Daily Papers

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding "slow nodes" at each edge that can mediate communication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths.

A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to oversmoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin

Message passing neural networks (MPNNs) have emerged as go-to models for learning on graph-structured data in the past decade. Despite their effectiveness, most of such models still incur severe issues such as over-smoothing and -correlation, due to their underlying objective of minimizing the Dirichlet energy and the derived neighborhood aggregation operations. In this paper, we propose the DDSM, a new MPNN model built on an optimization framework that includes the stress majorization and orthogonal regularization for overcoming the above issues. Further, we introduce the diffusion distances for nodes into the framework to guide the new message passing operations and develop efficient algorithms for distance approximations, both backed by rigorous theoretical analyses. Our comprehensive experiments showcase that DDSM consistently and considerably outperforms 15 strong baselines on both homophilic and heterophilic graphs.

Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.

Fairness in graph neural networks has been actively studied recently. However, existing works often do not explicitly consider the role of message passing in introducing or amplifying the bias. In this paper, we first investigate the problem of bias amplification in message passing. We empirically and theoretically demonstrate that message passing could amplify the bias when the 1-hop neighbors from different demographic groups are unbalanced. Guided by such analyses, we propose BeMap, a fair message passing method, that leverages a balance-aware sampling strategy to balance the number of the 1-hop neighbors of each node among different demographic groups. Extensive experiments on node classification demonstrate the efficacy of BeMap in mitigating bias while maintaining classification accuracy. The code is available at https://github.com/xiaolin-cs/BeMap.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of L-smooth and mu-strongly convex functions distributed over a given network of size n. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous, leading to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix chi_1 and the maximal resistance chi_2leq chi_1 of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires O(nfrac{L{mu}}log(1{epsilon})) local gradients and only O(nchi_1chi_2frac{L{mu}}log(1{epsilon})) communications to reach a precision epsilon, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. We also propose a SDP relaxation to find the optimal gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights. Our source code is released on a public repository.

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.

We design a low complexity decentralized learning algorithm to train a recently proposed large neural network in distributed processing nodes (workers). We assume the communication network between the workers is synchronized and can be modeled as a doubly-stochastic mixing matrix without having any master node. In our setup, the training data is distributed among the workers but is not shared in the training process due to privacy and security concerns. Using alternating-direction-method-of-multipliers (ADMM) along with a layerwise convex optimization approach, we propose a decentralized learning algorithm which enjoys low computational complexity and communication cost among the workers. We show that it is possible to achieve equivalent learning performance as if the data is available in a single place. Finally, we experimentally illustrate the time complexity and convergence behavior of the algorithm.

Message passing mechanism contributes to the success of GNNs in various applications, but also brings the oversquashing problem. Recent works combat oversquashing by improving the graph spectrums with rewiring techniques, disrupting the structural bias in graphs, and having limited improvement on oversquashing in terms of oversquashing measure. Motivated by unitary RNN, we propose Graph Unitary Message Passing (GUMP) to alleviate oversquashing in GNNs by applying unitary adjacency matrix for message passing. To design GUMP, a transformation is first proposed to make general graphs have unitary adjacency matrix and keep its structural bias. Then, unitary adjacency matrix is obtained with a unitary projection algorithm, which is implemented by utilizing the intrinsic structure of unitary adjacency matrix and allows GUMP to be permutation-equivariant. Experimental results show the effectiveness of GUMP in improving the performance on various graph learning tasks.

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

As multi-agent systems (MAS) become increasingly prevalent in autonomous systems, distributed control, and edge intelligence, efficient communication under resource constraints has emerged as a critical challenge. Traditional communication paradigms often emphasize message fidelity or bandwidth optimization, overlooking the task relevance of the exchanged information. In contrast, goal-oriented communication prioritizes the importance of information with respect to the agents' shared objectives. This review provides a comprehensive survey of goal-oriented communication in MAS, bridging perspectives from information theory, communication theory, and machine learning. We examine foundational concepts alongside learning-based approaches and emergent protocols. Special attention is given to coordination under communication constraints, as well as applications in domains such as swarm robotics, federated learning, and edge computing. The paper concludes with a discussion of open challenges and future research directions at the intersection of communication theory, machine learning, and multi-agent decision making.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive to information contained at distant nodes. Despite recent methods introduced to mitigate this issue, an understanding of the causes for over-squashing and of possible solutions are lacking. In this theoretical work, we prove that: (i) Neural network width can mitigate over-squashing, but at the cost of making the whole network more sensitive; (ii) Conversely, depth cannot help mitigate over-squashing: increasing the number of layers leads to over-squashing being dominated by vanishing gradients; (iii) The graph topology plays the greatest role, since over-squashing occurs between nodes at high commute (access) time. Our analysis provides a unified framework to study different recent methods introduced to cope with over-squashing and serves as a justification for a class of methods that fall under graph rewiring.

Despite much progress in training distributed artificial intelligence (AI), building cooperative multi-agent systems with multi-agent reinforcement learning (MARL) faces challenges in sample efficiency, interpretability, and transferability. Unlike traditional learning-based methods that require extensive interaction with the environment, large language models (LLMs) demonstrate remarkable capabilities in zero-shot planning and complex reasoning. However, existing LLM-based approaches heavily rely on text-based observations and struggle with the non-Markovian nature of multi-agent interactions under partial observability. We present COMPASS, a novel multi-agent architecture that integrates vision-language models (VLMs) with a dynamic skill library and structured communication for decentralized closed-loop decision-making. The skill library, bootstrapped from demonstrations, evolves via planner-guided tasks to enable adaptive strategies. COMPASS propagates entity information through multi-hop communication under partial observability. Evaluations on the improved StarCraft Multi-Agent Challenge (SMACv2) demonstrate COMPASS's strong performance against state-of-the-art MARL baselines across both symmetric and asymmetric scenarios. Notably, in the symmetric Protoss 5v5 task, COMPASS achieved a 57\% win rate, representing a 30 percentage point advantage over QMIX (27\%). Project page can be found at https://stellar-entremet-1720bb.netlify.app/.

Recent studies have demonstrated significant progress in aligning text-to-image diffusion models with human preference via Reinforcement Learning from Human Feedback. However, while existing methods achieve high scores on automated reward metrics, they often lead to Preference Mode Collapse (PMC)-a specific form of reward hacking where models converge on narrow, high-scoring outputs (e.g., images with monolithic styles or pervasive overexposure), severely degrading generative diversity. In this work, we introduce and quantify this phenomenon, proposing DivGenBench, a novel benchmark designed to measure the extent of PMC. We posit that this collapse is driven by over-optimization along the reward model's inherent biases. Building on this analysis, we propose Directional Decoupling Alignment (D^2-Align), a novel framework that mitigates PMC by directionally correcting the reward signal. Specifically, our method first learns a directional correction within the reward model's embedding space while keeping the model frozen. This correction is then applied to the reward signal during the optimization process, preventing the model from collapsing into specific modes and thereby maintaining diversity. Our comprehensive evaluation, combining qualitative analysis with quantitative metrics for both quality and diversity, reveals that D^2-Align achieves superior alignment with human preference.

Loopy Belief Propagation (LBP) is a widely used approximate inference algorithm in probabilistic graphical models, with applications in computer vision, error correction codes, protein folding, program analysis, etc. However, LBP faces significant computational challenges when applied to large-scale program analysis. While GPU (Graphics Processing Unit) parallel computing provides a promising solution, existing approaches lack support for flexible update strategies and have yet to integrate logical constraints with GPU acceleration, leading to suboptimal practical performance. This paper presents a GPU-accelerated LBP algorithm for program analysis. To support the diverse update strategies required by users, we propose a unified representation for specifying arbitrary user-defined update strategies, along with a dependency analysis algorithm. Furthermore, building on previous work that leverages the local structure of Horn clauses to simplify message passing, we group messages to minimize warp divergence and better utilize GPU resources. Experimental results on datarace analysis over eight real-world Java programs show that our approach achieves an average speedup of 2.14times over the state-of-the-art sequential approach and 5.56times over the state-of-the-art GPU-based approach, while maintaining high accuracy.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term shared simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.

We present a method for generating video sequences with coherent motion between a pair of input key frames. We adapt a pretrained large-scale image-to-video diffusion model (originally trained to generate videos moving forward in time from a single input image) for key frame interpolation, i.e., to produce a video in between two input frames. We accomplish this adaptation through a lightweight fine-tuning technique that produces a version of the model that instead predicts videos moving backwards in time from a single input image. This model (along with the original forward-moving model) is subsequently used in a dual-directional diffusion sampling process that combines the overlapping model estimates starting from each of the two keyframes. Our experiments show that our method outperforms both existing diffusion-based methods and traditional frame interpolation techniques.

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing graph neural network methods, and can naturally incorporate node features, unlike existing spectral methods. Extensive experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering when compared against 10 state-of-the-art methods from the literature, for a wide range of noise and sparsity levels, graph structures, and topologies, and even outperforms supervised methods.

Textual Inversion (TI) is an efficient approach to text-to-image personalization but often fails on complex prompts. We trace these failures to embedding norm inflation: learned tokens drift to out-of-distribution magnitudes, degrading prompt conditioning in pre-norm Transformers. Empirically, we show semantics are primarily encoded by direction in CLIP token space, while inflated norms harm contextualization; theoretically, we analyze how large magnitudes attenuate positional information and hinder residual updates in pre-norm blocks. We propose Directional Textual Inversion (DTI), which fixes the embedding magnitude to an in-distribution scale and optimizes only direction on the unit hypersphere via Riemannian SGD. We cast direction learning as MAP with a von Mises-Fisher prior, yielding a constant-direction prior gradient that is simple and efficient to incorporate. Across personalization tasks, DTI improves text fidelity over TI and TI-variants while maintaining subject similarity. Crucially, DTI's hyperspherical parameterization enables smooth, semantically coherent interpolation between learned concepts (slerp), a capability that is absent in standard TI. Our findings suggest that direction-only optimization is a robust and scalable path for prompt-faithful personalization.

Modern Vision-Language Models (VLMs) can solve a wide range of tasks requiring visual reasoning. In real-world scenarios, desirable properties for VLMs include fast inference and controllable generation (e.g., constraining outputs to adhere to a desired format). However, existing autoregressive (AR) VLMs like LLaVA struggle in these aspects. Discrete diffusion models (DMs) offer a promising alternative, enabling parallel decoding for faster inference and bidirectional context for controllable generation through text-infilling. While effective in language-only settings, DMs' potential for multimodal tasks is underexplored. We introduce LaViDa, a family of VLMs built on DMs. We build LaViDa by equipping DMs with a vision encoder and jointly fine-tune the combined parts for multimodal instruction following. To address challenges encountered, LaViDa incorporates novel techniques such as complementary masking for effective training, prefix KV cache for efficient inference, and timestep shifting for high-quality sampling. Experiments show that LaViDa achieves competitive or superior performance to AR VLMs on multi-modal benchmarks such as MMMU, while offering unique advantages of DMs, including flexible speed-quality tradeoff, controllability, and bidirectional reasoning. On COCO captioning, LaViDa surpasses Open-LLaVa-Next-8B by +4.1 CIDEr with 1.92x speedup. On bidirectional tasks, it achieves +59% improvement on Constrained Poem Completion. These results demonstrate LaViDa as a strong alternative to AR VLMs. Code and models will be released in the camera-ready version.

