arXiv subjects

Bruno Ribeiro

Publications and source records attributed to Bruno Ribeiro.

At least 19 recordsLinked to original sources

arXiv2026

Doubly critical mixed-order quasilinear equations: existence, multiplicity and regularity

We investigate a class of mixed-order quasilinear elliptic equations in $\mathbb R^N$ driven by the $q$-biharmonic and $p$-Laplacian operators, \[ Δ_q^2u-Δ_pu = λ\frac{|u|^{r_σ-2}u}{|x|^σ} +|u|^{p^*-2}u +|u|^{q^{**}-2}u, \] where $1<q<N/2$, $1<p<q^*$, $p\ne q$, $q\ne p^*$, and the weighted exponent is determined by the natural scaling of the equation. We establish compact weighted embeddings compatible with this mixed scaling and develop the corresponding variational framework. As an application, we prove existence and multiplicity of nontrivial solutions under suitable assumptions on the parameters. We also establish a local regularity result for the more general equation $Δ_q^2u-Δ_pu=f(x,u),$ where $f$ is a Carathéodory function with local critical growth. By combining nonlinear potential estimates, a regularity-lifting argument, and a finite bootstrap for an associated second-order system, we obtain higher local regularity of both $u$ and the nonlinear flux $|Δu|^{q-2}Δu$. This regularity result, which is also of independent interest, enables us to derive a Pohozaev-type identity for the equations under consideration.

math.AP↗

arXiv2026

Critical quasilinear elliptic systems with convex subcritical perturbations

We study a class of Dirichlet problems for coupled quasilinear elliptic systems driven by the $p$--Laplacian in a bounded domain, where the nonlinear terms split into a critical homogeneous part and a convex subcritical perturbation. Using variational methods, a nonlinear eigenvalue theory based on the Fadell--Rabinowitz $\mathbb Z_2$--cohomological index, and a refined linking construction, we prove the existence of a nontrivial solution for every parameter value under suitable dimensional assumptions. We also treat a nonhomogeneous version with small forcing terms by applying a recent abstract perturbation theorem, yielding the existence of two distinct nontrivial solutions.

math.AP↗

arXiv2026

Bridging Input Feature Spaces Towards Graph Foundation Models

Unlike vision and language domains, graph learning lacks a shared input space, as input features differ across graph datasets not only in semantics, but also in value ranges and dimensionality. This misalignment prevents graph models from generalizing across datasets, limiting their use as foundation models. In this work, we propose ALL-IN, a simple and theoretically grounded method that enables transferability across datasets with different input features. Our approach projects node features into a shared random space and constructs representations via covariance-based statistics, thus eliminating dependence on the original feature space. We show that the computed node-covariance operators and the resulting node representations are invariant in distribution to permutations of the input features. We further demonstrate that the expected operator exhibits invariance to general orthogonal transformations of the input features. Empirically, ALL-IN achieves strong performance across diverse node- and graph-level tasks on unseen datasets with new input features, without requiring architecture changes or retraining. These results point to a promising direction for input-agnostic, transferable graph models.

cs.LG↗

arXiv2026

Inhomogeneous nonlinear Schrödinger equations with competing singular nonlinearities

We study nonlinear elliptic equations that arise as stationary states of inhomogeneous nonlinear Schrödinger equations with competing singular nonlinearities. The model involves the Laplacian combined with weighted power-type terms and naturally leads to a variational formulation in a weighted Sobolev space obtained from the intersection of the homogeneous Sobolev space with a weighted Lebesgue space. Using sharp weighted Sobolev and Caffarelli--Kohn--Nirenberg type inequalities, we establish continuous and compact embeddings of this space into suitable weighted Lebesgue spaces. These embedding results, together with a natural scaling structure of the model, allow us to apply the abstract critical point framework of Mercuri and Perera (2026), yielding a sequence of nonlinear eigenvalues for the associated problem via a min--max scheme based on the Fadell--Rabinowitz cohomological index. Within this framework we obtain a broad collection of existence and multiplicity results for equations driven by sums of weighted power nonlinearities, covering interactions in both subcritical and critical cases. We also establish a nonexistence result derived from a Pohozaev-type identity. Finally, we analyze the radial setting, where improved radial Caffarelli--Kohn--Nirenberg inequalities allow us to enlarge some of the admissible embedding ranges. This leads to strengthened radial versions of our main results.

math.AP↗

arXiv2026

Window-based Membership Inference Attacks Against Fine-tuned Large Language Models

