arXiv subjects

Diego Mesquita

Publications and source records attributed to Diego Mesquita.

At least 19 recordsLinked to original sources

arXiv2026

Cooperative Sheaf Neural Networks

Sheaf diffusion has recently emerged as a promising design pattern for graph representation learning due to its inherent ability to handle heterophilic data and avoid oversmoothing. Meanwhile, cooperative message passing has also been proposed as a way to enhance the flexibility of information diffusion by allowing nodes to independently choose whether to propagate/gather information from/to neighbors. A natural question ensues: is sheaf diffusion capable of exhibiting this cooperative behavior? Here, we provide a negative answer to this question. In particular, we show that existing sheaf diffusion methods fail to achieve cooperative behavior due to the lack of message directionality. To circumvent this limitation, we introduce the notion of cellular sheaves over directed graphs and characterize their in- and out-degree Laplacians. We leverage our construction to propose Cooperative Sheaf Neural Networks (CSNNs). Theoretically, we characterize the receptive field of CSNN and show it allows nodes to selectively attend (listen) to arbitrarily far nodes while ignoring all others in their path, potentially mitigating oversquashing. Our experiments show that CSNN presents overall better performance compared to prior art on sheaf diffusion as well as cooperative graph neural networks.

cs.LG↗

arXiv2026

Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspective

Graph Neural Networks (GNNs) often struggle to capture long-range dependencies due to over-squashing -- a phenomenon in which the repeated compression of node embeddings into finite-size messages causes representations to collapse. Over-squashing is most often diagnosed as a property of the graph topology, with effective resistance serving as a principled measure of the bottleneck. We provide a complementary view on the matter: building on cellular sheaves, we introduce sheaf effective resistance, a generalization of effective resistance that depends on the sheaf attached to the graph, and we prove that for flat vector bundles, the over-squashing sensitivity in the Jacobian sense is upper bounded by a quantity related to the sheaf effective resistance between the nodes. The bottleneck thus need not lie in the graph itself: it can be relocated, and reduced, by adjusting the sheaf. We instantiate this idea in FlatNSD, a simple message-passing variant of Neural Sheaf Diffusion, and show that it implicitly learns to modulate total sheaf effective resistance, performing well on benchmarks designed to stress over-squashing without altering the original graph topology.

stat.ML↗

arXiv2026

Particle GFlowNets: Rethinking Generative Marginalization Models

Generative Marginalization Models (MaMs) have been recently introduced as efficient neural sampling models for any-order autoregressive modelling of discrete distributions. By learning both the marginal and conditional probabilities of a persistent-block Gibbs sampler, MaMs enable fast posterior evaluation with a single neural network forward pass. While prior work has considered MaMs to be distinct from Generative Flow Networks (GFlowNets), a well-established paradigm for inference in discrete stochastic models, we show that they are equivalent. Then, we also extend MaMs' sampling strategy to non-autoregressive generative processes. In particular, we describe an automatic criterion for full-state rejuvenation of the Gibbs sampler, derived from the Gelman-Rubin statistic, which plays a key role in speeding up learning convergence. Our experiments show that our method, called Particle GFlowNets, markedly accelerates training in large combinatorial spaces.

cs.LG↗

arXiv2026

Differentiable Lifting for Topological Neural Networks

Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.g., cycles and cliques) to boost the expressive power of message-passing neural networks. In turn, however, these structures are typically identified a priori through an unsupervised graph lifting operation. Notwithstanding, this choice is crucial and may have a drastic impact on a TNN's performance on downstream tasks. To circumvent this issue, we propose $\partial$lift (DiffLift), a general framework for learning graph liftings to hypergraphs and cellular- and simplicial complexes in an end-to-end fashion. In particular, our approach leverages learned vertex-level latent representations to identify and parameterize distributions over candidate higher-order cells for inclusion. This results in a scalable model which can be readily integrated into any TNN. Our experiments show that $\partial$lift outperforms existing lifting methods on multiple benchmarks for graph and node classification across different TNN architectures. Notably, our approach leads to gains of up to 45% over static liftings, including both connectivity- and feature-based ones.

