Katsuhiko Hayashi

Shintaro Ozaki, Kazuki Hayashi, Yusuke Sakai et al.

As the performance of Large-scale Vision Language Models (LVLMs) improves, they are increasingly capable of responding in multiple languages, and there is an expectation that the demand for explanations generated by LVLMs will grow. However, pre-training of Vision Encoder and the integrated training of LLMs with Vision Encoder are mainly conducted using English training data, leaving it uncertain whether LVLMs can completely handle their potential when generating explanations in languages other than English. In addition, multilingual QA benchmarks that create datasets using machine translation have cultural differences and biases, remaining issues for use as evaluation tasks. To address these challenges, this study created an extended dataset in multiple languages without relying on machine translation. This dataset that takes into account nuances and country-specific phrases was then used to evaluate the generation explanation abilities of LVLMs. Furthermore, this study examined whether Instruction-Tuning in resource-rich English improves performance in other languages. Our findings indicate that LVLMs perform worse in languages other than English compared to English. In addition, it was observed that LVLMs struggle to effectively manage the knowledge learned from English data. Our dataset is available at https://huggingface.co/datasets/naist-nlp/MultiExpArt

Hidetaka Kamigaito, Katsuhiko Hayashi

Negative sampling (NS) loss plays an important role in learning knowledge graph embedding (KGE) to handle a huge number of entities. However, the performance of KGE degrades without hyperparameters such as the margin term and number of negative samples in NS loss being appropriately selected. Currently, empirical hyperparameter tuning addresses this problem at the cost of computational time. To solve this problem, we theoretically analyzed NS loss to assist hyperparameter tuning and understand the better use of the NS loss in KGE learning. Our theoretical analysis showed that scoring methods with restricted value ranges, such as TransE and RotatE, require appropriate adjustment of the margin term or the number of negative samples different from those without restricted value ranges, such as RESCAL, ComplEx, and DistMult. We also propose subsampling methods specialized for the NS loss in KGE studied from a theoretical aspect. Our empirical analysis on the FB15k-237, WN18RR, and YAGO3-10 datasets showed that the results of actually trained models agree with our theoretical findings.

Xincan Feng, Hidetaka Kamigaito, Katsuhiko Hayashi et al.

Subsampling is effective in Knowledge Graph Embedding (KGE) for reducing overfitting caused by the sparsity in Knowledge Graph (KG) datasets. However, current subsampling approaches consider only frequencies of queries that consist of entities and their relations. Thus, the existing subsampling potentially underestimates the appearance probabilities of infrequent queries even if the frequencies of their entities or relations are high. To address this problem, we propose Model-based Subsampling (MBS) and Mixed Subsampling (MIX) to estimate their appearance probabilities through predictions of KGE models. Evaluation results on datasets FB15k-237, WN18RR, and YAGO3-10 showed that our proposed subsampling methods actually improved the KG completion performances for popular KGE models, RotatE, TransE, HAKE, ComplEx, and DistMult.

Hidetaka Kamigaito, Katsuhiko Hayashi, Taro Watanabe

In this paper, we propose a table and image generation task to verify how the knowledge about entities acquired from natural language is retained in Vision & Language (V&L) models. This task consists of two parts: the first is to generate a table containing knowledge about an entity and its related image, and the second is to generate an image from an entity with a caption and a table containing related knowledge of the entity. In both tasks, the model must know the entities used to perform the generation properly. We created the Wikipedia Table and Image Generation (WikiTIG) dataset from about 200,000 infoboxes in English Wikipedia articles to perform the proposed tasks. We evaluated the performance on the tasks with respect to the above research question using the V&L model OFA, which has achieved state-of-the-art results in multiple tasks. Experimental results show that OFA forgets part of its entity knowledge by pre-training as a complement to improve the performance of image related tasks.

Xincan Feng, Hidetaka Kamigaito, Katsuhiko Hayashi et al.