In this work, we propose Causal Autoregressive Diffusion (CARD), a novel framework that unifies the training efficiency of ARMs with the high-throughput inference of diffusion models. CARD reformulates the diffusion process within a strictly causal attention mask, enabling dense, per-token supervision in a single forward pass. To address the optimization instability of causal diffusion, we introduce a soft-tailed masking schema to preserve local context and a context-aware reweighting mechanism derived from signal-to-noise principles. This design enables dynamic parallel decoding, where the model leverages KV-caching to adaptively generate variable-length token sequences based on confidence. Empirically, CARD outperforms existing discrete diffusion baselines while reducing training latency by 3 times compared to block diffusion methods. Our results demonstrate that CARD achieves ARM-level data efficiency while unlocking the latency benefits of parallel generation, establishing a robust paradigm for next-generation efficient LLMs.

This paper tackles optimization problems whose objective and constraints involve a trained Neural Network (NN), where the goal is to maximize f(Phi(x)) subject to c(Phi(x)) leq 0, with f smooth, c general and non-stringent, and Phi an already trained and possibly nonwhite-box NN. We address two challenges regarding this problem: identifying ascent directions for local search, and ensuring reliable convergence towards relevant local solutions. To this end, we re-purpose the notion of directional NN attacks as efficient optimization subroutines, since directional NN attacks use the neural structure of Phi to compute perturbations of x that steer Phi(x) in prescribed directions. Precisely, we develop an attack operator that computes attacks of Phi at any x along the direction nabla f(Phi(x)). Then, we propose a hybrid algorithm combining the attack operator with derivative-free optimization (DFO) techniques, designed for numerical reliability by remaining oblivious to the structure of the problem. We consider the cDSM algorithm, which offers asymptotic guarantees to converge to a local solution under mild assumptions on the problem. The resulting method alternates between attack-based steps for heuristic yet fast local intensification and cDSM steps for certified convergence and numerical reliability. Experiments on three problems show that this hybrid approach consistently outperforms standard DFO baselines.

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique -- named NOTEARS -- is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.

The potential of applying diffusion models (DMs) for multiple antenna communications is discussed. A unified framework of applying DM for multiple antenna tasks is first proposed. Then, the tasks are innovatively divided into two categories, i.e., decision-making tasks and generation tasks, depending on whether an optimization of system parameters is involved. For each category, it is conceived 1) how the framework can be used for each task and 2) why the DM is superior to traditional artificial intelligence (TAI) and conventional optimization tasks. It is highlighted that the DMs are well-suited for scenarios with strong interference and noise, excelling in modeling complex data distribution and exploring better actions. A case study of learning beamforming with a DM is then provided, to demonstrate the superiority of the DMs with simulation results. Finally, the applications of DM for emerging multiple antenna technologies and promising research directions are discussed.

Message-passing graph neural networks (MPNNs) emerged as powerful tools for processing graph-structured input. However, they operate on a fixed input graph structure, ignoring potential noise and missing information. Furthermore, their local aggregation mechanism can lead to problems such as over-squashing and limited expressive power in capturing relevant graph structures. Existing solutions to these challenges have primarily relied on heuristic methods, often disregarding the underlying data distribution. Hence, devising principled approaches for learning to infer graph structures relevant to the given prediction task remains an open challenge. In this work, leveraging recent progress in exact and differentiable k-subset sampling, we devise probabilistically rewired MPNNs (PR-MPNNs), which learn to add relevant edges while omitting less beneficial ones. For the first time, our theoretical analysis explores how PR-MPNNs enhance expressive power, and we identify precise conditions under which they outperform purely randomized approaches. Empirically, we demonstrate that our approach effectively mitigates issues like over-squashing and under-reaching. In addition, on established real-world datasets, our method exhibits competitive or superior predictive performance compared to traditional MPNN models and recent graph transformer architectures.

Training a generative model with limited number of samples is a challenging task. Current methods primarily rely on few-shot model adaption to train the network. However, in scenarios where data is extremely limited (less than 10), the generative network tends to overfit and suffers from content degradation. To address these problems, we propose a novel phasic content fusing few-shot diffusion model with directional distribution consistency loss, which targets different learning objectives at distinct training stages of the diffusion model. Specifically, we design a phasic training strategy with phasic content fusion to help our model learn content and style information when t is large, and learn local details of target domain when t is small, leading to an improvement in the capture of content, style and local details. Furthermore, we introduce a novel directional distribution consistency loss that ensures the consistency between the generated and source distributions more efficiently and stably than the prior methods, preventing our model from overfitting. Finally, we propose a cross-domain structure guidance strategy that enhances structure consistency during domain adaptation. Theoretical analysis, qualitative and quantitative experiments demonstrate the superiority of our approach in few-shot generative model adaption tasks compared to state-of-the-art methods. The source code is available at: https://github.com/sjtuplayer/few-shot-diffusion.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

Autoregressive (AR) generation is the standard decoding paradigm for Large Language Models (LLMs), but its token-by-token nature limits parallelism at inference time. Diffusion Language Models (DLLMs) offer parallel decoding by recovering multiple masked tokens per step; however, in practice they often fail to translate this parallelism into deployment speed gains over optimized AR engines (e.g., vLLM). A key reason is that many DLLMs rely on bidirectional attention, which breaks standard prefix KV caching and forces repeated contextualization, undermining efficiency. We propose WeDLM, a diffusion decoding framework built entirely on standard causal attention to make parallel generation prefix-cache friendly. The core idea is to let each masked position condition on all currently observed tokens while keeping a strict causal mask, achieved by Topological Reordering that moves observed tokens to the physical prefix while preserving their logical positions. Building on this property, we introduce a streaming decoding procedure that continuously commits confident tokens into a growing left-to-right prefix and maintains a fixed parallel workload, avoiding the stop-and-wait behavior common in block diffusion methods. Experiments show that WeDLM preserves the quality of strong AR backbones while delivering substantial speedups, approaching 3x on challenging reasoning benchmarks and up to 10x in low-entropy generation regimes; critically, our comparisons are against AR baselines served by vLLM under matched deployment settings, demonstrating that diffusion-style decoding can outperform an optimized AR engine in practice.

We introduce directional routing, a lightweight mechanism that gives each transformer attention head learned suppression directions controlled by a shared router, at 3.9% parameter cost. We train a 433M-parameter model alongside an identical baseline in a single run, then trace the resulting circuits through mechanistic interpretability. Routing becomes the model's dominant computational pathway. Disabling it collapses factual recall to near-zero probability across all 8 test prompts and drops induction accuracy from 93.4% to 0.0%. Knocking out individual attention heads has negligible effect: the primary mover head's removal actually increases target probability, and induction heads retain 98.6% accuracy without their strongest member. The coordination mechanism is irreplaceable; the components it coordinates are not. The model also self-organizes, without explicit pressure, into two regimes: domain-adaptive routing in early layers and fixed syntactic pruning in late layers, where the least-varying layer is the most critical (+42.6 PPL when disabled). Routing reduces perplexity 31-56% relative to the baseline, though downstream multiple-choice benchmarks do not yet reflect these gains.

Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it suffers from two issues when applied to federated non-IID data. First, the variance of these estimates increases significantly. Second, delaying communication causes the Markov chains to diverge from the true posterior even for very simple models. To alleviate both these problems, we propose conducive gradients, a simple mechanism that combines local likelihood approximations to correct gradient updates. Notably, conducive gradients are easy to compute, and since we only calculate the approximations once, they incur negligible overhead. We apply conducive gradients to distributed stochastic gradient Langevin dynamics (DSGLD) and call the resulting method federated stochastic gradient Langevin dynamics (FSGLD). We demonstrate that our approach can handle delayed communication rounds, converging to the target posterior in cases where DSGLD fails. We also show that FSGLD outperforms DSGLD for non-IID federated data with experiments on metric learning and neural networks.

As large language models (LLMs) scale up, accuracy improves, but the autoregressive (AR) nature of decoding increases latency since each token requires a serial forward pass. Speculative decoding addresses this by employing a fast drafter to propose multi-token drafts, which are then verified in parallel by the target model. However, many deployments still rely on AR drafters, where sequential passes limit wall-clock gains. We revisit the drafting stage and present DiffuSpec, a training-free drop-in framework that uses a pretrained diffusion language model (DLM) to produce multi-token drafts in a single forward pass, while remaining compatible with standard AR verifiers. Because DLM drafts are generated under bidirectional conditioning, parallel per-position candidates form a token lattice in which the locally highest-probability token at each position need not form a causal left-to-right path. Moreover, DLM drafting requires pre-specifying a draft length, inducing a speed-quality trade-off. To address these challenges, we introduce two practical components: (i) a causal-consistency path search (CPS) over this lattice that extracts a left-to-right path aligned with AR verification; and (ii) an adaptive draft-length (ADL) controller that adjusts next proposal size based on recent acceptance feedback and realized generated length. Across benchmarks, DiffuSpec yields up to 3x wall-clock speedup, establishing diffusion-based drafting as a robust alternative to autoregressive drafters for speculative decoding.

Federated learning (FL) leverages client-server communications to train global models on decentralized data. However, communication noise or errors can impair model accuracy. To address this problem, we propose a novel FL algorithm that enhances robustness against communication noise while also reducing communication load. We derive the proposed algorithm through solving the weighted least-squares (WLS) regression problem as an illustrative example. We first frame WLS regression as a distributed convex optimization problem over a federated network employing random scheduling for improved communication efficiency. We then apply the alternating direction method of multipliers (ADMM) to iteratively solve this problem. To counteract the detrimental effects of cumulative communication noise, we introduce a key modification by eliminating the dual variable and implementing a new local model update at each participating client. This subtle yet effective change results in using a single noisy global model update at each client instead of two, improving robustness against additive communication noise. Furthermore, we incorporate another modification enabling clients to continue local updates even when not selected by the server, leading to substantial performance improvements. Our theoretical analysis confirms the convergence of our algorithm in both mean and the mean-square senses, even when the server communicates with a random subset of clients over noisy links at each iteration. Numerical results validate the effectiveness of our proposed algorithm and corroborate our theoretical findings.

