Conic10K: A Challenging Math Problem Understanding and Reasoning Dataset

Mathematical understanding and reasoning are crucial tasks for assessing the capabilities of artificial intelligence (AI). However, existing benchmarks either require just a few steps of reasoning, or only contain a small amount of data in one specific topic, making it hard to analyse AI's behaviour with reference to different problems within a specific topic in detail. In this work, we propose Conic10K, a challenging math problem dataset on conic sections in Chinese senior high school education. Our dataset contains various problems with different reasoning depths, while only the knowledge from conic sections is required. Since the dataset only involves a narrow range of knowledge, it is easy to separately analyse the knowledge a model possesses and the reasoning ability it has. For each problem, we provide a high-quality formal representation, the reasoning steps, and the final solution. Experiments show that existing large language models, including GPT-4, exhibit weak performance on complex reasoning. We hope that our findings could inspire more advanced techniques for precise natural language understanding and reasoning. Our dataset and codes are available at https://github.com/whyNLP/Conic10K.

Do PLMs Know and Understand Ontological Knowledge?

Ontological knowledge, which comprises classes and properties and their relationships, is integral to world knowledge. It is significant to explore whether Pretrained Language Models (PLMs) know and understand such knowledge. However, existing PLM-probing studies focus mainly on factual knowledge, lacking a systematic probing of ontological knowledge. In this paper, we focus on probing whether PLMs store ontological knowledge and have a semantic understanding of the knowledge rather than rote memorization of the surface form. To probe whether PLMs know ontological knowledge, we investigate how well PLMs memorize: (1) types of entities; (2) hierarchical relationships among classes and properties, e.g., Person is a subclass of Animal and Member of Sports Team is a subproperty of Member of ; (3) domain and range constraints of properties, e.g., the subject of Member of Sports Team should be a Person and the object should be a Sports Team. To further probe whether PLMs truly understand ontological knowledge beyond memorization, we comprehensively study whether they can reliably perform logical reasoning with given knowledge according to ontological entailment rules. Our probing results show that PLMs can memorize certain ontological knowledge and utilize implicit knowledge in reasoning. However, both the memorizing and reasoning performances are less than perfect, indicating incomplete knowledge and understanding.

COMBO: A Complete Benchmark for Open KG Canonicalization

Open knowledge graph (KG) consists of (subject, relation, object) triples extracted from millions of raw text. The subject and object noun phrases and the relation in open KG have severe redundancy and ambiguity and need to be canonicalized. Existing datasets for open KG canonicalization only provide gold entity-level canonicalization for noun phrases. In this paper, we present COMBO, a Complete Benchmark for Open KG canonicalization. Compared with existing datasets, we additionally provide gold canonicalization for relation phrases, gold ontology-level canonicalization for noun phrases, as well as source sentences from which triples are extracted. We also propose metrics for evaluating each type of canonicalization. On the COMBO dataset, we empirically compare previously proposed canonicalization methods as well as a few simple baseline methods based on pretrained language models. We find that properly encoding the phrases in a triple using pretrained language models results in better relation canonicalization and ontology-level canonicalization of the noun phrase. We release our dataset, baselines, and evaluation scripts at https://github.com/jeffchy/COMBO/tree/main.

Modeling Label Correlations for Ultra-Fine Entity Typing with Neural Pairwise Conditional Random Field

Ultra-fine entity typing (UFET) aims to predict a wide range of type phrases that correctly describe the categories of a given entity mention in a sentence. Most recent works infer each entity type independently, ignoring the correlations between types, e.g., when an entity is inferred as a president, it should also be a politician and a leader. To this end, we use an undirected graphical model called pairwise conditional random field (PCRF) to formulate the UFET problem, in which the type variables are not only unarily influenced by the input but also pairwisely relate to all the other type variables. We use various modern backbones for entity typing to compute unary potentials, and derive pairwise potentials from type phrase representations that both capture prior semantic information and facilitate accelerated inference. We use mean-field variational inference for efficient type inference on very large type sets and unfold it as a neural network module to enable end-to-end training. Experiments on UFET show that the Neural-PCRF consistently outperforms its backbones with little cost and results in a competitive performance against cross-encoder based SOTA while being thousands of times faster. We also find Neural- PCRF effective on a widely used fine-grained entity typing dataset with a smaller type set. We pack Neural-PCRF as a network module that can be plugged onto multi-label type classifiers with ease and release it in https://github.com/modelscope/adaseq/tree/master/examples/NPCRF.