Fourier methods have a long and proven track record as an excellent tool in data processing. We propose to integrate Fourier methods into complex recurrent neural network architectures and show accuracy improvements on prediction tasks as well as computational load reductions. We predict synthetic data drawn from synthetic-equations as well as real world power load data.
In machine learning, Fourier analysis is mostly associated with signal-processing heavy domains such as speech recognition @cite_1 , medical imaging @cite_21 and audio-processing @cite_25 @cite_12 . Recently, a comparison @cite_11 of the time versus frequency domain for audio event recognition with neural networks showed the discriminative gains of processing sound in the frequency domain.
@cite_21 @cite_1 @cite_25 @cite_12 @cite_11
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The task of MRI fingerprinting is to identify tissue parameters from complex-valued MRI signals. The prevalent approach is dictionary based, where a test MRI signal is compared to stored MRI signals with known tissue parameters and the most similar signals and tissue parameters retrieved. Such an approach does not scale with the number of parameters and is rather slow when the tissue parameter space is large. Our first novel contribution is to use deep learning as an efficient nonlinear inverse mapping approach. We generate synthetic (tissue, MRI) data from an MRI simulator, and use them to train a deep net to map the MRI signal to the tissue parameters directly. Our second novel contribution is to develop a complex-valued neural network with new cardioid activation functions. Our results demonstrate that complex-valued neural nets could be much more accurate than real-valued neural nets at complex-valued MRI fingerprinting. We present Listen, Attend and Spell (LAS), a neural speech recognizer that transcribes speech utterances directly to characters without pronunciation models, HMMs or other components of traditional speech recognizers. In LAS, the neural network architecture subsumes the acoustic, pronunciation and language models making it not only an end-to-end trained system but an end-to-end model. In contrast to DNN-HMM, CTC and most other models, LAS makes no independence assumptions about the probability distribution of the output character sequences given the acoustic sequence. Our system has two components: a listener and a speller. The listener is a pyramidal recurrent network encoder that accepts filter bank spectra as inputs. The speller is an attention-based recurrent network decoder that emits each character conditioned on all previous characters, and the entire acoustic sequence. On a Google voice search task, LAS achieves a WER of 14.1 without a dictionary or an external language model and 10.3 with language model rescoring over the top 32 beams. In comparison, the state-of-the-art CLDNN-HMM model achieves a WER of 8.0 on the same set. Content-based music information retrieval tasks have traditionally been solved using engineered features and shallow processing architectures. In recent years, there has been increasing interest in using feature learning and deep architectures instead, thus reducing the required engineering effort and the need for prior knowledge. However, this new approach typically still relies on mid-level representations of music audio, e.g. spectrograms, instead of raw audio signals. In this paper, we investigate whether it is possible to apply feature learning directly to raw audio signals. We train convolutional neural networks using both approaches and compare their performance on an automatic tagging task. Although they do not outperform a spectrogram-based approach, the networks are able to autonomously discover frequency decompositions from raw audio, as well as phase-and translation-invariant feature representations. This paper introduces a new large-scale music dataset, MusicNet, to serve as a source of supervision and evaluation of machine learning methods for music research. MusicNet consists of hundreds of freely-licensed classical music recordings by 10 composers, written for 11 instruments, together with instrument note annotations resulting in over 1 million temporal labels on 34 hours of chamber music performances under various studio and microphone conditions. @PARASPLIT The paper defines a multi-label classification task to predict notes in musical recordings, along with an evaluation protocol, and benchmarks several machine learning architectures for this task: i) learning from spectrogram features; ii) end-to-end learning with a neural net; iii) end-to-end learning with a convolutional neural net. These experiments show that end-to-end models trained for note prediction learn frequency selective filters as a low-level representation of audio. Recognizing acoustic events is an intricate problem for a machine and an emerging field of research. Deep neural networks achieve convincing results and are currently the state-of-the-art approach for many tasks. One advantage is their implicit feature learning, opposite to an explicit feature extraction of the input signal. In this work, we analyzed whether more discriminative features can be learned from either the time-domain or the frequency-domain representation of the audio signal. For this purpose, we trained multiple deep networks with different architectures on the Freiburg-106 and ESC-10 datasets. Our results show that feature learning from the frequency domain is superior to the time domain. Moreover, additionally using convolution and pooling layers, to explore local structures of the audio signal, significantly improves the recognition performance and achieves state-of-the-art results.