Knowledge Graphs (KGs) are fundamental resources in knowledge-intensive tasks in NLP. Due to the limitation of manually creating KGs, KG Completion (KGC) has an important role in automatically completing KGs by scoring their links with KG Embedding (KGE). To handle many entities in training, KGE relies on Negative Sampling (NS) loss that can reduce the computational cost by sampling. Since the appearance frequencies for each link are at most one in KGs, sparsity is an essential and inevitable problem. The NS loss is no exception. As a solution, the NS loss in KGE relies on smoothing methods like Self-Adversarial Negative Sampling (SANS) and subsampling. However, it is uncertain what kind of smoothing method is suitable for this purpose due to the lack of theoretical understanding. This paper provides theoretical interpretations of the smoothing methods for the NS loss in KGE and induces a new NS loss, Triplet Adaptive Negative Sampling (TANS), that can cover the characteristics of the conventional smoothing methods. Experimental results of TransE, DistMult, ComplEx, RotatE, HAKE, and HousE on FB15k-237, WN18RR, and YAGO3-10 datasets and their sparser subsets show the soundness of our interpretation and performance improvement by our TANS.

Yusuke Sakai, Hidetaka Kamigaito, Katsuhiko Hayashi et al.

Knowledge graphs (KGs) consist of links that describe relationships between entities. Due to the difficulty of manually enumerating all relationships between entities, automatically completing them is essential for KGs. Knowledge Graph Completion (KGC) is a task that infers unseen relationships between entities in a KG. Traditional embedding-based KGC methods, such as RESCAL, TransE, DistMult, ComplEx, RotatE, HAKE, HousE, etc., infer missing links using only the knowledge from training data. In contrast, the recent Pre-trained Language Model (PLM)-based KGC utilizes knowledge obtained during pre-training. Therefore, PLM-based KGC can estimate missing links between entities by reusing memorized knowledge from pre-training without inference. This approach is problematic because building KGC models aims to infer unseen links between entities. However, conventional evaluations in KGC do not consider inference and memorization abilities separately. Thus, a PLM-based KGC method, which achieves high performance in current KGC evaluations, may be ineffective in practical applications. To address this issue, we analyze whether PLM-based KGC methods make inferences or merely access memorized knowledge. For this purpose, we propose a method for constructing synthetic datasets specified in this analysis and conclude that PLMs acquire the inference abilities required for KGC through pre-training, even though the performance improvements mostly come from textual information of entities and relations.

Hidetaka Kamigaito, Katsuhiko Hayashi

In this article, we explain the recent advance of subsampling methods in knowledge graph embedding (KGE) starting from the original one used in word2vec.

Ken Nishida, Kojiro Machi, Kazuma Onishi et al.

The extreme multi-label classification~(XMC) task involves learning a classifier that can predict from a large label set the most relevant subset of labels for a data instance. While deep neural networks~(DNNs) have demonstrated remarkable success in XMC problems, the task is still challenging because it must deal with a large number of output labels, which make the DNN training computationally expensive. This paper addresses the issue by exploring the use of random circular vectors, where each vector component is represented as a complex amplitude. In our framework, we can develop an output layer and loss function of DNNs for XMC by representing the final output layer as a fully connected layer that directly predicts a low-dimensional circular vector encoding a set of labels for a data instance. We conducted experiments on synthetic datasets to verify that circular vectors have better label encoding capacity and retrieval ability than normal real-valued vectors. Then, we conducted experiments on actual XMC datasets and found that these appealing properties of circular vectors contribute to significant improvements in task performance compared with a previous model using random real-valued vectors, while reducing the size of the output layers by up to 99%.

Kazuki Hayashi, Yusuke Sakai, Hidetaka Kamigaito et al.

Large-scale vision-language models (LVLMs) output text from images and instructions, demonstrating advanced capabilities in text generation and comprehension. However, it has not been clarified to what extent LVLMs understand the knowledge necessary for explaining images, the complex relationships between various pieces of knowledge, and how they integrate these understandings into their explanations. To address this issue, we propose a new task: the artwork explanation generation task, along with its evaluation dataset and metric for quantitatively assessing the understanding and utilization of knowledge about artworks. This task is apt for image description based on the premise that LVLMs are expected to have pre-existing knowledge of artworks, which are often subjects of wide recognition and documented information. It consists of two parts: generating explanations from both images and titles of artworks, and generating explanations using only images, thus evaluating the LVLMs' language-based and vision-based knowledge. Alongside, we release a training dataset for LVLMs to learn explanations that incorporate knowledge about artworks. Our findings indicate that LVLMs not only struggle with integrating language and visual information but also exhibit a more pronounced limitation in acquiring knowledge from images alone. The datasets (ExpArt=Explain Artworks) are available at https://huggingface.co/datasets/naist-nlp/ExpArt.

