Derived label

See also: Machine learning terms

What is a derived label?

A derived label is a label that has been generated programmatically or inferred from other observable signals, rather than collected from direct human annotation of the variable a model is trying to predict. In short, a derived label is a training target produced by a process (a rule, a behavior log, a knowledge base, or another model) instead of by a person labeling each example by hand. The term is treated as a synonym for proxy label in Google's Machine Learning Glossary, and the two phrases are usually interchangeable in practice. Where they differ in emphasis, "proxy label" highlights the fact that the label is a stand-in for the true target, while "derived label" highlights the process by which the label was produced. This article focuses on the second angle: how labels get derived, what tools are used, and where the practice goes wrong.

Derived labels exist because gold-standard labels are expensive. Asking a radiologist to read 200,000 chest X-rays, or asking a Stanford PhD to annotate millions of social media posts for sentiment, is not financially or temporally realistic at the scale modern models require. Practitioners route around the problem by writing rules, mining behavior logs, querying knowledge bases, or asking another model to label data. The label that comes out the other end is a derived label, and the resulting training set is sometimes called a silver dataset, in contrast to a gold dataset produced by careful human annotation.

The practice is old. Information retrieval systems have trained on click logs since at least Thorsten Joachims's 2002 KDD paper on optimizing search engines from clickthrough data ^[3]. Distant supervision for relation extraction goes back to Mike Mintz and colleagues at ACL 2009, who paired Freebase with Wikipedia text to generate 1.8 million training instances spanning 102 relation classes and 940,000 entities, with no manual labeling at all ^[4]. What changed in the last decade is the surface area: derived labels now sit at the heart of large language model training, reinforcement learning from human feedback, and almost every recommender system in production.

How does a derived label differ from a proxy, weak, or noisy label?

The vocabulary in this corner of machine learning is messy and largely overlapping. The same idea travels under several names depending on the subfield and the era.

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Most real-world derived labels fit several of these categories at once. A click on a search result is a derived label (the team did not collect it as a relevance judgment), a proxy label (it stands in for relevance), a weak label (the labeling process is the user's behavior, not a careful annotator), and a noisy label (the click is wrong about relevance some fraction of the time). The labels in this article occupy the same space; the distinctions matter mostly when picking a denoising method.

It is also worth flagging what derived labels are not. They are not features. Feature engineering transforms the input variables a model sees. Label derivation produces the target the model is trained against. The two activities both involve transforming data, but they sit on opposite sides of the supervised-learning equation.

How are derived labels created?

There are seven common methods for deriving labels in modern ML pipelines. They differ in how much human input they require, how noisy the resulting labels tend to be, and how easy they are to audit.

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In practice, real pipelines combine several of these. A modern LLM pretraining corpus uses heuristic filters (length ratios, repetition checks, language detection), a quality classifier (itself trained on LLM-derived labels), and selective deduplication. Each stage produces labels that the next stage consumes. The Hugging Face FineWeb release documented this layered approach in detail ^[19].

How does programmatic labeling and weak supervision work?

The most influential research direction for derived labels in the last decade is programmatic labeling, where a user writes labeling functions and a software framework handles the noise. Alexander Ratner and collaborators at Stanford introduced the data programming paradigm at NeurIPS 2016 ^[8] and built Snorkel on top of it, published at VLDB 2017 ^[9]. The Snorkel paper reports that in a user study, "subject matter experts build models 2.8x faster and increase predictive performance an average 45.5% versus seven hours of hand labeling" ^[9]. Across two government deployments and four open-source datasets, the same paper found that Snorkel delivered 132% average improvements over prior heuristic approaches and came within an average of 3.60% of the predictive performance of large hand-curated training sets ^[9].

The core insight is that you can model the labeling functions themselves as noisy estimators of the true label, and learn their accuracies and correlations without ever seeing ground truth, by exploiting the patterns of agreement and disagreement among them. The output of the label model is a probabilistic label per training example, which downstream classifiers can train against directly.

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Snorkel and HoloClean operate before training: they take many noisy sources and produce a cleaner training set. Cleanlab operates after labeling: it takes an existing labeled dataset and finds the labels most likely to be wrong. Both approaches can be applied to derived labels, and they often are, in sequence.

