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Escaping Collapse: The Strength of Weak Data for Large Language Model Training
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Formalizes iterative LLM training on synthetic data plus a weak exogenous labeler, showing a boosting-style curation scheme provably avoids model collapse and converges to a correct LLM, validated with Gemma 2 2B on GSM8K and MBPP.
Problem
Synthetic data training of LLMs can plateau or collapse over iterations without curation; the paper asks how little exogenous curation is needed to guarantee continual improvement toward an optimal LLM.
Approach
Models iterative synthetic-data training with a strong learner (perfect distribution fitting) and weak data (a beta fraction of exogenous correct labels), and proposes a boosting-style algorithm that generates synthetic samples, filters correct ones, and sends persistently failed prompts to a weak labeler, weighting weak labels by alpha; this provably converges to near-perfect accuracy.
Key results
- On GSM8K, Boosting (A) reaches 0.849 train accuracy@8 and 0.456 test greedy accuracy after 5 rounds, versus 0.393 for Filter only and 0.129 for Do nothing.
- On MBPP, Boosting (A) reaches 0.844 train pass@32 versus 0.702 for Filter only and 0.386 for Do nothing.
- Iterative training without curation (Do nothing) degrades GSM8K test accuracy to 0.129 from 0.222 for the pre-trained model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add weak data (A) to filtered synthetic training | Boosting on GSM8K · GSM8K | test greedy accuracy: $.393_{.020} -> $.456_{.010} | Helped |
| Add weak data (A) to filtered synthetic training | Boosting on GSM8K · GSM8K | train accuracy@1: $.553_{.050} -> $.589_{.013} | Helped |
| Add weak data (A) to filtered synthetic training | Boosting on MBPP · MBPP | train pass@1: $.632_{.016} -> $.681_{.008} | Helped |
| Add weak data (A) to filtered synthetic training | Boosting on MBPP · MBPP | test greedy pass rate: $.329_{.022} -> $.329_{.004} | No clear effect |
| Focus weak labeling on challenging prompts rather than selecting prompts randomly (ablation) | Boosting (A) on GSM8K · GSM8K | train accuracy@1: $.550_{.008} -> $.589_{.013} | Helped |
| Focus weak labeling on challenging prompts rather than selecting prompts randomly (ablation) | Boosting (A) on GSM8K · GSM8K | test greedy accuracy: $.432_{.013} -> $.456_{.010} | Helped |
| Focus weak labeling on challenging prompts rather than selecting prompts randomly (ablation) | Boosting (A) on MBPP · MBPP | train pass@1: $.600_{.012} -> $.681_{.008} | Helped |
| Focus weak labeling on challenging prompts rather than selecting prompts randomly (ablation) | Boosting (A) on MBPP · MBPP | test greedy pass rate: $.336_{.011} -> $.329_{.004} | Hurt |
| Focus weak labeling on challenging prompts rather than selecting prompts randomly (ablation) | Boosting (B) on MBPP · MBPP | train pass@1: $.544_{.012} -> $.647_{.012} | Helped |
| Focus weak labeling on challenging prompts rather than selecting prompts randomly (ablation) | Boosting (B) on MBPP · MBPP | test greedy pass rate: $.327_{.009} -> $.326_{.009} | No clear effect |
| Remove curation and train iteratively on unfiltered model-generated responses | Iterative training on GSM8K · GSM8K | test greedy accuracy: $.222_{.003} -> $.129_{.022} | Hurt |
Surprising findings
- Boosting w/o focusing (random selection of prompts for the labeler) is a strong baseline, close to focused boosting on test accuracy.
- On MBPP, Boosting w/o focusing beats Boosting on test pass rate, and Filter only outperforms Boosting with weaker data (B), so training-accuracy gains do not uniformly translate to test gains.
Limitations
- Theory assumes strong learners that exactly fit the conditional distribution, which is not realistic in practice.
- Experiments are small (7000 GSM8K and 374 MBPP training problems) and limited to one model size and two tasks with verifiable rewards.
- Experiments accumulate updates rather than retraining on the full accumulated data, departing from the theoretical algorithm.
Experimental setup
Datasets: GSM8K MBPP
Benchmarks: GSM8K MBPP
Metrics: train accuracy@1 train accuracy@8 train pass@1 train pass@32 test greedy accuracy test pass rate
Baselines: Do nothing Filter only Gold SFT Boosting w/o focusing PT
Builds on: AdaBoost STaR ReST ReST-EM
Closest papers by meaning
- Strong Model Collapse (ICLR 2025 · similarity 0.90)
- Dynamic Loss-Based Sample Reweighting for Improved Large Language Model Pretraining (ICLR 2025 · similarity 0.90)
- Beyond Model Collapse: Scaling Up with Synthesized Data Requires Verification (ICLR 2025 · similarity 0.90)
- Rethinking Data Curation in LLM Training: Online Reweighting Offers Better Generalization than Offline Methods (ICLR 2026 · similarity 0.90)
- Benchmarking Optimizers for Large Language Model Pretraining (NeurIPS 2026 · similarity 0.89)
- Towards a Theoretical Understanding of Synthetic Data in LLM Post-Training: A Reverse-Bottleneck Perspective (ICLR 2025 · similarity 0.89)
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