Online high-dimensional regression requires algorithms that can update sequentially while preserving structural sparsity. We propose \textit{Adaptive Iterative Hard Thresholding (AIHT)}, an online sparse-regression framework that alternates stochastic subgradient updates with adaptively scheduled hard-thresholding steps. The key idea is to separate support discovery from local refinement: early in the learning process, AIHT delays thresholding so that weak but informative coordinates have time to accumulate signal, while later it increases the projection frequency to stabilize the sparse estimator and exploit local curvature. We develop the theory for high-dimensional online quantile regression, a challenging setting in which the loss is nonsmooth and the data may exhibit heterogeneity or heavy-tailed noise. Under restricted curvature and gradient-leakage conditions, AIHT remains in an inflated sparse cone, exhibits a two-phase convergence behavior, and attains logarithmic regret for the sliding-window objective. Simulations for online quantile regression, together with threshold-scheduling ablations, support the proposed mechanism and illustrate its advantage over standard online sparse-learning baselines.

A deep network's loss is invariant to continuous symmetries of its parameters: the logit shift, the ReLU rescaling, the LayerNorm scale, the per-head attention rotation. Adam's per-coordinate preconditioner drifts along each symmetry orbit, which pulls the trajectory off the symmetry quotient where the optimization lives and blurs the singular-learning rate the quotient makes readable. We build DDC, a Dead-Direction Conditioner that lifts a base optimizer into a $G$-equivariant one: it conditions the optimizer's state in the orbit decomposition of a $G$-invariant metric, so the trajectory stays a preconditioned gradient flow on the quotient $\barΘ= Θ/G$. The construction carries four architectural gauges (cross-entropy shift, ReLU and SwiGLU rescaling, LayerNorm and RMSNorm scale, and a per-head $O(d_{\rm head})$ attention rotation matched to RoPE), proves exactly equivariant on an Adam base, and composes with a Muon base through a gauge-equivariant orthogonaliser. Respecting the symmetry changes both the minimum the optimizer reaches and what it leaves measurable there. On a language model trained past the point of fit, DDCAdam resists the over-training collapse AdamW falls into, holding a validation-train loss gap of 0.67 against 5.88, and reads the dead-direction rate in 32 of 65 layer-by-observable cells where AdamW reads it in 7. A vision transformer trained from scratch reaches lower validation loss (1.71 against 2.12) while compressing spare feed-forward capacity a matched AdamW leaves intact. On a Muon base, where the rotation gauge composes exactly, DDCMuon groks ten of eleven seeds at depth 24 that a plain Muon never reaches. Built into the optimizer, a network's gauge symmetry sharpens the minimum it finds and turns that minimum's geometry into something the trajectory can measure.

Foundation models trained on large-scale de-identified electronic health records (EHRs) hold promise for clinical applications. However, their capacity to memorize patient information raises important privacy concerns. In this work, we introduce a suite of black-box evaluation tests to assess privacy-related memorization risks in foundation models trained on structured EHR data. Our framework includes methods for probing memorization at both the embedding and generative levels, and aims to distinguish between model generalization and harmful memorization in clinically relevant settings. We contextualize memorization in terms of its potential to compromise patient privacy, particularly for vulnerable subgroups.

Multimodal federated learning (MMFL) has gained increasing popularity due to its ability to leverage the correlation between various modalities, meanwhile preserving data privacy for different clients. However, recent studies show that correlation between modalities increase the vulnerability of federated learning against Gradient Inversion Attack (GIA). The complicated situation of MMFL privacy preserving can be summarized as follows: 1) different modality transmits different amounts of information, thus requires various protection strength; 2) correlation between modalities should be taken into account. This paper introduces an information theory perspective to analyze the leaked privacy in process of MMFL, and tries to propose a more reasonable protection method Sec-MMFL based on assessing different information leakage possibilities of each modality by conditional mutual information and adjust the corresponding protection strength. Moreover, we use mutual information to reduce the cross-modality information leakage in MMFL. Experiments have proven that our method can bring more balanced and comprehensive protection at an acceptable cost.

Side-channel analysis (SCA) poses a real-world threat by exploiting unintentional physical signals to extract secret information from secure devices. Evaluation labs also use the same techniques to certify device security. In recent years, deep learning has emerged as a prominent method for SCA, achieving state-ofthe-art attack performance at the cost of interpretability. Understanding how neural networks extract secrets is crucial for security evaluators aiming to defend against such attacks, as only by understanding the attack can one propose better countermeasures. In this work, we apply mechanistic interpretability to neural networks trained for SCA, revealing how models exploit what leakage in side-channel traces. We focus on sudden jumps in performance to reverse engineer learned representations, ultimately recovering secret masks and moving the evaluation process from blackbox to white-box. Our results show that mechanistic interpretability can scale to realistic SCA settings, even when relevant inputs are sparse, model accuracies are low, and side-channel protections prevent standard input interventions.

