A Model of Similarity: Metric In a Patch

In this paper, we present a novel model of similarity that adopts the metric approach, where the (dis)similarity between objects is represented as distance. However, our model distinguishes between two memory systems: a long-term memory (LTM) that functions as a comprehensive database and a short-term memory (STM) where similarity calculations occur. In our model, STM is conceptualized as a manifold-like metric space that dynamically changes both in terms of its content and metric. It represents a subset of information from LTM at any given time. Additionally, we introduce a discrete layer in the model to capture the limited sensitivity of our distinguishing capabilities, resulting in a "pixelization" of STM that reflects limited resolution. We argue that this limitation in STM is actually beneficial for the process of abstraction. Furthermore, we demonstrate how the probabilistic nature of LTM influences the varying representations of concepts and similarity judgments performed within STM. By integrating these elements, our model provides a comprehensive framework for understanding the dynamics of similarity assessment and concept representation in human cognition.