arXiv subjects

Moshe Eliasof

Publications and source records attributed to Moshe Eliasof.

At least 19 recordsLinked to original sources

arXiv2026

Module-Aware Optimization for Graph Neural Networks

Different optimizers impose different geometries on parameter updates. Adaptive methods such as Adam and AdamW use coordinate-wise updates, while matrix-aware optimizers such as Muon utilize weight-matrix structure through orthogonalized updates. For Graph Neural Networks (GNNs), however, the effective geometry of its weight matrices is shaped not only by its learned channel-mixing weights, but also by the graph-propagated representations it acts on. Thus, even if an update is well normalized as a matrix, its effect on the layer output can be amplified when applied to graph-propagated features. To address this gap, we introduce GraphMuon, a graph-aware optimizer that adapts Muon's matrix updates to the covariance structure of graph-propagated layer inputs. GraphMuon performs orthogonalization in a metric defined by these propagated representations and normalizes step sizes according to the update's induced effect on the layer representation. We show that theoretically, vanilla Muon can suffer from graph-induced update amplification, while our GraphMuon can mitigate this effect. As such, our GraphMuon yields a graph-metric analogue of Muon's polar update step. Empirically, GraphMuon achieves $1.32\times$-$2.42\times$ validation-loss time-to-target speedups over AdamW on three large-scale OGB benchmarks. Across 15 dataset-architecture configurations spanning node classification, inductive graph classification, and graph regression, it achieves lower time-to-target in 13 cases, while maintaining competitive or superior predictive performance. Code is available at https://github.com/guy-hadad/GraphMuon.

cs.LG↗

arXiv2026

PDE-SSM: A Spectral State Space Approach to Spatial Mixing in Diffusion Transformers

The success of vision transformers-especially for generative modeling-is limited by the quadratic cost and weak spatial inductive bias of self-attention. We propose PDE-SSM, a spatial state-space block that replaces attention with a learnable convection-diffusion-reaction partial differential equation. This operator encodes a strong spatial prior by modeling information flow via physically grounded dynamics rather than all-to-all token interactions. Solving the PDE in the Fourier domain yields global coupling with near-linear complexity of $O(N \log N)$, delivering a principled and scalable alternative to attention. We integrate PDE-SSM into a flow-matching generative model to obtain the PDE-based Diffusion Transformer PDE-SSM-DiT. Empirically, PDE-SSM-DiT matches or exceeds the performance of state-of-the-art Diffusion Transformers while substantially reducing compute. Our results show that, analogous to 1D settings where SSMs supplant attention, multi-dimensional PDE operators provide an efficient, inductive-bias-rich foundation for next-generation vision models.

cs.LG↗

arXiv2026

Towards Invariance to Node Identifiers in Graph Neural Networks

Message-Passing Graph Neural Networks (GNNs) are known to have limited expressive power, due to their message passing structure. One mechanism for circumventing this limitation is to add unique node identifiers (IDs), which break the symmetries that underlie the expressivity limitation. In this work, we highlight a key limitation of the ID framework, and propose an approach for addressing it. We begin by observing that the final output of the GNN should clearly not depend on the specific IDs used. We then show that in practice this does not hold, and thus the learned network does not possess this desired structural property. Such invariance to node IDs may be enforced in several ways, and we discuss their theoretical properties. We then propose a novel regularization method that effectively enforces ID invariance to the network. Extensive evaluations on both real-world and synthetic tasks demonstrate that our approach significantly improves ID invariance and, in turn, often boosts generalization performance.

cs.LG↗

arXiv2026

Preconditioned Flow Matching

Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions $p_t$. We identify a geometric optimization bottleneck in this regression problem: when the covariance $Σ_t$ of $p_t$ is ill-conditioned, gradient-based training rapidly fits high-variance directions while making slow progress along low-variance ones. In an exactly solvable Gaussian setting, we prove that the excess risk is weighted by $Σ_t$, and that both gradient descent and stochastic gradient descent inherit condition-number-dependent convergence. We then extend the analysis to Gaussian mixtures, showing that multimodality does not average away this effect; instead, the slowest and worst-conditioned component can control optimization. Motivated by this analysis, we propose $\textit{preconditioned flow matching}$, a precondition-then-match framework that transforms the target distribution into a more isotropic representation, trains the main flow in the transformed space, and maps generated samples back through the inverse transformation. We show theoretically that preconditioning reshapes the intermediate FM path and improves its conditioning. Across controlled Gaussian and Gaussian-mixture experiments, latent MNIST and other high resolution image datasets up to $512{\times}512$ resolution, preconditioning improves path-conditioning diagnostics, low-eigenvalue recovery, FID, MMD, precision, and recall. Compute-matched baselines and preconditioner-quality ablations further show that the gains are not explained merely by additional preconditioner parameters, but by improved geometry of the downstream flow matching problem. GitHub: https://github.com/ahxmeds/preconditioned-flow-matching.git.

