How to sketch a learning algorithm

arXiv:2604.07328v1 Announce Type: new Abstract: How does the choice of training data influence an AI model? This question is of central importance to interpretability, privacy, and basic science. At its core is the data deletion problem: after a reasonable amount of precomputation, quickly predict how the model would behave in a given situation if a given subset of training data had been excluded from the learning algorithm. We present a data deletion scheme capable of predicting model outputs with vanishing error arepsilon in the deep learning setting. Our precomputation and prediction algorithms are only poly(1/arepsilon) factors slower than regular training and inference, respectively. The storage requirements are those of poly(1/arepsilon) models. Our proof is based on an assumption that we call "stability." In contrast to the assumptions made by prior work, stability appears to be fully compatible with learning powerful AI models. In support of this, we show that stability is satisfied in a minimal set of experiments with microgpt. Our code is available at https://github.com/SamSpo1/microgpt-sketch. At a technical level, our work is based on a new method for locally sketching an arithmetic circuit by computing higher-order derivatives in random complex directions. Forward-mode automatic differentiation allows cheap computation of these derivatives.

Related

• Conditional flow matching for physics-constrained inverse problems with finite training data
• A comparative analysis of machine learning models in SHAP analysis
• ODE-free Neural Flow Matching for One-Step Generative Modeling

Source: arXiv cs.LG | 2026-04-10