Learning Functions Generated by Randomly Initialized MLPs and SRNs

In this paper, nonlinear functions generated by randomly initialized multilayer perceptrons (MLPs) and simultaneous recurrent neural networks (SRNs) and two benchmark functions are learned by MLPs and SRNs. Training SRNs is a challenging task and a new learning algorithm - PSO-QI is introduced. PSO-QI is a standard particle swarm optimization (PSO) algorithm with the addition of a quantum step utilizing the probability density property of a quantum particle. The results from PSO-QI are compared with the standard backpropagation (BP) and PSO algorithms. It is further verified that functions generated by SRNs are harder to learn than those generated by MLPs but PSO-QI provides learning capabilities of these functions by MLPs and SRNs compared to BP and PSO

Learning Nonlinear Functions with MLPs and SRNs

In this paper, nonlinear functions generated by randomly initialized multilayer perceptrons (MLPs) and simultaneous recurrent neural networks (SRNs) are learned by MLPs and SRNs. Training SRNs is a challenging task and a new learning algorithm - DEPSO is introduced. DEPSO is a standard particle swarm optimization (PSO) algorithm with the addition of a differential evolution step to aid in swarm convergence. The results from DEPSO are compared with the standard backpropagation (BP) and PSO algorithms. It is further verified that functions generated by SRNs are harder to learn than those generated by MLPs but DEPSO provides better learning capabilities for the functions generated by MLPs and SRNs as compared to BP and PSO. These three algorithms are also trained on several benchmark functions to confirm results

New Neural Network Design for Approximate Dynamic Programming and Optimal Multiuser Detection

In this thesis we demonstrate that a new neural network design can be used to solve a class of difficult function approximation problems which are crucial to the field of approximate dynamic programming (ADP). Although conventional neural networks have been proven to approximate smooth functions very well, the use of ADP for problems of intelligent control or planning requires the approximation of functions which are not so smooth. As an example, this thesis studies the problem of approximating the $J$ function of dynamic programming applied to the task of navigating mazes, in general, without the need to learn each individual maze. Conventional neural networks, like multi-layer perceptrons (MLPs), cannot learn this task. But a new type of neural network, simultaneous recurrent networks (SRNs), can accomplish the required learning as demonstrated by successful initial tests. In this thesis we also investigate the ability of recurrent neural networks to approximate MLPs and vice versa. Moreover, we present a comparison between using SRNs and MLPs to implement the optimal CDMA multiuser detector (OMD). This example is intended to demonstrate that SRNs can provide fast suboptimal solutions to hard combinatorial optimization problems, and achieve better bit- error-rate (BER) performance than MLPs

Adaptively Placed Multi-Grid Scene Representation Networks for Large-Scale Data Visualization

Scene representation networks (SRNs) have been recently proposed for compression and visualization of scientific data. However, state-of-the-art SRNs do not adapt the allocation of available network parameters to the complex features found in scientific data, leading to a loss in reconstruction quality. We address this shortcoming with an adaptively placed multi-grid SRN (APMGSRN) and propose a domain decomposition training and inference technique for accelerated parallel training on multi-GPU systems. We also release an open-source neural volume rendering application that allows plug-and-play rendering with any PyTorch-based SRN. Our proposed APMGSRN architecture uses multiple spatially adaptive feature grids that learn where to be placed within the domain to dynamically allocate more neural network resources where error is high in the volume, improving state-of-the-art reconstruction accuracy of SRNs for scientific data without requiring expensive octree refining, pruning, and traversal like previous adaptive models. In our domain decomposition approach for representing large-scale data, we train an set of APMGSRNs in parallel on separate bricks of the volume to reduce training time while avoiding overhead necessary for an out-of-core solution for volumes too large to fit in GPU memory. After training, the lightweight SRNs are used for realtime neural volume rendering in our open-source renderer, where arbitrary view angles and transfer functions can be explored. A copy of this paper, all code, all models used in our experiments, and all supplemental materials and videos are available at https://github.com/skywolf829/APMGSRN.Comment: Accepted to IEEE VIS 202

Cellular Simultanous Recurrent Networks for Image Processing

Artificial neural networks are inspired by the abilities of humans and animals to learn and adapt. Feed-forward networks are both fast and powerful, and are particularly useful for statistical pattern recognition. These networks are inspired by portions of the brain such as the visual cortex. However, feed-forward networks have been shown inadequate for complex applications such as long-term optimization, reinforced learning and image processing. Cellular Neural Networks (CNNs) are a type of recurrent network which have been used extensively for image processing. CNNs have shown limited success solving problems which involve topological relationships. Such problems include geometric transformations such as affine transformation and image registration. The Cellular Simultaneous Recurrent Network (CSRN) has been exploited to solve the 2D maze traversal problem, which is a long-term optimization problem with similar topological relations. From its inception, it has been speculated that the CSRN may have important implications in image processing. However, to date, very little work has been done to study CSRNs for image processing tasks. In this work, we investigate CSRNs for image processing. We propose a novel, generalized architecture for the CSRN suitable for generic image processing tasks. This architecture includes the use of sub-image processing which greatly improves the efficacy of CSRNs for image processing. We demonstrate the application of the CSRN with this generalized architecture across a variety of image processing problems including pixel level transformations, filtering, and geometric transformations. Results are evaluated and compared with standard MATLAB® functions. To better understand the inner workings of the CSRN we investigate the use of various CSRN cores including: 1) the original Generalized Multi-Layered Perceptron (GMLP) core used by Pang and Werbos to solve the 2D maze traversal problem, 2) the Elman Simultaneous Recurrent Network (ESRN), and 3) a novel ESRN core with multi-layered feedback. We compare the functionality of these cores in image processing applications. Further, we introduce the application of the unscented Kalman filter (UKF) for training of the CSRN. Results are compared with the standard Extended Kalman Filter (EKF) training method of CSRN. Finally, implications of current findings and proposed research directions are presented

