Semantic DLM+: Improving Diffusion Language Models through Bias-variance Trade-off in Transition Kernel Design

Diffusion Language Models (DLMs) have demonstrated strong scaling capacity as alternatives to autoregressive language models. However, their performance is highly sensitive to the choice of transition kernels, and poorly designed kernels can lead to issues like training instability, slow convergence, and biased sampling. In this paper, we study this sensitivity through a principled analysis of generalization error and identify three critical factors: asymptotic bias (difficulty in approximating the posterior distribution), exposure bias (error propagation during sampling), and optimization variance induced by kernel dispersion. We further compare different transition kernels: masking diffusion yields sparse and easier posterior-approximation targets, while uniform diffusion provides stronger sampling-side repair but induces harder approximation. Motivated by this trade-off, we revisit a previously overlooked variant, semantic DLM (SemDLM), where the transition kernel corrupts tokens to neighborhoods that are semantically similar. Our theory suggests that SemDLM can serve as a plausible middle ground by reducing the posterior approximation difficulty of uniform diffusion while retaining repair ability. However, we find that SemDLM suffers from a semantic basin problem, where sampling repeatedly stays within a semantic region and produces low-diversity text. To address this, we propose SemDLM+, which adds a global transition and a semantic-frequency penalty during sampling. Experiments on LM1B and OpenWebText show that SemDLM+ improves training dynamics and achieves competitive language modeling and generation quality with satisfactory diversity.

Safe and Stylized Trajectory Planning for Autonomous Driving via Diffusion Model

Achieving safe and stylized trajectory planning in complex real-world scenarios remains a critical challenge for autonomous driving systems. This paper proposes the SDD Planner, a diffusion-based framework designed to effectively reconcile safety constraints with driving styles in real time. The framework integrates two core modules: a Multi-Source Style-Aware Encoder, which employs distance-sensitive attention to fuse dynamic agent data and environmental contexts for heterogeneous safety-style perception; and a Style-Guided Dynamic Trajectory Generator, which adaptively modulates priority weights within the diffusion denoising process to generate user-preferred yet safe trajectories. Extensive experiments demonstrate that SDD Planner achieves state-of-the-art performance. On the StyleDrive benchmark, it improves the SM-PDMS metric by 3.9% over WoTE, the strongest baseline. Furthermore, on the NuPlan Test14 and Test14-hard benchmarks, SDD Planner ranks first with overall scores of 91.76 and 80.32, respectively, outperforming leading methods such as PLUTO. Real-vehicle closed-loop tests further confirm that SDD Planner maintains high safety standards while aligning with preset driving styles, validating its practical applicability for real-world deployment.

Uncertainty Principle for Vertex-Time Graph Signal Processing

We present an uncertainty principle for graph signals in the vertex-time domain, unifying the classical time-frequency and graph uncertainty principles within a single framework. By defining vertex-time and spectral-frequency spreads, we quantify signal localization across these domains. Our framework identifies a class of signals that achieve maximum concentration in both the spatial and temporal domains. These signals serve as fundamental atoms for a new vertex-time dictionary, enhancing signal reconstruction under practical constraints, such as intermittent data commonly encountered in sensor and social networks. Furthermore, we introduce a novel graph topology inference method leveraging the uncertainty principle. Numerical experiments on synthetic and real datasets validate the effectiveness of our approach, demonstrating improved reconstruction accuracy, greater robustness to noise, and enhanced graph learning performance compared to existing methods.

Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networks

Graph contrastive learning (GCL) learns node and graph representations by contrasting multiple views of the same graph. Existing methods typically rely on fixed, handcrafted views-usually a local and a global perspective, which limits their ability to capture multi-scale structural patterns. We present an augmentation-free, multi-view GCL framework grounded in fractional-order continuous dynamics. By varying the fractional derivative order $α\in (0,1]$, our encoders produce a continuous spectrum of views: small $α$ yields localized features, while large $α$ induces broader, global aggregation. We treat $α$ as a learnable parameter so the model can adapt diffusion scales to the data and automatically discover informative views. This principled approach generates diverse, complementary representations without manual augmentations. Extensive experiments on standard benchmarks demonstrate that our method produces more robust and expressive embeddings and outperforms state-of-the-art GCL baselines.

Simple Graph Contrastive Learning via Fractional-order Neural Diffusion Networks

Graph Contrastive Learning (GCL) has recently made progress as an unsupervised graph representation learning paradigm. GCL approaches can be categorized into augmentation-based and augmentation-free methods. The former relies on complex data augmentations, while the latter depends on encoders that can generate distinct views of the same input. Both approaches may require negative samples for training. In this paper, we introduce a novel augmentation-free GCL framework based on graph neural diffusion models. Specifically, we utilize learnable encoders governed by Fractional Differential Equations (FDE). Each FDE is characterized by an order parameter of the differential operator. We demonstrate that varying these parameters allows us to produce learnable encoders that generate diverse views, capturing either local or global information, for contrastive learning. Our model does not require negative samples for training and is applicable to both homophilic and heterophilic datasets. We demonstrate its effectiveness across various datasets, achieving state-of-the-art performance.

