Deciphering interventional dynamical causality from non-intervention systems

Detecting and quantifying causality is a focal topic in the fields of science, engineering, and interdisciplinary studies. However, causal studies on non-intervention systems attract much attention but remain extremely challenging. To address this challenge, we propose a framework named Interventional Dynamical Causality (IntDC) for such non-intervention systems, along with its computational criterion, Interventional Embedding Entropy (IEE), to quantify causality. The IEE criterion theoretically and numerically enables the deciphering of IntDC solely from observational (non-interventional) time-series data, without requiring any knowledge of dynamical models or real interventions in the considered system. Demonstrations of performance showed the accuracy and robustness of IEE on benchmark simulated systems as well as real-world systems, including the neural connectomes of C. elegans, COVID-19 transmission networks in Japan, and regulatory networks surrounding key circadian genes.

Predicting unobserved climate time series data at distant areas via spatial correlation using reservoir computing

Collecting time series data spatially distributed in many locations is often important for analyzing climate change and its impacts on ecosystems. However, comprehensive spatial data collection is not always feasible, requiring us to predict climate variables at some locations. This study focuses on a prediction of climatic elements, specifically near-surface temperature and pressure, at a target location apart from a data observation point. Our approach uses two prediction methods: reservoir computing (RC), known as a machine learning framework with low computational requirements, and vector autoregression models (VAR), recognized as a statistical method for analyzing time series data. Our results show that the accuracy of the predictions degrades with the distance between the observation and target locations. We quantitatively estimate the distance in which effective predictions are possible. We also find that in the context of climate data, a geographical distance is associated with data correlation, and a strong data correlation significantly improves the prediction accuracy with RC. In particular, RC outperforms VAR in predicting highly correlated data within the predictive range. These findings suggest that machine learning-based methods can be used more effectively to predict climatic elements in remote locations by assessing the distance to them from the data observation point in advance. Our study on low-cost and accurate prediction of climate variables has significant value for climate change strategies.

Chaos-based reinforcement learning with TD3

Chaos-based reinforcement learning (CBRL) is a method in which the agent's internal chaotic dynamics drives exploration. This approach offers a model for considering how the biological brain can create variability in its behavior and learn in an exploratory manner. At the same time, it is a learning model that has the ability to automatically switch between exploration and exploitation modes and the potential to realize higher explorations that reflect what it has learned so far. However, the learning algorithms in CBRL have not been well-established in previous studies and have yet to incorporate recent advances in reinforcement learning. This study introduced Twin Delayed Deep Deterministic Policy Gradients (TD3), which is one of the state-of-the-art deep reinforcement learning algorithms that can treat deterministic and continuous action spaces, to CBRL. The validation results provide several insights. First, TD3 works as a learning algorithm for CBRL in a simple goal-reaching task. Second, CBRL agents with TD3 can autonomously suppress their exploratory behavior as learning progresses and resume exploration when the environment changes. Finally, examining the effect of the agent's chaoticity on learning shows that extremely strong chaos negatively impacts the flexible switching between exploration and exploitation.

Trained Latent Space Navigation to Prevent Lack of Photorealism in Generated Images on Style-based Models

Recent studies on StyleGAN variants show promising performances for various generation tasks. In these models, latent codes have traditionally been manipulated and searched for the desired images. However, this approach sometimes suffers from a lack of photorealism in generated images due to a lack of knowledge about the geometry of the trained latent space. In this paper, we show a simple unsupervised method that provides well-trained local latent subspace, enabling latent code navigation while preserving the photorealism of the generated images. Specifically, the method identifies densely mapped latent spaces and restricts latent manipulations within the local latent subspace. Experimental results demonstrate that images generated within the local latent subspace maintain photorealism even when the latent codes are significantly and repeatedly manipulated. Moreover, experiments show that the method can be applied to latent code optimization for various types of style-based models. Our empirical evidence of the method will benefit applications in style-based models.

Sparse-firing regularization methods for spiking neural networks with time-to-first spike coding

The training of multilayer spiking neural networks (SNNs) using the error backpropagation algorithm has made significant progress in recent years. Among the various training schemes, the error backpropagation method that directly uses the firing time of neurons has attracted considerable attention because it can realize ideal temporal coding. This method uses time-to-first spike (TTFS) coding, in which each neuron fires at most once, and this restriction on the number of firings enables information to be processed at a very low firing frequency. This low firing frequency increases the energy efficiency of information processing in SNNs, which is important not only because of its similarity with information processing in the brain, but also from an engineering point of view. However, only an upper limit has been provided for TTFS-coded SNNs, and the information-processing capability of SNNs at lower firing frequencies has not been fully investigated. In this paper, we propose two spike timing-based sparse-firing (SSR) regularization methods to further reduce the firing frequency of TTFS-coded SNNs. The first is the membrane potential-aware SSR (M-SSR) method, which has been derived as an extreme form of the loss function of the membrane potential value. The second is the firing condition-aware SSR (F-SSR) method, which is a regularization function obtained from the firing conditions. Both methods are characterized by the fact that they only require information about the firing timing and associated weights. The effects of these regularization methods were investigated on the MNIST, Fashion-MNIST, and CIFAR-10 datasets using multilayer perceptron networks and convolutional neural network structures.