Hidetaka Kamigaito, Hiroyuki Deguchi, Yusuke Sakai et al.

Inference methods play an important role in eliciting the performance of large language models (LLMs). Currently, LLMs use inference methods utilizing generated multiple samples, which can be derived from Minimum Bayes Risk (MBR) Decoding. Previous studies have conducted empirical analyses to clarify the improvements in generation performance achieved by MBR decoding and have reported various observations. However, the theoretical underpinnings of these findings remain uncertain. To address this, we offer a new theoretical interpretation of MBR decoding from the perspective of bias-diversity decomposition. In this interpretation, the error in the quality estimation of hypotheses by MBR decoding is decomposed into two main factors: bias, which considers the closeness between the utility function and human evaluation, and diversity, which represents the variability in the quality estimation of the utility function. The theoretical analysis reveals the difficulty of simultaneously improving bias and diversity, confirming the validity of enhancing MBR decoding performance by increasing diversity. Furthermore, we reveal that diversity can explain one aspect of inference scaling laws that describe performance improvement by increasing sample size. Moreover, experiments across multiple NLP tasks yielded results consistent with these theoretical characteristics. Our code is available at https://github.com/naist-nlp/mbr-bias-diversity.

Katsuhiko Hayashi, Hidetaka Kamigaito

We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments confirm perfect separability under noise-free conditions, while real-data experiments on English morphology show that learned features align with well-known linguistic constraints. These results demonstrate that the subregular hierarchy provides a rigorous and interpretable foundation for modeling natural language structure. Our code used in real-data experiments is available at https://github.com/UTokyo-HayashiLab/subregular.

Kazuma Onishi, Katsuhiko Hayashi

Extreme multi-label learning (XML) is a task of assigning multiple labels from an extremely large set of labels to each data instance. Many current high-performance XML models are composed of a lot of hyperparameters, which complicates the tuning process. Additionally, the models themselves are adapted specifically to XML, which complicates their reimplementation. To remedy this problem, we propose a simple method based on ridge regression for XML. The proposed method not only has a closed-form solution but also is composed of a single hyperparameter. Since there are no precedents on applying ridge regression to XML, this paper verified the performance of the method by using various XML benchmark datasets. Furthermore, we enhanced the prediction of low-frequency labels in XML, which hold informative content. This prediction is essential yet challenging because of the limited amount of data. Here, we employed a simple frequency-based weighting. This approach greatly simplifies the process compared with existing techniques. Experimental results revealed that it can achieve levels of performance comparable to, or even exceeding, those of models with numerous hyperparameters. Additionally, we found that the frequency-based weighting significantly improved the predictive performance for low-frequency labels, while requiring almost no changes in implementation. The source code for the proposed method is available on github at https://github.com/cars1015/XML-ridge.

Katsuhiko Hayashi, Kazuma Onishi

Recently, in the field of recommendation systems, linear regression (autoencoder) models have been investigated as a way to learn item similarity. In this paper, we show a connection between a linear autoencoder model and ZCA whitening for recommendation data. In particular, we show that the dual form solution of a linear autoencoder model actually has ZCA whitening effects on feature vectors of items, while items are considered as input features in the primal problem of the autoencoder/regression model. We also show the correctness of applying a linear autoencoder to low-dimensional item vectors obtained using embedding methods such as Item2vec to estimate item-item similarities. Our experiments provide preliminary results indicating the effectiveness of whitening low-dimensional item embeddings.

Shintaro Ozaki, Yuta Kato, Siyuan Feng et al.

Retrieval Augmented Generation (RAG) complements the knowledge of Large Language Models (LLMs) by leveraging external information to enhance response accuracy for queries. This approach is widely applied in several fields by taking its advantage of injecting the most up-to-date information, and researchers are focusing on understanding and improving this aspect to unlock the full potential of RAG in such high-stakes applications. However, despite the potential of RAG to address these needs, the mechanisms behind the confidence levels of its outputs remain underexplored. Our study focuses on the impact of RAG, specifically examining whether RAG improves the confidence of LLM outputs in the medical domain. We conduct this analysis across various configurations and models. We evaluate confidence by treating the model's predicted probability as its output and calculating several evaluation metrics which include calibration error method, entropy, the best probability, and accuracy. Experimental results across multiple datasets confirmed that certain models possess the capability to judge for themselves whether an inserted document relates to the correct answer. These results suggest that evaluating models based on their output probabilities determine whether they function as generators in the RAG framework. Our approach allows us to evaluate whether the models handle retrieved documents.

