Why do some teaching examples click with an AI while similar-looking ones fall flat?
What makes some demonstration examples more useful than others?
This explores what separates a helpful example from a wasted one, whether the examples are few-shot demonstrations in a prompt or the small sets of examples used to train a model, and whether 'useful' depends on the example itself or on how it's chosen, ordered, and placed.
This explores what makes one example teach a model more than another, both for demonstrations placed in a prompt and for small training sets. The corpus's main answer is that an example isn't useful on its own. Its value depends on what the model already knows and on where the example sits. A few separate lines of research arrive at this from different directions.
The most common way to pick demonstrations is to retrieve the ones that look most like the test question. That turns out to be a weak rule. When example selection is treated as an experiment, choosing the examples that most reduce the model's uncertainty about the test set, the results beat similarity-based retrieval across small, medium and large models Can optimal experimental design improve few-shot example selection?. There's a useful parallel with analogy: GPT-4 retrieves analogies by surface resemblance and applies them indiscriminately, while people pick fewer analogies that share the underlying causal structure Does GPT-4 retrieve analogies differently than humans do?. An example that looks similar may not be similar in the way that matters.
Difficulty matters too, and the sweet spot is in the middle. In reinforcement learning on reasoning tasks, medium-difficulty problems produce the largest gains. Easy problems give no contrast because the model always succeeds, and very hard problems push it toward shortcuts Why do medium-difficulty problems teach reasoning better than hard ones?. The same logic explains why throwing out easy, redundant training examples can make data scaling far more efficient Can we prune training data without hurting model performance?. A less obvious finding is that an example can also be too good. Teacher-refined training data can hurt a student model when it goes beyond what that student is ready to learn, so a 'better' example can be a worse one for a particular learner Does teacher-refined data always improve student model performance?. Order matters as well: arranging demonstrations from hard to easy, using a signal read from the model's own internal activity, improves results without anyone labeling difficulty Can representation sparsity order few-shot demonstrations effectively?. Even position matters on its own. Moving the exact same block of demonstrations from the start of a prompt to the end can change accuracy by up to 20% and flip nearly half the answers How much does demo position alone affect in-context learning accuracy?.
The most surprising point concerns quantity versus contrast. A single training example can roughly double math performance Can a single training example unlock mathematical reasoning?, and one problem paired with critiques of right and wrong solutions does about as well Can a single problem unlock reasoning through solution critique?. What seems to do the teaching is seeing correct and incorrect reasoning side by side, and there may not need to be many examples at all. The same is true in prompting: letting a model get the demonstrations wrong first, then having it state the principles it learned from those mistakes, beats showing it clean examples Does learning from mistakes improve in-context learning?.
This points to the limit of learning from examples at all. Models trained on labeled examples of good arguments pick up surface patterns rather than the criteria behind them, and they only generalize once they're given the framework explicitly Can models learn argument quality from labeled examples alone?. Anthropic found the same thing for alignment: examples that include the reasoning behind a behavior carry over to unfamiliar situations much better than demonstrations of the behavior alone Does teaching ethical reasoning generalize better than demonstration training?. Taken together, the most useful examples make a principle visible, sit at the edge of what the learner can currently do, and include a contrast between right and wrong.
Sources 12 notes
AIPD frames demonstration selection as budgeted active learning, choosing examples that maximally reduce test-set uncertainty. Two algorithms (GO and SAL) outperformed similarity-based methods across small, medium, and large language models.
GPT-4 achieved perfect recall but near-zero precision, retrieving analogies based on surface features and over-applying them indiscriminately. Business students showed the opposite pattern: low recall but high precision, attempting fewer analogies but with stronger causal alignment.
RLVR learning follows an inverted-U curve across difficulty: medium problems yield strongest gains because they balance success frequency with informative failures, while easy samples lack variance and hard samples amplify shortcuts.
Research shows that ranking training examples by difficulty (EL2N, forgetting, memorization) and removing easy ones beats power-law scaling laws. On CIFAR-10, 50% of data was pruned without accuracy loss, and self-supervised metrics scaled the approach to ImageNet.
Teacher-refined data degrades performance when it exceeds the student's learning frontier, even if objectively higher quality. Students should filter refinements using their own statistical profile to retain only compatible improvements.
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Sparsity-Guided Curriculum In-Context Learning uses last-layer activation sparsity to order demonstrations from sparse (harder) to dense (easier), yielding considerable performance improvements. This approach requires no external difficulty labels and works across diverse in-context learning tasks.
Repositioning an identical demo block from prompt start to end swaps up to 20% accuracy and flips nearly half of predictions. This spatial effect operates independently of demo content and spans multiple task types.
A single example in RLVR boosts math performance from 36% to 73.6% and enables test accuracy to improve for 1,400 steps after training accuracy reaches 100%, revealing that minimal activation signals unlock latent reasoning capability.
Critique Fine-Tuning achieves reasoning activation comparable to RLVR using only one problem and teacher-generated critiques of varied solutions, with no reinforcement learning. This demonstrates that exposure to correct versus incorrect reasoning on a specific problem is the sufficient activation signal.
LEAP demonstrates that models achieve better performance on reasoning and math tasks by intentionally erring on few-shot examples, reflecting on mistakes, and deriving explicit task-specific principles—without additional labeled data or fine-tuning.
Fine-tuning on labeled examples fails to transfer quality criteria to new argument types. Models learn surface patterns rather than principled criteria. Explicit instruction using frameworks like RATIO or QOAM significantly improves performance and generalization.
Anthropic found that adding ethical deliberation to training responses cut agentic misalignment from 15% to 3%, and an out-of-distribution dataset matched this with 28x less data. Models trained on principled reasoning maintained alignment better when situations diverged from training examples.
Papers this line draws on 8
The research behind the notes this line reads — ranked by how closely each paper relates.
- In-Context Principle Learning from Mistakes
- STaR: Bootstrapping Reasoning With Reasoning
- LLMs can implicitly learn from mistakes in-context
- Where to show Demos in Your Prompt: A Positional Bias of In-Context Learning
- Evaluating Theory of Mind in Reasoning Models: Robustness over Reasoning
- Reinforcement Learning for Reasoning in Large Language Models with One Training Example
- Mechanistically Interpreting the Role of Sample Difficulty in RLVR for LLMs
- The Invisible Leash: Why RLVR May Not Escape Its Origin