AAAI 2024 论文列表

AAAI Conference on Artificial Intelligence

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Reinforcement Learning and Data-Generation for Syntax-Guided Synthesis

Julian Parsert, Elizabeth Polgreen

展开摘要

Program synthesis is the task of automatically generating code based on a specification. In Syntax-Guided Synthesis (SyGuS) this specification is a combination of a syntactic template and a logical formula, and the result is guaranteed to satisfy both. We present a reinforcement-learning guided algorithm for SyGuS which uses Monte-Carlo Tree Search (MCTS) to search the space of candidate solutions. Our algorithm learns policy and value functions which, combined with the upper confidence bound for trees, allow it to balance exploration and exploitation. A common challenge in applying machine learning approaches to syntax-guided synthesis is the scarcity of training data. To address this, we present a method for automatically generating training data for SyGuS based on anti-unification of existing first-order satisfiability problems, which we use to train our MCTS policy. We implement and evaluate this setup and demonstrate that learned policy and value improve the synthesis performance over a baseline by over 26 percentage points in the training and testing sets. Our tool outperforms state-of-the-art tool cvc5 on the training set and performs comparably in terms of the total number of problems solved on the testing set (solving 23% of the benchmarks on which cvc5 fails). We make our data set publicly available, to enable further application of machine learning methods to the SyGuS problem.

Technical
Reinforced Adaptive Knowledge Learning for Multimodal Fake News Detection

Litian Zhang, Xiaoming Zhang, Ziyi Zhou, Feiran Huang, Chaozhuo Li

展开摘要

Nowadays, detecting multimodal fake news has emerged as a foremost concern since the widespread dissemination of fake news may incur adverse societal impact. Conventional methods generally focus on capturing the linguistic and visual semantics within the multimodal content, which fall short in effectively distinguishing the heightened level of meticulous fabrications. Recently, external knowledge is introduced to provide valuable background facts as complementary to facilitate news detection. Nevertheless, existing knowledge-enhanced endeavors directly incorporate all knowledge contexts through static entity embeddings, resulting in the potential noisy and content-irrelevant knowledge. Moreover, the integration of knowledge entities makes it intractable to model the sophisticated correlations between multimodal semantics and knowledge entities. In light of these limitations, we propose a novel Adaptive Knowledge-Aware Fake News Detection model, dubbed AKA-Fake. For each news, AKA-Fake learns a compact knowledge subgraph under a reinforcement learning paradigm, which consists of a subset of entities and contextual neighbors in the knowledge graph, restoring the most informative knowledge facts. A novel heterogeneous graph learning module is further proposed to capture the reliable cross-modality correlations via topology refinement and modality-attentive pooling. Our proposal is extensively evaluated over three popular datasets, and experimental results demonstrate the superiority of AKA-Fake.

Technical
Regulating Intermediate 3D Features for Vision-Centric Autonomous Driving

Junkai Xu, Liang Peng, Haoran Cheng, Linxuan Xia, Qi Zhou, Dan Deng, Wei Qian, Wenxiao Wang, Deng Cai

展开摘要

Multi-camera perception tasks have gained significant attention in the field of autonomous driving. However, existing frameworks based on Lift-Splat-Shoot (LSS) in the multi-camera setting cannot produce suitable dense 3D features due to the projection nature and uncontrollable densification process. To resolve this problem, we propose to regulate intermediate dense 3D features with the help of volume rendering. Specifically, we employ volume rendering to process the dense 3D features to obtain corresponding 2D features (e.g., depth maps, semantic maps), which are supervised by associated labels in the training. This manner regulates the generation of dense 3D features on the feature level, providing appropriate dense and unified features for multiple perception tasks. Therefore, our approach is termed Vampire, stands for ``Volume rendering As Multi-camera Perception Intermediate feature REgulator''. Experimental results on the Occ3D and nuScenes datasets demonstrate that Vampire facilitates fine-grained and appropriate extraction of dense 3D features, and is competitive with existing SOTA methods across diverse downstream perception tasks like 3D occupancy prediction, LiDAR segmentation and 3D objection detection, while utilizing moderate GPU resources. We provide a video demonstration in the supplementary materials and Codes are available at github.com/cskkxjk/Vampire.

