Fourier Learning Machines: Nonharmonic Fourier-Based Neural Networks for Scientific Machine Learning

We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn the frequencies, amplitudes, and phase shifts of the series as trainable parameters. This design allows the model to create a problem-specific spectral basis adaptable to both periodic and nonperiodic functions. Unlike previous Fourier-inspired NN models, the FLM is the first architecture able to represent a complete, separable Fourier basis in multiple dimensions using a standard Multilayer Perceptron-like architecture. A one-to-one correspondence between the Fourier coefficients and amplitudes and phase-shifts is demonstrated, allowing for the translation between a full, separable basis form and the cosine phase--shifted one. Additionally, we evaluate the performance of FLMs on several scientific computing problems, including benchmark Partial Differential Equations (PDEs) and a family of Optimal Control Problems (OCPs). Computational experiments show that the performance of FLMs is comparable, and often superior, to that of established architectures like SIREN and vanilla feedforward NNs.

The Role of Handling Attributive Nouns in Improving Chinese-To-English Machine Translation

Translating between languages with drastically different grammatical conventions poses challenges, not just for human interpreters but also for machine translation systems. In this work, we specifically target the translation challenges posed by attributive nouns in Chinese, which frequently cause ambiguities in English translation. By manually inserting the omitted particle X ('DE'). In news article titles from the Penn Chinese Discourse Treebank, we developed a targeted dataset to fine-tune Hugging Face Chinese to English translation models, specifically improving how this critical function word is handled. This focused approach not only complements the broader strategies suggested by previous studies but also offers a practical enhancement by specifically addressing a common error type in Chinese-English translation.

Semantic Role Labeling of NomBank Partitives

This article is about Semantic Role Labeling for English partitive nouns (5%/REL of the price/ARG1; The price/ARG1 rose 5 percent/REL) in the NomBank annotated corpus. Several systems are described using traditional and transformer-based machine learning, as well as ensembling. Our highest scoring system achieves an F1 of 91.74% using "gold" parses from the Penn Treebank and 91.12% when using the Berkeley Neural parser. This research includes both classroom and experimental settings for system development.

Classification of US Supreme Court Cases using BERT-Based Techniques

Models based on bidirectional encoder representations from transformers (BERT) produce state of the art (SOTA) results on many natural language processing (NLP) tasks such as named entity recognition (NER), part-of-speech (POS) tagging etc. An interesting phenomenon occurs when classifying long documents such as those from the US supreme court where BERT-based models can be considered difficult to use on a first-pass or out-of-the-box basis. In this paper, we experiment with several BERT-based classification techniques for US supreme court decisions or supreme court database (SCDB) and compare them with the previous SOTA results. We then compare our results specifically with SOTA models for long documents. We compare our results for two classification tasks: (1) a broad classification task with 15 categories and (2) a fine-grained classification task with 279 categories. Our best result produces an accuracy of 80\% on the 15 broad categories and 60\% on the fine-grained 279 categories which marks an improvement of 8\% and 28\% respectively from previously reported SOTA results.

Comlex Syntax: Building a Computational Lexicon

We describe the design of Comlex Syntax, a computational lexicon providing detailed syntactic information for approximately 38,000 English headwords. We consider the types of errors which arise in creating such a lexicon, and how such errors can be measured and controlled.