Search arXiv⌕ Search

arXiv subjects

Alejandro Ribeiro

Publications and source records attributed to Alejandro Ribeiro.

At least 19 recordsLinked to original sources
arXiv2026

Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified learning theory for these settings has been lacking. To start addressing this gap, we introduce a novel convolutional learning framework for possibly infinite-dimensional signals supported on a manifold. Namely, we use the connection Laplacian associated with a Hilbert bundle as a convolutional operator, and we derive filters and neural networks, dubbed as \textit{HilbNets}. We make HilbNets and, more generally, the convolution operation, implementable via a two-stage sampling procedure. First, we show that sampling the manifold induces a Hilbert Cellular Sheaf, a generalized graph structure with Hilbert feature spaces and edge-wise coupling rules, and we prove that its sheaf Laplacian converges in probability to the underlying connection Laplacian as the sampling density increases. Notably, this result is a generalization to the infinite-dimensional bundle setting of the Belkin \& Niyogi \cite{BELKIN20081289} convergence result for the graph Laplacian to the manifold Laplacian, a theoretical cornerstone of geometric learning methods. Second, we discretize the signals and prove that the discretized (implementable) HilbNets converge to the underlying continuous architectures and are transferable across different samplings of the same bundle, providing consistency for learning. Finally, we validate our framework on synthetic and real-world tasks. Overall, our results broaden the scope of geometric learning as a whole by lifting classical Laplacian-based frameworks to settings where the signal at each point lives in its own Hilbert space.

cs.LG↗
arXiv2026

Scaling Graph Reasoning in Language Models with Learnable Graph Positional Encodings

Solving reasoning tasks supported on graphs typically requires providing a Language Reasoning Model (LRM) with a serialized description of the graph. This approach results in the input length growing with the number of edges, which limits the size of the problems that can be solved. Furthermore, even when graphs fit in context, performance sharply decays as the graphs grow. We propose to address this by augmenting LRMs with scalable and permutation equivariant graph positional encodings that modulate attention logits. An additional post-fusion-style module incorporates structural information into hidden states. We compute these positional encodings using a GNN followed by a Graph Transformer. This eliminates the need for serialized adjacencies, reducing the context burden to $O(N)$. We jointly fine-tune the positional encoder and the LRM LoRA adapters using optimal solutions generated by graph-theoretic solvers, resulting in a computationally efficient method. Trained on small graphs, the model exhibits improved size-generalization across graph-theoretic tasks on graphs with up to 1,000 nodes, and produces fewer tokens than a conventional LRM. Additionally, we observe that our model remains robust to node relabelings.

cs.LG↗
arXiv2026

Bilinear World Models: Learning Representations with Structured Dynamics for Efficient Control

World models jointly learn latent representations and dynamics that predict how high-dimensional observations evolve under actions. In this work, we propose a JEPA-style world model in which, rather than learning arbitrary latent dynamics, we restrict them to follow a bilinear parameterization. This structure enables efficient planning and control while shifting the modeling burden onto the encoder, encouraging richer representations that expose the controllable geometry of the system. In particular, this structured parameterization allows us to structurally enforce action recoverability, thereby preventing representation collapse by construction. Although prescribing a bilinear parametrization may appear restrictive, we show that a broad class of nonlinear dynamical systems admits a transformation under which the dynamics become bilinear. Empirically, we show across standard 2D and 3D control tasks that representations with bilinear-parameterized dynamics can be learned directly from high-dimensional observations, reducing planning time by nearly three orders of magnitude while retaining or even improving control accuracy. We also propose more demanding regimes of longer-horizon planning and real-time control, and demonstrate that our method succeeds in both, moving JEPA-style world models beyond short-horizon offline planning.

cs.RO↗
arXiv2026

Size-Transferability of Graph Transformers with Convolutional Positional Encodings

