Finding optimal paths in connected graphs requires determining the smallest total cost for traveling along the graph's edges. This problem can be solved by several classical algorithms where, usually, costs are predefined for all edges. Conventional planning methods can, thus, normally not be used when wanting to change costs in an adaptive way following the requirements of some task. Here we show that one can define a neural network representation of path finding problems by transforming cost values into synaptic weights, which allows for online weight adaptation using network learning mechanisms. When starting with an initial activity value of one, activity propagation in this network will lead to solutions, which are identical to those found by the Bellman-Ford algorithm. The neural network has the same algorithmic complexity as Bellman-Ford and, in addition, we can show that network learning mechanisms (such as Hebbian learning) can adapt the weights in the network augmenting the resulting paths according to some task at hand. We demonstrate this by learning to navigate in an environment with obstacles as well as by learning to follow certain sequences of path nodes. Hence, the here-presented novel algorithm may open up a different regime of applications where path-augmentation (by learning) is directly coupled with path finding in a natural way.

翻译：在连通图中寻找最优路径需要确定沿图边移动的最小总代价。该问题可通过若干经典算法求解，这些算法通常为所有边预定义代价。因此，当需要根据任务要求自适应调整代价时，传统规划方法通常无法使用。本文表明，通过将代价值转化为突触权重，可定义路径查找问题的神经网络表示，从而利用网络学习机制实现权重的在线适应。当初始活动值设为1时，该网络中的活动传播将得到与Bellman-Ford算法完全相同的解。该神经网络具有与Bellman-Ford算法相同的算法复杂度，且可证明网络学习机制（如赫布学习）能够根据当前任务调整网络权重，从而增强所获路径。我们通过在有障碍物的环境中导航以及遵循特定路径节点序列的学习任务展示了该方法的有效性。因此，本文提出的新型算法可能开辟一个全新的应用领域，其中路径增强（通过学习）以自然方式直接与路径查找相结合。