Technical
Regulating AI: Applying Insights from Behavioural Economics and Psychology to the Application of Article 5 of the EU AI Act

Huixin Zhong, Eamonn O'Neill, Janina A. Hoffmann

展开摘要

Article 5 of the European Union’s Artificial Intelligence Act is intended to regulate AI use to prevent potentially harmful consequences. Nevertheless, applying this legislation practically is likely to be challenging because of ambiguously used terminologies and because it fails to specify which manipulation techniques may be invoked by AI, potentially leading to significant harm. This paper aims to bridge this gap by defining key terms and demonstrating how AI may invoke these techniques, drawing from insights in psychology and behavioural economics. First, this paper provides definitions of the terms “subliminal techniques”, “manipulative techniques” and “deceptive techniques”. Secondly, we identified from the literature in cognitive psychology and behavioural economics three subliminal and five manipulative techniques and exemplify how AI might implement these techniques to manipulate users in real-world case scenarios. These illustrations may serve as a practical guide for stakeholders to detect cases of AI manipulation and consequently devise preventive measures. Article 5 has also been criticised for offering inadequate protection. We critically assess the protection offered by Article 5, proposing specific revisions to paragraph 1, points (a) and (b) of Article 5 to increase its protective effectiveness.

Technical
Regroup Median Loss for Combating Label Noise

Fengpeng Li, Kemou Li, Jinyu Tian, Jiantao Zhou

展开摘要

The deep model training procedure requires large-scale datasets of annotated data. Due to the difficulty of annotating a large number of samples, label noise caused by incorrect annotations is inevitable, resulting in low model performance and poor model generalization. To combat label noise, current methods usually select clean samples based on the small-loss criterion and use these samples for training. Due to some noisy samples similar to clean ones, these small-loss criterion-based methods are still affected by label noise. To address this issue, in this work, we propose Regroup Median Loss (RML) to reduce the probability of selecting noisy samples and correct losses of noisy samples. RML randomly selects samples with the same label as the training samples based on a new loss processing method. Then, we combine the stable mean loss and the robust median loss through a proposed regrouping strategy to obtain robust loss estimation for noisy samples. To further improve the model performance against label noise, we propose a new sample selection strategy and build a semi-supervised method based on RML. Compared to state-of-the-art methods, for both the traditionally trained and semi-supervised models, RML achieves a significant improvement on synthetic and complex real-world datasets. The source is at https://github.com/Feng-peng-Li/Regroup-Loss-Median-to-Combat-Label-Noise.

Technical
Regret Analysis of Repeated Delegated Choice

Mohammad Hajiaghayi, Mohammad Mahdavi, Keivan Rezaei, Suho Shin

展开摘要

We present a study on a repeated delegated choice problem, which is the first to consider an online learning variant of Kleinberg and Kleinberg, EC'18. In this model, a principal interacts repeatedly with an agent who possesses an exogenous set of solutions to search for efficient ones. Each solution can yield varying utility for both the principal and the agent, and the agent may propose a solution to maximize its own utility in a selfish manner. To mitigate this behavior, the principal announces an eligible set which screens out a certain set of solutions. The principal, however, does not have any information on the distribution of solutions nor the number of solutions in advance. Therefore, the principal dynamically announces various eligible sets to efficiently learn the distribution. The principal's objective is to minimize cumulative regret compared to the optimal eligible set in hindsight. We explore two dimensions of the problem setup, whether the agent behaves myopically or strategizes across the rounds, and whether the solutions yield deterministic or stochastic utility. We obtain sublinear regret upper bounds in various regimes, and derive corresponding lower bounds which implies the tightness of the results. Overall, we bridge a well-known problem in economics to the evolving area of online learning, and present a comprehensive study in this problem.

Technical
Regret Analysis of Policy Gradient Algorithm for Infinite Horizon Average Reward Markov Decision Processes

Qinbo Bai, Washim Uddin Mondal, Vaneet Aggarwal

展开摘要

In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm, liberating it from the constraints of assuming a linear MDP structure. We propose a vanilla policy gradient-based algorithm and show its global convergence property. We then prove that the proposed algorithm has O(T^3/4) regret. Remarkably, this paper marks a pioneering effort by presenting the first exploration into regret bound computation for the general parameterized policy gradient algorithm in the context of average reward scenarios.