Transformers have achieved remarkable success across domains, motivating the rise of Graph Transformers (GTs) as attention-based architectures for graph-structured data. A key design choice in GTs is the use of Graph Neural Network (GNN)-based positional encodings to incorporate structural information. In this work, we study GTs through the lens of manifold limit models for graph sequences and establish a theoretical connection between GTs with GNN positional encodings and Manifold Neural Networks (MNNs). Building on transferability results for GNNs under manifold convergence, we show that GTs inherit transferability guarantees from their positional encodings. In particular, GTs trained on small graphs provably generalize to larger graphs under mild assumptions. We complement our theory with extensive experiments on standard graph benchmarks, demonstrating that GTs exhibit scalable behavior on par with GNNs. To further show the efficiency in a real-world scenario, we implement GTs for shortest path distance estimation over terrains to better illustrate the efficiency of the transferable GTs. Our results provide new insights into the understanding of GTs and suggest practical directions for efficient training of GTs in large-scale settings.

cs.LG↗
arXiv2026

Colored Graph Signal Diffusion Models

Standard diffusion processes with isotropic noise corruption are not spectrally neutral. They inherit a coarse-to-fine generation hierarchy from the nonuniform data spectrum, because each frequency band loses signal-to-noise ratio (SNR) at its own rate. For signals on a graph, the relevant spectrum is that of the graph shift operator (GSO). A natural construction, therefore, builds both the diffusion dynamics and the denoiser from graph filters of the GSO, and any such design also takes a position on this hierarchy. We expose this hierarchy as a tunable axis through a family of colored score-based diffusions. Fixing the terminal prior to a Gaussian colored by the GSO couples the drift and diffusion through a positive spectral rate, which acts as a clock for each graph-frequency band. The clock sets when a band loses and recovers information, and the forward processes of standard and certain graph-aware diffusions appear as members of this family. A GSO-valued EDM preconditioning splits the denoiser into an analytic Wiener head that carries the Gaussian second-order structure and a graph neural network (GNN) that learns the remaining non-Gaussian dependencies. Numerical experiments show that colored diffusions reach a given generation quality in far fewer sampling steps than standard diffusion.

eess.SP↗
arXiv2026

Unrolled Neural Networks for Constrained Optimization

We develop unrolled neural networks to solve constrained optimization problems, offering accelerated, learnable counterparts to dual ascent (DA) algorithms. Our framework, termed constrained dual unrolling (CDU), comprises two coupled neural networks that jointly approximate the saddle point of the Lagrangian. The primal network emulates an iterative optimizer that finds a stationary point of the Lagrangian for a given dual multiplier, sampled from an unknown distribution. The dual network generates trajectories towards the optimal multipliers across its layers while querying the primal network at each layer. Unlike standard unrolling, which maps the updates of a prescribed iterative solver directly to network layers, CDU preserves the underlying optimization dynamics while learning the update mappings. The desired primal-dual dynamics are therefore induced through constrained learning by enforcing primal-descent and dual-ascent constraints. We formulate training the two networks as a nested optimization problem and propose an alternating procedure that updates the primal and dual networks in turn, mitigating uncertainty in the multiplier distribution required for primal network training. We establish theoretical guarantees on the feasibility and optimality of the coupled networks. We numerically evaluate the framework on quadratic programs (QPs) with linear constraints and power allocation in wireless networks.

cs.LG↗
arXiv2026

Constrained Diffusion Models with Primal-Dual Inference

This paper develops constrained diffusion models with primal-dual inference (PDI) to sample from optimal distributions of entropy-regularized optimization problems with \emph{average} constraints. We formalize constrained sampling in the Lagrangian dual domain, where the optimal distribution takes the form of a Gibbs distribution indexed by the optimal dual variable. Rather than estimating this dual multiplier before sampling and freezing it throughout generation, PDI jointly infers the optimal primal distribution and its parametrizing dual variable. Each reverse diffusion step denoises using the score field associated with the current multiplier and then updates the multiplier through dual ascent using the estimated constraint violation of the denoised samples. To enable this conditional score field, we train a single dual-conditioned score network over the family of Gibbs distributions induced by the dual variables encountered during inference. We prove that the dual iterates converge to a neighborhood of the dual optimum, and that the generated distribution approaches that of an oracle sampler that knows the optimal multiplier, up to a bias floor. We evaluate PDI on constrained sampling from a mixture of Gaussians, wireless resource allocation, and portfolio management.

