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Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets. However, this exponential growth property comes at a price of numerical instability such that training hyperbolic learning models will sometimes lead to catastrophic NaN problems, encountering unrepresentable values in floating point arithmetic. In this work, we carefully analyze the limitation of two popular models for the hyperbolic space, namely, the Poincar\'e ball and the Lorentz model. We first show that, under the 64 bit arithmetic system, the Poincar\'e ball has a relatively larger capacity than the Lorentz model for correctly representing points. Then, we theoretically validate the superiority of the Lorentz model over the Poincar\'e ball from the perspective of optimization. Given the numerical limitations of both models, we identify one Euclidean parametrization of the hyperbolic space which can alleviate these limitations. We further extend this Euclidean parametrization to hyperbolic hyperplanes and exhibits its ability in improving the performance of hyperbolic SVM.

Extracting a stable and compact representation of the environment is crucial for efficient reinforcement learning in high-dimensional, noisy, and non-stationary environments. Different categories of information coexist in such environments -- how to effectively extract and disentangle these information remains a challenging problem. In this paper, we propose IFactor, a general framework to model four distinct categories of latent state variables that capture various aspects of information within the RL system, based on their interactions with actions and rewards. Our analysis establishes block-wise identifiability of these latent variables, which not only provides a stable and compact representation but also discloses that all reward-relevant factors are significant for policy learning. We further present a practical approach to learning the world model with identifiable blocks, ensuring the removal of redundants but retaining minimal and sufficient information for policy optimization. Experiments in synthetic worlds demonstrate that our method accurately identifies the ground-truth latent variables, substantiating our theoretical findings. Moreover, experiments in variants of the DeepMind Control Suite and RoboDesk showcase the superior performance of our approach over baselines.

Fine-grained emotion classification (FEC) is a challenging task. Specifically, FEC needs to handle subtle nuance between labels, which can be complex and confusing. Most existing models only address text classification problem in the euclidean space, which we believe may not be the optimal solution as labels of close semantic (e.g., afraid and terrified) may not be differentiated in such space, which harms the performance. In this paper, we propose HypEmo, a novel framework that can integrate hyperbolic embeddings to improve the FEC task. First, we learn label embeddings in the hyperbolic space to better capture their hierarchical structure, and then our model projects contextualized representations to the hyperbolic space to compute the distance between samples and labels. Experimental results show that incorporating such distance to weight cross entropy loss substantially improves the performance with significantly higher efficiency. We evaluate our proposed model on two benchmark datasets and found 4.8% relative improvement compared to the previous state of the art with 43.2% fewer parameters and 76.9% less training time. Code is available at https: //github.com/dinobby/HypEmo.

Knowledge graphs (KGs), as structured representations of real world facts, are intelligent databases incorporating human knowledge that can help machine imitate the way of human problem solving. However, KGs are usually huge and there are inevitably missing facts in KGs, thus undermining applications such as question answering and recommender systems that are based on knowledge graph reasoning. Link prediction for knowledge graphs is the task aiming to complete missing facts by reasoning based on the existing knowledge. Two main streams of research are widely studied: one learns low-dimensional embeddings for entities and relations that can explore latent patterns, and the other gains good interpretability by mining logical rules. Unfortunately, the heterogeneity of modern KGs that involve entities and relations of various types is not well considered in the previous studies. In this paper, we propose DegreEmbed, a model that combines embedding-based learning and logic rule mining for inferring on KGs. Specifically, we study the problem of predicting missing links in heterogeneous KGs from the perspective of the degree of nodes. Experimentally, we demonstrate that our DegreEmbed model outperforms the state-of-the-art methods on real world datasets and the rules mined by our model are of high quality and interpretability.

How does language inform our downstream thinking? In particular, how do humans make meaning from language--and how can we leverage a theory of linguistic meaning to build machines that think in more human-like ways? In this paper, we propose rational meaning construction, a computational framework for language-informed thinking that combines neural language models with probabilistic models for rational inference. We frame linguistic meaning as a context-sensitive mapping from natural language into a probabilistic language of thought (PLoT)--a general-purpose symbolic substrate for generative world modeling. Our architecture integrates two computational tools that have not previously come together: we model thinking with probabilistic programs, an expressive representation for commonsense reasoning; and we model meaning construction with large language models (LLMs), which support broad-coverage translation from natural language utterances to code expressions in a probabilistic programming language. We illustrate our framework through examples covering four core domains from cognitive science: probabilistic reasoning, logical and relational reasoning, visual and physical reasoning, and social reasoning. In each, we show that LLMs can generate context-sensitive translations that capture pragmatically-appropriate linguistic meanings, while Bayesian inference with the generated programs supports coherent and robust commonsense reasoning. We extend our framework to integrate cognitively-motivated symbolic modules (physics simulators, graphics engines, and planning algorithms) to provide a unified commonsense thinking interface from language. Finally, we explore how language can drive the construction of world models themselves. We hope this work will provide a roadmap towards cognitive models and AI systems that synthesize the insights of both modern and classical computational perspectives.

