We introduce a manifold analysis technique for neural network representations. Normalized Space Alignment (NSA) compares pairwise distances between two point clouds derived from the same source and having the same size, while potentially possessing differing dimensionalities. NSA can act as both an analytical tool and a differentiable loss function, providing a robust means of comparing and aligning representations across different layers and models. It satisfies the criteria necessary for both a dissimilarity metric and a neural network loss function. We showcase NSA's versatility by illustrating its utility as a representation space analysis metric and a structure-preserving loss function. NSA is not only computationally efficient, but it can also approximate the global structural discrepancy during mini-batching, facilitating its use in a wide variety of neural network training paradigms.

The "Thinking, Fast and Slow" paradigm of Kahneman proposes that we use two different styles of thinking—a fast and intuitive System 1 for certain tasks, along with a slower but more analytical System 2 for others. While the idea of using this two-system style of thinking is gaining popularity in AI and robotics, our work considers how to interleave the two styles of decision-making, i.e., how System 1 and System 2 should be used together. For this, we propose a novel and general framework which includes a new System 0 to oversee Systems 1 and 2. At every point when a decision needs to be made, System 0 evaluates the situation and quickly hands over the decision-making process to either System 1 or System 2. We evaluate such a framework on a modified version of the classic Pac-Man game, with an already-trained RL algorithm for System 1, a Monte-Carlo tree search for System 2, and several different possible strategies for System 0. As expected, arbitrary switches between Systems 1 and 2 do not work, but certain strategies do well. With System 0, an agent is able to perform better than one that uses only System 1 or System 2.