Technical
Region-Disentangled Diffusion Model for High-Fidelity PPG-to-ECG Translation

Debaditya Shome, Pritam Sarkar, Ali Etemad

展开摘要

The high prevalence of cardiovascular diseases (CVDs) calls for accessible and cost-effective continuous cardiac monitoring tools. Despite Electrocardiography (ECG) being the gold standard, continuous monitoring remains a challenge, leading to the exploration of Photoplethysmography (PPG), a promising but more basic alternative available in consumer wearables. This notion has recently spurred interest in translating PPG to ECG signals. In this work, we introduce Region-Disentangled Diffusion Model (RDDM), a novel diffusion model designed to capture the complex temporal dynamics of ECG. Traditional Diffusion models like Denoising Diffusion Probabilistic Models (DDPM) face challenges in capturing such nuances due to the indiscriminate noise addition process across the entire signal. Our proposed RDDM overcomes such limitations by incorporating a novel forward process that selectively adds noise to specific regions of interest (ROI) such as QRS complex in ECG signals, and a reverse process that disentangles the denoising of ROI and non-ROI regions. Quantitative experiments demonstrate that RDDM can generate high-fidelity ECG from PPG in as few as 10 diffusion steps, making it highly effective and computationally efficient. Additionally, to rigorously validate the usefulness of the generated ECG signals, we introduce CardioBench, a comprehensive evaluation benchmark for a variety of cardiac-related tasks including heart rate and blood pressure estimation, stress classification, and the detection of atrial fibrillation and diabetes. Our thorough experiments show that RDDM achieves state-of-the-art performance on CardioBench. To the best of our knowledge, RDDM is the first diffusion model for cross-modal signal-to-signal translation in the bio-signal domain.

Technical
Region-Aware Exposure Consistency Network for Mixed Exposure Correction

Jin Liu, Huiyuan Fu, Chuanming Wang, Huadong Ma

展开摘要

Exposure correction aims to enhance images suffering from improper exposure to achieve satisfactory visual effects. Despite recent progress, existing methods generally mitigate either overexposure or underexposure in input images, and they still struggle to handle images with mixed exposure, i.e., one image incorporates both overexposed and underexposed regions. The mixed exposure distribution is non-uniform and leads to varying representation, which makes it challenging to address in a unified process. In this paper, we introduce an effective Region-aware Exposure Correction Network (RECNet) that can handle mixed exposure by adaptively learning and bridging different regional exposure representations. Specifically, to address the challenge posed by mixed exposure disparities, we develop a region-aware de-exposure module that effectively translates regional features of mixed exposure scenarios into an exposure-invariant feature space. Simultaneously, as de-exposure operation inevitably reduces discriminative information, we introduce a mixed-scale restoration unit that integrates exposure-invariant features and unprocessed features to recover local information. To further achieve a uniform exposure distribution in the global image, we propose an exposure contrastive regularization strategy under the constraints of intra-regional exposure consistency and inter-regional exposure continuity. Extensive experiments are conducted on various datasets, and the experimental results demonstrate the superiority and generalization of our proposed method. The code is released at: https://github.com/kravrolens/RECNet.

Technical
Regeneration Learning: A Learning Paradigm for Data Generation

Xu Tan, Tao Qin, Jiang Bian, Tie-Yan Liu, Yoshua Bengio

展开摘要

Machine learning methods for conditional data generation usually build a mapping from source conditional data X to target data Y. The target Y (e.g., text, speech, music, image, video) is usually high-dimensional and complex, and contains information that does not exist in source data, which hinders effective and efficient learning on the source-target mapping. In this paper, we present a learning paradigm called regeneration learning for data generation, which first generates Y' (an abstraction/representation of Y) from X and then generates Y from Y'. During training, Y' is obtained from Y through either handcrafted rules or self-supervised learning and is used to learn X-->Y' and Y'-->Y. Regeneration learning extends the concept of representation learning to data generation tasks, and can be regarded as a counterpart of traditional representation learning, since 1) regeneration learning handles the abstraction (Y') of the target data Y for data generation while traditional representation learning handles the abstraction (X') of source data X for data understanding; 2) both the processes of Y'-->Y in regeneration learning and X-->X' in representation learning can be learned in a self-supervised way (e.g., pre-training); 3) both the mappings from X to Y' in regeneration learning and from X' to Y in representation learning are simpler than the direct mapping from X to Y. We show that regeneration learning can be a widely-used paradigm for data generation (e.g., text generation, speech recognition, speech synthesis, music composition, image generation, and video generation) and can provide valuable insights into developing data generation methods.

