Graph condensation (GC) aims to distill the original graph into a small-scale graph, mitigating redundancy and accelerating GNN training. However, conventional GC approaches heavily rely on rigid GNNs and task-specific supervision. Such a dependency severely restricts their reusability and generalization across various tasks and architectures. In this work, we revisit the goal of ideal GC from the perspective of GNN optimization consistency, and then a generalized GC optimization objective is derived, by which those traditional GC methods can be viewed nicely as special cases of this optimization paradigm. Based on this, Pre-trained Graph Condensation (PreGC) via optimal transport is proposed to transcend the limitations of task-and architecture-dependent GC methods. Specifically, a hybrid-interval graph diffusion augmentation is presented to suppress the weak generalization ability of the condensed graph on particular architectures by enhancing the uncertainty of node states. Meanwhile, the matching between optimal graph transport plan and representation transport plan is tactfully established to maintain semantic consistencies across source graph and condensed graph spaces, thereby freeing graph condensation from task dependencies. To further facilitate the adaptation of condensed graphs to various downstream tasks, a traceable semantic harmonizer from source nodes to condensed nodes is proposed to bridge semantic associations through the optimized representation transport plan in pre-training. Extensive experiments verify the superiority and versatility of PreGC, demonstrating its task-independent nature and seamless compatibility with arbitrary GNNs.

Dataset condensation aims to synthesize compact yet informative datasets that1 retain the training efficacy of full-scale data, offering substantial gains in efficiency.2 Recent studies reveal that the condensation process can be vulnerable to backdoor3 attacks, where malicious triggers are injected into the condensation dataset, manipu-4 lating model behavior during inference. While prior approaches have made progress5 in balancing attack success rate and clean test accuracy, they often fall short in6 preserving stealthiness, especially in concealing the visual artifacts of condensed7 data or the perturbations introduced during inference. To address this challenge,8 we introduce SNEAKDOOR, which enhances stealthiness without compromising9 attack effectiveness. SNEAKDOOR exploits the inherent vulnerability of class deci-10 sion boundaries and incorporates a generative module that constructs input-aware11 triggers aligned with local feature geometry, thereby minimizing detectability. This12 joint design enables the attack to remain imperceptible to both human inspection13 and statistical detection. Extensive experiments across multiple datasets demon-14 strate that SNEAKDOOR achieves a compelling balance among attack success rate,15 clean test accuracy, and stealthiness, substantially improving the invisibility of both16 the synthetic data and triggered samples while maintaining high attack efficacy.17

Although transformer-based models have shown exceptional empirical performance, the fundamental principles governing their training dynamics are inadequately characterized beyond configuration-specific studies. Inspired by empirical evidence showing improved reasoning capabilities under small initialization scales in language models, we employ the gradient flow analytical framework established in Zhou et al. [2022] to systematically investigate linearized Transformer training dynamics.

Graph condensation, which reduces the size of a large-scale graph by synthesizing a small-scale condensed graph as its substitution, has immediate benefits for various graph learning tasks. However, existing graph condensation methods rely on the joint optimization of nodes and structures in the condensed graph, and overlook critical issues in effectiveness and generalization ability. In this paper, we advocate a new Structure-Free Graph Condensation paradigm, named SFGC, to distill a largescale graph into a small-scale graph node set without explicit graph structures, i.e., graph-free data. Our idea is to implicitly encode topology structure information into the node attributes in the synthesized graph-free data, whose topology is reduced to an identity matrix.

Graph condensation (GC) aims to distill the original graph into a small-scale graph, mitigating redundancy and accelerating GNN training. However, conventional GC approaches heavily rely on rigid GNNs and task-specific supervision. Such a dependency severely restricts their reusability and generalization across various tasks and architectures. In this work, we revisit the goal of ideal GC from the perspective of GNN optimization consistency, and then a generalized GC optimization objective is derived, by which those traditional GC methods can be viewed nicely as special cases of this optimization paradigm. Based on this, \textbf{Pre}-trained \textbf{G}raph \textbf{C}ondensation (\textbf{PreGC}) via optimal transport is proposed to transcend the limitations of task-and architecture-dependent GC methods. Specifically, a hybrid-interval graph diffusion augmentation is presented to suppress the weak generalization ability of the condensed graph on particular architectures by enhancing the uncertainty of node states. Meanwhile, the matching between optimal graph transport plan and representation transport plan is tactfully established to maintain semantic consistencies across source graph and condensed graph spaces, thereby freeing graph condensation from task dependencies. To further facilitate the adaptation of condensed graphs to various downstream tasks, a traceable semantic harmonizer from source nodes to condensed nodes is proposed to bridge semantic associations through the optimized representation transport plan in pre-training. Extensive experiments verify the superiority and versatility of PreGC, demonstrating its task-independent nature and seamless compatibility with arbitrary GNNs.

Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for learning such summaries from data assume that both the high- and low-dimensional structures are acyclic, which is helpful for causal effect identification and reasoning but excludes many high-dimensional models and thus limits applicability. We show that in the linear non-Gaussian (LiNG) setting, the high-dimensional acyclicity assumption can be relaxed while still allowing recovery of a low-dimensional causal directed acyclic graph (DAG). We further connect identifiability of this low-dimensional DAG to existing results: LiNG models with cycles are observationally identifiable only up to an equivalence class whose members differ by reversals of directed cycles; our low-dimensional DAG, which is invariant across all members of a given equivalence class, thus forms a natural representative of the class. While existing approaches for learning this observational equivalence class over high-dimensional variables have exponential time complexity, our low-dimensional summary is learned in worst-case cubic time and comes with explicit bounds on the sample complexity. We provide open source code and experiments on synthetic data to corroborate our theoretical results.

We present a new dataset condensation framework termed Squeeze (), Recover () and Relabel () (SRe2L) that decouples the bilevel optimization of model and architectures synthetic and data image during resolutions training, for to ef handle ficient dataset varying condensation.

Dataset condensation (DC) distills a large real-world dataset into a small synthetic dataset, with the goal of training a network from scratch on the latter that performs similarly to the former. State-of-the-art (SOTA) DC methods have achieved satisfactory results through techniques such as accuracy, gradient, training trajectory, or distribution matching. However, these works all perform matching in the high-dimension pixel space, ignoring that natural images are usually locally connected and have lower intrinsic dimensions, resulting in low condensation efficiency. In this work, we propose a simple-yet-efficient dataset condensation plugin that matches the raw and synthetic datasets in a low-dimensional manifold.

Graph Neural Networks (GNNs) are widely applied to graph learning problems such as node classification. When scaling up the underlying graphs of GNNs to a larger size, we are forced to either train on the complete graph and keep the full graph adjacency and node embeddings in memory (which is often infeasible) or mini-batch sample the graph (which results in exponentially growing computational complexities with respect to the number of GNN layers). Various sampling-based and historical-embedding-based methods are proposed to avoid this exponential growth of complexities. However, none of these solutions eliminates the linear dependence on graph size. This paper proposes a sketch-based algorithm whose training time and memory grow sublinearly with respect to graph size by training GNNs atop a few compact sketches of graph adjacency and node embeddings. Based on polynomial tensor-sketch (PTS) theory, our framework provides a novel protocol for sketching non-linear activations and graph convolution matrices in GNNs, as opposed to existing methods that sketch linear weights or gradients in neural networks. In addition, we develop a locality sensitive hashing (LSH) technique that can be trained to improve the quality of sketches. Experiments on large-graph benchmarks demonstrate the scalability and competitive performance of our Sketch-GNNs versus their full-size GNN counterparts.