Why Rectified Power Unit Networks Fail and How to Improve It: An Effective Theory Perspective

The Rectified Power Unit (RePU) activation functions, unlike the Rectified Linear Unit (ReLU), have the advantage of being a differentiable function when constructing neural networks. However, it can be experimentally observed when deep layers are stacked, neural networks constructed with RePU encounter critical issues. These issues include the values exploding or vanishing and failure of training. And these happen regardless of the hyperparameter initialization. From the perspective of effective theory, we aim to identify the causes of this phenomenon and propose a new activation function that retains the advantages of RePU while overcoming its drawbacks.

Neural Operators Learn the Local Physics of Magnetohydrodynamics

Magnetohydrodynamics (MHD) plays a pivotal role in describing the dynamics of plasma and conductive fluids, essential for understanding phenomena such as the structure and evolution of stars and galaxies, and in nuclear fusion for plasma motion through ideal MHD equations. Solving these hyperbolic PDEs requires sophisticated numerical methods, presenting computational challenges due to complex structures and high costs. Recent advances introduce neural operators like the Fourier Neural Operator (FNO) as surrogate models for traditional numerical analyses. This study explores a modified Flux Fourier neural operator model to approximate the numerical flux of ideal MHD, offering a novel approach that outperforms existing neural operator models by enabling continuous inference, generalization outside sampled distributions, and faster computation compared to classical numerical schemes.

Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Laws

Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based methods, such as physics-informed neural networks (PINNs) and neural operators, exhibit deficiencies in robustness and generalization. To address these issues, numerous studies have integrated classical numerical frameworks with machine learning techniques, incorporating neural networks into parts of traditional numerical methods. In this study, we focus on hyperbolic conservation laws by replacing traditional numerical fluxes with neural operators. To this end, we developed loss functions inspired by established numerical schemes related to conservation laws and approximated numerical fluxes using Fourier neural operators (FNOs). Our experiments demonstrated that our approach combines the strengths of both traditional numerical schemes and FNOs, outperforming standard FNO methods in several respects. For instance, we demonstrate that our method is robust, has resolution invariance, and is feasible as a data-driven method. In particular, our method can make continuous predictions over time and exhibits superior generalization capabilities with out-of-distribution (OOD) samples, which are challenges that existing neural operator methods encounter.

An Infinite-Width Analysis on the Jacobian-Regularised Training of a Neural Network

The recent theoretical analysis of deep neural networks in their infinite-width limits has deepened our understanding of initialisation, feature learning, and training of those networks, and brought new practical techniques for finding appropriate hyperparameters, learning network weights, and performing inference. In this paper, we broaden this line of research by showing that this infinite-width analysis can be extended to the Jacobian of a deep neural network. We show that a multilayer perceptron (MLP) and its Jacobian at initialisation jointly converge to a Gaussian process (GP) as the widths of the MLP's hidden layers go to infinity and characterise this GP. We also prove that in the infinite-width limit, the evolution of the MLP under the so-called robust training (i.e., training with a regulariser on the Jacobian) is described by a linear first-order ordinary differential equation that is determined by a variant of the Neural Tangent Kernel. We experimentally show the relevance of our theoretical claims to wide finite networks, and empirically analyse the properties of kernel regression solution to obtain an insight into Jacobian regularisation.

Virtual Action Actor-Critic Framework for Exploration (Student Abstract)

Efficient exploration for an agent is challenging in reinforcement learning (RL). In this paper, a novel actor-critic framework namely virtual action actor-critic (VAAC), is proposed to address the challenge of efficient exploration in RL. This work is inspired by humans' ability to imagine the potential outcomes of their actions without actually taking them. In order to emulate this ability, VAAC introduces a new actor called virtual actor (VA), alongside the conventional actor-critic framework. Unlike the conventional actor, the VA takes the virtual action to anticipate the next state without interacting with the environment. With the virtual policy following a Gaussian distribution, the VA is trained to maximize the anticipated novelty of the subsequent state resulting from a virtual action. If any next state resulting from available actions does not exhibit high anticipated novelty, training the VA leads to an increase in the virtual policy entropy. Hence, high virtual policy entropy represents that there is no room for exploration. The proposed VAAC aims to maximize a modified Q function, which combines cumulative rewards and the negative sum of virtual policy entropy. Experimental results show that the VAAC improves the exploration performance compared to existing algorithms.