Learning Reservoir Dynamics with Temporal Self-Modulation

Reservoir computing (RC) can efficiently process time-series data by transferring the input signal to randomly connected recurrent neural networks (RNNs), which are referred to as a reservoir. The high-dimensional representation of time-series data in the reservoir significantly simplifies subsequent learning tasks. Although this simple architecture allows fast learning and facile physical implementation, the learning performance is inferior to that of other state-of-the-art RNN models. In this paper, to improve the learning ability of RC, we propose self-modulated RC (SM-RC), which extends RC by adding a self-modulation mechanism. The self-modulation mechanism is realized with two gating variables: an input gate and a reservoir gate. The input gate modulates the input signal, and the reservoir gate modulates the dynamical properties of the reservoir. We demonstrated that SM-RC can perform attention tasks where input information is retained or discarded depending on the input signal. We also found that a chaotic state emerged as a result of learning in SM-RC. This indicates that self-modulation mechanisms provide RC with qualitatively different information-processing capabilities. Furthermore, SM-RC outperformed RC in NARMA and Lorentz model tasks. In particular, SM-RC achieved a higher prediction accuracy than RC with a reservoir 10 times larger in the Lorentz model tasks. Because the SM-RC architecture only requires two additional gates, it is physically implementable as RC, providing a new direction for realizing edge AI.

Timing-Based Backpropagation in Spiking Neural Networks Without Single-Spike Restrictions

We propose a novel backpropagation algorithm for training spiking neural networks (SNNs) that encodes information in the relative multiple spike timing of individual neurons without single-spike restrictions. The proposed algorithm inherits the advantages of conventional timing-based methods in that it computes accurate gradients with respect to spike timing, which promotes ideal temporal coding. Unlike conventional methods where each neuron fires at most once, the proposed algorithm allows each neuron to fire multiple times. This extension naturally improves the computational capacity of SNNs. Our SNN model outperformed comparable SNN models and achieved as high accuracy as non-convolutional artificial neural networks. The spike count property of our networks was altered depending on the time constant of the postsynaptic current and the membrane potential. Moreover, we found that there existed the optimal time constant with the maximum test accuracy. That was not seen in conventional SNNs with single-spike restrictions on time-to-fast-spike (TTFS) coding. This result demonstrates the computational properties of SNNs that biologically encode information into the multi-spike timing of individual neurons. Our code would be publicly available.

Entropic Herding

Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is inspired by the maximum entropy principle of statistical inference. In this paper, we propose an extension of the herding algorithm, called entropic herding, which generates a sequence of distributions instead of points. Entropic herding is derived as the optimization of the target function obtained from the maximum entropy principle. Using the proposed entropic herding algorithm as a framework, we discuss a closer connection between herding and the maximum entropy principle. Specifically, we interpret the original herding algorithm as a tractable version of entropic herding, the ideal output distribution of which is mathematically represented. We further discuss how the complex behavior of the herding algorithm contributes to optimization. We argue that the proposed entropic herding algorithm extends the application of herding to probabilistic modeling. In contrast to original herding, entropic herding can generate a smooth distribution such that both efficient probability density calculation and sample generation become possible. To demonstrate the viability of these arguments in this study, numerical experiments were conducted, including a comparison with other conventional methods, on both synthetic and real data.

Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamics

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of multiscale dynamics, we propose a reservoir computing model with diverse timescales by using a recurrent network of heterogeneous leaky integrator neurons. In prediction tasks with fast-slow chaotic dynamical systems including a large gap in timescales of their subsystems dynamics, we demonstrate that the proposed model has a higher potential than the existing standard model and yields a performance comparable to the best one of the standard model even without an optimization of the leak rate parameter. Our analysis reveals that the timescales required for producing each component of target dynamics are appropriately and flexibly selected from the reservoir dynamics by model training.

Effects of VLSI Circuit Constraints on Temporal-Coding Multilayer Spiking Neural Networks

The spiking neural network (SNN) has been attracting considerable attention not only as a mathematical model for the brain, but also as an energy-efficient information processing model for real-world applications. In particular, SNNs based on temporal coding are expected to be much more efficient than those based on rate coding, because the former requires substantially fewer spikes to carry out tasks. As SNNs are continuous-state and continuous-time models, it is favorable to implement them with analog VLSI circuits. However, the construction of the entire system with continuous-time analog circuits would be infeasible when the system size is very large. Therefore, mixed-signal circuits must be employed, and the time discretization and quantization of the synaptic weights are necessary. Moreover, the analog VLSI implementation of SNNs exhibits non-idealities, such as the effects of noise and device mismatches, as well as other constraints arising from the analog circuit operation. In this study, we investigated the effects of the time discretization and/or weight quantization on the performance of SNNs. Furthermore, we elucidated the effects the lower bound of the membrane potentials and the temporal fluctuation of the firing threshold. Finally, we propose an optimal approach for the mapping of mathematical SNN models to analog circuits with discretized time.