Where do derived labels show up in real systems?

Derived labels appear in nearly every large-scale machine learning system in production. The pattern is consistent: the team has a target it cannot measure directly at scale, and a related signal it can. The team derives labels from the related signal and trains on those.

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The last three rows in particular show how derived labels chain together in modern LLM training. Pretraining derives labels from the next token. Reward modeling derives labels from human preferences. Policy training derives reward signals from the reward model. Each stage adds another layer of indirection between the gradient updates and the actual goal of building a useful, safe model.

Why use derived labels instead of gold labels?

The motivation for derived labels is almost always cost. Hand annotation by domain experts is expensive in time and money, and at the scales modern models train on, it is not even possible. A few representative figures from the literature.

Gold relation-extraction labels for the standard benchmarks took graduate students months to produce; Mintz et al.'s distant supervision approach extracted 1.8 million training instances automatically from Freebase, with no manual annotation ^[4]. The CheXpert chest X-ray dataset would have required a radiologist hundreds of hours to label image-by-image; the team used an NLP labeler over the existing radiology reports and labeled 224,316 images at machine speed ^[11]. FineWeb-Edu used Llama-3-70B-Instruct to score 1.3 trillion tokens for educational quality, a task no human team could have completed at any plausible budget ^[19].

Derived labels also enable training on data that simply could not be labeled by hand even with infinite money. Click logs cannot be retroactively annotated by users. The next-token loss in language model pretraining cannot be reproduced by human labelers, because it requires labeling every token in every document. Self-supervised objectives generally fall into this category: the label is a function of the input, derived for free at training time.

A secondary benefit is iteration speed. Heuristic labelers and labeling functions can be modified and re-run in minutes, while a hand-labeled dataset is a fixed artifact. In the Snorkel user study, this speed advantage was measured directly: experts reached better models 2.8x faster than seven hours of hand labeling ^[9]. The team can change the labeling rules and regenerate the entire training set, then compare downstream model performance. This iteration loop is the central workflow of weak-supervision systems like Snorkel.

What are the risks of derived labels?

Derived labels are useful precisely because they are imperfect, so a serious training pipeline plans for the imperfections. The main failure modes recur across applications.

The proxy gap and Goodhart's law

If you optimize a derived label hard enough, you will eventually hurt the true objective. This is Goodhart's law in machine learning form. Recommender systems that derive engagement labels from clicks, then train rankers to maximize predicted clicks, end up promoting clickbait over content users actually value. Leo Gao, John Schulman, and Jacob Hilton's 2023 paper "Scaling Laws for Reward Model Overoptimization" measured the same effect in RLHF: as a policy optimizes a learned reward model harder, the proxy reward keeps climbing while the true reward, evaluated against a much larger gold reward model, eventually turns down ^[17]. Skalse et al.'s 2023 paper "Goodhart's Law in Reinforcement Learning" gave a geometric account of why this happens and proposed early-stopping rules to limit the damage ^[18].

Bias propagation

Derived labels are usually systematically biased rather than randomly noisy, which is a much harder problem to fix. A search ranker trained on clicks preferentially shows items that historically got clicked, perpetuating position bias and selection bias. A recidivism predictor trained on rearrest data inherits the policing patterns that produced the rearrests. The trained model can then amplify the bias in its own deployment data, creating feedback loops that are hard to detect from inside the system. The 2019 Obermeyer et al. paper on a widely deployed healthcare risk algorithm found that using cost as a derived label for health need produced strong racial bias, because the historical cost of care was systematically lower for Black patients with the same level of illness ^[12]. The bias was large: only 17.7% of patients the algorithm flagged for extra care were Black, whereas correcting the proxy raised that share to 46.5% ^[12].

Coverage gaps

Heuristic-based derivation tends to have high precision and low recall. A regex catches obvious cases and misses the rest. A model trained only on cases the regex labels will systematically underperform on the cases it missed. Practitioners typically combine multiple weak labelers with overlapping coverage, then use a generative model in the Snorkel style to combine them.