Enhanced Transformer Architecture for Natural Language Processing

Transformer is a state-of-the-art model in the field of natural language processing (NLP). Current NLP models primarily increase the number of transformers to improve processing performance. However, this technique requires a lot of training resources such as computing capacity. In this paper, a novel structure of Transformer is proposed. It is featured by full layer normalization, weighted residual connection, positional encoding exploiting reinforcement learning, and zero masked self-attention. The proposed Transformer model, which is called Enhanced Transformer, is validated by the bilingual evaluation understudy (BLEU) score obtained with the Multi30k translation dataset. As a result, the Enhanced Transformer achieves 202.96% higher BLEU score as compared to the original transformer with the translation dataset.

Road Redesign Technique Achieving Enhanced Road Safety by Inpainting with a Diffusion Model

Road infrastructure can affect the occurrence of road accidents. Therefore, identifying roadway features with high accident probability is crucial. Here, we introduce image inpainting that can assist authorities in achieving safe roadway design with minimal intervention in the current roadway structure. Image inpainting is based on inpainting safe roadway elements in a roadway image, replacing accident-prone (AP) features by using a diffusion model. After object-level segmentation, the AP features identified by the properties of accident hotspots are masked by a human operator and safe roadway elements are inpainted. With only an average time of 2 min for image inpainting, the likelihood of an image being classified as an accident hotspot drops by an average of 11.85%. In addition, safe urban spaces can be designed considering human factors of commuters such as gaze saliency. Considering this, we introduce saliency enhancement that suggests chrominance alteration for a safe road view.

Off-Policy Reinforcement Learning with Loss Function Weighted by Temporal Difference Error

Training agents via off-policy deep reinforcement learning (RL) requires a large memory, named replay memory, that stores past experiences used for learning. These experiences are sampled, uniformly or non-uniformly, to create the batches used for training. When calculating the loss function, off-policy algorithms assume that all samples are of the same importance. In this paper, we hypothesize that training can be enhanced by assigning different importance for each experience based on their temporal-difference (TD) error directly in the training objective. We propose a novel method that introduces a weighting factor for each experience when calculating the loss function at the learning stage. In addition to improving convergence speed when used with uniform sampling, the method can be combined with prioritization methods for non-uniform sampling. Combining the proposed method with prioritization methods improves sampling efficiency while increasing the performance of TD-based off-policy RL algorithms. The effectiveness of the proposed method is demonstrated by experiments in six environments of the OpenAI Gym suite. The experimental results demonstrate that the proposed method achieves a 33%~76% reduction of convergence speed in three environments and an 11% increase in returns and a 3%~10% increase in success rate for other three environments.

Reinforcement Learning for Predicting Traffic Accidents

As the demand for autonomous driving increases, it is paramount to ensure safety. Early accident prediction using deep learning methods for driving safety has recently gained much attention. In this task, early accident prediction and a point prediction of where the drivers should look are determined, with the dashcam video as input. We propose to exploit the double actors and regularized critics (DARC) method, for the first time, on this accident forecasting platform. We derive inspiration from DARC since it is currently a state-of-the-art reinforcement learning (RL) model on continuous action space suitable for accident anticipation. Results show that by utilizing DARC, we can make predictions 5\% earlier on average while improving in multiple metrics of precision compared to existing methods. The results imply that using our RL-based problem formulation could significantly increase the safety of autonomous driving.

Kick-motion Training with DQN in AI Soccer Environment

This paper presents a technique to train a robot to perform kick-motion in AI soccer by using reinforcement learning (RL). In RL, an agent interacts with an environment and learns to choose an action in a state at each step. When training RL algorithms, a problem called the curse of dimensionality (COD) can occur if the dimension of the state is high and the number of training data is low. The COD often causes degraded performance of RL models. In the situation of the robot kicking the ball, as the ball approaches the robot, the robot chooses the action based on the information obtained from the soccer field. In order not to suffer COD, the training data, which are experiences in the case of RL, should be collected evenly from all areas of the soccer field over (theoretically infinite) time. In this paper, we attempt to use the relative coordinate system (RCS) as the state for training kick-motion of robot agent, instead of using the absolute coordinate system (ACS). Using the RCS eliminates the necessity for the agent to know all the (state) information of entire soccer field and reduces the dimension of the state that the agent needs to know to perform kick-motion, and consequently alleviates COD. The training based on the RCS is performed with the widely used Deep Q-network (DQN) and tested in the AI Soccer environment implemented with Webots simulation software.