arXiv subjects

Moshe Eliasof

Publications and source records attributed to Moshe Eliasof.

At least 19 recordsLinked to original sources

arXiv2026

A Critical Audit of Spatiotemporal Forecasting Benchmark Datasets and Baselines

Graph neural networks (GNNs) are routinely employed for short-range forecasting on multivariate time series with a spatial graph structure. Despite the availability of many alternative datasets, method innovations within this domain are predominantly assessed against a rather limited set of benchmark datasets, most notably Chickenpox, PedalMe, WikiMaths, METR-LA, and PEMS-BAY. The evaluation protocols contain baselines spanning from historical averages to classical machine learning approaches. These baselines often show competitive performance compared to GNNs. In the present work, we take a step back and analyse the benchmark datasets via classical time series methods to uncover why spatially-unaware linear models pose a stronger competitor than previously reported, casting further doubt on the discriminative reliability of the aforementioned widely adopted datasets. Our statistical analysis provides a toolset for identifying significant spatial and temporal correlations, while revealing a structural bias introduced by first-order differenced datasets. We therefore recommend reducing the over-reliance on such datasets for method comparison, and instead advocate for more rigorous statistical evaluation. By applying the results of our analysis to a simple hybrid model, we show how our methodology can lead to novel ways of developing GNN models

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

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

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 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↗

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 $\Sigma_t$ 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 $\Sigma_t$, 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 \emph{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.

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

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↗

arXiv2025

Reversing Large Language Models for Efficient Training and Fine-Tuning

Large Language Models (LLMs) are known for their expensive and time-consuming training. Thus, oftentimes, LLMs are fine-tuned to address a specific task, given the pretrained weights of a pre-trained LLM considered a foundation model. In this work, we introduce memory-efficient, reversible architectures for LLMs, inspired by symmetric and symplectic differential equations, and investigate their theoretical properties. Different from standard, baseline architectures that store all intermediate activations, the proposed models use time-reversible dynamics to retrieve hidden states during backpropagation, relieving the need to store activations. This property allows for a drastic reduction in memory consumption, allowing for the processing of larger batch sizes for the same available memory, thereby offering improved throughput. In addition, we propose an efficient method for converting existing, non-reversible LLMs into reversible architectures through fine-tuning, rendering our approach practical for exploiting existing pre-trained models. Our results show comparable or improved performance on several datasets and benchmarks, on several LLMs, building a scalable and efficient path towards reducing the memory and computational costs associated with both training from scratch and fine-tuning of LLMs.

cs.CL↗

arXiv2025

Graph Neural Regularizers for PDE Inverse Problems

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme that alternates between FEM-based inversion and learned graph neural regularization. The forward problem is numerically solved using the finite element method (FEM), enabling applicability to a wide range of geometries and PDEs. By leveraging the graph structure inherent to FEM discretizations, we employ physics-inspired graph neural networks as learned regularizers, providing a robust, interpretable, and generalizable alternative to standard approaches. Numerical experiments demonstrate that our framework outperforms classical regularization techniques and achieves accurate reconstructions even in highly ill-posed scenarios.

math.NA↗

arXiv2025

Revisiting Node Affinity Prediction in Temporal Graphs

Node affinity prediction is a common task that is widely used in temporal graph learning with applications in social and financial networks, recommender systems, and more. Recent works have addressed this task by adapting state-of-the-art dynamic link property prediction models to node affinity prediction. However, simple heuristics, such as Persistent Forecast or Moving Average, outperform these models. In this work, we analyze the challenges in training current Temporal Graph Neural Networks for node affinity prediction and suggest appropriate solutions. Combining the solutions, we develop NAViS - Node Affinity prediction model using Virtual State, by exploiting the equivalence between heuristics and state space models. While promising, training NAViS is non-trivial. Therefore, we further introduce a novel loss function for node affinity prediction. We evaluate NAViS on TGB and show that it outperforms the state-of-the-art, including heuristics. Our source code is available at https://github.com/orfeld415/NAVIS

cs.LG↗

arXiv2025

On The Expressive Power of GNN Derivatives

Despite significant advances in Graph Neural Networks (GNNs), their limited expressivity remains a fundamental challenge. Research on GNN expressivity has produced many expressive architectures, leading to architecture hierarchies with models of increasing expressive power. Separately, derivatives of GNNs with respect to node features have been widely studied in the context of the oversquashing and over-smoothing phenomena, GNN explainability, and more. To date, these derivatives remain unexplored as a means to enhance GNN expressivity. In this paper, we show that these derivatives provide a natural way to enhance the expressivity of GNNs. We introduce High-Order Derivative GNN (HOD-GNN), a novel method that enhances the expressivity of Message Passing Neural Networks (MPNNs) by leveraging high-order node derivatives of the base model. These derivatives generate expressive structure-aware node embeddings processed by a second GNN in an end-to-end trainable architecture. Theoretically, we show that the resulting architecture family's expressive power aligns with the WL hierarchy. We also draw deep connections between HOD-GNN, Subgraph GNNs, and popular structural encoding schemes. For computational efficiency, we develop a message-passing algorithm for computing high-order derivatives of MPNNs that exploits graph sparsity and parallelism. Evaluations on popular graph learning benchmarks demonstrate HOD-GNN's strong performance on popular graph learning tasks.