We propose a gradient flow procedure for generative modeling by transporting particles from an initial source distribution to a target distribution, where the gradient field on the particles is given by a noise-adaptive Wasserstein Gradient of the Maximum Mean Discrepancy (MMD). The noise-adaptive MMD is trained on data distributions corrupted by increasing levels of noise, obtained via a forward diffusion process, as commonly used in denoising diffusion probabilistic models. The result is a generalization of MMD Gradient Flow, which we call Diffusion-MMD-Gradient Flow or DMMD. The divergence training procedure is related to discriminator training in Generative Adversarial Networks (GAN), but does not require adversarial training. We obtain competitive empirical performance in unconditional image generation on CIFAR10, MNIST, CELEB-A (64 x64) and LSUN Church (64 x 64). Furthermore, we demonstrate the validity of the approach when MMD is replaced by a lower bound on the KL divergence.

Graph-based recommender systems have achieved remarkable effectiveness by modeling high-order interactions between users and items. However, such approaches are significantly undermined by popularity bias, which distorts the interaction graph's structure, referred to as topology bias. This leads to overrepresentation of popular items, thereby reinforcing biases and fairness issues through the user-system feedback loop. Despite attempts to study this effect, most prior work focuses on the embedding or gradient level bias, overlooking how topology bias fundamentally distorts the message passing process itself. We bridge this gap by providing an empirical and theoretical analysis from a Dirichlet energy perspective, revealing that graph message passing inherently amplifies topology bias and consistently benefits highly connected nodes. To address these limitations, we propose Test-time Simplicial Propagation (TSP), which extends message passing to higher-order simplicial complexes. By incorporating richer structures beyond pairwise connections, TSP mitigates harmful topology bias and substantially improves the representation and recommendation of long-tail items during inference. Extensive experiments across five real-world datasets demonstrate the superiority of our approach in mitigating topology bias and enhancing recommendation quality.

Large Language Model-based Multi-Agent Systems (LLM-MAS) are increasingly applied to complex collaborative scenarios. However, their collaborative mechanisms may cause minor inaccuracies to gradually solidify into system-level false consensus through iteration. Such risks are difficult to trace since errors can propagate and amplify through message dependencies. Existing protections often rely on single-agent validation or require modifications to the collaboration architecture, which can weaken effective information flow and may not align with natural collaboration processes in real tasks. To address this, we propose a propagation dynamics model tailored for LLM-MAS that abstracts collaboration as a directed dependency graph and provides an early-stage risk criterion to characterize amplification risk. Through experiments on six mainstream frameworks, we identify three vulnerability classes: cascade amplification, topological sensitivity, and consensus inertia. We further instantiate an attack where injecting just a single atomic error seed leads to widespread failure. In response, we introduce a genealogy-graph-based governance layer, implemented as a message-layer plugin, that suppresses both endogenous and exogenous error amplification without altering the collaboration architecture. Experiments show that this approach raises the defense success rate from a baseline of 0.32 to over 0.89 and significantly mitigates the cascading spread of minor errors.

In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of k-hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.

Autoregressive (AR) diffusion offers a promising framework for generating videos of theoretically infinite length. However, a major challenge is maintaining temporal continuity while preventing the progressive quality degradation caused by error accumulation. To ensure continuity, existing methods typically condition on highly denoised contexts; yet, this practice propagates prediction errors with high certainty, thereby exacerbating degradation. In this paper, we argue that a highly clean context is unnecessary. Drawing inspiration from bidirectional diffusion models, which denoise frames at a shared noise level while maintaining coherence, we propose that conditioning on context at the same noise level as the current block provides sufficient signal for temporal consistency while effectively mitigating error propagation. Building on this insight, we propose HiAR, a hierarchical denoising framework that reverses the conventional generation order: instead of completing each block sequentially, it performs causal generation across all blocks at every denoising step, so that each block is always conditioned on context at the same noise level. This hierarchy naturally admits pipelined parallel inference, yielding a 1.8 wall-clock speedup in our 4-step setting. We further observe that self-rollout distillation under this paradigm amplifies a low-motion shortcut inherent to the mode-seeking reverse-KL objective. To counteract this, we introduce a forward-KL regulariser in bidirectional-attention mode, which preserves motion diversity for causal inference without interfering with the distillation loss. On VBench (20s generation), HiAR achieves the best overall score and the lowest temporal drift among all compared methods.

Despite the impressive performance of diffusion models such as Stable Diffusion (SD) in image generation, their slow inference limits practical deployment. Recent works accelerate inference by distilling multi-step diffusion into one-step generators. To better understand the distillation mechanism, we analyze U-Net/DiT weight changes between one-step students and their multi-step teacher counterparts. Our analysis reveals that changes in weight direction significantly exceed those in weight norm, highlighting it as the key factor during distillation. Motivated by this insight, we propose the Low-rank Rotation of weight Direction (LoRaD), a parameter-efficient adapter tailored to one-step diffusion distillation. LoRaD is designed to model these structured directional changes using learnable low-rank rotation matrices. We further integrate LoRaD into Variational Score Distillation (VSD), resulting in Weight Direction-aware Distillation (WaDi)-a novel one-step distillation framework. WaDi achieves state-of-the-art FID scores on COCO 2014 and COCO 2017 while using only approximately 10% of the trainable parameters of the U-Net/DiT. Furthermore, the distilled one-step model demonstrates strong versatility and scalability, generalizing well to various downstream tasks such as controllable generation, relation inversion, and high-resolution synthesis.

Message passing graph neural networks (GNNs) would appear to be powerful tools to learn distributed algorithms via gradient descent, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications, such as learning local communication policies between resource-constrained agents in, e.g., robotic swarms or sensor networks. In this work we explore why this failure occurs in common GNN architectures, and identify "implicitly-defined" GNNs as a class of architectures which is provably robust to partially asynchronous "hogwild" inference, adapting convergence guarantees from work in asynchronous and distributed optimization, e.g., Bertsekas (1982); Niu et al. (2011). We then propose a novel implicitly-defined GNN architecture, which we call an energy GNN. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems, and achieves competitive performance on real-world datasets.

We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing discrete diffusion approaches, while allowing significantly greater flexibility in the choice of corruption dynamics. The forward noising process relies on uniformization and enables fast arbitrary corruption. For the reverse process, we derive a simple evidence lower bound (ELBO) based on snapshot latents, instead of the entire noising path, that allows efficient training of standard generative modeling architectures with clear probabilistic interpretation. Our experiments on large-vocabulary discrete generation tasks suggest that the proposed framework outperforms existing discrete diffusion methods in terms of training efficiency and generation quality, and beats autoregressive models for the first time at this scale. We provide the code along with a blog post on the project page : https://oussamazekri.fr/gdds{https://oussamazekri.fr/gdds}.

In this work, we provide a systematic survey of Discrete Diffusion Language Models (dLLMs) and Discrete Diffusion Multimodal Language Models (dMLLMs). Unlike autoregressive (AR) models, dLLMs and dMLLMs adopt a multi-token, parallel decoding paradigm using full attention and a denoising-based generation strategy. This paradigm naturally enables parallel generation, fine-grained output controllability, and dynamic, response-aware perception. These capabilities are previously difficult to achieve with AR models. Recently, a growing number of industrial-scale proprietary d(M)LLMs, as well as a large number of open-source academic d(M)LLMs, have demonstrated performance comparable to their autoregressive counterparts, while achieving up to 10x acceleration in inference speed. The advancement of discrete diffusion LLMs and MLLMs has been largely driven by progress in two domains. The first is the development of autoregressive LLMs and MLLMs, which has accumulated vast amounts of data, benchmarks, and foundational infrastructure for training and inference. The second contributing domain is the evolution of the mathematical models underlying discrete diffusion. Together, these advancements have catalyzed a surge in dLLMs and dMLLMs research in early 2025. In this work, we present a comprehensive overview of the research in the dLLM and dMLLM domains. We trace the historical development of dLLMs and dMLLMs, formalize the underlying mathematical frameworks, and categorize representative models. We further analyze key techniques for training and inference, and summarize emerging applications across language, vision-language, and biological domains. We conclude by discussing future directions for research and deployment. Paper collection: https://github.com/LiQiiiii/DLLM-Survey

Denoising diffusion models have emerged as the go-to framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution (OOD) tasks, which remains an under-explored challenge. Realistic reconstructions inconsistent with the measured data can be generated, hallucinating image features that are uniquely present in the training dataset. To simultaneously enforce data-consistency and leverage data-driven priors, we introduce a novel sampling framework called Steerable Conditional Diffusion. This framework adapts the denoising network specifically to the available measured data. Utilising our proposed method, we achieve substantial enhancements in OOD performance across diverse imaging modalities, advancing the robust deployment of denoising diffusion models in real-world applications.

Despite significant progress in alignment, large language models (LLMs) remain vulnerable to adversarial attacks that elicit harmful behaviors. Activation steering techniques offer a promising inference-time intervention approach, but existing methods suffer from critical limitations: activation addition requires careful coefficient tuning and is sensitive to layer-specific norm variations, while directional ablation provides only binary control. Recent work on Angular Steering introduces continuous control via rotation in a 2D subspace, but its practical implementation violates norm preservation, causing distribution shift and generation collapse, particularly in models below 7B parameters. We propose Selective Steering, which addresses these limitations through two key innovations: (1) a mathematically rigorous norm-preserving rotation formulation that maintains activation distribution integrity, and (2) discriminative layer selection that applies steering only where feature representations exhibit opposite-signed class alignment. Experiments across nine models demonstrate that Selective Steering achieves 5.5x higher attack success rates than prior methods while maintaining zero perplexity violations and approximately 100\% capability retention on standard benchmarks. Our approach provides a principled, efficient framework for controllable and stable LLM behavior modification. Code: https://github.com/knoveleng/steering

Text-to-image diffusion models excel at generating photorealistic images, but commonly struggle to render accurate spatial relationships described in text prompts. We identify two core issues underlying this common failure: 1) the ambiguous nature of spatial-related data in existing datasets, and 2) the inability of current text encoders to accurately interpret the spatial semantics of input descriptions. We address these issues with CoMPaSS, a versatile training framework that enhances spatial understanding of any T2I diffusion model. CoMPaSS solves the ambiguity of spatial-related data with the Spatial Constraints-Oriented Pairing (SCOP) data engine, which curates spatially-accurate training data through a set of principled spatial constraints. To better exploit the curated high-quality spatial priors, CoMPaSS further introduces a Token ENcoding ORdering (TENOR) module to allow better exploitation of high-quality spatial priors, effectively compensating for the shortcoming of text encoders. Extensive experiments on four popular open-weight T2I diffusion models covering both UNet- and MMDiT-based architectures demonstrate the effectiveness of CoMPaSS by setting new state-of-the-arts with substantial relative gains across well-known benchmarks on spatial relationships generation, including VISOR (+98%), T2I-CompBench Spatial (+67%), and GenEval Position (+131%). Code will be available at https://github.com/blurgyy/CoMPaSS.

