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行进的最小总成本。这一问题可通过多种经典算法求解，通常所有边的成本是预先定义的。因此，当需要根据某些任务要求以自适应方式改变成本时，传统的规划方法通常无法使用。本文证明，通过将成本值转化为突触权重，可以构建路径查找问题的神经网络表示，从而利用网络学习机制在线调整权重。当初始激活值为1时，该网络中的活动传播将得到与Bellman-Ford算法相同的解。该神经网络具有与Bellman-Ford相同的算法复杂度，此外，我们还能证明网络学习机制（如赫布学习）可根据当前任务调整网络权重，增强所生成的路径。我们通过在存在障碍物的环境中学习导航以及学习遵循特定路径节点序列来演示这一能力。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）与路径查找以自然方式直接耦合。