cs.LG↗
arXiv2026

Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion

Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures such as graph transformers have shown promise for this task, yet the mechanisms through which attention denoises graphs remain poorly understood. We show that, under a graph denoising objective, standard attention scores learn an average spectral denoising filter across the training distribution and are suboptimal when the graph spectra vary. To address this limitation, we introduce spectral attention scores, which are attention scores that depend on the input graph spectrum. We characterize the improvement over standard attention scores in terms of the spectral diversity of the graph distribution. We then propose graph convolutional attention (GCA), a practical realization of spectral attention that uses graph-filtered queries and keys. For asymptotically large stochastic block models, we show that GCA matches the optimal denoising loss of spectral attention under suitable conditions. We also show that softmax can further reduce denoising error by approximately projecting noisy eigenvectors onto the clean eigenspace. Across synthetic and real datasets, replacing standard query--key projections with GCA improves graph denoising and diffusion, with denoising gains correlated with spectral diversity. Furthermore, replacing the DiGress architecture with a GCA-based architecture within the DiGress generative framework yields comparable generation quality with significantly faster inference.

cs.LG↗
arXiv2026

ConicFlow: constrained Inference-time optimal control for flow matching models

We propose ConicFlow, which frames constrained sampling from a flow matching model at inference time as an optimal control problem that balances deviation from the pretrained trajectory against reward, subject to hard terminal constraints. We discretize this problem and adapt receding-horizon control, optimizing only a short window of the trajectory at each step for computational tractability. We address the resulting sequence of receding-horizon subproblems with a receding-horizon primal-dual algorithm. Its dual multipliers capture the difficulty of satisfying each constraint and are refined throughout sampling, steering generation toward feasible final samples. We further propose a terminal-estimate variant that avoids accumulating local truncation errors by evaluating the reward and constraints at the predicted terminal point rather than at the end of the current horizon. Under standard regularity assumptions, we establish finite-horizon guarantees on suboptimality. Under convex-affine structure, we derive a sharper bound that scales linearly with omitted horizon length, and we show that the terminal-estimate variant is provably tighter when the flow dynamics change slowly. Experiments in both low- and high-dimensional settings with a recent large-scale flow matching model show that ConicFlow achieves high reward and strong constraint satisfaction while deviating less from the pretrained flow than recent baselines.

cs.AI↗
arXiv2026

Everywhere Learning: Artificial Intelligence with Pointwise Constraints

Everywhere learning is a new paradigm whereby Artificial Intelligence (AI) systems are trained to satisfy loss constraints with probability one over the data distribution. This is in contrast to the standard paradigm of training AI systems to minimize average losses. We develop an approximate duality theory to substantiate a generalization analysis that establishes the proximity between solutions of empirical and statistical everywhere learning problems. Our results show that dual variables reweigh the data distribution towards points in which loss constraints are more difficult to satisfy and that generalization is controlled by the mismatch between the concentration of mass of the data distribution and the concentration of mass on points where constraints are more difficult to satisfy. We further show that we can control generalization with a sparse L1 penalty on constraint relaxations. We illustrate the merits of everywhere learning with an experiment in agentic classification for language model tasks.

cs.LG↗
arXiv2026

Infinity Search: Approximate Vector Search with Projections on q-Metric Spaces

An ultrametric space or infinity-metric space is defined by a dissimilarity function that satisfies a strong triangle inequality in which every side of a triangle is not larger than the larger of the other two. We show that search in ultrametric spaces with a vantage point tree has worst-case complexity equal to the depth of the tree. Since datasets of interest are not ultrametric in general, we employ a projection operator that transforms an arbitrary dissimilarity function into an ultrametric space while preserving nearest neighbors. We further learn an approximation of this projection operator to efficiently compute ultrametric distances between query points and points in the dataset. We proceed to solve a more general problem in which we consider projections in $q$-metric spaces -- in which triangle sides raised to the power of $q$ are smaller than the sum of the $q$-powers of the other two. Notice that the use of learned approximations of projected $q$-metric distances renders the search pipeline approximate. We show in experiments that increasing values of $q$ result in faster search but lower recall. Overall, search in q-metric and infinity metric spaces is competitive with existing search methods.

cs.IR↗
arXiv2026

Learning Samples Importance: Parameterizing Dual Variables in Everywhere Learning

