Benefiting from pre-trained text-to-image (T2I) diffusion models, real-world image super-resolution (Real-ISR) methods can synthesize rich and realistic details. However, due to the inherent stochasticity of T2I models, different noise inputs often lead to outputs with varying perceptual quality. Although this randomness is sometimes seen as a limitation, it also introduces a wider perceptual quality range, which can be exploited to improve Real-ISR performance. To this end, we introduce Direct Perceptual Preference Optimization for Real-ISR (DP$^2$O-SR), a framework that aligns generative models with perceptual preferences without requiring costly human annotations. We construct a hybrid reward signal by combining full-reference and no-reference image quality assessment (IQA) models trained on large-scale human preference datasets. This reward encourages both structural fidelity and natural appearance. To better utilize perceptual diversity, we move beyond the standard best-vs-worst selection and construct multiple preference pairs from outputs of the same model. Our analysis reveals that the optimal selection ratio depends on model capacity: smaller models benefit from broader coverage, while larger models respond better to stronger contrast in supervision. Furthermore, we propose hierarchical preference optimization, which adaptively weights training pairs based on intra-group reward gaps and inter-group diversity, enabling more efficient and stable learning. Extensive experiments across both diffusion- and flow-based T2I backbones demonstrate that DP$^2$O-SR significantly improves perceptual quality and generalizes well to real-world benchmarks.

E-values have gained prominence as flexible tools for statistical inference and risk control, enabling anytime- and post-hoc-valid procedures under minimal assumptions. However, many real-world applications fundamentally rely on sensitive data, which can be leaked through e-values. To ensure their safe release, we propose a general framework to transform non-private e-values into differentially private ones. Towards this end, we develop a novel biased multiplicative noise mechanism that ensures our e-values remain statistically valid. We show that our differentially private e-values attain strong statistical power, and are asymptotically as powerful as their non-private counterparts. Experiments across online risk monitoring, private healthcare, and conformal e-prediction demonstrate our approach's effectiveness and illustrate its broad applicability.

Personalized federated learning (PFL) has garnered significant attention for its ability to address heterogeneous client data distributions while preserving data privacy. However, when local client data is limited, deep learning models often suffer from insufficient training, leading to suboptimal performance. Foundation models, such as CLIP (Contrastive Language-Image Pretraining), exhibit strong feature extraction capabilities and can alleviate this issue by fine-tuning on limited local data. Despite their potential, foundation models are rarely utilized in federated learning scenarios, and challenges related to integrating new clients remain largely unresolved. To address these challenges, we propose the Dual Prompt Personalized Federated Learning (DP2FL) framework, which introduces dual prompts and an adaptive aggregation strategy. DP2FL combines global task awareness with local data-driven insights, enabling local models to achieve effective generalization while remaining adaptable to specific data distributions. Moreover, DP2FL introduces a global model that enables prediction on new data sources and seamlessly integrates newly added clients without requiring retraining. Experimental results in highly heterogeneous environments validate the effectiveness of DP2FL's prompt design and aggregation strategy, underscoring the advantages of prediction on novel data sources and demonstrating the seamless integration of new clients into the federated learning framework.

Asynchronous event sequence clustering aims to group similar event sequences in an unsupervised manner. Mixture models of temporal point processes have been proposed to solve this problem, but they often suffer from overfitting, leading to excessive cluster generation with a lack of diversity. To overcome these limitations, we propose a Bayesian mixture model of Temporal Point Processes with Determinantal Point Process prior (TP$^2$DP$^2$) and accordingly an efficient posterior inference algorithm based on conditional Gibbs sampling. Our work provides a flexible learning framework for event sequence clustering, enabling automatic identification of the potential number of clusters and accurate grouping of sequences with similar features. It is applicable to a wide range of parametric temporal point processes, including neural network-based models. Experimental results on both synthetic and real-world data suggest that our framework could produce moderately fewer yet more diverse mixture components, and achieve outstanding results across multiple evaluation metrics.

Over the last 15-20 years we have been witnessing a rapid development of machine learning (ML) and neural networks (NN) concepts. As the need for efficient processing and interpretation of large data sets is estimated to further grow in the years to come, many fundamental algorithmic and theoretical NN breakthroughs are to be expected. To be able to adequately address upcoming challenges an excellent understanding of the ultimate limits of the employed technologies is needed. We in this paper study a mathematical problem that is directly connected to a notion of network capacity which is an example of such a limit. Characterizing presence or absence of injectivity as a property of random functions is the mathematical problem of our interest here. The mere definition of the functional injectivity implies its critical role in studying inverse problems. Namely, well-or ill-posedness of these problems is in a direct correspondence with the associated injectivity. Recent utilization of neural networks in studying (nonlinear) inverse problems therefore critically relies on their injectivity properties (see, e.g., [6,11,15,16,19,31,36,38]). Consequently, injectivity as a purely mathematical object is in these contexts transformed into a practically rather important NN architectures feature.