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

With the emergence of data marketplaces, the demand for methods to assess the value of data has increased significantly. While numerous techniques have been proposed for this purpose, none have specifically addressed graphs as the main data modality. Graphs are widely used across various fields, ranging from chemical molecules to social networks. In this study, we break down graphs into two main components: structural and featural, and we focus on evaluating data without relying on specific task-related metrics, making it applicable in practical scenarios where validation requirements may be lacking. We introduce a novel framework called blind message passing, which aligns the seller's and buyer's graphs using a shared node permutation based on graph matching. This allows us to utilize the graph Wasserstein distance to quantify the differences in the structural distribution of graph datasets, called the structural disparities. We then consider featural aspects of buyers' and sellers' graphs for data valuation and capture their statistical similarities and differences, referred to as relevance and diversity, respectively. Our approach ensures that buyers and sellers remain unaware of each other's datasets. Our experiments on real datasets demonstrate the effectiveness of our approach in capturing the relevance, diversity, and structural disparities of seller data for buyers, particularly in graph-based data valuation scenarios.

Diffusion Language Models (DLMs) have recently emerged as a strong alternative to autoregressive language models (LMs). DLMs offer comparable accuracy with faster inference speed via parallel decoding. However, standard DLM decoding strategies relying on high-confidence tokens encounter an inherent information-theoretic bottleneck that restricts decoding progress and ultimately slows generation. We demonstrate both theoretically and empirically that prioritizing high-confidence tokens is inherently inefficient. High-probability tokens carry negligible information and strictly relying on them limits the effective progress made in each decoding round. We prove that the number of decoding rounds must grow linearly with the sample's total information (negative log-likelihood) and inversely with the per-round information budget, establishing a bits-to-rounds principle. We also propose Explore-Then-Exploit (ETE), a training-free decoding strategy that maximizes information throughput and decoding efficiency. ETE combines cross-block decoding with targeted exploration of high-uncertainty tokens to reshape the conditional distribution and trigger cascades of confident predictions. Experiments verify our theoretical bounds and demonstrate that ETE consistently reduces the required number of decoding rounds compared to confidence-only baselines without compromising generation quality.

In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the academics and industries. However, analyses of large directed networks are often time-consuming and expensive because the complexities of a lot of graph algorithms are often polynomial with the size of the graph. Hence, sampling algorithms that can generate graphs preserving properties of original graph are of great importance because they can speed up the analysis process. We propose a promising framework to sample directed graphs: Construct a sample graph with linearly rescaled Joint Degree Matrix (JDM) and Degree Correlation Matrix (DCM). Previous work shows that graphs with the same JDM and DCM will have a range of very similar graph properties. We also conduct experiments on real-world datasets to show that the numbers of non-zero entries in JDM and DCM are quite small compared to the number of edges and nodes. Adopting this framework, we propose a novel graph sampling algorithm that can provably preserves in-degree and out-degree distributions, which are two most fundamental properties of a graph. We also prove the upper bound for deviations in the joint degree distribution and degree correlation distribution, which correspond to JDM and DCM. Besides, we prove that the deviations in these distributions are negatively correlated with the sparsity of the JDM and DCM. Considering that these two matrices are always quite sparse, we believe that proposed algorithm will have a better-than-theory performance on real-world large directed networks.

We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the amount of changes is arbitrary, lower complexity bounds and corresponding optimal algorithms are known, and the consensus acceleration is not possible. However, in practice the magnitude of network changes may be limited. We derive lower communication complexity bounds for several regimes of velocity of networks changes. Moreover, we show how to obtain accelerated communication rates for a certain class of time-varying graphs using a specific consensus algorithm.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is applicable to a wide range of use cases that have worst-case performance requirements. After defining the DMMV problem mathematically, we explore its properties to establish a foundational understanding. To tackle DMMV instance sizes of practical relevance, we develop a GPU-accelerated heuristic that takes advantage of the mathematical properties of DMMV for speeding up the solution process. We demonstrate the versatile applicability of our heuristic by solving three optimization problems as use cases: (1) post-training quantization of language models, (2) discrete tomography, and (3) Finite Impulse Response (FIR) filter design. In quantization without outlier separation, our heuristic achieves 14% improvement on average over existing methods. In discrete tomography, it reduces reconstruction error by 16% under uniform noise and accelerates computations by a factor of 6 on GPU. For FIR filter design, it nearly achieves 50% ripple reduction compared to using the commercial integer optimization solver, Gurobi. Our comparative results point to the benefits of studying DMMV as a context-free optimization problem and the advantages that our proposed heuristic offers on three distinct problems. Our GPU-accelerated heuristic will be made open-source to further stimulate research on DMMV and its other applications. The code is available at https://anonymous.4open.science/r/AMVM-5F3E/

Large language models (LLMs) excel at generation but dominant autoregressive (AR) decoding is inherently sequential, creating a throughput bottleneck. Diffusion Language Models (DLMs)--especially block-wise variants--enable parallel generation and intra-block bidirectional reasoning, yet training large DLMs from scratch is costly and wastes the knowledge in mature AR checkpoints. Prior "adaptation" attempts either modify logits or randomly grow attention masks to full-sequence diffusion, or simply transplant AR weights into a block-diffusion recipe, leaving a fundamental mismatch between AR causality and block-wise bidirectionality unaddressed. We reframe adaptation as a intra-paradigm path from AR to Block-Diffusion by viewing AR as Block-Diffusion with blocksize=1. Concretely, we design the pathway of adaptation as follows: we use a context-causal attention mask (causal in context, bidirectional only within the active block), an efficient parallel adaptation procedure, an auxiliary AR loss to maximize data utilization and retain pretrained knowledge, and gradual increment of the generation block size. The recipe integrates cleanly with masked block-diffusion and maintains train-inference consistency. Built on these components, NBDiff-7B (Base and Instruct) could inherit the long-context modeling and reasoning capabilities, and achieve state-of-the-art performance among the 7B-class DLMs, delivering strong gains on general-knowledge, math, and code benchmarks over strong baselines. These results demonstrate that principled AR-to-block-diffusion adaptation is an effective and compute-efficient alternative to training DLMs from scratch. Codes: https://github.com/YuchuanTian/NBDiff.

Autoregressive models excel in modeling sequential dependencies by enforcing causal constraints, yet they struggle to capture complex bidirectional patterns due to their unidirectional nature. In contrast, mask-based models leverage bidirectional context, enabling richer dependency modeling. However, they often assume token independence during prediction, which undermines the modeling of sequential dependencies. Additionally, the corruption of sequences through masking or absorption can introduce unnatural distortions, complicating the learning process. To address these issues, we propose Bidirectional Autoregressive Diffusion (BAD), a novel approach that unifies the strengths of autoregressive and mask-based generative models. BAD utilizes a permutation-based corruption technique that preserves the natural sequence structure while enforcing causal dependencies through randomized ordering, enabling the effective capture of both sequential and bidirectional relationships. Comprehensive experiments show that BAD outperforms autoregressive and mask-based models in text-to-motion generation, suggesting a novel pre-training strategy for sequence modeling. The codebase for BAD is available on https://github.com/RohollahHS/BAD.

Training large models with distributed data parallelism (DDP) requires frequent communication of gradients across workers, which can saturate bandwidth. Infrequent communication strategies (e.g., Local SGD) reduce this overhead but, when applied to adaptive optimizers, often suffer a performance gap relative to fully synchronous DDP. We trace this gap to a time-scale mismatch: the optimizer's fast-moving momentum, tuned for frequent updates, decays too quickly to smooth gradients over long intervals, leading to noise-dominated optimization. To address this, we propose MT-DAO, a family of optimizers that employs multiple slow- and fast-moving first momenta or the gradient to track update dynamics across different time scales, for which we provide the first convergence guarantees. Empirically, for language-model pre-training, this eliminates the performance gap with DDP, outperforming infrequent-communication baselines in perplexity and reducing iso-token wall-clock time by 6-27% on Ethernet interconnects. At the 720M scale, MT-DAO reaches a target perplexity in 24% fewer steps and 35% less time than the single-momentum DDP baseline. MT-DAO enables effective cross-datacenter training and training over wide geographic areas.

In this paper, we propose decentralized and scalable algorithms for Gaussian process (GP) training and prediction in multi-agent systems. To decentralize the implementation of GP training optimization algorithms, we employ the alternating direction method of multipliers (ADMM). A closed-form solution of the decentralized proximal ADMM is provided for the case of GP hyper-parameter training with maximum likelihood estimation. Multiple aggregation techniques for GP prediction are decentralized with the use of iterative and consensus methods. In addition, we propose a covariance-based nearest neighbor selection strategy that enables a subset of agents to perform predictions. The efficacy of the proposed methods is illustrated with numerical experiments on synthetic and real data.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

Efficient video transmission is essential for seamless communication and collaboration within the visually-driven digital landscape. To achieve low latency and high-quality video transmission over a bandwidth-constrained noisy wireless channel, we propose a stable diffusion (SD)-based goal-oriented semantic communication (GSC) framework. In this framework, we first design a semantic encoder that effectively identify the keyframes from video and extract the relevant semantic information (SI) to reduce the transmission data size. We then develop a semantic decoder to reconstruct the keyframes from the received SI and further generate the full video from the reconstructed keyframes using frame interpolation to ensure high-quality reconstruction. Recognizing the impact of wireless channel noise on SI transmission, we also propose an SD-based denoiser for GSC (SD-GSC) condition on an instantaneous channel gain to remove the channel noise from the received noisy SI under a known channel. For scenarios with an unknown channel, we further propose a parallel SD denoiser for GSC (PSD-GSC) to jointly learn the distribution of channel gains and denoise the received SI. It is shown that, with the known channel, our proposed SD-GSC outperforms state-of-the-art ADJSCC, Latent-Diff DNSC, DeepWiVe and DVST, improving Peak Signal-to-Noise Ratio (PSNR) by 69%, 58%, 33% and 38%, reducing mean squared error (MSE) by 52%, 50%, 41% and 45%, and reducing Fréchet Video Distance (FVD) by 38%, 32%, 22% and 24%, respectively. With the unknown channel, our PSD-GSC achieves a 17% improvement in PSNR, a 29% reduction in MSE, and a 19% reduction in FVD compared to MMSE equalizer-enhanced SD-GSC. These significant performance improvements demonstrate the robustness and superiority of our proposed methods in enhancing video transmission quality and efficiency under various channel conditions.