cs.LG↗

arXiv2026

Gaussian Sheaf Neural Networks

Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better represented by probability distributions than real vectors. Concretely, when node features are Gaussians, characterized by a mean and a covariance matrix, naively concatenating their parameters into a single vector and applying standard message passing discards the geometric and algebraic structure that governs means and covariances. We propose Gaussian Sheaf Neural Networks (GSNNs), a principled framework that incorporates these inductive biases into graph-based learning. Building on the theory of cellular sheaves, we derive a new Laplacian operator that generalizes the sheaf Laplacian to this setting and preserves its key properties. We complement our theoretical contributions with experiments on synthetic and real-world data that illustrate the practical relevance of GSNNs.

cs.LG↗

arXiv2026

On the Identifiability of Tensor Ranks via Prior Predictive Matching

Selecting the latent dimensions (ranks) in tensor factorization is a central challenge that often relies on heuristic methods. This paper introduces a rigorous approach to determine rank identifiability in probabilistic tensor models, based on prior predictive moment matching. We transform a set of moment matching conditions into a log-linear system of equations in terms of marginal moments, prior hyperparameters, and ranks; establishing an equivalence between rank identifiability and the solvability of such system. We apply this framework to four foundational tensor-models, demonstrating that the linear structure of the PARAFAC/CP model, the chain structure of the Tensor Train model, and the closed-loop structure of the Tensor Ring model yield solvable systems, making their ranks identifiable. In contrast, we prove that the symmetric topology of the Tucker model leads to an underdetermined system, rendering the ranks unidentifiable by this method. For the identifiable models, we derive explicit closed-form rank estimators based on the moments of observed data only. We empirically validate these estimators and evaluate the robustness of the proposal.

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arXiv2026

MATH-PT: A Math Reasoning Benchmark for European and Brazilian Portuguese

The use of large language models (LLMs) for complex mathematical reasoning is an emergent area of research, with fast progress in methods, models, and benchmark datasets. However, most mathematical reasoning evaluations exhibit a significant linguistic bias, with the vast majority of benchmark datasets being exclusively in English or (at best) translated from English. We address this limitation by introducing {\sc Math-PT}, a novel dataset comprising 1,729 mathematical problems written in European and Brazilian Portuguese. {\sc Math-PT} is curated from a variety of high-quality native sources, including mathematical Olympiads, competitions, and exams from Portugal and Brazil. We present a comprehensive benchmark of current state-of-the-art LLMs on {\sc Math-PT}, revealing that frontier reasoning models achieve strong performance in multiple choice questions compared to open weight models, but that their performance decreases for questions with figures or open-ended questions. To facilitate future research, we release the benchmark dataset and model outputs.

cs.CL↗

arXiv2026

Boosted GFlowNets: Improving Exploration via Sequential Learning

Generative Flow Networks (GFlowNets) are powerful samplers for compositional objects that, by design, sample proportionally to a given non-negative reward. Nonetheless, in practice, they often struggle to explore the reward landscape evenly: trajectories toward easy-to-reach regions dominate training, while hard-to-reach modes receive vanishing or uninformative gradients, leading to poor coverage of high-reward areas. We address this imbalance with Boosted GFlowNets, a method that sequentially trains an ensemble of GFlowNets, each optimizing a residual reward that compensates for the mass already captured by previous models. This residual principle reactivates learning signals in underexplored regions and, under mild assumptions, ensures a monotone non-degradation property: adding boosters cannot worsen the learned distribution and typically improves it. Empirically, Boosted GFlowNets achieve substantially better exploration and sample diversity on multimodal synthetic benchmarks and peptide design tasks, while preserving the stability and simplicity of standard trajectory-balance training.