Technical
Refining Latent Homophilic Structures over Heterophilic Graphs for Robust Graph Convolution Networks

Chenyang Qiu, Guoshun Nan, Tianyu Xiong, Wendi Deng, Di Wang, Zhiyang Teng, Lijuan Sun, Qimei Cui, Xiaofeng Tao

展开摘要

Graph convolution networks (GCNs) are extensively utilized in various graph tasks to mine knowledge from spatial data. Our study marks the pioneering attempt to quantitatively investigate the GCN robustness over omnipresent heterophilic graphs for node classification. We uncover that the predominant vulnerability is caused by the structural out-of-distribution (OOD) issue. This finding motivates us to present a novel method that aims to harden GCNs by automatically learning Latent Homophilic Structures over heterophilic graphs. We term such a methodology as LHS. To elaborate, our initial step involves learning a latent structure by employing a novel self-expressive technique based on multi-node interactions. Subsequently, the structure is refined using a pairwisely constrained dual-view contrastive learning approach. We iteratively perform the above procedure, enabling a GCN model to aggregate information in a homophilic way on heterophilic graphs. Armed with such an adaptable structure, we can properly mitigate the structural OOD threats over heterophilic graphs. Experiments on various benchmarks show the effectiveness of the proposed LHS approach for robust GCNs.

Technical
Refined Characterizations of Approval-Based Committee Scoring Rules

Chris Dong, Patrick Lederer

展开摘要

In approval-based committee (ABC) elections, the goal is to select a fixed-size subset of the candidates, a so-called committee, based on the voters' approval ballots over the candidates. One of the most popular classes of ABC voting rules are ABC scoring rules, for which voters give points to each committee and the committees with maximal total points are chosen. While the set of ABC scoring rules has recently been characterized in a model where the output is a ranking of all committees, no full characterization of these rules exists in the standard model where a set of winning committees is returned. We address this issue by characterizing two important subclasses of ABC scoring rules in the standard ABC election model, thereby both extending the result for ABC ranking rules to the standard setting and refining it to subclasses. In more detail, by relying on a consistency axiom for variable electorates, we characterize (i) the prominent class of Thiele rules and (ii) a new class of ABC voting rules called ballot size weighted approval voting. Based on these theorems, we also infer characterizations of three well-known ABC voting rules, namely multi-winner approval voting, proportional approval voting, and satisfaction approval voting.

Technical
Referred by Multi-Modality: A Unified Temporal Transformer for Video Object Segmentation

Shilin Yan, Renrui Zhang, Ziyu Guo, Wenchao Chen, Wei Zhang, Hongyang Li, Yu Qiao, Hao Dong, Zhongjiang He, Peng Gao

展开摘要

Recently, video object segmentation (VOS) referred by multi-modal signals, e.g., language and audio, has evoked increasing attention in both industry and academia. It is challenging for exploring the semantic alignment within modalities and the visual correspondence across frames. However, existing methods adopt separate network architectures for different modalities, and neglect the inter-frame temporal interaction with references. In this paper, we propose MUTR, a Multi-modal Unified Temporal transformer for Referring video object segmentation. With a unified framework for the first time, MUTR adopts a DETR-style transformer and is capable of segmenting video objects designated by either text or audio reference. Specifically, we introduce two strategies to fully explore the temporal relations between videos and multi-modal signals. Firstly, for low-level temporal aggregation before the transformer, we enable the multi-modal references to capture multi-scale visual cues from consecutive video frames. This effectively endows the text or audio signals with temporal knowledge and boosts the semantic alignment between modalities. Secondly, for high-level temporal interaction after the transformer, we conduct inter-frame feature communication for different object embeddings, contributing to better object-wise correspondence for tracking along the video. On Ref-YouTube-VOS and AVSBench datasets with respective text and audio references, MUTR achieves +4.2% and +8.7% J&F improvements to state-of-the-art methods, demonstrating our significance for unified multi-modal VOS. Code is released at https://github.com/OpenGVLab/MUTR.

