Search is an ability foundational in many important tasks, and recent studies have shown that large language models (LLMs) struggle to perform search robustly. It is unknown whether this inability is due to a lack of data, insufficient model parameters, or fundamental limitations of the transformer architecture. In this work, we use the foundational graph connectivity problem as a testbed to generate effectively limitless high-coverage data to train small transformers and test whether they can learn to perform search. We find that, when given the right training distribution, the transformer is able to learn to search. We analyze the algorithm that the transformer has learned through a novel mechanistic interpretability technique that enables us to extract the computation graph from the trained model. We find that for each vertex in the input graph, transformers compute the set of vertices reachable from that vertex. Each layer then progressively expands these sets, allowing the model to search over a number of vertices exponential in the number of layers. However, we find that as the input graph size increases, the transformer has greater difficulty in learning the task. This difficulty is not resolved even as the number of parameters is increased, suggesting that increasing model scale will not lead to robust search abilities. We also find that performing search in-context (i.e., chain-of-thought) does not resolve this inability to learn to search on larger graphs.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to compositional proofs. However, they have difficulty generalizing to longer proofs, and they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Recent years have witnessed much interest in temporal reasoning over knowledge graphs (KG) for complex question answering (QA), but there remains a substantial gap in human capabilities. We explore how to generalize relational graph convolutional networks (RGCN) for temporal KGQA. Specifically, we propose a novel, intuitive and interpretable scheme to modulate the messages passed through a KG edge during convolution, based on the relevance of its associated time period to the question. We also introduce a gating device to predict if the answer to a complex temporal question is likely to be a KG entity or time and use this prediction to guide our scoring mechanism. We evaluate the resulting system, which we call TwiRGCN, on TimeQuestions, a recently released, challenging dataset for multi-hop complex temporal QA. We show that TwiRGCN significantly outperforms state-of-the-art systems on this dataset across diverse question types. Notably, TwiRGCN improves accuracy by 9--10 percentage points for the most difficult ordinal and implicit question types.

Graph neural networks (GNNs) work well when the graph structure is provided. However, this structure may not always be available in real-world applications. One solution to this problem is to infer a task-specific latent structure and then apply a GNN to the inferred graph. Unfortunately, the space of possible graph structures grows super-exponentially with the number of nodes and so the task-specific supervision may be insufficient for learning both the structure and the GNN parameters. In this work, we propose the Simultaneous Learning of Adjacency and GNN Parameters with Self-supervision, or SLAPS, a method that provides more supervision for inferring a graph structure through self-supervision. A comprehensive experimental study demonstrates that SLAPS scales to large graphs with hundreds of thousands of nodes and outperforms several models that have been proposed to learn a task-specific graph structure on established benchmarks.

Many important problems can be formulated as reasoning in knowledge graphs. Representation learning has proved extremely effective for transductive reasoning, in which one needs to make new predictions for already observed entities. This is true for both attributed graphs(where each entity has an initial feature vector) and non-attributed graphs (where the only initial information derives from known relations with other entities). For out-of-sample reasoning, where one needs to make predictions for entities that were unseen at training time, much prior work considers attributed graph. However, this problem is surprisingly under-explored for non-attributed graphs. In this paper, we study the out-of-sample representation learning problem for non-attributed knowledge graphs, create benchmark datasets for this task, develop several models and baselines, and provide empirical analyses and comparisons of the proposed models and baselines.

Knowledge graphs (KGs) typically contain temporal facts indicating relationships among entities at different times. Due to their incompleteness, several approaches have been proposed to infer new facts for a KG based on the existing ones-a problem known as KG completion. KG embedding approaches have proved effective for KG completion, however, they have been developed mostly for static KGs. Developing temporal KG embedding models is an increasingly important problem. In this paper, we build novel models for temporal KG completion through equipping static models with a diachronic entity embedding function which provides the characteristics of entities at any point in time. This is in contrast to the existing temporal KG embedding approaches where only static entity features are provided. The proposed embedding function is model-agnostic and can be potentially combined with any static model. We prove that combining it with SimplE, a recent model for static KG embedding, results in a fully expressive model for temporal KG completion. Our experiments indicate the superiority of our proposal compared to existing baselines.

Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static graphs. However, many applications involve evolving graphs. This introduces important challenges for learning and inference since nodes, attributes, and edges change over time. In this survey, we review the recent advances in representation learning for dynamic graphs, including dynamic knowledge graphs. We describe existing models from an encoder-decoder perspective, categorize these encoders and decoders based on the techniques they employ, and analyze the approaches in each category. We also review several prominent applications and widely used datasets, and highlight directions for future research.

Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links among the entities. Tensor factorization approaches have proved promising for such link prediction problems. Proposed in 1927, Canonical Polyadic (CP) decomposition is among the first tensor factorization approaches. CP generally performs poorly for link prediction as it learns two independent embedding vectors for each entity, whereas they are really tied. We present a simple enhancement of CP (which we call SimplE) to allow the two embeddings of each entity to be learned dependently. The complexity of SimplE grows linearly with the size of embeddings. The embeddings learned through SimplE are interpretable, and certain types of background knowledge can be incorporated into these embeddings through weight tying. We prove SimplE is fully expressive and derive a bound on the size of its embeddings for full expressivity. We show empirically that, despite its simplicity, SimplE outperforms several state-of-the-art tensor factorization techniques. SimplE's code is available on GitHub at https://github.com/Mehran-k/SimplE.

Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links among the entities. Tensor factorization approaches have proved promising for such link prediction problems. Proposed in 1927, Canonical Polyadic (CP) decomposition is among the first tensor factorization approaches. CP generally performs poorly for link prediction as it learns two independent embedding vectors for each entity, whereas they are really tied. We present a simple enhancement of CP (which we call SimplE) to allow the two embeddings of each entity to be learned dependently. The complexity of SimplE grows linearly with the size of embeddings. The embeddings learned through SimplE are interpretable, and certain types of background knowledge can be incorporated into these embeddings through weight tying. We prove SimplE is fully expressive and derive a bound on the size of its embeddings for full expressivity. We show empirically that, despite its simplicity, SimplE outperforms several state-of-the-art tensor factorization techniques. SimplE's code is available on GitHub at https://github.com/Mehran-k/SimplE.

Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links among the entities. Tensor factorization approaches have proved promising for such link prediction problems. Proposed in 1927, Canonical Polyadic (CP) decomposition is among the first tensor factorization approaches. CP generally performs poorly for link prediction as it learns two independent embedding vectors for each entity, whereas they are really tied. We present a simple enhancement of CP (which we call SimplE) to allow the two embeddings of each entity to be learned dependently. The complexity of SimplE grows linearly with the size of embeddings. The embeddings learned through SimplE are interpretable, and certain types of background knowledge can be incorporated into these embeddings through weight tying. We prove SimplE is fully expressive and derive a bound on the size of its embeddings for full expressivity. We show empirically that, despite its simplicity, SimplE outperforms several state-of-the-art tensor factorization techniques. SimplE's code is available on GitHub at https://github.com/Mehran-k/SimplE.