cs.LG↗

arXiv2026

Expert-Aided Causal Discovery of Ancestral Graphs

Causal discovery (CD) is an important component of many scientific applications, yet most techniques produce unreliable point estimates that often contradict expert knowledge. To mitigate this, recent research has focused on ex-ante incorporation of background knowledge into the CD process, typically under an unrealistic causal sufficiency assumption. When probing experts is costly (e.g., hidden behind expensive LLM APIs), however, ex-post model refinement that maximizes query utility is preferable. Also, when independent experts provide conflicting but better-than-random feedback, a principled aggregation method is required. In this context, we introduce the first CD algorithm that enables (i) distributional inference over ancestral graphs (AGs), which represent causal systems under latent confounding, and (ii) integration of both ex-ante and uncertain ex-post expert knowledge. Briefly, our method is a diversity-seeking reinforcement learning algorithm, termed Ancestral GFlowNet (AGFN), whose policy we iteratively refine based on a Bayesian model of the noisy expert feedback. Importantly, we prove convergence to the true AG given sufficiently accurate responses. Through validation on synthetic and realistic datasets using simulated humans and LLMs, we show AGFN is competitive with or superior to strong baselines in terms of structural Hamming distance and Bayesian Information Criterion.

cs.LG↗

arXiv2026

Avoid What You Know: Divergent Trajectory Balance for GFlowNets

Generative Flow Networks (GFlowNets) are a flexible family of amortized samplers trained to generate discrete and compositional objects with probability proportional to a reward function. However, learning efficiency is constrained by the model's ability to rapidly explore diverse high-probability regions during training. To mitigate this issue, recent works have focused on incentivizing the exploration of unvisited and valuable states via curiosity-driven search and self-supervised random network distillation, which tend to waste samples on already well-approximated regions of the state space. In this context, we propose Adaptive Complementary Exploration (ACE), a principled algorithm for the effective exploration of novel and high-probability regions when learning GFlowNets. To achieve this, ACE introduces an exploration GFlowNet explicitly trained to search for high-reward states in regions underexplored by the canonical GFlowNet, which learns to sample from the target distribution. Through extensive experiments, we show that ACE significantly improves upon prior work in terms of approximation accuracy to the target distribution and discovery rate of diverse high-reward states.

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arXiv2025

Differentially Private E-Values

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.

stat.ME↗

arXiv2025

Infinite Neural Operators: Gaussian processes on functions

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.

stat.ML↗

arXiv2025

Differentially Private Selection using Smooth Sensitivity

Differentially private selection mechanisms offer strong privacy guarantees for queries aiming to identify the top-scoring element r from a finite set R, based on a dataset-dependent utility function. While selection queries are fundamental in data science, few mechanisms effectively ensure their privacy. Furthermore, most approaches rely on global sensitivity to achieve differential privacy (DP), which can introduce excessive noise and impair downstream inferences. To address this limitation, we propose the Smooth Noisy Max (SNM) mechanism, which leverages smooth sensitivity to yield provably tighter (upper bounds on) expected errors compared to global sensitivity-based methods. Empirical results demonstrate that SNM is more accurate than state-of-the-art differentially private selection methods in three applications: percentile selection, greedy decision trees, and random forests.

cs.LG↗

arXiv2024

Streaming Bayes GFlowNets

Bayes' rule naturally allows for inference refinement in a streaming fashion, without the need to recompute posteriors from scratch whenever new data arrives. In principle, Bayesian streaming is straightforward: we update our prior with the available data and use the resulting posterior as a prior when processing the next data chunk. In practice, however, this recipe entails i) approximating an intractable posterior at each time step; and ii) encapsulating results appropriately to allow for posterior propagation. For continuous state spaces, variational inference (VI) is particularly convenient due to its scalability and the tractability of variational posteriors. For discrete state spaces, however, state-of-the-art VI results in analytically intractable approximations that are ill-suited for streaming settings. To enable streaming Bayesian inference over discrete parameter spaces, we propose streaming Bayes GFlowNets (abbreviated as SB-GFlowNets) by leveraging the recently proposed GFlowNets -- a powerful class of amortized samplers for discrete compositional objects. Notably, SB-GFlowNet approximates the initial posterior using a standard GFlowNet and subsequently updates it using a tailored procedure that requires only the newly observed data. Our case studies in linear preference learning and phylogenetic inference showcase the effectiveness of SB-GFlowNets in sampling from an unnormalized posterior in a streaming setting. As expected, we also observe that SB-GFlowNets is significantly faster than repeatedly training a GFlowNet from scratch to sample from the full posterior.