Technical
Referee-Meta-Learning for Fast Adaptation of Locational Fairness

Weiye Chen, Yiqun Xie, Xiaowei Jia, Erhu He, Han Bao, Bang An, Xun Zhou

展开摘要

When dealing with data from distinct locations, machine learning algorithms tend to demonstrate an implicit preference of some locations over the others, which constitutes biases that sabotage the spatial fairness of the algorithm. This unfairness can easily introduce biases in subsequent decision-making given broad adoptions of learning-based solutions in practice. However, locational biases in AI are largely understudied. To mitigate biases over locations, we propose a locational meta-referee (Meta-Ref) to oversee the few-shot meta-training and meta-testing of a deep neural network. Meta-Ref dynamically adjusts the learning rates for training samples of given locations to advocate a fair performance across locations, through an explicit consideration of locational biases and the characteristics of input data. We present a three-phase training framework to learn both a meta-learning-based predictor and an integrated Meta-Ref that governs the fairness of the model. Once trained with a distribution of spatial tasks, Meta-Ref is applied to samples from new spatial tasks (i.e., regions outside the training area) to promote fairness during the fine-tune step. We carried out experiments with two case studies on crop monitoring and transportation safety, which show Meta-Ref can improve locational fairness while keeping the overall prediction quality at a similar level.

Technical
Reducing Spatial Fitting Error in Distillation of Denoising Diffusion Models

Shengzhe Zhou, Zejian Li, Shengyuan Zhang, Lefan Hou, Changyuan Yang, Guang Yang, Zhiyuan Yang, Lingyun Sun

展开摘要

Denoising Diffusion models have exhibited remarkable capabilities in image generation. However, generating high-quality samples requires a large number of iterations. Knowledge distillation for diffusion models is an effective method to address this limitation with a shortened sampling process but causes degraded generative quality. Based on our analysis with bias-variance decomposition and experimental observations, we attribute the degradation to the spatial fitting error occurring in the training of both the teacher and student model in the distillation. Accordingly, we propose Spatial Fitting-Error Reduction Distillation model (SFERD). SFERD utilizes attention guidance from the teacher model and a designed semantic gradient predictor to reduce the student's fitting error. Empirically, our proposed model facilitates high-quality sample generation in a few function evaluations. We achieve an FID of 5.31 on CIFAR-10 and 9.39 on ImageNet 64x64 with only one step, outperforming existing diffusion methods. Our study provides a new perspective on diffusion distillation by highlighting the intrinsic denoising ability of models.

Technical
Redefining the Laparoscopic Spatial Sense: AI-Based Intra- and Postoperative Measurement from Stereoimages

Leopold Müller, Patrick Hemmer, Moritz Queisner, Igor Sauer, Simeon Allmendinger, Johannes Jakubik, Michael Vössing, Niklas Kühl

展开摘要

A significant challenge in image-guided surgery is the accurate measurement task of relevant structures such as vessel segments, resection margins, or bowel lengths. While this task is an essential component of many surgeries, it involves substantial human effort and is prone to inaccuracies. In this paper, we develop a novel human-AI-based method for laparoscopic measurements utilizing stereo vision that has been guided by practicing surgeons. Based on a holistic qualitative requirements analysis, this work proposes a comprehensive measurement method, which comprises state-of-the-art machine learning architectures, such as RAFT-Stereo and YOLOv8. The developed method is assessed in various realistic experimental evaluation environments. Our results outline the potential of our method achieving high accuracies in distance measurements with errors below 1 mm. Furthermore, on-surface measurements demonstrate robustness when applied in challenging environments with textureless regions. Overall, by addressing the inherent challenges of image-guided surgery, we lay the foundation for a more robust and accurate solution for intra- and postoperative measurements, enabling more precise, safe, and efficient surgical procedures.

Technical
Redefining ABA+ Semantics via Abstract Set-to-Set Attacks

Yannis Dimopoulos, Wolfgang Dvořák, Matthias König, Anna Rapberger, Markus Ulbricht, Stefan Woltran

展开摘要

Assumption-based argumentation (ABA) is a powerful defeasible reasoning formalism which is based on the interplay of assumptions, their contraries, and inference rules. ABA with preferences (ABA+) generalizes the basic model by allowing qualitative comparison between assumptions. The integration of preferences however comes with a cost. In ABA+, the evaluation under two central and well-established semantics---grounded and complete semantics---is not guaranteed to yield an outcome. Moreover, while ABA frameworks without preferences allow for a graph-based representation in Dung-style frameworks, an according instantiation for general ABA+ frameworks has not been established so far. In this work, we tackle both issues: First, we develop a novel abstract argumentation formalism based on set-to-set attacks. We show that our so-called Hyper Argumentation Frameworks (HYPAFs) capture ABA+. Second, we propose relaxed variants of complete and grounded semantics for HYPAFs that yield an extension for all frameworks by design, while still faithfully generalizing the established semantics of Dung-style Argumentation Frameworks. We exploit the newly established correspondence between ABA+ and HYPAFs to obtain variants for grounded and complete ABA+ semantics that are guaranteed to yield an outcome. Finally, we discuss basic properties and provide a complexity analysis. Along the way, we settle the computational complexity of several ABA+ semantics.

