Extrapolation and Interpolation: Unraveling Complexity

Understanding the distinction between extrapolation and interpolation depends on recognizing the underlying latent space that connects seemingly disparate phenomena. In physics, for instance, the relationship between falling apples and planetary orbits stems from the same fundamental law, F equals MA. What may appear as an extrapolation from one context to another can actually be viewed as interpolation within the correct latent space. Similarly, in machine learning, the ability of language models to tackle a variety of tasks may be rooted in a limited set of foundational skills, suggesting that new tasks can be understood as combinations of these basic skills rather than entirely new challenges.