Most membership inference attacks (MIAs) against Large Language Models (LLMs) rely on global signals, like average loss, to identify training data. This approach, however, dilutes the subtle, localized signals of memorization, reducing attack effectiveness. We challenge this global-averaging paradigm, positing that membership signals are more pronounced within localized contexts. We introduce WBC (Window-Based Comparison), which exploits this insight through a sliding window approach with sign-based aggregation. Our method slides windows of varying sizes across text sequences, with each window casting a binary vote on membership based on loss comparisons between target and reference models. By ensembling votes across geometrically spaced window sizes, we capture memorization patterns from token-level artifacts to phrase-level structures. Extensive experiments across eleven datasets demonstrate that WBC substantially outperforms established baselines, achieving higher AUC scores and 2-3 times improvements in detection rates at low false positive thresholds. Our findings reveal that aggregating localized evidence is fundamentally more effective than global averaging, exposing critical privacy vulnerabilities in fine-tuned LLMs.

cs.CL↗

arXiv2026

Membership Inference Attacks Against Fine-tuned Diffusion Language Models

Diffusion Language Models (DLMs) represent a promising alternative to autoregressive language models, using bidirectional masked token prediction. Yet their susceptibility to privacy leakage via Membership Inference Attacks (MIA) remains critically underexplored. This paper presents the first systematic investigation of MIA vulnerabilities in DLMs. Unlike the autoregressive models' single fixed prediction pattern, DLMs' multiple maskable configurations exponentially increase attack opportunities. This ability to probe many independent masks dramatically improves detection chances. To exploit this, we introduce SAMA (Subset-Aggregated Membership Attack), which addresses the sparse signal challenge through robust aggregation. SAMA samples masked subsets across progressive densities and applies sign-based statistics that remain effective despite heavy-tailed noise. Through inverse-weighted aggregation prioritizing sparse masks' cleaner signals, SAMA transforms sparse memorization detection into a robust voting mechanism. Experiments on nine datasets show SAMA achieves 30% relative AUC improvement over the best baseline, with up to 8 times improvement at low false positive rates. These findings reveal significant, previously unknown vulnerabilities in DLMs, necessitating the development of tailored privacy defenses.

cs.LG↗

arXiv2026

Differentiable Constraint-Based Causal Discovery

Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly categorized as constraint-based or score-based approaches. Constraint-based methods offer rigorous causal discovery but are often hindered by small sample sizes, while score-based methods provide flexible optimization but typically forgo explicit conditional independence testing. This work explores a third avenue: developing differentiable $d$-separation scores, obtained through a percolation theory using soft logic. This enables the implementation of a new type of causal discovery method: gradient-based optimization of conditional independence constraints. Empirical evaluations demonstrate the robust performance of our approach in low-sample regimes, surpassing traditional constraint-based and score-based baselines on a real-world dataset. Code and data of the proposed method are publicly available at https://github$.$com/PurdueMINDS/DAGPA.

cs.LG↗

arXiv2026

Imitative Membership Inference Attack

A Membership Inference Attack (MIA) assesses how much a target machine learning model reveals about its training data by determining whether specific query instances were part of the training set. State-of-the-art MIAs rely on training hundreds of shadow models that are independent of the target model, leading to significant computational overhead. In this paper, we introduce Imitative Membership Inference Attack (IMIA), which employs a novel imitative training technique to strategically construct a small number of target-informed imitative models that closely replicate the target model's behavior for inference. Extensive experimental results demonstrate that IMIA substantially outperforms existing MIAs in various attack settings while only requiring less than 5% of the computational cost of state-of-the-art approaches.

cs.CR↗

arXiv2025

Viability of general relativity and modified gravity cosmologies using high-redshift cosmic probes

Several models based on General Relativity and Modified Gravity aim to reproduce the observed universe with precision comparable to the flat-$Λ$CDM cosmological model. In this study, we investigate the consistency of some of these models with current high-redshift cosmic data, assessing their ability to simultaneously describe both the background expansion and matter clustering, using measurements of the Hubble parameter $H(z)$, the luminosity distance $D_L(z)$, and the growth rate of structures $[fσ_8](z)$ through parametric and non-parametric methods. Our results indicate that background observables alone offer limited capacity to distinguish between models, while the inclusion of growth of structures data proves useful in revealing deviations, even if small. An $F(Q)$ model, the non-flat $Λ$CDM and the $ω$CDM emerge as alternatives well supported by data, closely matching the growth data and showing performance comparable to $Λ$CDM, as revealed by the Akaike Information Criterion. In contrast, $F(R)$ models are strongly disfavored compared to $Λ$CDM and $F(Q)$. However, according to the Bayesian Information Criterion, $Λ$CDM remains the preferred model among the models analysed. These analyses illustrate the usefulness of both parametric and non-parametric approaches to explore the observational viability of alternative cosmological models.

