Extrapolation Learning

Learning for Extrapolation

Traditional ML is Only Capable of Interpolation Due to the iid Assumption

Current AI and Machine Learning generalizes only within its training data (interpolation). It cannot adapt to or learn from truly novel situations (extrapolation).

• Interpolation (working within the known): This means making sense of, or generating responses for, situations that fall within the boundaries of the data the AI was trained on. It's like connecting the dots between known points. The model is essentially performing sophisticated pattern matching and averaging based on the examples it has seen. The learning process frequently converges on surface-level statistical regularities that are highly predictive in the training set but fail to capture the fundamental principles of the task.
• Extrapolation (reasoning beyond the known): This means making inferences, predictions, or adapting to situations that lie outside the boundaries of its training data. This requires reasoning, understanding underlying principles, and applying them to novel cases or contexts. Thus, the capacity for extrapolation is contingent on the discovery or learning of the task's underlying generative or causal structure, rather than superficial statistical correlations.

Current AI is a powerful tool for working within the known; the next frontier is building AI that can venture intelligently into the unknown, which needs learning for extrapolation as well as agent self-motivation, aautonomy, and continual learning.

• Perhaps, we should stop using 'generalization' as a catch-all term. A model's adaptability has two distinct facets: interpolative power and extrapolative power.

The Reality of Deployment

The real world is an open environment that can be highly complex and full of unknowns. It is impossible to gather enough data to cover all possible scenarios or corner cases in a sophisticated application, e.g., self-driving. The real world is also unpredictable, in constant flux. Trends change, user preferences evolve, new products are launched, and unforeseen events (like a pandemic or a new social media platform) occur. Interpolation knowledge learned using current learning methods based on the past data cannot handle such complexities. The abilities to learn principled knowledge that can extrapolate to unfamilar contexts and to adapt and apply such knowledge in these contexts are absolutely necessary.

The Human Advantage: Masters of Extrapolation

Humans excel at extrapolation because of our ability to form mental models of the world and learn the true and interpretable rules rather than short-cut or overfitting patterns.

• Abstract Reasoning and Theory of Mind: We understand abstract concepts like "physics," "intent," "causality," and "goals." If we see a novel object, we can characterize it and infer its potential properties based on its shape, material, movement, etc. For example, we can predict people's behavior based on their beliefs and desires, even if we've never seen them in that exact situation before.
• Learning from Few Examples: A child only needs to see a few examples of "gravity" (dropping a toy, spilling milk) to build a basic mental model of it and extrapolate that if they drop another object, it will also fall. An AI would need to see millions of examples of falling objects to interpolate the pattern, and even then, it wouldn't understand the why.

Towards AI That Can Extrapolate

This interpolation bottleneck is the single biggest challenge in the quest for Artificial General Intelligence (AGI). This research is to explore ways to overcome it to achieve the extrapolation capability, which requires AI agents to learn principled knowledge and apply it to novel situations.

Artificial Creativity: Creativity is the act of generating novel and valuable ideas, solutions, or artifacts. The ability to extrapolate is of critical importance for creativity because it acts as the fundamental bridge between the known and the unknown. It is well known that creativity happens when one realizes a piece of existing knowledge learned from one context can be used in a very different context, i.e., making novel connections between concepts that already in your brain but were previously unlinked.

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