arXiv subjects

Alba Carballo-Castro

Publications and source records attributed to Alba Carballo-Castro.

7 recordsLinked to original sources

arXiv2026

PolarFlow: Spectral Geometric Flow Matching for Directed Graph Generation via Polar Decomposition

Directed graphs model asymmetric relationships in biology, transportation, social networks, and electronic design automation. Recent discrete diffusion and flow-matching methods generate directed graphs effectively, but their edge-wise categorical formulations require dense predictions over all ordered node pairs and repeated categorical updates during generation. This motivates a fundamental question: can comparable generative quality be achieved through a more computationally efficient formulation that better exploits the structure of directed adjacency matrices? Existing benchmarks also cover limited network structures, restricting comprehensive evaluation. We introduce PolarFlow, a continuous geometric flow-matching framework based on polar decomposition and truncated spectral coordinates. Its representation comprises four coupled components: a Stiefel frame and rotation angles encoding the orthogonal factor, and a second Stiefel frame and nonnegative eigenvalues characterizing the positive-semidefinite factor. PolarFlow learns a joint velocity field along geometry-aware conditional paths on this product space, reconstructs a continuous adjacency-score matrix, and discretizes it into a binary directed graph. By replacing discrete edge-wise generation with joint continuous transport, PolarFlow improves computational efficiency while retaining global adjacency structure. To broaden evaluation, we introduce complementary Circuit and Twitter benchmarks spanning engineered functional and naturally evolved social networks. Across synthetic and real-world datasets, PolarFlow achieves generative quality comparable to competitive discrete methods while substantially reducing training and sampling time.

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arXiv2026

Efficient Edge-aware Attention Network for Graph Generation

Graph generative models commonly use graph-specific Transformer architectures to jointly update node and edge features. However, these architectures do not directly benefit from recent hardware-aware attention implementations, limiting their scalability. The adaptation is, however, non-trivial: edge and graph-level features must be injected into pairwise attention scores, graph masks must be respected, and dynamic edge updates remain a major source of quadratic memory usage. We propose an edge-aware attention layer for graph generation that incorporates structural information through head-wise score modulation, while updating edge representations with a lightweight residual mechanism that retains attention-score dependent edge updates. This layer can be effectively implemented using PyTorch's FlexAttention. We achieve similar generation quality to our baseline while reducing peak GPU memory by around 65% and substantially improving training and sampling throughput. These results suggest that the proposed architecture is a practical step toward scalable graph foundation models.

cs.LG↗

arXiv2026

Recursive Scaling in Masked Diffusion Models

Masked diffusion models (MDMs) generate sequences by iteratively refining a partially masked state and committing tokens in parallel. We introduce recursion in MDMs and propose new Recursive Masked Diffusion Models (R-MDMs), which apply a shared denoising transformer $L$ times within each denoising step, adding recursive depth as an additional compute axis without increasing parameter count. Across structured generation tasks, recursive depth improves quality at fixed parameter budget, matches substantially larger non-recursive models at matched FLOPs, and can reduce the number of denoising steps needed to reach a target quality. We interpret these gains with a dependence--fidelity decomposition of parallel decoding error: recursion refines model marginals at a fixed masked state, whereas denoising steps change that state by committing tokens. Building on this analysis, we propose to treat decoding as a two-axis decision (how many loops to run and which tokens to commit) and show that entropy-guided adaptive rules improve the quality--compute frontier over fixed schedules, transferring across various tasks on Sudoku, Countdown, RNA, and executable math generation. Together, these results establish recursive depth as a practical, complementary test-time scaling mechanism for MDMs.