astro-ph.CO↗

arXiv2025

Fractional Schrödinger-Poisson-Slater equations in Coulomb-Sobolev spaces

We prove existence and multiplicity results for the fractional Schroedinger--Poisson--Slater equation $(-Δ)^s u + (I_α* u^2)u = f(|x|,u)$ in $\mathbb{R}^N$, where $0<s<1$ and $α\in (1,N)$. We seek solutions in a fractional Coulomb-Sobolev space and employ new tools in critical point theory that link the behavior of $f$ at zero and at infinity to the scaling properties of the left-hand side. For several regimes of $f$, we establish compactness for an associated action functional and obtain multiple solutions as critical points, with the number governed by the interaction of $f$ with a sequence of eigenvalues $\{λ_k\}$ defined via the $\mathbb{Z}_2$ cohomological index of Fadell and Rabinowitz (rather than the classical Krasnosel'skii genus). In this fractional setting we also prove new regularity results and necessary conditions for the existence of solutions.

math.AP↗

arXiv2025

Critical p-biharmonic problems and applications to Hamiltonian systems

We study fourth-order quasilinear elliptic problems that involve the p-biharmonic operator and Navier boundary conditions. The nonlinear term grows at the critical Sobolev rate. Starting from a Hamiltonian system of two second-order equations, we use an inversion step to reduce it to a single p-biharmonic equation with a lower-order perturbation. We handle both non-resonant and resonant cases and show that the problem admits non-trivial solutions when the forcing term and the superscaled perturbation are small enough. The proof combines concentration-compactness with an abstract critical point method based on the cohomological index. Our theorems cover both homogeneous and nonhomogeneous settings and extend Tarantello's classical results for the Laplacian, improving earlier work on p-biharmonic equations (including the case p = 2) and on critical Hamiltonian systems.

math.AP↗

arXiv2025

Cascading and Proxy Membership Inference Attacks

A Membership Inference Attack (MIA) assesses how much a trained machine learning model reveals about its training data by determining whether specific query instances were included in the dataset. We classify existing MIAs into adaptive or non-adaptive, depending on whether the adversary is allowed to train shadow models on membership queries. In the adaptive setting, where the adversary can train shadow models after accessing query instances, we highlight the importance of exploiting membership dependencies between instances and propose an attack-agnostic framework called Cascading Membership Inference Attack (CMIA), which incorporates membership dependencies via conditional shadow training to boost membership inference performance. In the non-adaptive setting, where the adversary is restricted to training shadow models before obtaining membership queries, we introduce Proxy Membership Inference Attack (PMIA). PMIA employs a proxy selection strategy that identifies samples with similar behaviors to the query instance and uses their behaviors in shadow models to perform a membership posterior odds test for membership inference. We provide theoretical analyses for both attacks, and extensive experimental results demonstrate that CMIA and PMIA substantially outperform existing MIAs in both settings, particularly in the low false-positive regime, which is crucial for evaluating privacy risks.

cs.CR↗

arXiv2025

Castle: Causal Cascade Updates in Relational Databases with Large Language Models

This work introduces Castle, the first framework for schema-only cascade update generation using large language models (LLMs). Despite recent advances in LLMs for Text2SQL code generation, existing approaches focus primarily on SELECT queries, neglecting the challenges of SQL update operations and their ripple effects. Traditional CASCADE UPDATE constraints are static and unsuitable for modern, denormalized databases, which demand dynamic, context-aware updates. Castle enables natural language instructions to trigger multi-column, causally consistent SQL UPDATE statements, without revealing table content to the model. By framing UPDATE SQL generation as a divide-and-conquer task with LLMs' reasoning capacity, Castle can determine not only which columns must be directly updated, but also how those updates propagate through the schema, causing cascading updates -- all via nested queries and substructures that ensure data confidentiality. We evaluate it on real-world causal update scenarios, demonstrating its ability to produce accurate SQL updates, and thereby highlighting the reasoning ability of LLMs in automated DBMS.

cs.DB↗

arXiv2025

Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounders

We consider the task of out-of-distribution (OOD) generalization, where the distribution shift is due to an unobserved confounder ($Z$) affecting both the covariates ($X$) and the labels ($Y$). This confounding introduces heterogeneity in the predictor, i.e., $P(Y | X) = E_{P(Z | X)}[P(Y | X,Z)]$, making traditional covariate and label shift assumptions unsuitable. OOD generalization differs from traditional domain adaptation in that it does not assume access to the covariate distribution ($X^\text{te}$) of the test samples during training. These conditions create a challenging scenario for OOD robustness: (a) $Z^\text{tr}$ is an unobserved confounder during training, (b) $P^\text{te}(Z) \neq P^\text{tr}(Z)$, (c) $X^\text{te}$ is unavailable during training, and (d) the predictive distribution depends on $P^\text{te}(Z)$. While prior work has developed complex predictors requiring multiple additional variables for identifiability of the latent distribution, we explore a set of identifiability assumptions that yield a surprisingly simple predictor using only a single additional variable. Our approach demonstrates superior empirical performance on several benchmark tasks.