Graph neural networks generalize conventional neural networks to graph-structured data and have received widespread attention due to their impressive representation ability. In spite of the remarkable achievements, the performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry, especially for datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution, owing to its exponential growth property. In this survey, we comprehensively revisit the technical details of the current hyperbolic graph neural networks, unifying them into a general framework and summarizing the variants of each component. More importantly, we present various HGNN-related applications. Last, we also identify several challenges, which potentially serve as guidelines for further flourishing the achievements of graph learning in hyperbolic spaces.

Knowledge Graph Embedding (KGE) aims to learn representations for entities and relations. Most KGE models have gained great success, especially on extrapolation scenarios. Specifically, given an unseen triple (h, r, t), a trained model can still correctly predict t from (h, r, ?), or h from (?, r, t), such extrapolation ability is impressive. However, most existing KGE works focus on the design of delicate triple modeling function, which mainly tells us how to measure the plausibility of observed triples, but offers limited explanation of why the methods can extrapolate to unseen data, and what are the important factors to help KGE extrapolate. Therefore in this work, we attempt to study the KGE extrapolation of two problems: 1. How does KGE extrapolate to unseen data? 2. How to design the KGE model with better extrapolation ability? For the problem 1, we first discuss the impact factors for extrapolation and from relation, entity and triple level respectively, propose three Semantic Evidences (SEs), which can be observed from train set and provide important semantic information for extrapolation. Then we verify the effectiveness of SEs through extensive experiments on several typical KGE methods. For the problem 2, to make better use of the three levels of SE, we propose a novel GNN-based KGE model, called Semantic Evidence aware Graph Neural Network (SE-GNN). In SE-GNN, each level of SE is modeled explicitly by the corresponding neighbor pattern, and merged sufficiently by the multi-layer aggregation, which contributes to obtaining more extrapolative knowledge representation. Finally, through extensive experiments on FB15k-237 and WN18RR datasets, we show that SE-GNN achieves state-of-the-art performance on Knowledge Graph Completion task and performs a better extrapolation ability.

Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that jointly learn representations and transformations of text are very data-inefficient, and it is hard to analyse their reasoning process. These issues are addressed by end-to-end differentiable reasoning systems such as Neural Theorem Provers (NTPs), although they can only be used with small-scale symbolic KBs. In this paper we first propose Greedy NTPs (GNTPs), an extension to NTPs addressing their complexity and scalability limitations, thus making them applicable to real-world datasets. This result is achieved by dynamically constructing the computation graph of NTPs and including only the most promising proof paths during inference, thus obtaining orders of magnitude more efficient models. Then, we propose a novel approach for jointly reasoning over KBs and textual mentions, by embedding logic facts and natural language sentences in a shared embedding space. We show that GNTPs perform on par with NTPs at a fraction of their cost while achieving competitive link prediction results on large datasets, providing explanations for predictions, and inducing interpretable models. Source code, datasets, and supplementary material are available online at //github.com/uclnlp/gntp.

In this paper, we propose Latent Relation Language Models (LRLMs), a class of language models that parameterizes the joint distribution over the words in a document and the entities that occur therein via knowledge graph relations. This model has a number of attractive properties: it not only improves language modeling performance, but is also able to annotate the posterior probability of entity spans for a given text through relations. Experiments demonstrate empirical improvements over both a word-based baseline language model and a previous approach that incorporates knowledge graph information. Qualitative analysis further demonstrates the proposed model's ability to learn to predict appropriate relations in context.

We consider the problem of zero-shot recognition: learning a visual classifier for a category with zero training examples, just using the word embedding of the category and its relationship to other categories, which visual data are provided. The key to dealing with the unfamiliar or novel category is to transfer knowledge obtained from familiar classes to describe the unfamiliar class. In this paper, we build upon the recently introduced Graph Convolutional Network (GCN) and propose an approach that uses both semantic embeddings and the categorical relationships to predict the classifiers. Given a learned knowledge graph (KG), our approach takes as input semantic embeddings for each node (representing visual category). After a series of graph convolutions, we predict the visual classifier for each category. During training, the visual classifiers for a few categories are given to learn the GCN parameters. At test time, these filters are used to predict the visual classifiers of unseen categories. We show that our approach is robust to noise in the KG. More importantly, our approach provides significant improvement in performance compared to the current state-of-the-art results (from 2 ~ 3% on some metrics to whopping 20% on a few).