Robust GNN Watermarking via Implicit Perception of Topological Invariants

Graph Neural Networks (GNNs) are valuable intellectual property, yet many watermarks rely on backdoor triggers that break under common model edits and create ownership ambiguity. We present InvGNN-WM, which ties ownership to a model's implicit perception of a graph invariant, enabling trigger-free, black-box verification with negligible task impact. A lightweight head predicts normalized algebraic connectivity on an owner-private carrier set; a sign-sensitive decoder outputs bits, and a calibrated threshold controls the false-positive rate. Across diverse node and graph classification datasets and backbones, InvGNN-WM matches clean accuracy while yielding higher watermark accuracy than trigger- and compression-based baselines. It remains strong under unstructured pruning, fine-tuning, and post-training quantization; plain knowledge distillation (KD) weakens the mark, while KD with a watermark loss (KD+WM) restores it. We provide guarantees for imperceptibility and robustness, and we prove that exact removal is NP-complete.

Unleashing the True Potential of LLMs: A Feedback-Triggered Self-Correction with Long-Term Multipath Decoding

Large Language Models (LLMs) have achieved remarkable performance across diverse tasks, yet their susceptibility to generating incorrect content during inference remains a critical unsolved challenge. While self-correction methods offer potential solutions, their effectiveness is hindered by two inherent limitations: (1) the absence of reliable guidance signals for error localization, and (2) the restricted reasoning depth imposed by conventional next-token decoding paradigms. To address these issues, we propose Feedback-Triggered Regeneration (FTR), a novel framework that synergizes user feedback with enhanced decoding dynamics. Specifically, FTR activates response regeneration only upon receiving negative user feedback, thereby circumventing error propagation from faulty self-assessment while preserving originally correct outputs. Furthermore, we introduce Long-Term Multipath (LTM) decoding, which enables systematic exploration of multiple reasoning trajectories through delayed sequence evaluation, effectively overcoming the myopic decision-making characteristic of standard next-token prediction. Extensive experiments on mathematical reasoning and code generation benchmarks demonstrate that our framework achieves consistent and significant improvements over state-of-the-art prompt-based self-correction methods.

Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Models

Explicit noise-level conditioning is widely regarded as essential for the effective operation of Graph Diffusion Models (GDMs). In this work, we challenge this assumption by investigating whether denoisers can implicitly infer noise levels directly from corrupted graph structures, potentially eliminating the need for explicit noise conditioning. To this end, we develop a theoretical framework centered on Bernoulli edge-flip corruptions and extend it to encompass more complex scenarios involving coupled structure-attribute noise. Extensive empirical evaluations on both synthetic and real-world graph datasets, using models such as GDSS and DiGress, provide strong support for our theoretical findings. Notably, unconditional GDMs achieve performance comparable or superior to their conditioned counterparts, while also offering reductions in parameters (4-6%) and computation time (8-10%). Our results suggest that the high-dimensional nature of graph data itself often encodes sufficient information for the denoising process, opening avenues for simpler, more efficient GDM architectures.

Uncertainty Quantification With Noise Injection in Neural Networks: A Bayesian Perspective

Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural networks by introducing randomness. In this paper, we establish a connection between noise injection and uncertainty quantification from a Bayesian standpoint. We theoretically demonstrate that injecting noise into the weights of a neural network is equivalent to Bayesian inference on a deep Gaussian process. Consequently, we introduce a Monte Carlo Noise Injection (MCNI) method, which involves injecting noise into the parameters during training and performing multiple forward propagations during inference to estimate the uncertainty of the prediction. Through simulation and experiments on regression and classification tasks, our method demonstrates superior performance compared to the baseline model.

Robustness Enhancement in Neural Networks with Alpha-Stable Training Noise

With the increasing use of deep learning on data collected by non-perfect sensors and in non-perfect environments, the robustness of deep learning systems has become an important issue. A common approach for obtaining robustness to noise has been to train deep learning systems with data augmented with Gaussian noise. In this work, we challenge the common choice of Gaussian noise and explore the possibility of stronger robustness for non-Gaussian impulsive noise, specifically alpha-stable noise. Justified by the Generalized Central Limit Theorem and evidenced by observations in various application areas, alpha-stable noise is widely present in nature. By comparing the testing accuracy of models trained with Gaussian noise and alpha-stable noise on data corrupted by different noise, we find that training with alpha-stable noise is more effective than Gaussian noise, especially when the dataset is corrupted by impulsive noise, thus improving the robustness of the model. The generality of this conclusion is validated through experiments conducted on various deep learning models with image and time series datasets, and other benchmark corrupted datasets. Consequently, we propose a novel data augmentation method that replaces Gaussian noise, which is typically added to the training data, with alpha-stable noise.