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Behnoosh Zamanlooy

Behnoosh Zamanlooy appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Artificial IntelligenceMachine Learningmath.FANeural and Evolutionary Computingmath.MGmath.NANumerical Analysis

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Published work

3 published item(s)

preprint2026arXiv

On Privacy Leakage in Tabular Diffusion Models: Influential Factors, Attacker Knowledge, and Metrics

Tabular data plays an important role in many fields and industries, including those with elevated privacy considerations and risks. As such, there is a rising interest in generating high-quality synthetic proxies for real tabular data as a means of reducing privacy risk and proprietary data exposure. With tabular diffusion models (TDMs) demonstrating leading performance in synthesizing such data, understanding and measuring the privacy risks associated with these models is imperative. Leveraging state-of-the-art membership inference attacks for TDMs in both black- and white-box settings, this work quantifies the impact of training setup, synthesis choices, and attacker knowledge on privacy leakage. Moreover, the results demonstrate that adversaries need not have perfect knowledge of the training setup, identical data distributions, or massive compute resources to construct successful attacks. Finally, the pitfalls associated with applying heuristic privacy metrics, such as distance-to-closest record, are revealed.

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preprint2022arXiv

Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?

We study the problem of approximating compactly-supported integrable functions while implementing their support set using feedforward neural networks. Our first main result transcribes this "structured" approximation problem into a universality problem. We do this by constructing a refinement of the usual topology on the space $L^1_{\operatorname{loc}}(\mathbb{R}^d,\mathbb{R}^D)$ of locally-integrable functions in which compactly-supported functions can only be approximated in $L^1$-norm by functions with matching discretized support. We establish the universality of ReLU feedforward networks with bilinear pooling layers in this refined topology. Consequentially, we find that ReLU feedforward networks with bilinear pooling can approximate compactly supported functions while implementing their discretized support. We derive a quantitative uniform version of our universal approximation theorem on the dense subclass of compactly-supported Lipschitz functions. This quantitative result expresses the depth, width, and the number of bilinear pooling layers required to construct this ReLU network via the target function's regularity, the metric capacity and diameter of its essential support, and the dimensions of the inputs and output spaces. Conversely, we show that polynomial regressors and analytic feedforward networks are not universal in this space.

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preprint2022arXiv

Universal Approximation Under Constraints is Possible with Transformers

Many practical problems need the output of a machine learning model to satisfy a set of constraints, $K$. Nevertheless, there is no known guarantee that classical neural network architectures can exactly encode constraints while simultaneously achieving universality. We provide a quantitative constrained universal approximation theorem which guarantees that for any non-convex compact set $K$ and any continuous function $f:\mathbb{R}^n\rightarrow K$, there is a probabilistic transformer $\hat{F}$ whose randomized outputs all lie in $K$ and whose expected output uniformly approximates $f$. Our second main result is a "deep neural version" of Berge's Maximum Theorem (1963). The result guarantees that given an objective function $L$, a constraint set $K$, and a family of soft constraint sets, there is a probabilistic transformer $\hat{F}$ that approximately minimizes $L$ and whose outputs belong to $K$; moreover, $\hat{F}$ approximately satisfies the soft constraints. Our results imply the first universal approximation theorem for classical transformers with exact convex constraint satisfaction. They also yield that a chart-free universal approximation theorem for Riemannian manifold-valued functions subject to suitable geodesically convex constraints.

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