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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Related Experiment Video

Updated: Feb 4, 2026

Cloud-Based Phrase Mining and Analysis of User-Defined Phrase-Category Association in Biomedical Publications
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Alignment-Supervised Bidimensional Attention-Based Recursive Autoencoders for Bilingual Phrase Representation.

Biao Zhang, Deyi Xiong, Jinsong Su

    IEEE Transactions on Cybernetics
    |October 2, 2018
    PubMed
    Summary

    We developed alignment-supervised bidimensional attention-based recursive autoencoders (ABattRAE) to create better bilingual phrase embeddings. This method significantly improves machine translation performance by capturing semantic interactions.

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    Area of Science:

    • Natural Language Processing
    • Machine Learning
    • Computational Linguistics

    Background:

    • Generating effective bilingual phrase embeddings is essential for cross-lingual tasks.
    • Existing methods struggle to capture nuanced semantic interactions between phrases in different languages.
    • Hierarchical phrase structures offer a promising avenue for richer representations.

    Purpose of the Study:

    • To propose a novel model, alignment-supervised bidimensional attention-based recursive autoencoders (ABattRAE), for learning bilingual phrase embeddings.
    • To leverage semantic interactions at various granularities for improved representation quality.
    • To enhance machine translation systems through better bilingual phrase understanding.

    Main Methods:

    • Employing two recursive autoencoders to derive hierarchical tree structures for bilingual phrases.
    • Introducing a bidimensional attention network to quantify semantic matching between cross-lingual linguistic items.
    • Utilizing word alignments as supervision signals to refine attention weights during end-to-end training.
    • Optimizing for semantic similarity of translation equivalents and minimizing similarity for non-translation pairs.

    Main Results:

    • Achieved substantial improvements in BLEU scores on NIST Chinese-English (up to 2.86 points) and WMT English-German (up to 1.09 points) datasets.
    • Demonstrated superior performance in learning bilingual phrase embeddings compared to baseline methods.
    • Validated the effectiveness of the learned embeddings when integrated into a machine translation system for translation selection.

    Conclusions:

    • ABattRAE effectively captures semantic interactions between bilingual phrases through a novel attention mechanism.
    • The proposed model offers a significant advancement in bilingual phrase representation learning.
    • The integration of these enhanced embeddings leads to tangible improvements in machine translation quality.