The rapid adoption of generative AI and Large Language Models (LLMs) has spurred interest in synthetic data as a privacy-preserving alternative to sensitive real-world datasets. However, generating high-utility synthetic data often carries the risk of memorizing and regurgitating private information from the training corpus. In this work, we present a customizable empirical auditing framework designed to detect and explain such data disclosures. Our framework introduces a mechanism to distinguish between "true disclosures"-where the system directly reproduces a user's information-and "phantom disclosures''-where the system incidentally generates a user's data. By partitioning input data into training and holdout sets and applying rigorous statistical hypothesis testing, we determine if observed disclosures are consistent with strict privacy baselines, such as zero-learning or specific Differential Privacy (DP) bounds. Crucially, this approach requires no model access, no canary insertion, and no reference model training -only the synthetic output and a held-out control set. We demonstrate that this framework effectively functions as a membership inference attack, providing empirical lower bounds on privacy leakage that are tighter than prior data-based auditing methods. Our approach is model-agnostic, applies to any synthetic data generation mechanism, and requires orders of magnitude fewer computational resources than shadow-model or canary-based alternatives.

Evaluating large language models (LLMs) poses significant challenges, particularly due to issues of data contamination and the leakage of correct answers. To address these challenges, we introduce ThinkBench, a novel evaluation framework designed to robustly evaluate the reasoning capability of LLMs. ThinkBench proposes a dynamic data generation method for constructing out-of-distribution (OOD) datasets and offers an OOD dataset that contains 2,912 samples drawn from reasoning tasks.

Diffusion Models have gained significant popularity due to their remarkable capabilities in image generation, albeit at the cost of intensive computation requirement. Meanwhile, despite their widespread deployment in inference services such as Midjourney, concerns about the potential leakage of sensitive information in uploaded user prompts have arisen. Existing solutions either fail to strike an effective balance between utility and efficiency, or lack rigorous privacy guarantees. To bridge this gap, we propose ObCLIP, a plug-and-play safeguard that enables oblivious cloud-device hybrid generation scheme. By oblivious, each input prompt is transformed into a set of semantically similar candidate prompts that differ only in sensitive attributes (e.g., gender, ethnicity).

Parameter-efficient fine-tuning of large language models (LLMs) can exhibit problematic memorization of individual training examples. Empirical privacy auditing (EPA) quantifies this risk by measuring realistic data leakage on membership inference (MI) or reconstruction attacks. A key challenge in EPA is designing ``canary'' examples that are mixed with the privacy-sensitive training data. We propose generating synthetic canaries via high-temperature sampling ($T \geq 0.8$) from LLMs, using prompts tailored to the privacy-sensitive training data. These canaries act as high-influence outliers, ensuring high identifiability and hence strong audits. Further, since the canaries are themselves non-private, they are inspectable and can be inserted with repetition without jeopardizing the privacy of the real data. An important use of models fine-tuned on privacy-sensitive data is the generation of synthetic data. This also comes with privacy risk. We introduce a powerful synthetic data audit based on fine-tuning an auxiliary model on the synthetic data. Auditing the auxiliary model for the original canaries then provides a strong estimate of the privacy leakage through the synthetic data. Finally, leveraging our strong auditing methodologies, we perform a systematic investigation into the interacting effects of model capacity and canary entropy on memorization.

Selecting a finite dictionary of observables whose span is Koopman-invariant is a central challenge in data-driven Koopman operator approximation. We address this problem by exploiting zero-block structure in Extended Dynamic Mode Decomposition (EDMD) matrices. We show that any sub-dictionary whose span is Koopman-invariant induces an exact zero block in the EDMD matrix, even for finite data. We then show that such blocks can be detected by applying PageRank to a row-normalized EDMD matrix constructed from a large initial dictionary. The theory extends to approximately invariant subspaces and yields stronger guarantees for personalized PageRank (PPR) when the seed observables lie inside the target block and reach all observables in that block. Combining EDMD concentration bounds with PageRank perturbation theory gives end-to-end detection guarantees with $O(1/\sqrt{M})$ finite-sample scaling and explicit constants. More generally, without assuming an invariant subspace exists, high PPR mass on a sub-dictionary controls discounted multi-step leakage from the seed observables. Numerical experiments on the Duffing oscillator, Van der Pol oscillator, Lorenz system, and a three-well Ramachandran potential suggest that the method identifies compact, interpretable dictionaries with accurate predictions.