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 intersection space


Is the Hard-Label Cryptanalytic Model Extraction Really Polynomial?

arXiv.org Artificial Intelligence

Deep Neural Networks (DNNs) have attracted significant attention, and their internal models are now considered valuable intellectual assets. Extracting these internal models through access to a DNN is conceptually similar to extracting a secret key via oracle access to a block cipher. Consequently, cryptanalytic techniques, particularly differential-like attacks, have been actively explored recently. ReLU-based DNNs are the most commonly and widely deployed architectures. While early works (e.g., Crypto 2020, Eurocrypt 2024) assume access to exact output logits, which are usually invisible, more recent works (e.g., Asiacrypt 2024, Eurocrypt 2025) focus on the hard-label setting, where only the final classification result (e.g., "dog" or "car") is available to the attacker. Notably, Carlini et al. (Eurocrypt 2025) demonstrated that model extraction is feasible in polynomial time even under this restricted setting. In this paper, we first show that the assumptions underlying their attack become increasingly unrealistic as the attack-target depth grows. In practice, satisfying these assumptions requires an exponential number of queries with respect to the attack depth, implying that the attack does not always run in polynomial time. To address this critical limitation, we propose a novel attack method called CrossLayer Extraction. Instead of directly extracting the secret parameters (e.g., weights and biases) of a specific neuron, which incurs exponential cost, we exploit neuron interactions across layers to extract this information from deeper layers. This technique significantly reduces query complexity and mitigates the limitations of existing model extraction approaches.


Approximating Intersections and Differences Between Linear Statistical Shape Models Using Markov Chain Monte Carlo

arXiv.org Artificial Intelligence

To date, the comparison of Statistical Shape Models (SSMs) is often solely performance-based, carried out by means of simplistic metrics such as compactness, generalization, or specificity. Any similarities or differences between the actual shape spaces can neither be visualized nor quantified. In this paper, we present a new method to qualitatively compare two linear SSMs in dense correspondence by computing approximate intersection spaces and set-theoretic differences between the (hyper-ellipsoidal) allowable shape domains spanned by the models. To this end, we approximate the distribution of shapes lying in the intersection space using Markov chain Monte Carlo and subsequently apply Principal Component Analysis (PCA) to the posterior samples, eventually yielding a new SSM of the intersection space. We estimate differences between linear SSMs in a similar manner; here, however, the resulting spaces are no longer convex and we do not apply PCA but instead use the posterior samples for visualization. We showcase the proposed algorithm qualitatively by computing and analyzing intersection spaces and differences between publicly available face models, focusing on gender-specific male and female as well as identity and expression models. Our quantitative evaluation based on SSMs built from synthetic and real-world data sets provides detailed evidence that the introduced method is able to recover ground-truth intersection spaces and differences accurately.