cs.LG↗

arXiv2026

Graph Transductive Sharpening: Leveraging Unlabeled Predictions in Node Classification

In the transductive setting, where the full graph is observed but node labels are only partially available, progress in semi-supervised node classification has largely focused on architectural innovation. In this paper, we revisit an orthogonal axis: the training objective. We start from a simple observation: transductive models produce predictions for every node during training, including nodes without labels. These unlabeled-node predictions may contain useful training signal, but standard supervised objectives discard them because no ground-truth labels are available. Inspired by the decomposition of cross-entropy into a label-dependent alignment term and a label-independent entropy term, we propose prediction confidence as a natural way to extract this signal in the absence of labels. This motivates Transductive Sharpening (TS): a loss-level modification that minimizes prediction entropy on unlabeled nodes while counterbalancing this effect on labeled nodes. We evaluate Transductive Sharpening across a wide range of node-classification benchmarks and observe consistent performance improvements without requiring any changes to the backbone architecture. Code is available at https://github.com/transductive-sharpening/tunedGNN.

cs.LG↗

arXiv2026

CrossMean: Model Merging by Pairing Merged and Expert Activations

Model merging combines fine-tuned experts into one network without retraining, and closed-form methods compute each merged layer from statistics of its input activations. However, these statistics are measured on a single expert, while in the merged model, each layer receives activations from the merged layers that precede it. Recent work re-measures these statistics in the merged model but still forms them from a single network. We formulate closed-form methods as a linear system and show that they use the same matrix on both sides. We then introduce CrossMean, which replaces this matrix on one side with a bilinear statistic that pairs merged and expert activations. From the same statistics, we also derive a label-free criterion that indicates the task sets in which accounting for the merged activations improves the merge more. Empirically, task sets with a lower criterion value show a larger improvement. On the eight-task benchmark of each vision backbone that we tested and on BERT encoders, CrossMean improves on merging with statistics measured on the experts, and with all linear layers merged, it also improves on re-measuring these statistics in the merged model. These results suggest that merging benefits from pairing merged and expert activations.

cs.LG↗

arXiv2026

A Critical Audit of Spatiotemporal Forecasting Benchmark Datasets and Models

Graph neural networks (GNNs) are routinely employed for spatiotemporal forecasting, yet their performance across widely used benchmark datasets is inconsistent. Here, we perform an audit of dataset properties and baseline models to assess the quality of the benchmarks, and the robustness of the conclusions drawn from them. Using classical statistical tools, we characterise spatiotemporal lagged dependencies in benchmarks, and examine how temporal differencing changes these relationships and affects model rankings. Motivated by this, we re-evaluate temporal linear baselines, significantly reducing the apparent gains from GNNs on several benchmarks, and surpassing GNNs on others. Suspecting that GNNs struggle to extract linear, node-wise signals, we find that supplying them with autoregressive residuals improves their performance particularly on non-traffic benchmarks. Finally, controlled synthetic experiments reveal that GNNs are sensitive to heterogeneity in temporal dynamics and spatial graph interactions. Together, our findings demonstrate that baseline specification, data pre-processing and system heterogeneity shape the interpretations drawn from benchmark rankings, informing the design and robust evaluation of GNNs.

cs.LG↗

arXiv2026

Get a GRIP, this will be a long TRIP: A Quantifiable Long-Range Framework for Verifying Over-squashing

Empirical claims about the connection between over-squashing and long-range interactions in GNNs, can only be trusted if the benchmarks used to validate them genuinely require long-range interactions. The de-facto standard, the Long Range Graph Benchmark, has been repeatedly shown to be saturated by tuned short-range models, with existing synthetic alternatives being tied to specific topologies. As such, there is a lack of principled certificate of long-rangedness on arbitrary graphs. This state reflects the absence of a precise characterization of long-ranged benchmarks. We address this fundamental gap by introducing four verifiable axioms: Predictability, Tightness, Strictly $k$-Range, and Topology-Invariance, that any task claiming to test $k$-hop interactions must satisfy. We formally prove that violating any one of them admits failure modes that undermine conclusions drawn from the task. Based on these axioms, we introduce TRIP (Truly Ranged Interactions Problem) and its generalisation GRIP (Generally Ranged Interactions Problem), constructive procedures that turn any graph into a provably long-ranged task by drawing features from stable distributions. Moreover, by construction, GRIP admits a closed-form, per-range Maximum-Likelihood oracle that yields the first a priori per-range lower bound on test error available on any benchmark. Using our framework, we: (i) audit 4 common long-range benchmarks and identify their failures modes with respect to our axioms; (ii) on TRIP-instantiated topologies, we find a popular notion of curvature is uncorrelated with GNN performance, supporting topological-vs-computational bottleneck distinction; and (iii) we show that a novel benchmark's over-squashing measures factors beyond pure long-rangedness. Code to use the framework and reproduce experiments is released https://github.com/ferranhernandezc/graph-grip.

