Canlin Zhang

Canlin Zhang, Xiuwen Liu

Link prediction is a crucial research area in knowledge graphs, with many downstream applications. In many real-world scenarios, inductive link prediction is required, where predictions have to be made among unseen entities. Embedding-based models usually need fine-tuning on new entity embeddings, and hence are difficult to be directly applied to inductive link prediction tasks. Logical rules captured by rule-based models can be directly applied to new entities with the same graph typologies, but the captured rules are discrete and usually lack generosity. Graph neural networks (GNNs) can generalize topological information to new graphs taking advantage of deep neural networks, which however may still need fine-tuning on new entity embeddings. In this paper, we propose SiaILP, a path-based model for inductive link prediction using siamese neural networks. Our model only depends on relation and path embeddings, which can be generalized to new entities without fine-tuning. Experiments show that our model achieves several new state-of-the-art performances in link prediction tasks using inductive versions of WN18RR, FB15k-237, and Nell995. Our code is available at \url{https://github.com/canlinzhang/SiaILP}.

Canlin Zhang, Xiuwen Liu

Deep neural networks trained through end-to-end learning have achieved remarkable success across various domains in the past decade. However, the end-to-end learning strategy, originally designed to minimize predictive loss in a black-box manner, faces two fundamental limitations: the struggle to form explainable representations in a self-supervised manner, and the inability to compress information rigorously following the Minimum Description Length (MDL) principle. These two limitations point to a deeper issue: an end-to-end learning model is not able to "understand" what it learns. In this paper, we establish a novel theory connecting these two limitations. We design the Spectrum VAE, a novel deep learning architecture whose minimum description length (MDL) can be rigorously evaluated. Then, we introduce the concept of latent dimension combinations, or what we term spiking patterns, and demonstrate that the observed spiking patterns should be as few as possible based on the training data in order for the Spectrum VAE to achieve the MDL. Finally, our theory demonstrates that when the MDL is achieved with respect to the given data distribution, the Spectrum VAE will naturally produce explainable latent representations of the data. In other words, explainable representations--or "understanding"--can emerge in a self-supervised manner simply by making the deep network obey the MDL principle. In our opinion, this also implies a deeper insight: To understand is to compress. At its core, our theory advocates for a shift in the training objective of deep networks: not only to minimize predictive loss, but also to minimize the description length regarding the given data. That is, a deep network should not only learn, but also understand what it learns. This work is entirely theoretical and aims to inspire future research toward self-supervised, explainable AI grounded in the MDL principle.

Canlin Zhang, Xiuwen Liu

Deep neural networks trained in an end-to-end manner are proven to be efficient in a wide range of machine learning tasks. However, there is one drawback of end-to-end learning: The learned features and information are implicitly represented in neural network parameters, which cannot be used as regularities, concepts or knowledge to explicitly represent the data probability distribution. To resolve this issue, we propose in this paper a new machine learning theory, which defines in mathematics what are regularities. Briefly, regularities are concise representations of the non-random features, or 'non-randomness' in the data probability distribution. Combining this with information theory, we claim that regularities can also be regarded as a small amount of information encoding a large amount of information. Our theory is based on spiking functions. That is, if a function can react to, or spike on specific data samples more frequently than random noise inputs, we say that such a function discovers non-randomness from the data distribution. Also, we say that the discovered non-randomness is encoded into regularities if the function is simple enough. Our theory also discusses applying multiple spiking functions to the same data distribution. In this process, we claim that the 'best' regularities, or the optimal spiking functions, are those who can capture the largest amount of information from the data distribution, and then encode the captured information in the most concise way. Theorems and hypotheses are provided to describe in mathematics what are 'best' regularities and optimal spiking functions. Finally, we propose a machine learning approach, which can potentially obtain the optimal spiking functions regarding the given dataset in practice.

Canlin Zhang, Chun-Nan Hsu, Yannis Katsis et al.

Discovering precise and interpretable rules from knowledge graphs is regarded as an essential challenge, which can improve the performances of many downstream tasks and even provide new ways to approach some Natural Language Processing research topics. In this paper, we present a fundamental theory for rule-based knowledge graph reasoning, based on which the connectivity dependencies in the graph are captured via multiple rule types. It is the first time for some of these rule types in a knowledge graph to be considered. Based on these rule types, our theory can provide precise interpretations to unknown triples. Then, we implement our theory by what we call the RuleDict model. Results show that our RuleDict model not only provides precise rules to interpret new triples, but also achieves state-of-the-art performances on one benchmark knowledge graph completion task, and is competitive on other tasks.

Canlin Zhang, Xiuwen Liu

In this paper, we provide a novel way to generate low dimensional vector embeddings for the noun and verb synsets in WordNet, where the hypernym-hyponym relationship is preserved in the embeddings. We call this embedding the Sense Spectrum (and Sense Spectra for embeddings). In order to create suitable labels for the training of sense spectra, we designed a new similarity measurement for noun and verb synsets in WordNet. We call this similarity measurement the Hypernym Intersection Similarity (HIS), since it compares the common and unique hypernyms between two synsets. Our experiments show that on the noun and verb pairs of the SimLex-999 dataset, HIS outperforms the three similarity measurements in WordNet. Moreover, to the best of our knowledge, the sense spectra provide the first dense synset embeddings that preserve the semantic relationships in WordNet.

Canlin Zhang, Xiuwen Liu, Daniel Bis

To improve the generalization of the representations for natural language processing tasks, words are commonly represented using vectors, where distances among the vectors are related to the similarity of the words. While word2vec, the state-of-the-art implementation of the skip-gram model, is widely used and improves the performance of many natural language processing tasks, its mechanism is not yet well understood. In this work, we derive the learning rules for the skip-gram model and establish their close relationship to competitive learning. In addition, we provide the global optimal solution constraints for the skip-gram model and validate them by experimental results.

Shaeke Salman, Canlin Zhang, Xiuwen Liu et al.

Understanding the underlying mechanisms that enable the empirical successes of deep neural networks is essential for further improving their performance and explaining such networks. Towards this goal, a specific question is how to explain the "surprising" behavior of the same over-parametrized deep neural networks that can generalize well on real datasets and at the same time "memorize" training samples when the labels are randomized. In this paper, we demonstrate that deep ReLU networks generalize from training samples to new points via piece-wise linear interpolation. We provide a quantified analysis on the generalization ability of a deep ReLU network: Given a fixed point $\mathbf{x}$ and a fixed direction in the input space $\mathcal{S}$, there is always a segment such that any point on the segment will be classified the same as the fixed point $\mathbf{x}$. We call this segment the $generalization \ interval$. We show that the generalization intervals of a ReLU network behave similarly along pairwise directions between samples of the same label in both real and random cases on the MNIST and CIFAR-10 datasets. This result suggests that the same interpolation mechanism is used in both cases. Additionally, for datasets using real labels, such networks provide a good approximation of the underlying manifold in the data, where the changes are much smaller along tangent directions than along normal directions. On the other hand, however, for datasets with random labels, generalization intervals along mid-lines of triangles with the same label are much smaller than those on the datasets with real labels, suggesting different behaviors along other directions. Our systematic experiments demonstrate for the first time that such deep neural networks generalize through the same interpolation and explain the differences between their performance on datasets with real and random labels.