Shintaro Ozaki, Wataru Hashimoto, Hidetaka Kamigaito et al.

While large language models (LLMs) improve performance by explicit reasoning, their responses are often overconfident, even though they include linguistic expressions demonstrating uncertainty. In this work, we identify what linguistic expressions are related to confidence by applying the regression method. Specifically, we predict confidence of those linguistic expressions in the reasoning parts of LLMs as the dependent variables and analyze the relationship between a specific $n$-gram and confidence. Across multiple models and QA benchmarks, we show that LLMs remain overconfident when reasoning is involved and attribute this behavior to specific linguistic information. Interestingly, several of the extracted expressions coincide with cue phrases intentionally inserted on test-time scaling to improve reasoning performance. Through our test on causality and verification that the extracted linguistic information truly affects confidence, we reveal that confidence calibration is possible by simply suppressing those overconfident expressions without drops in performance.

Hidetaka Kamigaito, Ying Zhang, Jingun Kwon et al.

Transformers deliver outstanding performance across a wide range of tasks and are now a dominant backbone architecture for large language models (LLMs). Their task-solving performance is improved by increasing parameter size, as shown in the recent studies on parameter scaling laws. Although recent mechanistic-interpretability studies have deepened our understanding of the internal behavior of Transformers by analyzing their residual stream, the relationship between these internal mechanisms and the parameter scaling laws remains unclear. To bridge this gap, we focus on layers and their size, which mainly decide the parameter size of Transformers. For this purpose, we first theoretically investigate the layers within the residual stream through a bias-diversity decomposition. The decomposition separates (i) bias, the error of each layer's output from the ground truth, and (ii) diversity, which indicates how much the outputs of each layer differ from each other. Analyzing Transformers under this theory reveals that performance improves when individual layers make predictions close to the correct answer and remain mutually diverse. We show that diversity becomes especially critical when individual layers' outputs are far from the ground truth. Finally, we introduce an information-theoretic diversity and show our main findings that adding layers enhances performance only when those layers behave differently, i.e., are diverse. We also reveal the performance gains from increasing the number of layers exhibit submodularity: marginal improvements diminish as additional layers increase, mirroring the logarithmic convergence predicted by the parameter scaling laws. Experiments on multiple semantic-understanding tasks with various LLMs empirically confirm the theoretical properties derived in this study.

Shintaro Ozaki, Kazuki Hayashi, Yusuke Sakai et al.

Generating images from prompts containing specific entities requires models to retain as much entity-specific knowledge as possible. However, fully memorizing such knowledge is impractical due to the vast number of entities and their continuous emergence. To address this, we propose Text-based Intelligent Generation with Entity prompt Refinement (TextTIGER), which augments knowledge on entities included in the prompts and then summarizes the augmented descriptions using Large Language Models (LLMs) to mitigate performance degradation from longer inputs. To evaluate our method, we introduce WiT-Cub (WiT with Captions and Uncomplicated Background-explanations), a dataset comprising captions, images, and an entity list. Experiments on four image generation models and five LLMs show that TextTIGER improves image generation performance in standard metrics (IS, FID, and CLIPScore) compared to caption-only prompts. Additionally, multiple annotators' evaluation confirms that the summarized descriptions are more informative, validating LLMs' ability to generate concise yet rich descriptions. These findings demonstrate that refining prompts with augmented and summarized entity-related descriptions enhances image generation capabilities. The code and dataset will be available upon acceptance.

Masayo Tomita, Katsuhiko Hayashi, Tomoyuki Kaneko

Vision-Language Models (VLMs) occasionally generate outputs that contradict input images, constraining their reliability in real-world applications. While visual prompting is reported to suppress hallucinations by augmenting prompts with relevant area inside an image, the effectiveness in terms of the area remains uncertain. This study analyzes success and failure cases of Attention-driven visual prompting in object hallucination, revealing that preserving background context is crucial for mitigating object hallucination.

Takashi Harada, Takehiro Motomitsu, Katsuhiko Hayashi et al.