cs.LG↗

arXiv2026

Trajectory Stitching for Solving Inverse Problems with Flow-Based Models

Flow-based generative models have emerged as powerful priors for solving inverse problems. One option is to directly optimize the initial latent code (noise), such that the flow output solves the inverse problem. However, this requires backpropagating through the entire generative trajectory, incurring high memory costs and numerical instability. We propose MS-Flow, which represents the trajectory as a sequence of intermediate latent states rather than a single initial code. By enforcing the flow dynamics locally and coupling segments through trajectory-matching penalties, MS-Flow alternates between updating intermediate latent states and enforcing consistency with observed data. This reduces memory consumption while improving reconstruction quality. We demonstrate the effectiveness of MS-Flow over existing methods on image recovery and inverse problems, including inpainting, super-resolution, and computed tomography.

eess.IV↗

arXiv2026

GeoCFM: Positive-Only Conditional Flow Matching for Mineral Occurrence Sampling

Critical mineral discovery is a positive-only problem: deposits are observed as sparse locations, while unlabeled regions are not reliable negatives, and similar geophysical signatures can arise from different subsurface states. We therefore model mineral targeting as learning a conditional spatial distribution over occurrence locations, $π(p\mid d)$, given geo-images $d$, rather than predicting a deterministic per-pixel score map. We introduce GeoCFM, a conditional flow-matching model that generates mineral occurrence point sets conditioned on multi-channel geo-images; GeoCFM learns a point-wise transport field in $\mathbb{R}^2$, using UNet features with point-conditioned velocity prediction to bridge dense rasters and sparse supervision without pseudo-negatives. On a synthetic magnetics--geochemistry benchmark with latent activation and on USGS Earth MRI data with a spatially disjoint tile split, GeoCFM improves geometric agreement with observed occurrences over score-map and non-conditional baselines, while representing epistemic uncertainty through conditional sampling.

cs.LG↗

arXiv2026

Attention Graphons: A Graph Limit Perspective on Graph Transformers

Graph Transformers produce, for each attention head, a dense $n\times n$ matrix of learned pairwise interactions. We ask a fundamental question: do these attention-induced graphs converge to a stable limit object as $n$ grows, or does the learned interaction pattern remain unstructured and size-dependent? We answer this using dense graph limit theory, treating each attention matrix as a finite sample from an underlying kernel---an \emph{attention graphon}---and studying concentration around this limit under the cut-distance. We derive a worst-case variance bound requiring no assumptions on the graphon, and a sharper regularity-aware bound based on nonparametric estimation theory. To operationalize the theory, we propose a canonicalize-then-block-average pipeline for estimating dataset-level attention graphons, and a variance-based diagnostic for testing whether attention admits a stable continuum description. Experiments across multiple graph benchmarks show that learned attention stabilizes to dataset-specific graphon structure on several datasets; that empirical cut-distance and cut-norm variance decreases with $n$ consistent with our bounds; and that attention graphons transfer to larger graph sizes with error decreasing in $n$.

cs.LG↗

arXiv2026

Iterative Flow Matching: Path Correction and Gradual Refinement for Enhanced Generative Modeling

Generative models for image generation are now commonly used for a wide variety of applications, ranging from guided image generation for entertainment to solving inverse problems. Nonetheless, training a generator is a non-trivial feat that requires fine-tuning and can lead to so-called hallucinations, that is, the generation of images that are unrealistic. In this work, we explore image generation using flow matching. We explain and demonstrate why flow matching can generate hallucinations, and propose an iterative process to improve the generation process. Our iterative process can be integrated into virtually any generative modeling technique, thereby enhancing the performance and robustness of image synthesis systems.

cs.LG↗

arXiv2026

FLASH: Flexible Learning of Adaptive Sampling from History in Temporal Graph Neural Networks