In recent multimodal research, the diffusion paradigm has emerged as a promising alternative to the autoregressive paradigm (AR), owing to its unique decoding advantages. However, due to the capability limitations of the base diffusion language model, the performance of the diffusion vision language model (dVLM) still lags significantly behind that of mainstream models. This leads to a simple yet fundamental question: Is it possible to construct dVLMs based on existing powerful AR models? In response, we propose DiffusionVL, a dVLM family that could be translated from any powerful AR models. Through simple fine-tuning, we successfully adapt AR pre-trained models into the diffusion paradigm. This approach yields two key observations: (1) The paradigm shift from AR-based multimodal models to diffusion is remarkably effective. (2) Direct conversion of an AR language model to a dVLM is also feasible, achieving performance competitive with LLaVA-style visual-instruction-tuning. Further, we introduce a block-decoding design into dVLMs that supports arbitrary-length generation and KV cache reuse, achieving a significant inference speedup. We conduct a large number of experiments. Despite training with less than 5% of the data required by prior methods, DiffusionVL achieves a comprehensive performance improvement-a 34.4% gain on the MMMU-Pro (vision) bench and 37.5% gain on the MME (Cog.) bench-alongside a 2x inference speedup. The model and code are released at https://github.com/hustvl/DiffusionVL.

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.

Diffusion models have emerged as a powerful class of generative models across various modalities, including image, video, and audio synthesis. However, their deployment is often limited by significant inference latency, primarily due to the inherently sequential nature of the denoising process. While existing parallelization strategies attempt to accelerate inference by distributing computation across multiple devices, they typically incur high communication overhead, hindering deployment on commercial hardware. To address this challenge, we propose ParaStep, a novel parallelization method based on a reuse-then-predict mechanism that parallelizes diffusion inference by exploiting similarity between adjacent denoising steps. Unlike prior approaches that rely on layer-wise or stage-wise communication, ParaStep employs lightweight, step-wise communication, substantially reducing overhead. ParaStep achieves end-to-end speedups of up to 3.88times on SVD, 2.43times on CogVideoX-2b, and 6.56times on AudioLDM2-large, while maintaining generation quality. These results highlight ParaStep as a scalable and communication-efficient solution for accelerating diffusion inference, particularly in bandwidth-constrained environments.

We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph including connected components, connectivity, and cycle structures even with no features. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at https://github.com/KrishnaswamyLab/DYMAG.

A variety of Auto-Regressive Video Diffusion Models (ARVDM) have achieved remarkable successes in generating realistic long-form videos. However, theoretical analyses of these models remain scant. In this work, we develop theoretical underpinnings for these models and use our insights to improve the performance of existing models. We first develop Meta-ARVDM, a unified framework of ARVDMs that subsumes most existing methods. Using Meta-ARVDM, we analyze the KL-divergence between the videos generated by Meta-ARVDM and the true videos. Our analysis uncovers two important phenomena inherent to ARVDM -- error accumulation and memory bottleneck. By deriving an information-theoretic impossibility result, we show that the memory bottleneck phenomenon cannot be avoided. To mitigate the memory bottleneck, we design various network structures to explicitly use more past frames. We also achieve a significantly improved trade-off between the mitigation of the memory bottleneck and the inference efficiency by compressing the frames. Experimental results on DMLab and Minecraft validate the efficacy of our methods. Our experiments also demonstrate a Pareto-frontier between the error accumulation and memory bottleneck across different methods.

Large Language Models have shown remarkable efficacy in generating streaming data such as text and audio, thanks to their temporally uni-directional attention mechanism, which models correlations between the current token and previous tokens. However, video streaming remains much less explored, despite a growing need for live video processing. State-of-the-art video diffusion models leverage bi-directional temporal attention to model the correlations between the current frame and all the surrounding (i.e. including future) frames, which hinders them from processing streaming videos. To address this problem, we present Live2Diff, the first attempt at designing a video diffusion model with uni-directional temporal attention, specifically targeting live streaming video translation. Compared to previous works, our approach ensures temporal consistency and smoothness by correlating the current frame with its predecessors and a few initial warmup frames, without any future frames. Additionally, we use a highly efficient denoising scheme featuring a KV-cache mechanism and pipelining, to facilitate streaming video translation at interactive framerates. Extensive experiments demonstrate the effectiveness of the proposed attention mechanism and pipeline, outperforming previous methods in terms of temporal smoothness and/or efficiency.

Diffusion-based large language models (Diffusion LLMs) have shown promise for non-autoregressive text generation with parallel decoding capabilities. However, the practical inference speed of open-sourced Diffusion LLMs often lags behind autoregressive models due to the lack of Key-Value (KV) Cache and quality degradation when decoding multiple tokens simultaneously. To bridge this gap, we introduce a novel block-wise approximate KV Cache mechanism tailored for bidirectional diffusion models, enabling cache reuse with negligible performance drop. Additionally, we identify the root cause of generation quality degradation in parallel decoding as the disruption of token dependencies under the conditional independence assumption. To address this, we propose a confidence-aware parallel decoding strategy that selectively decodes tokens exceeding a confidence threshold, mitigating dependency violations and maintaining generation quality. Experimental results on LLaDA and Dream models across multiple LLM benchmarks demonstrate up to 27.6times throughput improvement with minimal accuracy loss, closing the performance gap with autoregressive models and paving the way for practical deployment of Diffusion LLMs.

Multi-round LLM-based multi-agent systems rely on effective communication structures to support collaboration across rounds. However, most existing methods employ a fixed communication topology during inference, which falls short in many realistic applications where the agents' roles may change across rounds due to dynamic adversary, task progression, or time-varying constraints such as communication bandwidth. In this paper, we propose addressing this issue through TodyComm, a task-oriented dynamic communication algorithm. It produces behavior-driven collaboration topologies that adapt to the dynamics at each round, optimizing the utility for the task through policy gradient. Experiments on five benchmarks demonstrate that under both dynamic adversary and communications budgets, TodyComm delivers superior task effectiveness while retaining token efficiency and scalability.

Denoising diffusion models have shown great promise in human motion synthesis conditioned on natural language descriptions. However, integrating spatial constraints, such as pre-defined motion trajectories and obstacles, remains a challenge despite being essential for bridging the gap between isolated human motion and its surrounding environment. To address this issue, we propose Guided Motion Diffusion (GMD), a method that incorporates spatial constraints into the motion generation process. Specifically, we propose an effective feature projection scheme that manipulates motion representation to enhance the coherency between spatial information and local poses. Together with a new imputation formulation, the generated motion can reliably conform to spatial constraints such as global motion trajectories. Furthermore, given sparse spatial constraints (e.g. sparse keyframes), we introduce a new dense guidance approach to turn a sparse signal, which is susceptible to being ignored during the reverse steps, into denser signals to guide the generated motion to the given constraints. Our extensive experiments justify the development of GMD, which achieves a significant improvement over state-of-the-art methods in text-based motion generation while allowing control of the synthesized motions with spatial constraints.

We consider distributed linear bandits where M agents learn collaboratively to minimize the overall cumulative regret incurred by all agents. Information exchange is facilitated by a central server, and both the uplink and downlink communications are carried over channels with fixed capacity, which limits the amount of information that can be transmitted in each use of the channels. We investigate the regret-communication trade-off by (i) establishing information-theoretic lower bounds on the required communications (in terms of bits) for achieving a sublinear regret order; (ii) developing an efficient algorithm that achieves the minimum sublinear regret order offered by centralized learning using the minimum order of communications dictated by the information-theoretic lower bounds. For sparse linear bandits, we show a variant of the proposed algorithm offers better regret-communication trade-off by leveraging the sparsity of the problem.

This paper analyses a set of simple adaptations that transform standard message-passing Graph Neural Networks (GNN) into provably powerful directed multigraph neural networks. The adaptations include multigraph port numbering, ego IDs, and reverse message passing. We prove that the combination of these theoretically enables the detection of any directed subgraph pattern. To validate the effectiveness of our proposed adaptations in practice, we conduct experiments on synthetic subgraph detection tasks, which demonstrate outstanding performance with almost perfect results. Moreover, we apply our proposed adaptations to two financial crime analysis tasks. We observe dramatic improvements in detecting money laundering transactions, improving the minority-class F1 score of a standard message-passing GNN by up to 30%, and closely matching or outperforming tree-based and GNN baselines. Similarly impressive results are observed on a real-world phishing detection dataset, boosting three standard GNNs' F1 scores by around 15% and outperforming all baselines.

A popular approach to post-training control of large language models (LLMs) is the steering of intermediate latent representations. Namely, identify a well-chosen direction depending on the task at hand and perturbs representations along this direction at inference time. While many propositions exist to pick this direction, considerably less is understood about how to choose the magnitude of the move, whereas its importance is clear: too little and the intended behavior does not emerge, too much and the model's performance degrades beyond repair. In this work, we propose the first theoretical analysis of steering strength. We characterize its effect on next token probability, presence of a concept, and cross-entropy, deriving precise qualitative laws governing these quantities. Our analysis reveals surprising behaviors, including non-monotonic effects of steering strength. We validate our theoretical predictions empirically on eleven language models, ranging from a small GPT architecture to modern models.

Diffusion models (DMs) have achieved remarkable success in image and video generation. However, they still struggle with (1) physical alignment and (2) out-of-distribution (OOD) instruction following. We argue that these issues stem from the models' failure to learn causal directions and to disentangle causal factors for novel recombination. We introduce the Causal Scene Graph (CSG) and the Physical Alignment Probe (PAP) dataset to enable diagnostic interventions. This analysis yields three key insights. First, DMs struggle with multi-hop reasoning for elements not explicitly determined in the prompt. Second, the prompt embedding contains disentangled representations for texture and physics. Third, visual causal structure is disproportionately established during the initial, computationally limited denoising steps. Based on these findings, we introduce LINA (Learning INterventions Adaptively), a novel framework that learns to predict prompt-specific interventions, which employs (1) targeted guidance in the prompt and visual latent spaces, and (2) a reallocated, causality-aware denoising schedule. Our approach enforces both physical alignment and OOD instruction following in image and video DMs, achieving state-of-the-art performance on challenging causal generation tasks and the Winoground dataset. Our project page is at https://opencausalab.github.io/LINA.