In recent years, there has been a notable increase in research on machine learning models for music retrieval and generation systems that are capable of taking natural language sentences as inputs. However, there is a scarcity of large-scale publicly available datasets, consisting of music data and their corresponding natural language descriptions known as music captions. In particular, non-musical information such as suitable situations for listening to a track and the emotions elicited upon listening is crucial for describing music. This type of information is underrepresented in existing music caption datasets due to the challenges associated with extracting it directly from music data. To address this issue, we propose a method for generating music caption data that incorporates non-musical aspects inferred from music thumbnail images, and validated the effectiveness of our approach through human evaluations. Additionally, we created a dataset with approximately 360,000 captions containing non-musical aspects. Leveraging this dataset, we trained a music retrieval model and demonstrated its effectiveness in music retrieval tasks through evaluation.

Siyuan Feng, Teruya Yoshinaga, Katsuhiko Hayashi et al.

Today, manga has gained worldwide popularity. However, the question of how various elements of manga, such as characters, text, and panel layouts, reflect the uniqueness of a particular work, or even define it, remains an unexplored area. In this paper, we aim to quantitatively and qualitatively analyze the visual characteristics of manga works, with a particular focus on panel layout features. As a research method, we used facing page images of manga as input to train a deep learning model for predicting manga titles, examining classification accuracy to quantitatively analyze these features. Specifically, we conducted ablation studies by limiting page image information to panel frames to analyze the characteristics of panel layouts. Through a series of quantitative experiments using all 104 works, 12 genres, and 10,122 facing page images from the Manga109 dataset, as well as qualitative analysis using Grad-CAM, our study demonstrates that the uniqueness of manga works is strongly reflected in their panel layouts.

Kazuki Hayashi, Kazuma Onishi, Toma Suzuki et al.

Large-scale Vision-Language Models (LVLMs) process both images and text, excelling in multimodal tasks such as image captioning and description generation. However, while these models excel at generating factual content, their ability to generate and evaluate texts reflecting perspectives on the same image, depending on the context, has not been sufficiently explored. To address this, we propose IRR: Image Review Rank, a novel evaluation framework designed to assess critic review texts from multiple perspectives. IRR evaluates LVLMs by measuring how closely their judgments align with human interpretations. We validate it using a dataset of images from 15 categories, each with five critic review texts and annotated rankings in both English and Japanese, totaling over 2,000 data instances. The datasets are available at https://hf.co/datasets/naist-nlp/Wiki-ImageReview1.0. Our results indicate that, although LVLMs exhibited consistent performance across languages, their correlation with human annotations was insufficient, highlighting the need for further advancements. These findings highlight the limitations of current evaluation methods and the need for approaches that better capture human reasoning in Vision & Language tasks.

Hidetaka Kamigaito, Katsuhiko Hayashi

In knowledge graph embedding, the theoretical relationship between the softmax cross-entropy and negative sampling loss functions has not been investigated. This makes it difficult to fairly compare the results of the two different loss functions. We attempted to solve this problem by using the Bregman divergence to provide a unified interpretation of the softmax cross-entropy and negative sampling loss functions. Under this interpretation, we can derive theoretical findings for fair comparison. Experimental results on the FB15k-237 and WN18RR datasets show that the theoretical findings are valid in practical settings.

Akiko Aizawa, Frederic Bergeron, Junjie Chen et al.

The global pandemic of COVID-19 has made the public pay close attention to related news, covering various domains, such as sanitation, treatment, and effects on education. Meanwhile, the COVID-19 condition is very different among the countries (e.g., policies and development of the epidemic), and thus citizens would be interested in news in foreign countries. We build a system for worldwide COVID-19 information aggregation containing reliable articles from 10 regions in 7 languages sorted by topics. Our reliable COVID-19 related website dataset collected through crowdsourcing ensures the quality of the articles. A neural machine translation module translates articles in other languages into Japanese and English. A BERT-based topic-classifier trained on our article-topic pair dataset helps users find their interested information efficiently by putting articles into different categories.

Koki Kishimoto, Katsuhiko Hayashi, Genki Akai et al.

Methods based on vector embeddings of knowledge graphs have been actively pursued as a promising approach to knowledge graph completion.However, embedding models generate storage-inefficient representations, particularly when the number of entities and relations, and the dimensionality of the real-valued embedding vectors are large. We present a binarized CANDECOMP/PARAFAC(CP) decomposition algorithm, which we refer to as B-CP, where real-valued parameters are replaced by binary values to reduce model size. Moreover, we show that a fast score computation technique can be developed with bitwise operations. We prove that B-CP is fully expressive by deriving a bound on the size of its embeddings. Experimental results on several benchmark datasets demonstrate that the proposed method successfully reduces model size by more than an order of magnitude while maintaining task performance at the same level as the real-valued CP model.

