A variety of contextualised language models have been proposed in the NLP community, which are trained on diverse corpora to produce numerous Neural Language Models (NLMs). However, different NLMs have reported different levels of performances in downstream NLP applications when used as text representations. We propose a sentence-level meta-embedding learning method that takes independently trained contextualised word embedding models and learns a sentence embedding that preserves the complementary strengths of the input source NLMs. Our proposed method is unsupervised and is not tied to a particular downstream task, which makes the learnt meta-embeddings in principle applicable to different tasks that require sentence representations. Specifically, we first project the token-level embeddings obtained by the individual NLMs and learn attention weights that indicate the contributions of source embeddings towards their token-level meta-embeddings. Next, we apply mean and max pooling to produce sentence-level meta-embeddings from token-level meta-embeddings. Experimental results on semantic textual similarity benchmarks show that our proposed unsupervised sentence-level meta-embedding method outperforms previously proposed sentence-level meta-embedding methods as well as a supervised baseline.

This paper introduces a new music signal processing method to extract multiple fundamental frequencies, which we call specmurt analysis. In contrast with cepstrum which is the inverse Fourier transform of log-scaled power spectrum with linear frequency, specmurt is defined as the inverse Fourier transform of linear power spectrum with log-scaled frequency. Assuming that all tones in a polyphonic sound have a common harmonic pattern, the sound spectrum can be regarded as a sum of linearly stretched common harmonic structures along frequency. In the log-frequency domain, it is formulated as the convolution of a common harmonic structure and the distribution density of the fundamental frequencies of multiple tones. The fundamental frequency distribution can be found by deconvolving the observed spectrum with the assumed common harmonic structure, where the common harmonic structure is given heuristically or quasi-optimized with an iterative algorithm. The efficiency of specmurt analysis is experimentally demonstrated through generation of a piano-roll-like display from a polyphonic music signal and automatic sound-to-MIDI conversion. Multipitch estimation accuracy is evaluated over several polyphonic music signals and compared with manually annotated MIDI data.