Deep Recurrent Learning for Efficient Image Recognition Using Small Data

Recognition is fundamental yet open and challenging problem in computer vision. Recognition involves the detection and interpretation of complex shapes of objects or persons from previous encounters or knowledge. Biological systems are considered as the most powerful, robust and generalized recognition models. The recent success of learning based mathematical models known as artificial neural networks, especially deep neural networks, have propelled researchers to utilize such architectures for developing bio-inspired computational recognition models. However, the computational complexity of these models increases proportionally to the challenges posed by the recognition problem, and more importantly, these models require a large amount of data for successful learning. Additionally, the feedforward-based hierarchical models do not exploit another important biological learning paradigm, known as recurrency, which ubiquitously exists in the biological visual system and has been shown to be quite crucial for recognition. Consequently, this work aims to develop novel biologically relevant deep recurrent learning models for robust recognition using limited training data. First, we design an efficient deep simultaneous recurrent network (DSRN) architecture for solving several challenging image recognition tasks. The use of simultaneous recurrency in the proposed model improves the recognition performance and offers reduced computational complexity compared to the existing hierarchical deep learning models. Moreover, the DSRN architecture inherently learns meaningful representations of data during the training process which is essential to achieve superior recognition performance. However, probabilistic models such as deep generative models are particularly adept at learning representations directly from unlabeled input data. Accordingly, we show the generalization of the proposed deep simultaneous recurrency concept by developing a probabilistic deep simultaneous recurrent belief network (DSRBN) architecture which is more efficient in learning the underlying representation of the data compared to the state-of-the-art generative models. Finally, we propose a deep recurrent learning framework for solving the image recognition task using small data. We incorporate Bayesian statistics to the DSRBN generative model to propose a deep recurrent generative Bayesian model that addresses the challenge of learning from a small amount of data. Our findings suggest that the proposed deep recurrent Bayesian framework demonstrates better image recognition performance compared to the state-of-the-art models in a small data learning scenario. In conclusion, this dissertation proposes novel deep recurrent learning pipelines, which utilize not only limited training data to achieve improved image recognition performance but also require significantly reduced training parameters

Mitigation of Catastrophic Interference in Neural Networks and Ensembles using a Fixed Expansion Layer

Catastrophic forgetting (also known in the literature as catastrophic interference) is the phenomenon by which learning systems exhibit a severe exponential loss of learned information when exposed to relatively small amounts of new training data. This loss of information is not caused by constraints due to the lack of resources available to the learning system, but rather is caused by representational overlap within the learning system and by side-effects of the training methods used. Catastrophic forgetting in auto-associative pattern recognition is a well-studied attribute of most parameterized supervised learning systems. A variation of this phenomenon, in the context of feedforward neural networks, arises when non-stationary inputs lead to loss of previously learned mappings. The majority of the schemes proposed in the literature for mitigating catastrophic forgetting are not data-driven, but rather rely on storage of prior representations of the learning system. We introduce the Fixed Expansion Layer (FEL) feedforward neural network that embeds an expansion layer which sparsely encodes the information contained within the hidden layer, in order to help mitigate forgetting of prior learned representations. The fixed expansion layer approach is generally applicable to feedforward neural networks, as demonstrated by the application of the FEL technique to a recurrent neural network algorithm built on top of a standard feedforward neural network. Additionally, we investigate a novel framework for training ensembles of FEL networks, based on exploiting an information-theoretic measure of diversity between FEL learners, to further control undesired plasticity. The proposed methodology is demonstrated on a several tasks, clearly emphasizing its advantages over existing techniques. The architecture proposed can be applied to address a range of computational intelligence tasks, including classification problems, regression problems and system control

Neural Radiance Fields: Past, Present, and Future

The various aspects like modeling and interpreting 3D environments and surroundings have enticed humans to progress their research in 3D Computer Vision, Computer Graphics, and Machine Learning. An attempt made by Mildenhall et al in their paper about NeRFs (Neural Radiance Fields) led to a boom in Computer Graphics, Robotics, Computer Vision, and the possible scope of High-Resolution Low Storage Augmented Reality and Virtual Reality-based 3D models have gained traction from res with more than 1000 preprints related to NeRFs published. This paper serves as a bridge for people starting to study these fields by building on the basics of Mathematics, Geometry, Computer Vision, and Computer Graphics to the difficulties encountered in Implicit Representations at the intersection of all these disciplines. This survey provides the history of rendering, Implicit Learning, and NeRFs, the progression of research on NeRFs, and the potential applications and implications of NeRFs in today's world. In doing so, this survey categorizes all the NeRF-related research in terms of the datasets used, objective functions, applications solved, and evaluation criteria for these applications.Comment: 413 pages, 9 figures, 277 citation