cs.LG↗

arXiv2025

A Cloud-native Agile approach to cyber platform prototyping and integration for astronomy: the ENGAGE SKA case

The Square Kilometre Array (SKA) Observatory is gearing up the formal construction of its two radio interferometers in Australia and South Africa after the end of design and pre-construction phases. Agile methodologies, the Cloud native Computing technologies and the DevOps software ideas are influencing the design of compute infrastructures that will be key to reduce the operational costs of SKA while improving the control and monitoring of the SKA antennas and ancillary systems, Correlators, HPC facilities or related data centre tiered systems. These tools will likely include advanced power metering technologies and efficient distribution automation and Network Operation Centres (NOC). SKA will become the world's largest radio telescope and is expected to achieve its first science by 2026. To cope with this dimension and complexity, a key part of this distributed Observatory is the overall software control and monitoring system embodied in the Observatory Management and Control (OMC) and the Services Teams that requires specialized Agile Teams to assist in software and cyber infrastructure building using an Agile development environment that includes test automation, Continuous Integration, and Continuous Deployment. To manage such a large and distributed machine, the Agile approach was adopted for the core software package of the SKA Telescope aimed at scheduling observations, controlling their execution, monitoring the telescope status and ensuring scalability and reliability. Here, we report on the ENGAGE SKA ciberinfrastructure prototyping support to the SKA Agile Software Development Life Cycle (SDLC).

astro-ph.IM↗

arXiv2025

DiTASK: Multi-Task Fine-Tuning with Diffeomorphic Transformations

Pre-trained Vision Transformers now serve as powerful tools for computer vision. Yet, efficiently adapting them for multiple tasks remains a challenge that arises from the need to modify the rich hidden representations encoded by the learned weight matrices, without inducing interference between tasks. Current parameter-efficient methods like LoRA, which apply low-rank updates, force tasks to compete within constrained subspaces, ultimately degrading performance. We introduce DiTASK a novel Diffeomorphic Multi-Task Fine-Tuning approach that maintains pre-trained representations by preserving weight matrix singular vectors, while enabling task-specific adaptations through neural diffeomorphic transformations of the singular values. By following this approach, DiTASK enables both shared and task-specific feature modulations with minimal added parameters. Our theoretical analysis shows that DITASK achieves full-rank updates during optimization, preserving the geometric structure of pre-trained features, and establishing a new paradigm for efficient multi-task learning (MTL). Our experiments on PASCAL MTL and NYUD show that DiTASK achieves state-of-the-art performance across four dense prediction tasks, using 75% fewer parameters than existing methods. Our code is available [here](https://github.com/ipsitmantri/DiTASK).

cs.CV↗

arXiv2025

Boosting Relational Deep Learning with Pretrained Tabular Models

Relational databases, organized into tables connected by primary-foreign key relationships, are a common format for organizing data. Making predictions on relational data often involves transforming them into a flat tabular format through table joins and feature engineering, which serve as input to tabular methods. However, designing features that fully capture complex relational patterns remains challenging. Graph Neural Networks (GNNs) offer a compelling alternative by inherently modeling these relationships, but their time overhead during inference limits their applicability for real-time scenarios. In this work, we aim to bridge this gap by leveraging existing feature engineering efforts to enhance the efficiency of GNNs in relational databases. Specifically, we use GNNs to capture complex relationships within relational databases, patterns that are difficult to featurize, while employing engineered features to encode temporal information, thereby avoiding the need to retain the entire historical graph and enabling the use of smaller, more efficient graphs. Our \textsc{LightRDL} approach not only improves efficiency, but also outperforms existing models. Experimental results on the RelBench benchmark demonstrate that our framework achieves up to $33\%$ performance improvement and a $526\times$ inference speedup compared to GNNs, making it highly suitable for real-time inference.

cs.DB↗

arXiv2025

TRIX: A More Expressive Model for Zero-shot Domain Transfer in Knowledge Graphs

Fully inductive knowledge graph models can be trained on multiple domains and subsequently perform zero-shot knowledge graph completion (KGC) in new unseen domains. This is an important capability towards the goal of having foundation models for knowledge graphs. In this work, we introduce a more expressive and capable fully inductive model, dubbed TRIX, which not only yields strictly more expressive triplet embeddings (head entity, relation, tail entity) compared to state-of-the-art methods, but also introduces a new capability: directly handling both entity and relation prediction tasks in inductive settings. Empirically, we show that TRIX outperforms the state-of-the-art fully inductive models in zero-shot entity and relation predictions in new domains, and outperforms large-context LLMs in out-of-domain predictions. The source code is available at https://github.com/yuchengz99/TRIX.

cs.LG↗