Everywhere learning provides a principled framework for training AI models under constraints that must hold throughout the data distribution. In the dual domain, these pointwise constraints give rise to functional dual variables. In this work, we propose to learn these dual variables, motivated by the fact that their values encode useful information about the underlying constrained problem. By representing the dual variable as a parametric function of each sample, we enable the learned multiplier to be evaluated on new, unseen samples. This contrasts with standard empirical dual formulations, which assign an independent multiplier to each training sample. We characterize the error in the recovered primal solution induced by restricting the dual variable to a parametric function class and show that it is controlled by how well this class approximates the optimal statistical multiplier. Moreover, we show that the learned parametric multiplier retains the sensitivity interpretation of the optimal statistical multiplier, yielding approximate sensitivity guarantees that extend beyond the samples used for training. We empirically validate our theory across a variety of everywhere learning tasks, showing that the resulting constrained problems can be solved efficiently and that the learned dual variables provide meaningful representations of sample-level sensitivity.

cs.LG↗
arXiv2026

Ceiling of a Task: When Can a Transformer Succeed Without Its Chain of Thought?

Reasoning models generate long chains of thought before they answer, yet it is debated whether the content of these chains does real computational work or is largely decorative. We study this question by viewing a transformer as a shallow circuit. One forward pass through a fixed number of layers has constant depth, so any procedure that runs the model a constant number of times is a shallow circuit. We call the best accuracy that a shallow circuit can reach on a task the ceiling of the task, and a task is serial if its ceiling lies below one. We prove three results on serial tasks that hold for every transformer, no matter how it was trained. Necessity: replacing the chain by anything that does not depend on its content, such as filler tokens or a restatement of the question, drives the accuracy down to the ceiling, and on a maximally serial task down to chance. Depth: no shallow computation can write the chain of a model whose accuracy exceeds the ceiling, not even approximately. Locality: the answer is one shallow pass away from the finished chain, so all of the serial reasoning happens in the chain. On word problems of finite groups, whose ceilings are known, small transformers trained from scratch, with or without reinforcement learning, attain the predicted numbers: chain-trained models solve every input length and fall to chance when the chain is erased, chainless models collapse to the ceiling as the input length grows, and open-weight reasoning models given the same problem in words return to the baseline without their chain. On MATH-500 and AIME, erasing the chain costs open reasoning models 0.52 to 0.82 accuracy, a sentence shuffle is harmless, and a token shuffle is as harmful as erasing; the same holds for checkpoints trained by GRPO with a correct or a random reward. The ceiling of a task therefore answers when a transformer can succeed without its chain of thought.

cs.AI↗
arXiv2026

A Scalable Multi-Robot Framework for Decentralized and Asynchronous Perception-Action-Communication Loops

We develop a decentralized Perception-Action-Communication (PAC) system for multi-robot teams that enables them to collaborate in large scale, outdoor environments. Our system natively supports deployments at any scale by leveraging a graph neural network (GNN) to diffuse information hop-by-hop across the fleet's network. This achieves global collaboration from individual robots limited to local sensing and communication. Fully asynchronous, the core modules of PAC: perception, inter-robot communication, message aggregation and action are clocked at different frequencies with information flowing between them through buffers. We implement the PAC system as a series of highly extensible ROS2 nodes to serve as the foundational infrastructure for deployable swarm systems. PAC is validated in the real world with outdoor experiments with up to N=20 quadrotor robots and in simulations based on real-world data with up to N=100. These validations show that our system upholds crucial properties for field-deployable robot collectives: scalability, resiliency and repeatability.

cs.RO↗
arXiv2026

Controlling Collectives of AI Agents in Reasoning Space with Spatial Transformers

Large Language Models (LLMs) introduce an exciting new paradigm for planning and navigation in robotics, but fail on even simple multi-robot tasks as team sizes grow. We propose COMPASS, a scalable, decentralized multi-robot architecture for controlling large collectives of agentic robots with reasoning space feedback control. Feedback is generated locally on each robot by a spatial transformer which aggregates multi-hop messages across the fleet into a learned feedback token. Our experiments find that collectives of language models demonstrate performance gains from structured diversity of the input command, which can cancel biases; an advantage that is held across scale. Compared against a centralized frontier LLM policy and a language-only communication ablation, we find that the coupled design of COMPASS decisively produces cohesive flocking formations that accurately fly the commanded intent. We show that reasoning feedback works best when composed with a compact learned token. Our ablations show that hand engineered feedback with raw state appearing in the language channel obliterates cohesion. COMPASS generalizes zero-shot to unseen instructions of ambiguous meaning while commanding flocks up to 16 times its training scale, flying up to 1024 robots under natural language commands.