Graph Neural Networks (GNNs) have shown promising potential in graph representation learning. The majority of GNNs define a local message-passing mechanism, propagating information over the graph by stacking multiple layers. These methods, however, are known to suffer from two major limitations: over-squashing and poor capturing of long-range dependencies. Recently, Graph Transformers (GTs) emerged as a powerful alternative to Message-Passing Neural Networks (MPNNs). GTs, however, have quadratic computational cost, lack inductive biases on graph structures, and rely on complex Positional/Structural Encodings (SE/PE). In this paper, we show that while Transformers, complex message-passing, and SE/PE are sufficient for good performance in practice, neither is necessary. Motivated by the recent success of State Space Models (SSMs), such as Mamba, we present Graph Mamba Networks (GMNs), a general framework for a new class of GNNs based on selective SSMs. We discuss and categorize the new challenges when adopting SSMs to graph-structured data, and present four required and one optional steps to design GMNs, where we choose (1) Neighborhood Tokenization, (2) Token Ordering, (3) Architecture of Bidirectional Selective SSM Encoder, (4) Local Encoding, and dispensable (5) PE and SE. We further provide theoretical justification for the power of GMNs. Experiments demonstrate that despite much less computational cost, GMNs attain an outstanding performance in long-range, small-scale, large-scale, and heterophilic benchmark datasets.

We introduce Directional Stimulus Prompting, a novel framework for guiding black-box large language models (LLMs) toward specific desired outputs. Instead of directly adjusting LLMs, our method employs a small tunable policy model (e.g., T5) to generate an auxiliary directional stimulus prompt for each input instance. These directional stimulus prompts act as nuanced, instance-specific hints and clues to guide LLMs in generating desired outcomes, such as including specific keywords in the generated summary. Our approach sidesteps the challenges of direct LLM tuning by optimizing the policy model to explore directional stimulus prompts that align LLMs with desired behaviors. The policy model can be optimized through 1) supervised fine-tuning using labeled data and 2) reinforcement learning from offline or online rewards based on the LLM's output. We assess our method across summarization, dialogue response generation, and chain-of-thought reasoning tasks. Our experiments demonstrate that the framework consistently improves LLMs' (e.g., ChatGPT, Codex, InstructGPT) performance on these supervised tasks using minimal labeled data. Notably, using just 80 dialogues on the MultiWOZ dataset, our approach enhances ChatGPT's performance by an impressive 41.4%, matching or surpassing some fully supervised start-of-the-art models. Additionally, the instance-specific chain-of-thought prompt generated by our approach improves InstructGPT's reasoning accuracy compared to human-crafted or automatically generated prompts. The code and data are publicly available at https://github.com/Leezekun/Directional-Stimulus-Prompting.

Message passing graph neural networks (GNNs) are a popular learning architectures for graph-structured data. However, one problem GNNs experience is oversquashing, where a GNN has difficulty sending information between distant nodes. Understanding and mitigating oversquashing has recently received significant attention from the research community. In this paper, we continue this line of work by analyzing oversquashing through the lens of the effective resistance between nodes in the input graph. Effective resistance intuitively captures the ``strength'' of connection between two nodes by paths in the graph, and has a rich literature spanning many areas of graph theory. We propose to use total effective resistance as a bound of the total amount of oversquashing in a graph and provide theoretical justification for its use. We further develop an algorithm to identify edges to be added to an input graph to minimize the total effective resistance, thereby alleviating oversquashing. We provide empirical evidence of the effectiveness of our total effective resistance based rewiring strategies for improving the performance of GNNs.

Multi-agent collaboration enhances the perception capabilities of individual agents through information sharing. However, in real-world applications, differences in sensors and models across heterogeneous agents inevitably lead to domain gaps during collaboration. Existing approaches based on adaptation and reconstruction fail to support pragmatic heterogeneous collaboration due to two key limitations: (1) Intrusive retraining of the encoder or core modules disrupts the established semantic consistency among agents; and (2) accommodating new agents incurs high computational costs, limiting scalability. To address these challenges, we present a novel Generative Communication mechanism (GenComm) that facilitates seamless perception across heterogeneous multi-agent systems through feature generation, without altering the original network, and employs lightweight numerical alignment of spatial information to efficiently integrate new agents at minimal cost. Specifically, a tailored Deformable Message Extractor is designed to extract spatial message for each collaborator, which is then transmitted in place of intermediate features. The Spatial-Aware Feature Generator, utilizing a conditional diffusion model, generates features aligned with the ego agent's semantic space while preserving the spatial information of the collaborators. These generated features are further refined by a Channel Enhancer before fusion. Experiments conducted on the OPV2V-H, DAIR-V2X and V2X-Real datasets demonstrate that GenComm outperforms existing state-of-the-art methods, achieving an 81% reduction in both computational cost and parameter count when incorporating new agents. Our code is available at https://github.com/jeffreychou777/GenComm.

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `h-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The h-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) models, offering sub-linear generation latency and bidirectional capabilities that are particularly appealing for code generation and editing. Achieving sub-linear latency in discrete DLMs requires predicting multiple tokens in parallel. However, standard DLMs sample tokens independently from conditional marginal distributions, failing to capture the joint dependencies among concurrently generated tokens. As a result, they often lead to syntactic inconsistencies and break multi-token structures. In this work, we introduce CoDiLA (Coherent Diffusion with Local Autoregression), a method that reconciles parallel sampling with local dependency modeling. Rather than forcing the DLM to resolve fine-grained syntax, CoDiLA delegates local decoding to a small, auxiliary AR model operating on the diffusion latents. This design allows for parallel block generation while ensuring sequential validity within each block and maintaining core DLM capabilities, including bidirectional modeling across blocks. We demonstrate that using a highly compact auxiliary AR model (e.g., 0.6B parameters) effectively eliminates coherence artifacts, establishing a new Pareto frontier for accuracy and speed in code generation benchmarks.

We study differentially private (DP) machine learning algorithms as instances of noisy fixed-point iterations, in order to derive privacy and utility results from this well-studied framework. We show that this new perspective recovers popular private gradient-based methods like DP-SGD and provides a principled way to design and analyze new private optimization algorithms in a flexible manner. Focusing on the widely-used Alternating Directions Method of Multipliers (ADMM) method, we use our general framework to derive novel private ADMM algorithms for centralized, federated and fully decentralized learning. For these three algorithms, we establish strong privacy guarantees leveraging privacy amplification by iteration and by subsampling. Finally, we provide utility guarantees using a unified analysis that exploits a recent linear convergence result for noisy fixed-point iterations.

Finite symmetric groups S_n are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over S_n poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce SymmetricDiffusers, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over S_n by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performances on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at https://github.com/DSL-Lab/SymmetricDiffusers.

To measure the difference between two probability distributions, referred to as the source and target, respectively, we exploit both the chain rule and Bayes' theorem to construct conditional transport (CT), which is constituted by both a forward component and a backward one. The forward CT is the expected cost of moving a source data point to a target one, with their joint distribution defined by the product of the source probability density function (PDF) and a source-dependent conditional distribution, which is related to the target PDF via Bayes' theorem. The backward CT is defined by reversing the direction. The CT cost can be approximated by replacing the source and target PDFs with their discrete empirical distributions supported on mini-batches, making it amenable to implicit distributions and stochastic gradient descent-based optimization. When applied to train a generative model, CT is shown to strike a good balance between mode-covering and mode-seeking behaviors and strongly resist mode collapse. On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing generative adversarial network with CT is shown to consistently improve the performance. PyTorch code is provided.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

Current diffusion-based image restoration methods feed degraded input images as conditions into the noise estimation network. However, interpreting this diffusion process is challenging since it essentially generates the target image from the noise. To establish a unified and more interpretable model for image generation and restoration, we propose residual denoising diffusion models (RDDM). In contrast to existing diffusion models (e.g., DDPM or DDIM) that focus solely on noise estimation, our RDDM predicts residuals to represent directional diffusion from the target domain to the input domain, while concurrently estimating noise to account for random perturbations in the diffusion process. The introduction of residuals allows us to redefine the forward diffusion process, wherein the target image progressively diffuses into a purely noisy image or a noise-carrying input image, thus unifying image generation and restoration. We demonstrate that our sampling process is consistent with that of DDPM and DDIM through coefficient transformation, and propose a partially path-independent generation process to better understand the reverse process. Notably, with native support for conditional inputs, our RDDM enables a generic UNet, trained with only an ell _1 loss and a batch size of 1, to compete with state-of-the-art image restoration methods. We provide code and pre-trained models to encourage further exploration, application, and development of our innovative framework (https://github.com/nachifur/RDDM).

In multi-agent reinforcement learning (MARL), effective communication improves agent performance, particularly under partial observability. We propose MARL-CPC, a framework that enables communication among fully decentralized, independent agents without parameter sharing. MARL-CPC incorporates a message learning model based on collective predictive coding (CPC) from emergent communication research. Unlike conventional methods that treat messages as part of the action space and assume cooperation, MARL-CPC links messages to state inference, supporting communication in non-cooperative, reward-independent settings. We introduce two algorithms -Bandit-CPC and IPPO-CPC- and evaluate them in non-cooperative MARL tasks. Benchmarks show that both outperform standard message-as-action approaches, establishing effective communication even when messages offer no direct benefit to the sender. These results highlight MARL-CPC's potential for enabling coordination in complex, decentralized environments.

Decentralized learning provides a scalable alternative to traditional parameter-server-based training, yet its performance is often hindered by limited peer-to-peer communication. In this paper, we study how communication should be scheduled over time, including determining when and how frequently devices synchronize. Our empirical results show that concentrating communication budgets in the later stages of decentralized training markedly improves global generalization. Surprisingly, we uncover that fully connected communication at the final step, implemented by a single global merging, is sufficient to match the performance of server-based training. We further show that low communication in decentralized learning preserves the mergeability of local models throughout training. Our theoretical contributions, which explains these phenomena, are first to establish that the globally merged model of decentralized SGD can converge faster than centralized mini-batch SGD. Technically, we novelly reinterpret part of the discrepancy among local models, which were previously considered as detrimental noise, as constructive components that accelerate convergence. This work challenges the common belief that decentralized learning generalizes poorly under data heterogeneity and limited communication, while offering new insights into model merging and neural network loss landscapes.

This work proposes a novel channel estimator based on diffusion models (DMs), one of the currently top-rated generative models. Contrary to related works utilizing generative priors, a lightweight convolutional neural network (CNN) with positional embedding of the signal-to-noise ratio (SNR) information is designed by learning the channel distribution in the sparse angular domain. Combined with an estimation strategy that avoids stochastic resampling and truncates reverse diffusion steps that account for lower SNR than the given pilot observation, the resulting DM estimator has both low complexity and memory overhead. Numerical results exhibit better performance than state-of-the-art channel estimators utilizing generative priors.