cs.LG↗

arXiv2026

Balancing Symmetry and Efficiency in Graph Flow Matching

Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs. However, strict equivariance can increase computational cost due to added architectural constraints, and can slow down convergence because the model must be consistent across a large space of possible node permutations. We study this trade-off for graph generative models. Specifically, we start from an equivariant discrete flow-matching model, and relax its equivariance during training via a controllable symmetry modulation scheme based on sinusoidal positional encodings and node permutations. Experiments first show that symmetry-breaking can accelerate early training by providing an easier learning signal, but at the expense of encouraging shortcut solutions that can cause overfitting, where the model repeatedly generates graphs that are duplicates of the training set. On the contrary, properly modulating the symmetry signal can delay overfitting while accelerating convergence, allowing the model to reach stronger performance with $19\%$ of the baseline training epochs.

cs.LG↗

arXiv2026

Fixed-Point Masked Generative Modeling

Masked Generative Models (MGMs) enable parallel decoding and achieve strong performance across modalities, but require full-sequence bidirectional transformers at every step, making training costly and degrading quality under low sampling budgets. Existing work improves efficiency via better samplers or cheaper fixed-depth denoisers, but they still allocate a fixed amount of denoiser computation to each refinement step. We introduce Fixed-Point Masked Generative Models (FP-MGMs), which replace part of the denoiser with a fixed-point solver over shared attention layers to enable adaptive depth with fewer parameters. To make it more effective for masked generation, we first introduce a cross-step consistency loss, which aligns hidden representations at neighboring denoising steps and, second, three-state reuse (3SR) which warm-starts the solver using the previous solution by treating differently unchanged, still-masked, and newly revealed tokens respectively. Together, these components define our complete training-to-inference framework for fixed-point masked generation, \emph{CoFRe}. We also show that pre-trained MGMs can be converted into FP-MGMs with short fine-tuning, avoiding full retraining. Across modalities, CoFRe improves the quality and cost trade-off. On OpenWebText, CoFRe reduces parameters by 38.8\%, training time by 11.5\%, and VRAM by 16.9\%, while improving generative perplexity from 830.8 to 101.8 at a budget of $96$ transformer-block forward passes, compared to MDLM. In ImageNette, CoFRe reduces training time by 48.6\% and VRAM by 50.7\%, while improving FID in all sample budgets tested. Overall, CoFRe offers a practical framework for cheaper training and stronger low-budget masked generation.

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arXiv2026

Generating Directed Graphs with Dual Attention and Asymmetric Encoding

Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data augmentation and novel instance discovery; however, directed graph generation remains underexplored. We identify two key factors limiting progress in this direction: first, modeling edge directionality introduces a substantially larger dependency space, making the underlying distribution harder to learn; second, the absence of standardized benchmarks hinders rigorous evaluation. Addressing the former requires more expressive models that are sensitive to directional topologies. We propose Directo, the first generative model for directed graphs built upon the discrete flow matching framework. Our approach combines: (i) principled positional encodings tailored to asymmetric pairwise relations, (ii) a dual-attention mechanism capturing both incoming and outgoing dependencies, and (iii) a robust, discrete generative framework. To support evaluation, we introduce a benchmark suite covering synthetic and real-world datasets. It shows that our method performs strongly across diverse settings and even competes with specialized models for particular classes, such as directed acyclic graphs. Our results highlight the effectiveness and generality of our approach, establishing a solid foundation for future research in directed graph generation.

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arXiv2024

Exploiting Interpretable Capabilities with Concept-Enhanced Diffusion and Prototype Networks

Concept-based machine learning methods have increasingly gained importance due to the growing interest in making neural networks interpretable. However, concept annotations are generally challenging to obtain, making it crucial to leverage all their prior knowledge. By creating concept-enriched models that incorporate concept information into existing architectures, we exploit their interpretable capabilities to the fullest extent. In particular, we propose Concept-Guided Conditional Diffusion, which can generate visual representations of concepts, and Concept-Guided Prototype Networks, which can create a concept prototype dataset and leverage it to perform interpretable concept prediction. These results open up new lines of research by exploiting pre-existing information in the quest for rendering machine learning more human-understandable.

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