cs.RO↗
arXiv2026

Visual Navigation Transformer with Pose Attention

Learned navigation policies typically consume observations as a temporally ordered history, with positional encodings tying each observation to when it was seen, making it difficult to reuse experience from earlier traversals of an environment. Systems that do reuse such experience usually construct an explicit representation, such as a map or a topological graph, and plan on it. We propose VNT-PA (Visual Navigation Transformer with Pose Attention), a transformer planner whose context is a set of depth keyframes indexed by camera pose. With camera poses as positional encoding, attention depends on the pose differences between keyframes rather than on their temporal order. VNT-PA is trained to imitate a shortest-path planner operating on the ground-truth scene mesh, predicting actions by querying the spatial context with only its current pose and the goal position. On point-goal navigation in HM3D validation scenes, VNT-PA reaches 93.3% success and 90.4% success weighted by path length (SPL), outperforming baselines that encode the same context as a temporal sequence or treat pose as an input feature, in both navigation performance and training efficiency. Because the spatial context is a pose-indexed set, frames from different trajectories can be fused at test time. The planner also degrades more gracefully under localization noise than a conventional baseline which plans on explicit maps. These results show that pose-stamped experience can serve directly as the environment representation for a learned planner, and that making attention depend on pose differences, rather than on temporal order, speeds up training and improves long-horizon navigation.

cs.RO↗
arXiv2026

Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs

This feature article provides an overview of the theoretical foundations for coVariance neural networks (VNNs), i.e., graph neural networks (GNNs) operating on covariance matrices as graphs. Covariance matrices are ubiquitous across domains, and hence, the deployment of GNNs often leverages graphs of pairwise statistical dependencies. Existing theoretical contributions on GNNs consider abstract graph representations and cannot accommodate the data-driven nuances associated with covariance matrices. This tutorial brings into focus various novel theoretical insights via mathematical analyses of VNNs that have broad signal processing implications, including: (i) a conceptual equivalence between VNNs and principal component analysis (PCA)-based information processing; (ii) refined stability bounds on predictive outcomes in the presence of finite sample-induced covariance matrix perturbations; and (iii) refined characterization of transferability of VNNs across multiscale datasets. The theoretical insights discussed herein provide the underlying principles and justification towards adopting VNNs over workhorse PCA-based learning pipelines, in applications where covariance matrices are useful descriptors of data structure. We also convey how impact of these foundational advances permeates to \textit{principled} designs and applications of learning methods across broad domains where covariance matrices emerge. Notably, we elucidate the conceptual insights facilitated by VNNs to the specific task of characterizing brain age gap for neurodegenerative conditions using neuroimaging datasets, a timely problem in computational neuroscience. Broader impacts to other application domains are discussed as well.

cs.LG↗
arXiv2026

Scalability of Graph Neural Network Policies in Wireless Communication Networks

Graph Neural Networks (GNNs) offer scalable solutions for wireless resource allocation, yet existing formal performance guarantees across varying scales for spatial and sparse graphs do not directly apply to these settings. Scalability theories rely on dense graphon limits or continuous manifold approximations, both of which fail under the sparse, bounded-degree regimes and Euclidean metric constraints of physical wireless environments. This paper establishes a theoretical framework for GNN transferability over sparse Random Geometric Graphs (RGGs), capturing distance-dependent channel decay and spatial interference. We model sparse RGGs as spatial perturbations of regular Deterministic Grid Graphs (DGGs) and employ spatial windowing operators to compare networks across differing scales. Assuming Lipschitz continuity of GNN architectures and signal stationarity, we prove scalability over DGGs and bound same-scale transferability between DGGs and RGGs. Combining these results establishes formal scalability bounds across sparse RGG topologies. Finally, we extend this framework to conflict graph models, deriving equivalent scalability guarantees for link-level resource allocation policies. We verify our results for scalability with two experiment settings: power allocation and wireless link scheduling. The simulations show GNNs exhibit the expected scalable behavior, and analyze the relevance of our theoretical assumptions in practical deployment.

eess.SP↗