The Watts-Strogatz small-world model has been an influential random graph model since its proposal in 1998 due to the ubiquity of the small-world phenomenon in complex networks [WS98, Wat04]. In this model, there are n vertices with latent positions on a circle, and the vertices are more likely to be connected to their k-nearest geometric neighbors than to more distant vertices. In other words, a denser cycle of length n and width k is "planted" in the sparser ambient random graph on n vertices. Informally, the small-world model can also be viewed as an interpolation between a random geometric graph [Pen03], where edges exist only between vertices with nearby locations on a circle, and an Erdős-Rényi graph [ER59], where edges are random and independent. As a consequence, a small-world network tends to have a high clustering coefficient due to the geometry while preserving low distances between vertices in a random graph. While there has been extensive literature on small-world networks and geometric graphs, the associated statistical problems, such as detection and recovery of the latent geometry from the observed random graph, have only gained attention more recently.

World models can represent potentially high-dimensional pixel observations in compact latent spaces, making it tractable to model the dynamics of the environment. However, the latent dynamics inferred by these models may still be highly complex. Abstracting the dynamics of the environment with simple models can have several benefits. If the latent dynamics are simple, the model may generalize better to novel transitions, and discover useful latent representations of environment states. We propose a regularization scheme that simplifies the world model's latent dynamics. Our model, the Parsimonious Latent Space Model (PLSM), minimizes the mutual information between latent states and the dynamics that arise between them. This makes the dynamics softly state-invariant, and the effects of the agent's actions more predictable. We combine the PLSM with three different model classes used for i) future latent state prediction, ii) video prediction, and iii) planning. We find that our regularization improves accuracy, generalization, and performance in downstream tasks.

Message passing Graph Neural Networks (GNNs) are known to be limited in expressive power by the 1-WL color-refinement test for graph isomorphism. Other more expressive models either are computationally expensive or need preprocessing to extract structural features from the graph. In this work, we propose to make GNNs universal by guiding the learning process with exact isomorphism solver techniques which operate on the paradigm of Individualization and Refinement (IR), a method to artificially introduce asymmetry and further refine the coloring when 1-WL stops. Isomorphism solvers generate a search tree of colorings whose leaves uniquely identify the graph. However, the tree grows exponentially large and needs hand-crafted pruning techniques which are not desirable from a learning perspective. We take a probabilistic view and approximate the search tree of colorings (i.e. embeddings) by sampling multiple paths from root to leaves of the search tree. To learn more discriminative representations, we guide the sampling process with particle filter updates, a principled approach for sequential state estimation. Our algorithm is end-to-end differentiable, can be applied with any GNN as backbone and learns richer graph representations with only linear increase in runtime. Experimental evaluation shows that our approach consistently outperforms leading GNN models on both synthetic benchmarks for isomorphism detection as well as real-world datasets.

Two studies of a human-AI collaborative design tool were carried out in order to understand the influence design recommendations have on the design process. The tool investigated is based on an evolutionary algorithm attempting to design a virtual car to travel as far as possible in a fixed time. Participants were able to design their own cars, make recommendations to the algorithm and view sets of recommendations from the algorithm. The algorithm-recommended sets were designs which had been previously tested; some sets were simply randomly picked and other sets were picked using MAP-Elites. In the first study 808 design sessions were recorded as part of a science outreach program, each with analytical data of how each participant used the tool. To provide context to this quantitative data, a smaller double-blind lab study was also carried out with 12 participants. In the lab study the same quantitative data from the large scale study was collected alongside responses to interview questions. Although there is some evidence that the MAP-Elites provide higher-quality individual recommendations, neither study provides convincing evidence that these recommendations have a more positive influence on the design process than simply a random selection of designs. In fact, it seems that providing a combination of MAP-Elites and randomly selected recommendations is beneficial to the process. Furthermore, simply viewing recommendations from the MAP-Elites had a positive influence on engagement in the design task and the quality of the final design produced. Our findings are significant both for researchers designing new mixed-initiative tools, and those who wish to evaluate existing tools. Most significantly, we found that metrics researchers currently use to evaluate the success of human-AI collaborative algorithms do not measure the full influence these algorithms have on the design process.

Current approaches of knowledge editing struggle to effectively propagate updates to interconnected facts. In this work, we delve into the barriers that hinder the appropriate propagation of updated knowledge within these models for accurate reasoning. To support our analysis, we introduce a novel reasoning-based benchmark -- ReCoE (Reasoning-based Counterfactual Editing dataset) -- which covers six common reasoning schemes in real world. We conduct a thorough analysis of existing knowledge editing techniques, including input augmentation, finetuning, and locate-and-edit. We found that all model editing methods show notably low performance on this dataset, especially in certain reasoning schemes. Our analysis over the chain-of-thought generation of edited models further uncover key reasons behind the inadequacy of existing knowledge editing methods from a reasoning standpoint, involving aspects on fact-wise editing, fact recall ability, and coherence in generation. We will make our benchmark publicly available.

