Oscillations enhance time-series prediction in reservoir computing with feedback

Reservoir computing, a machine learning framework used for modeling the brain, can predict temporal data with little observations and minimal computational resources. However, it is difficult to accurately reproduce the long-term target time series because the reservoir system becomes unstable. This predictive capability is required for a wide variety of time-series processing, including predictions of motor timing and chaotic dynamical systems. This study proposes oscillation-driven reservoir computing (ODRC) with feedback, where oscillatory signals are fed into a reservoir network to stabilize the network activity and induce complex reservoir dynamics. The ODRC can reproduce long-term target time series more accurately than conventional reservoir computing methods in a motor timing and chaotic time-series prediction tasks. Furthermore, it generates a time series similar to the target in the unexperienced period, that is, it can learn the abstract generative rules from limited observations. Given these significant improvements made by the simple and computationally inexpensive implementation, the ODRC would serve as a practical model of various time series data. Moreover, we will discuss biological implications of the ODRC, considering it as a model of neural oscillations and their cerebellar processors.

Positional Encoding Helps Recurrent Neural Networks Handle a Large Vocabulary

This study discusses the effects of positional encoding on recurrent neural networks (RNNs) utilizing synthetic benchmarks. Positional encoding "time-stamps" data points in time series and complements the capabilities of Transformer neural networks, which lack an inherent mechanism for representing the data order. By contrast, RNNs can encode the temporal information of data points on their own, rendering their use of positional encoding seemingly "redundant". Nonetheless, empirical investigations reveal the effectiveness of positional encoding even when coupled with RNNs, specifically for handling a large vocabulary that yields diverse observations. These findings pave the way for a new line of research on RNNs, concerning the combination of input-driven and autonomous time representation. Additionally, biological implications of the computational/simulational results are discussed, in the light of the affinity between the sinusoidal implementation of positional encoding and neural oscillations in biological brains.

Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discovery

We propose a new parameter-adaptive uncertainty-penalized Bayesian information criterion (UBIC) to prioritize the parsimonious partial differential equation (PDE) that sufficiently governs noisy spatial-temporal observed data with few reliable terms. Since the naive use of the BIC for model selection has been known to yield an undesirable overfitted PDE, the UBIC penalizes the found PDE not only by its complexity but also the quantified uncertainty, derived from the model supports' coefficient of variation in a probabilistic view. We also introduce physics-informed neural network learning as a simulation-based approach to further validate the selected PDE flexibly against the other discovered PDE. Numerical results affirm the successful application of the UBIC in identifying the true governing PDE. Additionally, we reveal an interesting effect of denoising the observed data on improving the trade-off between the BIC score and model complexity. Code is available at https://github.com/Pongpisit-Thanasutives/UBIC.

Noise-aware Physics-informed Machine Learning for Robust PDE Discovery

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying performance against noisy data, partly owing to suboptimal estimated derivatives and found PDE coefficients. We address the issues by introducing a noise-aware physics-informed machine learning (nPIML) framework to discover the governing PDE from data following arbitrary distributions. Our proposals are twofold. First, we propose a couple of neural networks, namely solver and preselector, which yield an interpretable neural representation of the hidden physical constraint. After they are jointly trained, the solver network approximates potential candidates, e.g., partial derivatives, which are then fed to the sparse regression algorithm that initially unveils the most likely parsimonious PDE, decided according to the information criterion. Second, we propose the denoising physics-informed neural networks (dPINNs), based on Discrete Fourier Transform (DFT), to deliver a set of the optimal finetuned PDE coefficients respecting the noise-reduced variables. The denoising PINNs' structures are compartmentalized into forefront projection networks and a PINN, by which the formerly learned solver initializes. Our extensive experiments on five canonical PDEs affirm that the proposed framework presents a robust and interpretable approach for PDE discovery, applicable to a wide range of systems, possibly complicated by noise.

