Aymane El Firdoussi

Aymane El Firdoussi, Mohamed El Amine Seddik, Soufiane Hayou et al.

Synthetic data has gained attention for training large language models, but poor-quality data can harm performance (see, e.g., Shumailov et al. (2023); Seddik et al. (2024)). A potential solution is data pruning, which retains only high-quality data based on a score function (human or machine feedback). Previous work Feng et al. (2024) analyzed models trained on synthetic data as sample size increases. We extend this by using random matrix theory to derive the performance of a binary classifier trained on a mix of real and pruned synthetic data in a high dimensional setting. Our findings identify conditions where synthetic data could improve performance, focusing on the quality of the generative model and verification strategy. We also show a smooth phase transition in synthetic label noise, contrasting with prior sharp behavior in infinite sample limits. Experiments with toy models and large language models validate our theoretical results.

Aymane El Firdoussi, Mohamed El Amine Seddik

This paper provides theoretical insights into high-dimensional binary classification with class-conditional noisy labels. Specifically, we study the behavior of a linear classifier with a label noisiness aware loss function, when both the dimension of data $p$ and the sample size $n$ are large and comparable. Relying on random matrix theory by supposing a Gaussian mixture data model, the performance of the linear classifier when $p,n\to \infty$ is shown to converge towards a limit, involving scalar statistics of the data. Importantly, our findings show that the low-dimensional intuitions to handle label noise do not hold in high-dimension, in the sense that the optimal classifier in low-dimension dramatically fails in high-dimension. Based on our derivations, we design an optimized method that is shown to be provably more efficient in handling noisy labels in high dimensions. Our theoretical conclusions are further confirmed by experiments on real datasets, where we show that our optimized approach outperforms the considered baselines.