cs.LG↗

arXiv2025

Quadratic Binary Optimization with Graph Neural Networks

We investigate a link between Graph Neural Networks (GNNs) and Quadratic Unconstrained Binary Optimization (QUBO) problems, laying the groundwork for GNNs to approximate solutions for these computationally challenging tasks. By analyzing the sensitivity of QUBO formulations, we frame the solution of QUBO problems as a heterophilic node classification task. We then propose QUBO-GNN, an architecture that integrates graph representation learning techniques with QUBO-aware features to approximate solutions efficiently. Additionally, we introduce a self-supervised data generation mechanism to enable efficient and scalable training data acquisition even for large-scale QUBO instances. Experimental evaluations of QUBO-GNN across diverse QUBO problem sizes demonstrate its superior performance compared to exhaustive search and heuristic methods. Finally, we discuss open challenges in the emerging intersection between QUBO optimization and GNN-based learning.

cs.LG↗

arXiv2025

TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows

We introduce TANGO -- a dynamical systems inspired framework for graph representation learning that governs node feature evolution through a learned energy landscape and its associated descent dynamics. At the core of our approach is a learnable Lyapunov function over node embeddings, whose gradient defines an energy-reducing direction that guarantees convergence and stability. To enhance flexibility while preserving the benefits of energy-based dynamics, we incorporate a novel tangential component, learned via message passing, that evolves features while maintaining the energy value. This decomposition into orthogonal flows of energy gradient descent and tangential evolution yields a flexible form of graph dynamics, and enables effective signal propagation even in flat or ill-conditioned energy regions, that often appear in graph learning. Our method mitigates oversquashing and is compatible with different graph neural network backbones. Empirically, TANGO achieves strong performance across a diverse set of node and graph classification and regression benchmarks, demonstrating the effectiveness of jointly learned energy functions and tangential flows for graph neural networks.

cs.LG↗

arXiv2025

Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks

ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness in capturing local graph structure. Despite their success, MPNNs are limited in their ability to capture long-range dependencies between nodes. This has led researchers to adapt MPNNs through rewiring or make use of Graph Transformers, which compromises the computational efficiency that characterized early spatial message-passing architectures, and typically disregards the graph structure. Almost a decade after its original introduction, we revisit ChebNet to shed light on its ability to model distant node interactions. We find that out-of-box, ChebNet already shows competitive advantages relative to classical MPNNs and GTs on long-range benchmarks, while maintaining good scalability properties for high-order polynomials. However, we uncover that this polynomial expansion leads ChebNet to an unstable regime during training. To address this limitation, we cast ChebNet as a stable and non-dissipative dynamical system, which we coin Stable-ChebNet. Our Stable-ChebNet model allows for stable information propagation, and has controllable dynamics which do not require the use of eigendecompositions, positional encodings, or graph rewiring. Across several benchmarks, Stable-ChebNet achieves near state-of-the-art performance.

cs.LG↗

arXiv2025

Understanding and Improving Laplacian Positional Encodings For Temporal GNNs

Temporal graph learning has applications in recommendation systems, traffic forecasting, and social network analysis. Although multiple architectures have been introduced, progress in positional encoding for temporal graphs remains limited. Extending static Laplacian eigenvector approaches to temporal graphs through the supra-Laplacian has shown promise, but also poses key challenges: high eigendecomposition costs, limited theoretical understanding, and ambiguity about when and how to apply these encodings. In this paper, we address these issues by (1) offering a theoretical framework that connects supra-Laplacian encodings to per-time-slice encodings, highlighting the benefits of leveraging additional temporal connectivity, (2) introducing novel methods to reduce the computational overhead, achieving up to 56x faster runtimes while scaling to graphs with 50,000 active nodes, and (3) conducting an extensive experimental study to identify which models, tasks, and datasets benefit most from these encodings. Our findings reveal that while positional encodings can significantly boost performance in certain scenarios, their effectiveness varies across different models.

cs.LG↗

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↗