Exploring TTS without T Using Biologically/Psychologically Motivated Neural Network Modules (ZeroSpeech 2020)

In this study, we reported our exploration of Text-To-Speech without Text (TTS without T) in the Zero Resource Speech Challenge 2020, in which participants proposed an end-to-end, unsupervised system that learned speech recognition and TTS together. We addressed the challenge using biologically/psychologically motivated modules of Artificial Neural Networks (ANN), with a particular interest in unsupervised learning of human language as a biological/psychological problem. The system first processes Mel Frequency Cepstral Coefficient (MFCC) frames with an Echo-State Network (ESN), and simulates computations in cortical microcircuits. The outcome is discretized by our original Variational Autoencoder (VAE) that implements the Dirichlet-based Bayesian clustering widely accepted in computational linguistics and cognitive science. The discretized signal is then reverted into sound waveform via a neural-network implementation of the source-filter model for speech production.

Neural Language Models as Psycholinguistic Subjects: Representations of Syntactic State

We deploy the methods of controlled psycholinguistic experimentation to shed light on the extent to which the behavior of neural network language models reflects incremental representations of syntactic state. To do so, we examine model behavior on artificial sentences containing a variety of syntactically complex structures. We test four models: two publicly available LSTM sequence models of English (Jozefowicz et al., 2016; Gulordava et al., 2018) trained on large datasets; an RNNG (Dyer et al., 2016) trained on a small, parsed dataset; and an LSTM trained on the same small corpus as the RNNG. We find evidence that the LSTMs trained on large datasets represent syntactic state over large spans of text in a way that is comparable to the RNNG, while the LSTM trained on the small dataset does not or does so only weakly.

Superregular grammars do not provide additional explanatory power but allow for a compact analysis of animal song

A pervasive belief with regard to the differences between human language and animal vocal sequences (song) is that they belong to different classes of computational complexity, with animal song belonging to regular languages, whereas human language is superregular. This argument, however, lacks empirical evidence since superregular analyses of animal song are understudied. The goal of this paper is to perform a superregular analysis of animal song, using data from gibbons as a case study, and demonstrate that a superregular analysis can be effectively used with non-human data. A key finding is that a superregular analysis does not increase explanatory power but rather provides for compact analysis. For instance, fewer grammatical rules are necessary once superregularity is allowed. This pattern is analogous to a previous computational analysis of human language, and accordingly, the null hypothesis, that human language and animal song are governed by the same type of grammatical systems, cannot be rejected.

RNNs as psycholinguistic subjects: Syntactic state and grammatical dependency

Recurrent neural networks (RNNs) are the state of the art in sequence modeling for natural language. However, it remains poorly understood what grammatical characteristics of natural language they implicitly learn and represent as a consequence of optimizing the language modeling objective. Here we deploy the methods of controlled psycholinguistic experimentation to shed light on to what extent RNN behavior reflects incremental syntactic state and grammatical dependency representations known to characterize human linguistic behavior. We broadly test two publicly available long short-term memory (LSTM) English sequence models, and learn and test a new Japanese LSTM. We demonstrate that these models represent and maintain incremental syntactic state, but that they do not always generalize in the same way as humans. Furthermore, none of our models learn the appropriate grammatical dependency configurations licensing reflexive pronouns or negative polarity items.

What do RNN Language Models Learn about Filler-Gap Dependencies?

RNN language models have achieved state-of-the-art perplexity results and have proven useful in a suite of NLP tasks, but it is as yet unclear what syntactic generalizations they learn. Here we investigate whether state-of-the-art RNN language models represent long-distance filler-gap dependencies and constraints on them. Examining RNN behavior on experimentally controlled sentences designed to expose filler-gap dependencies, we show that RNNs can represent the relationship in multiple syntactic positions and over large spans of text. Furthermore, we show that RNNs learn a subset of the known restrictions on filler-gap dependencies, known as island constraints: RNNs show evidence for wh-islands, adjunct islands, and complex NP islands. These studies demonstrates that state-of-the-art RNN models are able to learn and generalize about empty syntactic positions.