It is well acknowledged that incorporating explicit knowledge graphs (KGs) can benefit question answering. Existing approaches typically follow a grounding-reasoning pipeline in which entity nodes are first grounded for the query (question and candidate answers), and then a reasoning module reasons over the matched multi-hop subgraph for answer prediction. Although the pipeline largely alleviates the issue of extracting essential information from giant KGs, efficiency is still an open challenge when scaling up hops in grounding the subgraphs. In this paper, we target at finding semantically related entity nodes in the subgraph to improve the efficiency of graph reasoning with KG. We propose a grounding-pruning-reasoning pipeline to prune noisy nodes, remarkably reducing the computation cost and memory usage while also obtaining decent subgraph representation. In detail, the pruning module first scores concept nodes based on the dependency distance between matched spans and then prunes the nodes according to score ranks. To facilitate the evaluation of pruned subgraphs, we also propose a graph attention network (GAT) based module to reason with the subgraph data. Experimental results on CommonsenseQA and OpenBookQA demonstrate the effectiveness of our method.

Geometry problem solving presents a formidable challenge within the NLP community. Existing approaches often rely on models designed for solving math word problems, neglecting the unique characteristics of geometry math problems. Additionally, the current research predominantly focuses on geometry calculation problems, while overlooking other essential aspects like proving. In this study, we address these limitations by proposing the Geometry-Aware Problem Solver (GAPS) model. GAPS is specifically designed to generate solution programs for geometry math problems of various types with the help of its unique problem-type classifier. To achieve this, GAPS treats the solution program as a composition of operators and operands, segregating their generation processes. Furthermore, we introduce the geometry elements enhancement method, which enhances the ability of GAPS to recognize geometry elements accurately. By leveraging these improvements, GAPS showcases remarkable performance in resolving geometry math problems. Our experiments conducted on the UniGeo dataset demonstrate the superiority of GAPS over the state-of-the-art model, Geoformer. Specifically, GAPS achieves an accuracy improvement of more than 5.3% for calculation tasks and an impressive 41.1% for proving tasks. Notably, GAPS achieves an impressive accuracy of 97.5% on proving problems, representing a significant advancement in solving geometry proving tasks.

Neural radiance fields (NeRFs) have exhibited potential in synthesizing high-fidelity views of 3D scenes but the standard training paradigm of NeRF presupposes an equal importance for each image in the training set. This assumption poses a significant challenge for rendering specific views presenting intricate geometries, thereby resulting in suboptimal performance. In this paper, we take a closer look at the implications of the current training paradigm and redesign this for more superior rendering quality by NeRFs. Dividing input views into multiple groups based on their visual similarities and training individual models on each of these groups enables each model to specialize on specific regions without sacrificing speed or efficiency. Subsequently, the knowledge of these specialized models is aggregated into a single entity via a teacher-student distillation paradigm, enabling spatial efficiency for online render-ing. Empirically, we evaluate our novel training framework on two publicly available datasets, namely NeRF synthetic and Tanks&Temples. Our evaluation demonstrates that our DaC training pipeline enhances the rendering quality of a state-of-the-art baseline model while exhibiting convergence to a superior minimum.

As a novel and effective fine-tuning paradigm based on large-scale pre-trained language models (PLMs), prompt-tuning aims to reduce the gap between downstream tasks and pre-training objectives. While prompt-tuning has yielded continuous advancements in various tasks, such an approach still remains a persistent defect: prompt-tuning methods fail to generalize to specific few-shot patterns. From the perspective of distribution analyses, we disclose that the intrinsic issues behind the phenomenon are the over-multitudinous conceptual knowledge contained in PLMs and the abridged knowledge for target downstream domains, which jointly result in that PLMs mis-locate the knowledge distributions corresponding to the target domains in the universal knowledge embedding space. To this end, we intuitively explore to approximate the unabridged target domains of downstream tasks in a debiased manner, and then abstract such domains to generate discriminative prompts, thereby providing the de-ambiguous guidance for PLMs. Guided by such an intuition, we propose a simple yet effective approach, namely BayesPrompt, to learn prompts that contain the domain discriminative information against the interference from domain-irrelevant knowledge. BayesPrompt primitively leverages known distributions to approximate the debiased factual distributions of target domains and further uniformly samples certain representative features from the approximated distributions to generate the ultimate prompts for PLMs. We provide theoretical insights with the connection to domain adaptation. Empirically, our method achieves state-of-the-art performance on benchmarks.

In recent years, spectral graph neural networks, characterized by polynomial filters, have garnered increasing attention and have achieved remarkable performance in tasks such as node classification. These models typically assume that eigenvalues for the normalized Laplacian matrix are distinct from each other, thus expecting a polynomial filter to have a high fitting ability. However, this paper empirically observes that normalized Laplacian matrices frequently possess repeated eigenvalues. Moreover, we theoretically establish that the number of distinguishable eigenvalues plays a pivotal role in determining the expressive power of spectral graph neural networks. In light of this observation, we propose an eigenvalue correction strategy that can free polynomial filters from the constraints of repeated eigenvalue inputs. Concretely, the proposed eigenvalue correction strategy enhances the uniform distribution of eigenvalues, thus mitigating repeated eigenvalues, and improving the fitting capacity and expressive power of polynomial filters. Extensive experimental results on both synthetic and real-world datasets demonstrate the superiority of our method.