Sahel Torkamani

Sahel Torkamani, Henry Gouk, Rik Sarkar

Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of a metric space. The proposed distance incorporates a tunable scaling parameter, $t$, that controls the sensitivity to global structure (small $t$) and finer details (large $t$). We prove several theoretical properties of magnitude distance, including its limiting behavior across scales and conditions under which it satisfies key metric properties. In contrast to classical distances, we show that magnitude distance remains discriminative in high-dimensional settings when the scale is appropriately tuned. We further demonstrate how magnitude distance can be used as a training objective for push-forward generative models. Our experimental results support our theoretical analysis and demonstrate that magnitude distance provides meaningful signals, comparable to established distance-based generative approaches.

Wan Ki Wong, Sahel Torkamani, Michele Ciampi et al.

Evaluating the relevance of data is a critical task for model builders seeking to acquire datasets that enhance model performance. Ideally, such evaluation should allow the model builder to assess the utility of candidate data without exposing proprietary details of the model. At the same time, data providers must be assured that no information about their data - beyond the computed utility score - is disclosed to the model builder. In this paper, we present PrivaDE, a cryptographic protocol for privacy-preserving utility scoring and selection of data for machine learning. While prior works have proposed data evaluation protocols, our approach advances the state of the art through a practical, blockchain-centric design. Leveraging the trustless nature of blockchains, PrivaDE enforces malicious-security guarantees and ensures strong privacy protection for both models and datasets. To achieve efficiency, we integrate several techniques - including model distillation, model splitting, and cut-and-choose zero-knowledge proofs - bringing the runtime to a practical level. Furthermore, we propose a unified utility scoring function that combines empirical loss, predictive entropy, and feature-space diversity, and that can be seamlessly integrated into active-learning workflows. Evaluation shows that PrivaDE performs data evaluation effectively, achieving online runtimes within 15 minutes even for models with millions of parameters. Our work lays the foundation for fair and automated data marketplaces in decentralized machine learning ecosystems.