cs.LG↗

arXiv2024

On Divergence Measures for Training GFlowNets

Generative Flow Networks (GFlowNets) are amortized inference models designed to sample from unnormalized distributions over composable objects, with applications in generative modeling for tasks in fields such as causal discovery, NLP, and drug discovery. Traditionally, the training procedure for GFlowNets seeks to minimize the expected log-squared difference between a proposal (forward policy) and a target (backward policy) distribution, which enforces certain flow-matching conditions. While this training procedure is closely related to variational inference (VI), directly attempting standard Kullback-Leibler (KL) divergence minimization can lead to proven biased and potentially high-variance estimators. Therefore, we first review four divergence measures, namely, Renyi-$α$'s, Tsallis-$α$'s, reverse and forward KL's, and design statistically efficient estimators for their stochastic gradients in the context of training GFlowNets. Then, we verify that properly minimizing these divergences yields a provably correct and empirically effective training scheme, often leading to significantly faster convergence than previously proposed optimization. To achieve this, we design control variates based on the REINFORCE leave-one-out and score-matching estimators to reduce the variance of the learning objectives' gradients. Our work contributes by narrowing the gap between GFlowNets training and generalized variational approximations, paving the way for algorithmic ideas informed by the divergence minimization viewpoint.

cs.LG↗

arXiv2024

Meta-analysis of Bayesian analyses

Meta-analysis aims to generalize results from multiple related statistical analyses through a combined analysis. While the natural outcome of a Bayesian study is a posterior distribution, traditional Bayesian meta-analyses proceed by combining summary statistics (i.e., point-valued estimates) computed from data. In this paper, we develop a framework for combining posterior distributions from multiple related Bayesian studies into a meta-analysis. Importantly, the method is capable of reusing pre-computed posteriors from computationally costly analyses, without needing the implementation details from each study. Besides providing a consensus across studies, the method enables updating the local posteriors post-hoc and therefore refining them by sharing statistical strength between the studies, without rerunning the original analyses. We illustrate the wide applicability of the framework by combining results from likelihood-free Bayesian analyses, which would be difficult to carry out using standard methodology.

stat.ME↗

arXiv2024

Embarrassingly Parallel GFlowNets

GFlowNets are a promising alternative to MCMC sampling for discrete compositional random variables. Training GFlowNets requires repeated evaluations of the unnormalized target distribution or reward function. However, for large-scale posterior sampling, this may be prohibitive since it incurs traversing the data several times. Moreover, if the data are distributed across clients, employing standard GFlowNets leads to intensive client-server communication. To alleviate both these issues, we propose embarrassingly parallel GFlowNet (EP-GFlowNet). EP-GFlowNet is a provably correct divide-and-conquer method to sample from product distributions of the form $R(\cdot) \propto R_1(\cdot) ... R_N(\cdot)$ -- e.g., in parallel or federated Bayes, where each $R_n$ is a local posterior defined on a data partition. First, in parallel, we train a local GFlowNet targeting each $R_n$ and send the resulting models to the server. Then, the server learns a global GFlowNet by enforcing our newly proposed \emph{aggregating balance} condition, requiring a single communication step. Importantly, EP-GFlowNets can also be applied to multi-objective optimization and model reuse. Our experiments illustrate the EP-GFlowNets's effectiveness on many tasks, including parallel Bayesian phylogenetics, multi-objective multiset, sequence generation, and federated Bayesian structure learning.

cs.LG↗

arXiv2024

Distill n' Explain: explaining graph neural networks using simple surrogates

Explaining node predictions in graph neural networks (GNNs) often boils down to finding graph substructures that preserve predictions. Finding these structures usually implies back-propagating through the GNN, bonding the complexity (e.g., number of layers) of the GNN to the cost of explaining it. This naturally begs the question: Can we break this bond by explaining a simpler surrogate GNN? To answer the question, we propose Distill n' Explain (DnX). First, DnX learns a surrogate GNN via knowledge distillation. Then, DnX extracts node or edge-level explanations by solving a simple convex program. We also propose FastDnX, a faster version of DnX that leverages the linear decomposition of our surrogate model. Experiments show that DnX and FastDnX often outperform state-of-the-art GNN explainers while being orders of magnitude faster. Additionally, we support our empirical findings with theoretical results linking the quality of the surrogate model (i.e., distillation error) to the faithfulness of explanations.

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