Does an AI only handle new problems that resemble the examples you showed it, or can it stretch beyond them?

This explores whether the range of operations and situations that examples actually show, in a prompt or in training demonstrations, sets the limit on what a model can do with new problems. The corpus has no paper that measures 'operation coverage' directly. But several notes point the same way: models generalize along the lines their examples drew, and they stall where the examples stop.

The clearest evidence is on the failure side. Chain-of-thought reasoning degrades predictably when a task, a length, or a format moves away from what the model saw, and the model still produces fluent but logically inconsistent steps (Does chain-of-thought reasoning actually generalize beyond training data?). The suggested reason is that chain-of-thought reproduces familiar reasoning patterns rather than applying an operation in the abstract (Does chain-of-thought reasoning reveal genuine inference or pattern matching?). So an operation shown in a few contexts is often learned as 'what this kind of answer looks like', not as a rule that carries over. The same pattern shows up in training. Instruction tuning mostly transfers knowledge of the output space, since deliberately wrong instructions score about the same as correct ones (Does instruction tuning teach task understanding or output format?). Agents trained on expert demonstrations are capped by what the curators imagined (Can agents learn beyond what their training data shows?).

Coverage also has a shape, not just a size. For sequential decision-making, in-context learning needs whole or partial trajectories from the same environment level, and isolated examples don't work. The demonstration has to show how steps chain together, not only what single steps look like (Why do trajectories matter more than individual examples for in-context learning?). The same idea appears in function calling. Splitting it into seven explicit subtasks (nested calls, chaining, parallel calls, parameter detection and so on) generalized better than one umbrella dataset, presumably because each operation was covered on its own (Can breaking function calling into subtasks improve model generalization?).

There are two ways around the ceiling. One is to add the principle to the examples. Fine-tuning on labeled argument examples didn't transfer to new argument types, because models learned surface patterns. Explicit theoretical frameworks did transfer (Can models learn argument quality from labeled examples alone?). LEAP points the same way. It has the model err on its few-shot examples and then write down the principles behind its mistakes, which improved reasoning and math performance with no extra labeled data (Does learning from mistakes improve in-context learning?). The other way is to choose the examples deliberately. Treating demonstration selection as an experimental-design problem, picking the examples that most reduce uncertainty on the test set, beat plain similarity retrieval (Can optimal experimental design improve few-shot example selection?). Ordering matters too. Arranging demonstrations from sparse (harder) to dense (easier) representations improved results without any difficulty labels (Can representation sparsity order few-shot demonstrations effectively?).

The corpus suggests that examples in a prompt work more like a map of where the model can go than like a lesson. An operation generalizes when the examples cover its variations, show it in sequence, or come with the rule that explains it. Without those, the model matches the pattern it saw.