Label noise

Derived labels are usually noisier than gold labels, which slows training and lowers the eventual model quality. Benoit Frenay and Michel Verleysen's 2014 IEEE survey "Classification in the Presence of Label Noise" grouped the response into three buckets: noise-robust algorithms (loss functions that are inherently less sensitive), noise cleansing (find and fix the wrong labels), and noise-tolerant methods (model the noise process explicitly during training) ^[6]. Confident learning, introduced by Curtis Northcutt, Lu Jiang, and Isaac Chuang in their 2021 JAIR paper, falls into the cleansing bucket: estimate the joint distribution of noisy and true labels using out-of-sample predicted probabilities, then prune the examples most likely to be mislabeled ^[14]. The same authors' Cleanlab library implements the method.

Validation on a gold set

The single habit that prevents most disasters is keeping a small, carefully labeled gold evaluation set that the model never trains on. A model trained on derived labels can score perfectly on the derived labels and still fail on the gold set; the size of that gap is the proxy gap, made visible. Without a gold set, there is no way to tell whether the model is learning the derived signal or the underlying task.

What are best practices for using derived labels?

A few recurring pieces of advice from teams that have used derived labels at scale.

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The pattern most teams converge on is a tiered labeling stack. A large noisy training set comes from derived labels. A medium validation set is hand-labeled by non-experts (often crowd workers). A small gold test set is hand-labeled by domain experts and treated as ground truth. The model is trained on the first, tuned on the second, and reported on the third.

Why do derived labels matter for modern AI?

Derived labels became more important, not less, with the rise of large models. The data scales involved in training a current frontier model exceed anything humans can label by hand by several orders of magnitude. Pretraining a GPT-class model uses next-token prediction on trillions of tokens scraped from the web; the supervision signal is the actual next token, which is a derived label produced by the data itself. This self-supervised objective is the cheapest possible derivation.

Quality filtering of pretraining corpora now relies heavily on derived labels. The Hugging Face FineWeb pipeline used over 50 candidate heuristic filters and ablated them down to a small effective set ^[19]. FineWeb-Edu trained a DeBERTa quality classifier on synthetic annotations from Llama-3-70B-Instruct, then used it to filter 1.3 trillion tokens ^[19]. FinerWeb-10BT used GPT-4o mini to label 20,000 documents at the line level with quality categories, then trained a classifier to scale the filter to 10 billion tokens. Each of these is a chain of derived labels: the LLM derives labels for a small set, the classifier derives labels for the large set, and the resulting filtered corpus derives the next generation of pretraining data.

Fine-tuning pipelines for instruction-following and chat behavior depend on derived labels in a similar way. LLM-as-judge protocols use a strong frontier model to grade responses from a smaller model, producing reward or preference labels that the smaller model trains against. Knowledge distillation, formalized by Geoffrey Hinton, Oriol Vinyals, and Jeff Dean in 2015, treats the teacher's soft probability outputs as derived labels that carry more information than the original hard labels ^[7].

Reinforcement learning from human feedback (RLHF) layers two stages of derivation. Human labelers provide pairwise preferences over model outputs. A reward model is trained on those preferences and serves as a derived labeler for new outputs. The policy is then trained against the reward model, which is itself a derived stand-in for what humans want. Each stage of derivation introduces error, and the failure modes of the resulting system are usually traceable to one of those stages. The constitutional AI approach (Anthropic 2022) takes the chain a step further: the model itself generates critiques and revisions of its own outputs, and those self-derived labels become the training signal ^[16].

The practical effect is that almost every modern AI system above a certain scale is trained primarily on derived labels, with a thin layer of gold labels reserved for evaluation. Knowing where each label came from, and how it can fail, is a core part of the job for anyone working on these systems.

Explain like I'm 5 (ELI5)

Imagine you want to teach a robot which berries in the forest are safe to eat. The best way would be to have a botanist tour the whole forest with the robot and point at every berry, saying "safe" or "not safe." That would take forever and cost a lot.

So you cheat a little. You write down a few rules: berries that grow on this kind of bush are usually safe, berries that birds eat are usually safe, berries that smell sour are usually not safe. You walk through the forest applying your rules and labeling berries. The labels you produce this way are not as good as a botanist's labels, but you produced thousands of them in an afternoon. These are derived labels. You did not look at each berry and carefully decide; you derived the label from a rule.

