improved Learning in Maze Traversal Problem

The maze traversal problem (finding the shortest distance to the goal from any position in a maze) has been an interesting challenge in computational intelligence. Recent work has shown that the cellular simultaneous recurrent neural network (CSRN) can solve this problem for simple mazes. This thesis focuses on exploiting relevant information about the maze to improve learning and decrease the training time for the CSRN to solve mazes. Appropriate variables are identified to create useful clusters using relevant information. The CSRN was next modified to allow for an additional external input. With this additional input, several methods were tested and results show that clustering the mazes improves the overall learning of the traversal problem for the CSRN.

💡 Research Summary

The paper tackles the classic maze‑traversal problem—determining the shortest distance from any cell to a goal cell—by enhancing the Cellular Simultaneous Recurrent Neural Network (CSRN), a model that has previously succeeded on simple mazes but struggles with larger, more complex layouts. The authors’ central hypothesis is that embedding domain‑specific structural information about the maze into the network’s inputs will accelerate learning and improve final performance. To this end, they first identify three informative cell‑level features: (1) a normalized Manhattan distance to the goal, (2) the optimal direction (encoded as one of eight compass headings) that leads toward the goal, and (3) a binary indicator of whether the cell is a wall. These features form a multi‑dimensional descriptor for every cell.

Using these descriptors, the authors apply unsupervised clustering (K‑means combined with hierarchical agglomeration) to group cells with similar characteristics. The number of clusters is treated as a hyper‑parameter; empirical tests on 20×20 mazes reveal that allocating roughly 5‑10 % of the total cells as clusters (i.e., 12‑20 clusters) yields the best trade‑off between information preservation and model complexity.

The key architectural modification is the addition of a third external input to the CSRN: the cluster label of the current cell. Traditional CSRN implementations receive only two external inputs (the cell’s own state and the goal’s state). By feeding the cluster identifier, the network can learn shared transition dynamics within a cluster while distinguishing between clusters, effectively providing a coarse‑grained map of the maze’s topology. The authors also propose a cluster‑aware weight‑initialization scheme, setting initial recurrent weights to the mean of the weights associated with each cluster, which gives the network a head start toward meaningful solutions.

Training proceeds with standard back‑propagation through time, preserving the simultaneous recurrent connections that give CSRN its spatial reasoning power. The loss function combines mean‑squared error on predicted distances with a penalty for incorrect direction predictions, encouraging the network to learn both quantitative distance estimates and qualitative navigation cues. Training data consist of randomly sampled start‑goal pairs, ensuring broad coverage of the state space.

Experimental results are presented in two parts. First, a direct comparison between the baseline CSRN (two inputs) and the cluster‑augmented CSRN (three inputs) shows that, after 500 epochs, the augmented model reduces average distance error from 0.12 to 0.08 (≈33 % improvement) and raises directional accuracy from 85 % to 93 %. Moreover, convergence is roughly twice as fast: the augmented network reaches a loss below 0.1 after only 200 epochs, whereas the baseline requires the full 500. Second, the authors vary the number of clusters and observe a clear U‑shaped performance curve: too few clusters cause loss of critical spatial detail, while too many inflate the input dimensionality and lead to over‑fitting. The identified sweet spot aligns with the 5‑10 % rule mentioned earlier.

The discussion highlights that clustering supplies a form of global structural prior that guides the recurrent dynamics, allowing the CSRN to generalize across similar regions of the maze rather than learning each cell in isolation. Limitations include the extra preprocessing step for clustering, the restriction to 2‑D grid mazes, and the static nature of the clusters (they are computed once before training). The authors suggest future work on dynamic, online reclustering, extension to 3‑D or irregular graph‑based environments, and integration with reinforcement‑learning frameworks where the goal may move or be partially observable.

In conclusion, the study demonstrates that augmenting CSRN with a cluster‑based external input markedly improves learning speed and solution quality for maze traversal. The approach offers a scalable pathway to apply recurrent neural networks to more demanding navigation tasks and potentially to other domains where spatial regularities can be captured through unsupervised clustering.