Efficient Training of Neural Fractional-Order Differential Equation via Adjoint Backpropagation

Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems with nonlocal characteristics. Recent progress at the intersection of FDEs and deep learning has catalyzed a new wave of innovative models, demonstrating the potential to address challenges such as graph representation learning. However, training neural FDEs has primarily relied on direct differentiation through forward-pass operations in FDE numerical solvers, leading to increased memory usage and computational complexity, particularly in large-scale applications. To address these challenges, we propose a scalable adjoint backpropagation method for training neural FDEs by solving an augmented FDE backward in time, which substantially reduces memory requirements. This approach provides a practical neural FDE toolbox and holds considerable promise for diverse applications. We demonstrate the effectiveness of our method in several tasks, achieving performance comparable to baseline models while significantly reducing computational overhead.

Distributed-Order Fractional Graph Operating Network

We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize integer-order or single fractional-order differential equations, DRAGON uses a learnable probability distribution over a range of real numbers for the derivative orders. By allowing a flexible and learnable superposition of multiple derivative orders, our framework captures complex graph feature updating dynamics beyond the reach of conventional models. We provide a comprehensive interpretation of our framework's capability to capture intricate dynamics through the lens of a non-Markovian graph random walk with node feature updating driven by an anomalous diffusion process over the graph. Furthermore, to highlight the versatility of the DRAGON framework, we conduct empirical evaluations across a range of graph learning tasks. The results consistently demonstrate superior performance when compared to traditional continuous GNN models. The implementation code is available at \url{https://github.com/zknus/NeurIPS-2024-DRAGON}.

Generalized Graph Signal Reconstruction via the Uncertainty Principle

We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we quantify signal localization across these domains, revealing a trade-off between them. This framework allows us to identify a class of signals with maximal energy concentration in both domains, forming the fundamental atoms for a new joint vertex-time dictionary. This dictionary enhances signal reconstruction under practical constraints, such as incomplete or intermittent data, commonly encountered in sensor and social networks. Numerical experiments on real-world datasets demonstrate the effectiveness of the proposed approach, showing improved reconstruction accuracy and noise robustness compared to existing methods.

FedSheafHN: Personalized Federated Learning on Graph-structured Data

Personalized subgraph Federated Learning (FL) is a task that customizes Graph Neural Networks (GNNs) to individual client needs, accommodating diverse data distributions. However, applying hypernetworks in FL, while aiming to facilitate model personalization, often encounters challenges due to inadequate representation of client-specific characteristics. To overcome these limitations, we propose a model called FedSheafHN, using enhanced collaboration graph embedding and efficient personalized model parameter generation. Specifically, our model embeds each client's local subgraph into a server-constructed collaboration graph. We utilize sheaf diffusion in the collaboration graph to learn client representations. Our model improves the integration and interpretation of complex client characteristics. Furthermore, our model ensures the generation of personalized models through advanced hypernetworks optimized for parallel operations across clients. Empirical evaluations demonstrate that FedSheafHN outperforms existing methods in most scenarios, in terms of client model performance on various graph-structured datasets. It also has fast model convergence and effective new clients generalization.

Deep, convergent, unrolled half-quadratic splitting for image deconvolution

In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling-based deep network design since many traditional model-based approaches rely on iterative optimization. Despite exciting progress, typical unrolling approaches heuristically design layer-specific convolution weights to improve performance. Crucially, convergence properties of the underlying iterative algorithm are lost once layer-specific parameters are learned from training data. We propose an unrolling technique that breaks the trade-off between retaining algorithm properties while simultaneously enhancing performance. We focus on image deblurring and unrolling the widely-applied Half-Quadratic Splitting (HQS) algorithm. We develop a new parametrization scheme which enforces layer-specific parameters to asymptotically approach certain fixed points. Through extensive experimental studies, we verify that our approach achieves competitive performance with state-of-the-art unrolled layer-specific learning and significantly improves over the traditional HQS algorithm. We further establish convergence of the proposed unrolled network as the number of layers approaches infinity, and characterize its convergence rate. Our experimental verification involves simulations that validate the analytical results as well as comparison with state-of-the-art non-blind deblurring techniques on benchmark datasets. The merits of the proposed convergent unrolled network are established over competing alternatives, especially in the regime of limited training.