Aggregating temporal signals from historic interactions is a key step in future link prediction on dynamic graphs. However, incorporating long histories is resource-intensive. Hence, temporal graph neural networks (TGNNs) often rely on historical neighbors sampling heuristics such as uniform sampling or recent neighbors selection. These heuristics are static and fail to adapt to the underlying graph structure. We introduce FLASH, a learnable and graph-adaptive neighborhood selection mechanism that generalizes existing heuristics. FLASH integrates seamlessly into TGNNs and is trained end-to-end using a self-supervised ranking loss. We provide theoretical evidence that commonly used heuristics hinder TGNNs performance, motivating our design. Extensive experiments across multiple benchmarks demonstrate consistent and significant performance improvements for TGNNs equipped with FLASH.

cs.LG↗

arXiv2026

Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modeling

The recent success of State-Space Models (SSMs) in sequence modeling has motivated their adaptation to graph learning, giving rise to Graph State-Space Models (GSSMs). However, existing GSSMs operate by applying SSM modules to sequences extracted from graphs, often compromising core properties such as permutation equivariance, message-passing compatibility, and computational efficiency. In this paper, we introduce a new perspective by embedding the key principles of modern SSM computation directly into the Message-Passing Neural Network framework, resulting in a unified methodology for both static and temporal graphs. Our approach, MP-SSM, enables efficient, permutation-equivariant, and long-range information propagation while preserving the architectural simplicity of message passing. Crucially, MP-SSM enables an exact sensitivity analysis, which we use to theoretically characterize information flow and evaluate issues like vanishing gradients and over-squashing in the deep regime. Furthermore, our design choices allow for a highly optimized parallel implementation akin to modern SSMs. We validate MP-SSM across a wide range of tasks, including node classification, graph property prediction, long-range benchmarks, and spatiotemporal forecasting, demonstrating both its versatility and strong empirical performance.

cs.LG↗

arXiv2026

Learning from Historical Activations in Graph Neural Networks

Graph Neural Networks (GNNs) have demonstrated remarkable success in various domains such as social networks, molecular chemistry, and more. A crucial component of GNNs is the pooling procedure, in which the node features calculated by the model are combined to form an informative final descriptor to be used for the downstream task. However, previous graph pooling schemes rely on the last GNN layer features as an input to the pooling or classifier layers, potentially under-utilizing important activations of previous layers produced during the forward pass of the model, which we regard as historical graph activations. This gap is particularly pronounced in cases where a node's representation can shift significantly over the course of many graph neural layers, and worsened by graph-specific challenges such as over-smoothing in deep architectures. To bridge this gap, we introduce HISTOGRAPH, a novel two-stage attention-based final aggregation layer that first applies a unified layer-wise attention over intermediate activations, followed by node-wise attention. By modeling the evolution of node representations across layers, our HISTOGRAPH leverages both the activation history of nodes and the graph structure to refine features used for final prediction. Empirical results on multiple graph classification benchmarks demonstrate that HISTOGRAPH offers strong performance that consistently improves traditional techniques, with particularly strong robustness in deep GNNs.

cs.LG↗

arXiv2026

Conservative Flows: A New Paradigm of Generative Models

Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized from data-supported states rather than from noise. The framework can utilize any pretrained flow model. We develop two probability-preserving sampling mechanisms, a corrected Langevin dynamics with a Metropolis adjustment and a predictor-corrector flow, that operate directly on existing checkpoints. We validate the framework on a synthetic Swiss-roll target, ImageNet-256 and Oxford Flowers-102, where our samplers consistently improve over the original generation procedures.

cs.LG↗

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

Towards Improved Sentence Representations using Token Graphs

Obtaining a single-vector representation from a Large Language Model's (LLM) token-level outputs is a critical step for nearly all sentence-level tasks. However, standard pooling methods like mean or max aggregation treat tokens as an independent set, discarding the rich relational structure captured by the model's self-attention layers and making them susceptible to signal dilution. To address this, we introduce GLOT, a lightweight, structure-aware pooling module that reframes pooling as relational learning followed by aggregation. Operating on the outputs of a frozen LLM, GLOT first constructs a latent token-similarity graph, then refines token representations with a graph neural network, and finally aggregates them using a readout layer. Experimentally, our approach is remarkably robust and efficient: on a diagnostic stress test where 90% of tokens are random distractors, GLOT maintains over 97% accuracy while baseline methods collapse. Furthermore, it is competitive with state-of-the-art techniques on benchmarks like GLUE and MTEB with 20x fewer trainable parameters and speeds up the training time by over 100x compared with parameter-efficient fine-tuning methods. Supported by a theoretical analysis of its expressive power, our work shows that learning over token graphs is a powerful paradigm for the efficient adaptation of frozen LLMs. Our code is published at https://github.com/ipsitmantri/GLOT.

cs.LG↗