Large-scale distributed training in production datacenters constitutes a challenging workload bottlenecked by network communication. In response, both major industry players (e.g., Ultra Ethernet Consortium) and parts of academia have surprisingly, and almost unanimously, agreed that packet spraying is necessary to improve the performance of large-scale distributed training workloads. In this paper, we challenge this prevailing belief and pose the question: How close can a singlepath transport approach an optimal multipath transport? We demonstrate that singlepath transport (from a NIC's perspective) is sufficient and can perform nearly as well as an ideal multipath transport with packet spraying, particularly in the context of distributed training in leaf-spine topologies. Our assertion is based on four key observations about workloads driven by collective communication patterns: (i) flows within a collective start almost simultaneously, (ii) flow sizes are nearly equal, (iii) the completion time of a collective is more crucial than individual flow completion times, and (iv) flows can be split upon arrival. We analytically prove that singlepath transport, using minimal flow splitting (at the application layer), is equivalent to an ideal multipath transport with packet spraying in terms of maximum congestion. Our preliminary evaluations support our claims. This paper suggests an alternative agenda for developing next-generation transport protocols tailored for large-scale distributed training.

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT

Maximizing a monotone submodular function is a fundamental task in machine learning, economics, and statistics. In this paper, we present two communication-efficient decentralized online algorithms for the monotone continuous DR-submodular maximization problem, both of which reduce the number of per-function gradient evaluations and per-round communication complexity from T^{3/2} to 1. The first one, One-shot Decentralized Meta-Frank-Wolfe (Mono-DMFW), achieves a (1-1/e)-regret bound of O(T^{4/5}). As far as we know, this is the first one-shot and projection-free decentralized online algorithm for monotone continuous DR-submodular maximization. Next, inspired by the non-oblivious boosting function zhang2022boosting, we propose the Decentralized Online Boosting Gradient Ascent (DOBGA) algorithm, which attains a (1-1/e)-regret of O(T). To the best of our knowledge, this is the first result to obtain the optimal O(T) against a (1-1/e)-approximation with only one gradient inquiry for each local objective function per step. Finally, various experimental results confirm the effectiveness of the proposed methods.

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset.

Bayesian persuasion studies how an informed sender should influence beliefs of rational receivers who take decisions through Bayesian updating of a common prior. We focus on the online Bayesian persuasion framework, in which the sender repeatedly faces one or more receivers with unknown and adversarially selected types. First, we show how to obtain a tight tilde O(T^{1/2}) regret bound in the case in which the sender faces a single receiver and has partial feedback, improving over the best previously known bound of tilde O(T^{4/5}). Then, we provide the first no-regret guarantees for the multi-receiver setting under partial feedback. Finally, we show how to design no-regret algorithms with polynomial per-iteration running time by exploiting type reporting, thereby circumventing known intractability results on online Bayesian persuasion. We provide efficient algorithms guaranteeing a O(T^{1/2}) regret upper bound both in the single- and multi-receiver scenario when type reporting is allowed.

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not always the case in real-world applications. For example, in inverse graphics, the goal is to generate samples from a distribution of 3D scenes that align with a given image, but ground-truth 3D scenes are unavailable and only 2D images are accessible. To address this limitation, we propose a novel class of denoising diffusion probabilistic models that learn to sample from distributions of signals that are never directly observed. Instead, these signals are measured indirectly through a known differentiable forward model, which produces partial observations of the unknown signal. Our approach involves integrating the forward model directly into the denoising process. This integration effectively connects the generative modeling of observations with the generative modeling of the underlying signals, allowing for end-to-end training of a conditional generative model over signals. During inference, our approach enables sampling from the distribution of underlying signals that are consistent with a given partial observation. We demonstrate the effectiveness of our method on three challenging computer vision tasks. For instance, in the context of inverse graphics, our model enables direct sampling from the distribution of 3D scenes that align with a single 2D input image.

We propose a targeted communication architecture for multi-agent reinforcement learning, where agents learn both what messages to send and whom to address them to while performing cooperative tasks in partially-observable environments. This targeting behavior is learnt solely from downstream task-specific reward without any communication supervision. We additionally augment this with a multi-round communication approach where agents coordinate via multiple rounds of communication before taking actions in the environment. We evaluate our approach on a diverse set of cooperative multi-agent tasks, of varying difficulties, with varying number of agents, in a variety of environments ranging from 2D grid layouts of shapes and simulated traffic junctions to 3D indoor environments, and demonstrate the benefits of targeted and multi-round communication. Moreover, we show that the targeted communication strategies learned by agents are interpretable and intuitive. Finally, we show that our architecture can be easily extended to mixed and competitive environments, leading to improved performance and sample complexity over recent state-of-the-art approaches.

Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D methods do not fully exploit the 3D distribution prior. To address this, we propose a novel approach using two perpendicular pre-trained 2D diffusion models to solve the 3D inverse problem. By modeling the 3D data distribution as a product of 2D distributions sliced in different directions, our method effectively addresses the curse of dimensionality. Our experimental results demonstrate that our method is highly effective for 3D medical image reconstruction tasks, including MRI Z-axis super-resolution, compressed sensing MRI, and sparse-view CT. Our method can generate high-quality voxel volumes suitable for medical applications.

Diffusion Language Models (DLMs) offer a promising parallel generation paradigm but suffer from slow inference due to numerous refinement steps and the inability to use standard KV caching. We introduce CDLM (Consistency Diffusion Language Models), a training-based acceleration method that simultaneously tackles both bottlenecks. CDLM integrates consistency modeling to drastically reduce the number of required sampling steps by enabling multi-token finalization. Furthermore, we enforce a block-wise causal attention mask during fine-tuning, making the model fully compatible with KV caching. Experiments show CDLM achieves 3.6x-14.5x lower latency while maintaining competitive accuracy on math and coding tasks. The full training and evaluation code is available at https://github.com/SqueezeAILab/CDLM.

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer. However, as an emerging domain, several challenges remain, including 1) The lack of global convergence guarantees, 2) Slow convergence towards solutions, and 3) Cubic time complexity with regard to feature dimensions. In this paper, we propose a novel optimization framework for deep learning via ADMM (dlADMM) to address these challenges simultaneously. The parameters in each layer are updated backward and then forward so that the parameter information in each layer is exchanged efficiently. The time complexity is reduced from cubic to quadratic in (latent) feature dimensions via a dedicated algorithm design for subproblems that enhances them utilizing iterative quadratic approximations and backtracking. Finally, we provide the first proof of global convergence for an ADMM-based method (dlADMM) in a deep neural network problem under mild conditions. Experiments on benchmark datasets demonstrated that our proposed dlADMM algorithm outperforms most of the comparison methods.

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be explored. In this work, we show that we can indeed solve a family of blind inverse problems by constructing another diffusion prior for the forward operator. Specifically, parallel reverse diffusion guided by gradients from the intermediate stages enables joint optimization of both the forward operator parameters as well as the image, such that both are jointly estimated at the end of the parallel reverse diffusion procedure. We show the efficacy of our method on two representative tasks -- blind deblurring, and imaging through turbulence -- and show that our method yields state-of-the-art performance, while also being flexible to be applicable to general blind inverse problems when we know the functional forms.

We present Seed Diffusion Preview, a large-scale language model based on discrete-state diffusion, offering remarkably fast inference speed. Thanks to non-sequential, parallel generation, discrete diffusion models provide a notable speedup to mitigate the inherent latency of token-by-token decoding, as demonstrated recently (e.g., Mercury Coder, Gemini Diffusion). Seed Diffusion Preview achieves an inference speed of 2,146 token/s over H20 GPUs while maintaining competitive performance across a sweep of standard code evaluation benchmarks, significantly faster than contemporary Mercury and Gemini Diffusion, establishing new state of the art on the speed-quality Pareto frontier for code models.

One of the most compelling features of global discrete diffusion language models is their global bidirectional contextual capability. However, existing block-based diffusion studies tend to introduce autoregressive priors, which, while offering benefits, can cause models to lose this global coherence at the macro level. To regain global contextual understanding while preserving the advantages of the semi-autoregressive paradigm, we propose Diffusion in Diffusion, a 'draft-then-refine' framework designed to overcome the irreversibility and myopia problems inherent in block diffusion models. Our approach first employs block diffusion to generate rapid drafts using small blocks, then refines these drafts through global bidirectional diffusion with a larger bidirectional receptive field. We utilize snapshot confidence remasking to identify the most critical tokens that require modification, and apply mix-scale training to expand the block diffusion model's global capabilities. Empirical results demonstrate that our approach sets a new benchmark for discrete diffusion models on the OpenWebText dataset. Using only 26% of the fine-tuning budget of baseline models, we reduce generative perplexity from 25.7 to 21.9, significantly narrowing the performance gap with autoregressive models.

We propose a new partial-observability model for online learning problems where the learner, besides its own loss, also observes some noisy feedback about the other actions, depending on the underlying structure of the problem. We represent this structure by a weighted directed graph, where the edge weights are related to the quality of the feedback shared by the connected nodes. Our main contribution is an efficient algorithm that guarantees a regret of O(α^* T) after T rounds, where α^* is a novel graph property that we call the effective independence number. Our algorithm is completely parameter-free and does not require knowledge (or even estimation) of α^*. For the special case of binary edge weights, our setting reduces to the partial-observability models of Mannor and Shamir (2011) and Alon et al. (2013) and our algorithm recovers the near-optimal regret bounds.

Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two augmentation schemes. Here we propose a novel family of positional encoding schemes which draws a link between the above two approaches and improves over both. The new approach, named Random Feature Propagation (RFP), is inspired by the power iteration method and its generalizations. It concatenates several intermediate steps of an iterative algorithm for computing the dominant eigenvectors of a propagation matrix, starting from random node features. Notably, these propagation steps are based on graph-dependent propagation operators that can be either predefined or learned. We explore the theoretical and empirical benefits of RFP. First, we provide theoretical justifications for using random features, for incorporating early propagation steps, and for using multiple random initializations. Then, we empirically demonstrate that RFP significantly outperforms both spectral PE and random features in multiple node classification and graph classification benchmarks.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

A multilayer perceptron can behave as a generative classifier by applying bidirectional learning (BL). It consists of training an undirected neural network to map input to output and vice-versa; therefore it can produce a classifier in one direction, and a generator in the opposite direction for the same data. The learning process of BL tries to reproduce the neuroplasticity stated in Hebbian theory using only backward propagation of errors. In this paper, two novel learning techniques are introduced which use BL for improving robustness to white noise static and adversarial examples. The first method is bidirectional propagation of errors, which the error propagation occurs in backward and forward directions. Motivated by the fact that its generative model receives as input a constant vector per class, we introduce as a second method the hybrid adversarial networks (HAN). Its generative model receives a random vector as input and its training is based on generative adversarial networks (GAN). To assess the performance of BL, we perform experiments using several architectures with fully and convolutional layers, with and without bias. Experimental results show that both methods improve robustness to white noise static and adversarial examples, and even increase accuracy, but have different behavior depending on the architecture and task, being more beneficial to use the one or the other. Nevertheless, HAN using a convolutional architecture with batch normalization presents outstanding robustness, reaching state-of-the-art accuracy on adversarial examples of hand-written digits.