Federated learning (FL) is a distributed machine learning approach that allows multiple clients to collaboratively train a model without sharing their raw data. To prevent sensitive information from being inferred through the model updates shared in FL, differentially private federated learning (DPFL) has been proposed. DPFL ensures formal and rigorous privacy protection in FL by clipping and adding random noise to the shared model updates. However, the existing DPFL methods often result in severe model utility degradation, especially in settings with data heterogeneity. To enhance model utility, we propose a novel DPFL method named DP$^2$-FedSAM: Differentially Private and Personalized Federated Learning with Sharpness-Aware Minimization. DP$^2$-FedSAM leverages personalized partial model-sharing and sharpness-aware minimization optimizer to mitigate the adverse impact of noise addition and clipping, thereby significantly improving model utility without sacrificing privacy. From a theoretical perspective, we provide a rigorous theoretical analysis of the privacy and convergence guarantees of our proposed method. To evaluate the effectiveness of DP$^2$-FedSAM, we conduct extensive evaluations based on common benchmark datasets. Our results verify that our method improves the privacy-utility trade-off compared to the existing DPFL methods, particularly in heterogeneous data settings.

We consider the classical \emph{spherical} perceptrons and study their capacities. The famous zero-threshold case was solved in the sixties of the last century (see, \cite{Wendel62,Winder,Cover65}) through the high-dimensional combinatorial considerations. The general threshold, $\kappa$, case though turned out to be much harder and stayed out of reach for the following several decades. A substantial progress was then made in \cite{SchTir02} and \cite{StojnicGardGen13} where the \emph{positive} threshold ($\kappa\geq 0$) scenario was finally fully settled. While the negative counterpart ($\kappa\leq 0$) remained out of reach, \cite{StojnicGardGen13} did show that the random duality theory (RDT) is still powerful enough to provide excellent upper bounds. Moreover, in \cite{StojnicGardSphNeg13}, a \emph{partially lifted} RDT variant was considered and it was shown that the upper bounds of \cite{StojnicGardGen13} can be lowered. After recent breakthroughs in studying bilinearly indexed (bli) random processes in \cite{Stojnicsflgscompyx23,Stojnicnflgscompyx23}, \emph{fully lifted} random duality theory (fl RDT) was developed in \cite{Stojnicflrdt23}. We here first show that the \emph{negative spherical perceptrons} can be fitted into the frame of the fl RDT and then employ the whole fl RDT machinery to characterize the capacity. To be fully practically operational, the fl RDT requires a substantial numerical work. We, however, uncover remarkable closed form analytical relations among key lifting parameters. Such a discovery enables performing the needed numerical calculations to obtain concrete capacity values. We also observe that an excellent convergence (with the relative improvement $\sim 0.1\%$) is achieved already on the third (second non-trivial) level of the \emph{stationarized} full lifting.

The Adam optimizer is a popular choice in contemporary deep learning, due to its strong empirical performance. However we observe that in privacy sensitive scenarios, the traditional use of Differential Privacy (DP) with the Adam optimizer leads to sub-optimal performance on several tasks. We find that this performance degradation is due to a DP bias in Adam's second moment estimator, introduced by the addition of independent noise in the gradient computation to enforce DP guarantees. This DP bias leads to a different scaling for low variance parameter updates, that is inconsistent with the behavior of non-private Adam. We propose DP-AdamBC, an optimization algorithm which removes the bias in the second moment estimation and retrieves the expected behaviour of Adam. Empirically, DP-AdamBC significantly improves the optimization performance of DP-Adam by up to 3.5% in final accuracy in image, text, and graph node classification tasks.

Prompt-based pre-trained language models (PLMs) paradigm have succeeded substantially in few-shot natural language processing (NLP) tasks. However, prior discrete prompt optimization methods require expert knowledge to design the base prompt set and identify high-quality prompts, which is costly, inefficient, and subjective. Meanwhile, existing continuous prompt optimization methods improve the performance by learning the ideal prompts through the gradient information of PLMs, whose high computational cost, and low readability and generalizability are often concerning. To address the research gap, we propose a Dialogue-comprised Policy-gradient-based Discrete Prompt Optimization ($DP_2O$) method. We first design a multi-round dialogue alignment strategy for readability prompt set generation based on GPT-4. Furthermore, we propose an efficient prompt screening metric to identify high-quality prompts with linear complexity. Finally, we construct a reinforcement learning (RL) framework based on policy gradients to match the prompts to inputs optimally. By training a policy network with only 0.67% of the PLM parameter size on the tasks in the few-shot setting, $DP_2O$ outperforms the state-of-the-art (SOTA) method by 1.52% in accuracy on average on four open-source datasets. Moreover, subsequent experiments also demonstrate that $DP_2O$ has good universality, robustness, and generalization ability.

Privacy noise may negate the benefits of using adaptive optimizers in differentially private model training. Prior works typically address this issue by using auxiliary information (e.g., public data) to boost the effectiveness of adaptive optimization. In this work, we explore techniques to estimate and efficiently adapt to gradient geometry in private adaptive optimization without auxiliary data. Motivated by the observation that adaptive methods can tolerate stale preconditioners, we propose differentially private adaptive training with delayed preconditioners (DP^2), a simple method that constructs delayed but less noisy preconditioners to better realize the benefits of adaptivity. Theoretically, we provide convergence guarantees for our method for both convex and non-convex problems, and analyze trade-offs between delay and privacy noise reduction. Empirically, we explore DP^2 across several real-world datasets, demonstrating that it can improve convergence speed by as much as 4x relative to non-adaptive baselines and match the performance of state-of-the-art optimization methods that require auxiliary data.