In this paper, we focus on the prediction phase of a random forest and study the problem of representing a bag of decision trees using a smaller bag of decision trees, where we only consider binary decision problems on the binary domain and simple decision trees in which an internal node is limited to querying the Boolean value of a single variable. As a main result, we show that the majority function of $n$ variables can be represented by a bag of $T$ ($< n$) decision trees each with polynomial size if $n-T$ is a constant, where $n$ and $T$ must be odd (in order to avoid the tie break). We also show that a bag of $n$ decision trees can be represented by a bag of $T$ decision trees each with polynomial size if $n-T$ is a constant and a small classification error is allowed. A related result on the $k$-out-of-$n$ functions is presented too.

The generation of lyrics tightly connected to accompanying melodies involves establishing a mapping between musical notes and syllables of lyrics. This process requires a deep understanding of music constraints and semantic patterns at syllable-level, word-level, and sentence-level semantic meanings. However, pre-trained language models specifically designed at the syllable level are publicly unavailable. To solve these challenging issues, we propose to exploit fine-tuning character-level language models for syllable-level lyrics generation from symbolic melody. In particular, our method endeavors to incorporate linguistic knowledge of the language model into the beam search process of a syllable-level Transformer generator network. Additionally, by exploring ChatGPT-based evaluation for generated lyrics, along with human subjective evaluation, we demonstrate that our approach enhances the coherence and correctness of the generated lyrics, eliminating the need to train expensive new language models.

Lyrics-to-melody generation is an interesting and challenging topic in AI music research field. Due to the difficulty of learning the correlations between lyrics and melody, previous methods suffer from low generation quality and lack of controllability. Controllability of generative models enables human interaction with models to generate desired contents, which is especially important in music generation tasks towards human-centered AI that can facilitate musicians in creative activities. To address these issues, we propose a controllable lyrics-to-melody generation network, ConL2M, which is able to generate realistic melodies from lyrics in user-desired musical style. Our work contains three main novelties: 1) To model the dependencies of music attributes cross multiple sequences, inter-branch memory fusion (Memofu) is proposed to enable information flow between multi-branch stacked LSTM architecture; 2) Reference style embedding (RSE) is proposed to improve the quality of generation as well as control the musical style of generated melodies; 3) Sequence-level statistical loss (SeqLoss) is proposed to help the model learn sequence-level features of melodies given lyrics. Verified by evaluation metrics for music quality and controllability, initial study of controllable lyrics-to-melody generation shows better generation quality and the feasibility of interacting with users to generate the melodies in desired musical styles when given lyrics.

Table answering questions from business documents has many challenges that require understanding tabular structures, cross-document referencing, and additional numeric computations beyond simple search queries. This paper introduces a novel pipeline, named TabIQA, to answer questions about business document images. TabIQA combines state-of-the-art deep learning techniques 1) to extract table content and structural information from images and 2) to answer various questions related to numerical data, text-based information, and complex queries from structured tables. The evaluation results on VQAonBD 2023 dataset demonstrate the effectiveness of TabIQA in achieving promising performance in answering table-related questions. The TabIQA repository is available at https://github.com/phucty/itabqa.

Knowledge graph completion is an important task that aims to predict the missing relational link between entities. Knowledge graph embedding methods perform this task by representing entities and relations as embedding vectors and modeling their interactions to compute the matching score of each triple. Previous work has usually treated each embedding as a whole and has modeled the interactions between these whole embeddings, potentially making the model excessively expensive or requiring specially designed interaction mechanisms. In this work, we propose the multi-partition embedding interaction (MEI) model with block term format to systematically address this problem. MEI divides each embedding into a multi-partition vector to efficiently restrict the interactions. Each local interaction is modeled with the Tucker tensor format and the full interaction is modeled with the block term tensor format, enabling MEI to control the trade-off between expressiveness and computational cost, learn the interaction mechanisms from data automatically, and achieve state-of-the-art performance on the link prediction task. In addition, we theoretically study the parameter efficiency problem and derive a simple empirically verified criterion for optimal parameter trade-off. We also apply the framework of MEI to provide a new generalized explanation for several specially designed interaction mechanisms in previous models.

The trends of open science have enabled several open scholarly datasets which include millions of papers and authors. Managing, exploring, and utilizing such large and complicated datasets effectively are challenging. In recent years, the knowledge graph has emerged as a universal data format for representing knowledge about heterogeneous entities and their relationships. The knowledge graph can be modeled by knowledge graph embedding methods, which represent entities and relations as embedding vectors in semantic space, then model the interactions between these embedding vectors. However, the semantic structures in the knowledge graph embedding space are not well-studied, thus knowledge graph embedding methods are usually only used for knowledge graph completion but not data representation and analysis. In this paper, we propose to analyze these semantic structures based on the well-studied word embedding space and use them to support data exploration. We also define the semantic queries, which are algebraic operations between the embedding vectors in the knowledge graph embedding space, to solve queries such as similarity and analogy between the entities on the original datasets. We then design a general framework for data exploration by semantic queries and discuss the solution to some traditional scholarly data exploration tasks. We also propose some new interesting tasks that can be solved based on the uncanny semantic structures of the embedding space.

Knowledge graph is a popular format for representing knowledge, with many applications to semantic search engines, question-answering systems, and recommender systems. Real-world knowledge graphs are usually incomplete, so knowledge graph embedding methods, such as Canonical decomposition/Parallel factorization (CP), DistMult, and ComplEx, have been proposed to address this issue. These methods represent entities and relations as embedding vectors in semantic space and predict the links between them. The embedding vectors themselves contain rich semantic information and can be used in other applications such as data analysis. However, mechanisms in these models and the embedding vectors themselves vary greatly, making it difficult to understand and compare them. Given this lack of understanding, we risk using them ineffectively or incorrectly, particularly for complicated models, such as CP, with two role-based embedding vectors, or the state-of-the-art ComplEx model, with complex-valued embedding vectors. In this paper, we propose a multi-embedding interaction mechanism as a new approach to uniting and generalizing these models. We derive them theoretically via this mechanism and provide empirical analyses and comparisons between them. We also propose a new multi-embedding model based on quaternion algebra and show that it achieves promising results using popular benchmarks.