We study distributed contextual linear bandits with stochastic contexts, where N agents act cooperatively to solve a linear bandit-optimization problem with d-dimensional features over the course of T rounds. For this problem, we derive the first ever information-theoretic lower bound Omega(dN) on the communication cost of any algorithm that performs optimally in a regret minimization setup. We then propose a distributed batch elimination version of the LinUCB algorithm, DisBE-LUCB, where the agents share information among each other through a central server. We prove that the communication cost of DisBE-LUCB matches our lower bound up to logarithmic factors. In particular, for scenarios with known context distribution, the communication cost of DisBE-LUCB is only mathcal{O}(dN) and its regret is {mathcal{O}}(dNT), which is of the same order as that incurred by an optimal single-agent algorithm for NT rounds. We also provide similar bounds for practical settings where the context distribution can only be estimated. Therefore, our proposed algorithm is nearly minimax optimal in terms of both regret and communication cost. Finally, we propose DecBE-LUCB, a fully decentralized version of DisBE-LUCB, which operates without a central server, where agents share information with their immediate neighbors through a carefully designed consensus procedure.

Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is no need to maintain a high dimensionality in the evolution process, especially in the early generation phase. To this end, we make a theoretical generalization of the forward diffusion process via signal decomposition. Concretely, we manage to decompose an image into multiple orthogonal components and control the attenuation of each component when perturbing the image. That way, along with the noise strength increasing, we are able to diminish those inconsequential components and thus use a lower-dimensional signal to represent the source, barely losing information. Such a reformulation allows to vary dimensions in both training and inference of diffusion models. Extensive experiments on a range of datasets suggest that our approach substantially reduces the computational cost and achieves on-par or even better synthesis performance compared to baseline methods. We also show that our strategy facilitates high-resolution image synthesis and improves FID of diffusion model trained on FFHQ at 1024times1024 resolution from 52.40 to 10.46. Code and models will be made publicly available.

Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions. Recent work has shown that such models can separate generic pairs of non-isomorphic geometric graphs, though they may fail to separate some rare and complicated instances. However, these results assume a fully connected graph, where each node possesses complete knowledge of all other nodes. In contrast, often, in application, every node only possesses knowledge of a small number of nearest neighbors. This paper shows that generic pairs of non-isomorphic geometric graphs can be separated by message-passing networks with rotation equivariant features as long as the underlying graph is connected. When only invariant intermediate features are allowed, generic separation is guaranteed for generically globally rigid graphs. We introduce a simple architecture, EGENNET, which achieves our theoretical guarantees and compares favorably with alternative architecture on synthetic and chemical benchmarks. Our code is available at https://github.com/yonatansverdlov/E-GenNet.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

Open-ended text generation with autoregressive language models (LMs) is one of the core tasks in natural language processing. However, maximization-based decoding methods (e.g., greedy/beam search) often lead to the degeneration problem, i.e., the generated text is unnatural and contains undesirable repetitions. Existing solutions to this problem either introduce randomness prone to incoherence or require a look-ahead mechanism that demands extra computational overhead. In this study, we formulate open-ended text generation from a new perspective, i.e., we view it as an exploration process within a directed graph. Thereby, we understand the phenomenon of degeneration as circular loops within the directed graph. Based on our formulation, we propose a novel decoding method -- momentum decoding -- which encourages the LM to greedily explore new nodes outside the current graph. Meanwhile, it also allows the LM to return to the existing nodes with a momentum downgraded by a pre-defined resistance function. We extensively test our approach on three benchmarks from different domains through automatic and human evaluations. The results show that momentum decoding performs comparably with the current state of the art while enjoying notably improved inference speed and computation FLOPs. Furthermore, we conduct a detailed analysis to reveal the merits and inner workings of our approach. Our codes and other related resources are publicly available at https://github.com/gmftbyGMFTBY/MomentumDecoding.

Text-guided diffusion models such as DALLE-2, IMAGEN, and Stable Diffusion are able to generate an effectively endless variety of images given only a short text prompt describing the desired image content. In many cases the images are very high quality as well. However, these models often struggle to compose scenes containing several key objects such as characters in specified positional relationships. Unfortunately, this capability to ``direct'' the placement of characters and objects both within and across images is crucial in storytelling, as recognized in the literature on film and animation theory. In this work we take a particularly straightforward approach to providing the needed direction, by injecting ``activation'' at desired positions in the cross-attention maps corresponding to the objects under control, while attenuating the remainder of the map. The resulting approach is a step toward generalizing the applicability of text-guided diffusion models beyond single images to collections of related images, as in storybooks. To the best of our knowledge, our Directed Diffusion method is the first diffusion technique that provides positional control over multiple objects, while making use of an existing pre-trained model and maintaining a coherent blend between the positioned objects and the background. Moreover, it requires only a few lines to implement.

Multi-agent systems (MAS) based on Large Language Models (LLMs) have the potential to solve tasks that are beyond the reach of any single LLM. However, this potential can only be realized when the collaboration mechanism between agents is optimized. Specifically, optimizing the communication structure between agents is critical for fruitful collaboration. Most existing approaches rely on fixed topologies, pretrained graph generators, optimization over edges, or employ external LLM judges, thereby adding to the complexity. In this work, we introduce a response-conditioned framework that adapts communication on-the-fly. Agents independently generate responses to the user query and assess peer contributions using an approximation of the Shapley value. A directed acyclic graph (DAG) is then constructed to regulate the propagation of the responses among agents, which ensures stable and efficient message transmission from high-contributing agents to others. This graph is dynamically updated based on the agent responses from the previous collaboration round. Since the proposed framework enables the self-organization of agents without additional supervision or training, we refer to it as SelfOrg. The SelfOrg framework goes beyond task- and query-level optimization and takes into account the stochastic nature of agent responses. Experiments with both strong and weak LLM backends demonstrate robust performance, with significant gains in the weak regime where prior methods collapse. We also theoretically show that multiple agents increase the chance of correctness and that the correct responses naturally dominate the information flow.

Large language model (LLM)-based multi-agent systems (MAS) have demonstrated exceptional capabilities in solving complex tasks, yet their effectiveness depends heavily on the underlying communication topology that coordinates agent interactions. Within these systems, successful problem-solving often necessitates task-specific group structures to divide and conquer subtasks. However, most existing approaches generate communication topologies in a node-centric manner, leaving group structures to emerge implicitly from local connectivity decisions rather than modeling them explicitly, often leading to suboptimal coordination and unnecessary communication overhead. To address this limitation, we propose GoAgent (Group-of-Agents), a communication topology generation method that explicitly treats collaborative groups as the atomic units of MAS construction. Specifically, GoAgent first enumerates task-relevant candidate groups through an LLM and then autoregressively selects and connects these groups as atomic units to construct the final communication graph, jointly capturing intra-group cohesion and inter-group coordination. To mitigate communication redundancy and noise propagation inherent in expanding topologies, we further introduce a conditional information bottleneck (CIB) objective that compresses inter-group communication, preserving task-relevant signals while filtering out redundant historical noise. Extensive experiments on six benchmarks demonstrate the state-of-the-art performance of GoAgent with 93.84% average accuracy while reducing token consumption by about 17%.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Collaborative perception (CP) is emerging as a promising solution to the inherent limitations of stand-alone intelligence. However, current wireless communication systems are unable to support feature-level and raw-level collaborative algorithms due to their enormous bandwidth demands. In this paper, we propose DiffCP, a novel CP paradigm that utilizes a specialized diffusion model to efficiently compress the sensing information of collaborators. By incorporating both geometric and semantic conditions into the generative model, DiffCP enables feature-level collaboration with an ultra-low communication cost, advancing the practical implementation of CP systems. This paradigm can be seamlessly integrated into existing CP algorithms to enhance a wide range of downstream tasks. Through extensive experimentation, we investigate the trade-offs between communication, computation, and performance. Numerical results demonstrate that DiffCP can significantly reduce communication costs by 14.5-fold while maintaining the same performance as the state-of-the-art algorithm.

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.

Masked diffusion language models (MDLMs) have recently emerged as a promising alternative to autoregressive (AR) language models, offering properties such as parallel decoding, flexible generation orders, and the potential for fewer inference steps. Despite these advantages, decoding strategies and reinforcement learning (RL) algorithms tailored for MDLMs remain underexplored. A naive approach is to directly transfer techniques well-established for AR models to MDLMs. However, this raises an immediate question: Is such a naive transfer truly optimal? For example, 1) Block-wise and semi-AR decoding strategies are not employed during the training of MDLMs, so why do they outperform full diffusion-style decoding during inference? 2) Applying RL algorithms designed for AR models directly to MDLMs exhibits a training-inference inconsistency, since MDLM decoding are non-causal (parallel). This results in inconsistencies between the rollout trajectory and the optimization trajectory. To address these challenges, we propose EOS Early Rejection (EOSER) and Ascending Step-Size (ASS) decoding scheduler, which unlock the potential of MDLMs to perform full diffusion-style decoding, achieving competitive performance with fewer decoding steps. Additionally, we introduce Consistency Trajectory Group Relative Policy Optimization (CJ-GRPO) for taming MDLMs, which emphasizes the consistency between rollout trajectory and optimization trajectory, and reduces the optimization errors caused by skip-step optimization. We conduct extensive experiments on reasoning tasks, such as mathematical and planning benchmarks, using LLaDA-8B-Instruct. The results demonstrate that the proposed EOSER and ASS mechanisms, together with CJ-GRPO, hold significant promise for effectively and efficiently taming MDLMs. Code: https://github.com/yjyddq/EOSER-ASS-RL.

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.

The continued improvements in language model capability have unlocked their widespread use as drivers of autonomous agents, for example in coding or computer use applications. However, the core of these systems has not changed much since early instruction-tuned models like ChatGPT. Even advanced AI agents function on message exchange formats, successively exchanging messages with users, systems, with itself (i.e. chain-of-thought) and tools in a single stream of computation. This bottleneck to a single stream in chat models leads to a number of limitations: the agent cannot act (generate output) while reading, and in reverse, cannot react to new information while writing. Similarly, the agent cannot act while thinking and cannot think while reading or acting on information. In this work, we show that models can be unblocked by switching from instruction-tuning for sequential message formats to instruction-tuning for multiple, parallel streams of computation, splitting each role into a separate stream. Every forward pass of the language model then simultaneously reads from multiple input streams and generates tokens in multiple output streams, all of which causally depend on earlier timesteps. We argue that this data-driven change remedies a number of usability limitations as outlined above, improves model efficiency through parallelization, improves model security through better separation of concerns and can further improve model monitorability.