Katsuhiko Hayashi, Masashi Shimbo

Bilinear diagonal models for knowledge graph embedding (KGE), such as DistMult and ComplEx, balance expressiveness and computational efficiency by representing relations as diagonal matrices. Although they perform well in predicting atomic relations, composite relations (relation paths) cannot be modeled naturally by the product of relation matrices, as the product of diagonal matrices is commutative and hence invariant with the order of relations. In this paper, we propose a new bilinear KGE model, called BlockHolE, based on block circulant matrices. In BlockHolE, relation matrices can be non-commutative, allowing composite relations to be modeled by matrix product. The model is parameterized in a way that covers a spectrum ranging from diagonal to full relation matrices. A fast computation technique is developed on the basis of the duality of the Fourier transform of circulant matrices.

Koki Kishimoto, Katsuhiko Hayashi, Genki Akai et al.

Tensor factorization has become an increasingly popular approach to knowledge graph completion(KGC), which is the task of automatically predicting missing facts in a knowledge graph. However, even with a simple model like CANDECOMP/PARAFAC(CP) tensor decomposition, KGC on existing knowledge graphs is impractical in resource-limited environments, as a large amount of memory is required to store parameters represented as 32-bit or 64-bit floating point numbers. This limitation is expected to become more stringent as existing knowledge graphs, which are already huge, keep steadily growing in scale. To reduce the memory requirement, we present a method for binarizing the parameters of the CP tensor decomposition by introducing a quantization function to the optimization problem. This method replaces floating point-valued parameters with binary ones after training, which drastically reduces the model size at run time. We investigate the trade-off between the quality and size of tensor factorization models for several KGC benchmark datasets. In our experiments, the proposed method successfully reduced the model size by more than an order of magnitude while maintaining the task performance. Moreover, a fast score computation technique can be developed with bitwise operations.

Tomoki Matsuno, Katsuhiko Hayashi, Takahiro Ishihara et al.

Currently, the biaffine classifier has been attracting attention as a method to introduce an attention mechanism into the modeling of binary relations. For instance, in the field of dependency parsing, the Deep Biaffine Parser by Dozat and Manning has achieved state-of-the-art performance as a graph-based dependency parser on the English Penn Treebank and CoNLL 2017 shared task. On the other hand, it is reported that parameter redundancy in the weight matrix in biaffine classifiers, which has O(n^2) parameters, results in overfitting (n is the number of dimensions). In this paper, we attempted to reduce the parameter redundancy by assuming either symmetry or circularity of weight matrices. In our experiments on the CoNLL 2017 shared task dataset, our model achieved better or comparable accuracy on most of the treebanks with more than 16% parameter reduction.

Hitoshi Manabe, Katsuhiko Hayashi, Masashi Shimbo

Embedding-based methods for knowledge base completion (KBC) learn representations of entities and relations in a vector space, along with the scoring function to estimate the likelihood of relations between entities. The learnable class of scoring functions is designed to be expressive enough to cover a variety of real-world relations, but this expressive comes at the cost of an increased number of parameters. In particular, parameters in these methods are superfluous for relations that are either symmetric or antisymmetric. To mitigate this problem, we propose a new L1 regularizer for Complex Embeddings, which is one of the state-of-the-art embedding-based methods for KBC. This regularizer promotes symmetry or antisymmetry of the scoring function on a relation-by-relation basis, in accordance with the observed data. Our empirical evaluation shows that the proposed method outperforms the original Complex Embeddings and other baseline methods on the FB15k dataset.

Katsuhiko Hayashi, Masashi Shimbo

We show the equivalence of two state-of-the-art link prediction/knowledge graph completion methods: Nickel et al's holographic embedding and Trouillon et al.'s complex embedding. We first consider a spectral version of the holographic embedding, exploiting the frequency domain in the Fourier transform for efficient computation. The analysis of the resulting method reveals that it can be viewed as an instance of the complex embedding with certain constraints cast on the initial vectors upon training. Conversely, any complex embedding can be converted to an equivalent holographic embedding.