Technical
RedCore: Relative Advantage Aware Cross-Modal Representation Learning for Missing Modalities with Imbalanced Missing Rates

Jun Sun, Xinxin Zhang, Shoukang Han, Yu-Ping Ruan, Taihao Li

展开摘要

Multimodal learning is susceptible to modality missing, which poses a major obstacle for its practical applications and, thus, invigorates increasing research interest. In this paper, we investigate two challenging problems: 1) when modality missing exists in the training data, how to exploit the incomplete samples while guaranteeing that they are properly supervised? 2) when the missing rates of different modalities vary, causing or exacerbating the imbalance among modalities, how to address the imbalance and ensure all modalities are well-trained. To tackle these two challenges, we first introduce the variational information bottleneck (VIB) method for the cross-modal representation learning of missing modalities, which capitalizes on the available modalities and the labels as supervision. Then, accounting for the imbalanced missing rates, we define relative advantage to quantify the advantage of each modality over others. Accordingly, a bi-level optimization problem is formulated to adaptively regulate the supervision of all modalities during training. As a whole, the proposed approach features Relative advantage aware Cross-modal representation learning (abbreviated as RedCore) for missing modalities with imbalanced missing rates. Extensive empirical results demonstrate that RedCore outperforms competing models in that it exhibits superior robustness against either large or imbalanced missing rates. The code is available at: https://github.com/sunjunaimer/RedCore.

Technical
Recurrent Partial Kernel Network for Efficient Optical Flow Estimation

Henrique Morimitsu, Xiaobin Zhu, Xiangyang Ji, Xu-Cheng Yin

展开摘要

Optical flow estimation is a challenging task consisting of predicting per-pixel motion vectors between images. Recent methods have employed larger and more complex models to improve the estimation accuracy. However, this impacts the widespread adoption of optical flow methods and makes it harder to train more general models since the optical flow data is hard to obtain. This paper proposes a small and efficient model for optical flow estimation. We design a new spatial recurrent encoder that extracts discriminative features at a significantly reduced size. Unlike standard recurrent units, we utilize Partial Kernel Convolution (PKConv) layers to produce variable multi-scale features with a single shared block. We also design efficient Separable Large Kernels (SLK) to capture large context information with low computational cost. Experiments on public benchmarks show that we achieve state-of-the-art generalization performance while requiring significantly fewer parameters and memory than competing methods. Our model ranks first in the Spring benchmark without finetuning, improving the results by over 10% while requiring an order of magnitude fewer FLOPs and over four times less memory than the following published method without finetuning. The code is available at github.com/hmorimitsu/ptlflow/tree/main/ptlflow/models/rpknet.

Technical
Recurrent Graph Neural Networks and Their Connections to Bisimulation and Logic

Maximilian Pflueger, David Tena Cucala, Egor V. Kostylev

展开摘要

The success of Graph Neural Networks (GNNs) in practice has motivated extensive research on their theoretical properties. This includes recent results that characterise node classifiers expressible by GNNs in terms of first order logic. Most of the analysis, however, has been focused on GNNs with fixed number of message-passing iterations (i.e., layers), which cannot realise many simple classifiers such as reachability of a node with a given label. In this paper, we start to fill this gap and study the foundations of GNNs that can perform more than a fixed number of message-passing iterations. We first formalise two generalisations of the basic GNNs: recurrent GNNs (RecGNNs), which repeatedly apply message-passing iterations until the node classifications become stable, and graph-size GNNs (GSGNNs), which exploit a built-in function of the input graph size to decide the number of message-passings. We then formally prove that GNN classifiers are strictly less expressive than RecGNN ones, and RecGNN classifiers are strictly less expressive than GSGNN ones. To get this result, we identify novel semantic characterisations of the three formalisms in terms of suitable variants of bisimulation, which we believe have their own value for our understanding of GNNs. Finally, we prove syntactic logical characterisations of RecGNNs and GSGNNs analogous to the logical characterisation of plain GNNs, where we connect the two formalisms to monadic monotone fixpoint logic---a generalisation of first-order logic that supports recursion.

Technical