The robot now learns from your rule-derived labels. It will probably be pretty good, because most of your labels are right. But it might also pick up your mistakes. If your rule about birds is wrong (some berries are safe for birds but not for people), the robot will learn that mistake too.

So you also keep a small bag of berries that the botanist did label. You never use these for teaching the robot; you only use them to test the robot. If the robot gets the botanist's labels right, you trust it. If it does not, you go back and fix your rules. That small carefully labeled test bag is the only thing standing between you and a robot that confidently picks the wrong berries.

References

1. Google for Developers. "Datasets: Labels." Machine Learning Crash Course. https://developers.google.com/machine-learning/crash-course/overfitting/labels
2. Google for Developers. "Machine Learning Glossary." Entries for "proxy labels" and "derived label". https://developers.google.com/machine-learning/glossary
3. Joachims, T. (2002). "Optimizing Search Engines using Clickthrough Data." Proceedings of KDD 2002. ↩
4. Mintz, M., Bills, S., Snow, R., and Jurafsky, D. (2009). "Distant supervision for relation extraction without labeled data." Proceedings of the Joint Conference of the 47th Annual Meeting of the ACL and the 4th International Joint Conference on Natural Language Processing of the AFNLP, pp. 1003-1011. https://aclanthology.org/P09-1113/ ↩
5. Lee, D.-H. (2013). "Pseudo-Label: The Simple and Efficient Semi-Supervised Learning Method for Deep Neural Networks." ICML 2013 Workshop on Challenges in Representation Learning. ↩
6. Frenay, B., and Verleysen, M. (2014). "Classification in the Presence of Label Noise: A Survey." IEEE Transactions on Neural Networks and Learning Systems, 25(5), 845-869. ↩
7. Hinton, G., Vinyals, O., and Dean, J. (2015). "Distilling the Knowledge in a Neural Network." NIPS 2014 Deep Learning Workshop. arXiv:1503.02531. ↩
8. Ratner, A., De Sa, C., Wu, S., Selsam, D., and Re, C. (2016). "Data Programming: Creating Large Training Sets, Quickly." Advances in Neural Information Processing Systems 29. ↩
9. Ratner, A., Bach, S. H., Ehrenberg, H., Fries, J., Wu, S., and Re, C. (2017). "Snorkel: Rapid Training Data Creation with Weak Supervision." Proceedings of the VLDB Endowment, 11(3), 269-282. https://arxiv.org/abs/1711.10160 ↩
10. Zhou, Z.-H. (2018). "A brief introduction to weakly supervised learning." National Science Review, 5(1), 44-53.
11. Irvin, J. et al. (2019). "CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison." AAAI 2019. arXiv:1901.07031. ↩
12. Obermeyer, Z., Powers, B., Vogeli, C., and Mullainathan, S. (2019). "Dissecting racial bias in an algorithm used to manage the health of populations." Science, 366(6464), 447-453. https://www.science.org/doi/10.1126/science.aax2342 ↩
13. Bach, S. H. et al. (2019). "Snorkel DryBell: A Case Study in Deploying Weak Supervision at Industrial Scale." SIGMOD 2019.
14. Northcutt, C., Jiang, L., and Chuang, I. (2021). "Confident Learning: Estimating Uncertainty in Dataset Labels." Journal of Artificial Intelligence Research, 70, 1373-1411. arXiv:1911.00068. ↩
15. Lison, P., Barnes, J., and Hubin, A. (2021). "skweak: Weak Supervision Made Easy for NLP." ACL 2021 System Demonstrations.
16. Bai, Y. et al. (2022). "Constitutional AI: Harmlessness from AI Feedback." Anthropic. arXiv:2212.08073. ↩
17. Gao, L., Schulman, J., and Hilton, J. (2023). "Scaling Laws for Reward Model Overoptimization." Proceedings of the 40th International Conference on Machine Learning. arXiv:2210.10760. ↩
18. Skalse, J., Howe, N., Krasheninnikov, D., and Krueger, D. (2023). "Goodhart's Law in Reinforcement Learning." arXiv:2310.09144. ↩
19. Penedo, G. et al. (2024). "The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale." NeurIPS 2024 Datasets and Benchmarks Track. https://arxiv.org/abs/2406.17557 ↩