Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Doctor of Philosophy

dissertationMicrowave/millimeter-wave imaging systems have become ubiquitous and have found applications in areas like astronomy, bio-medical diagnostics, remote sensing, and security surveillance. These areas have so far relied on conventional imaging devices (empl

Laughing Hyena Distillery: Extracting Compact Recurrences From Convolutions

Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In particular, long convolution sequence models have achieved state-of-the-art performance in many domains, but incur a significant cost during auto-regressive inference workloads -- naively requiring a full pass (or caching of activations) over the input sequence for each generated token -- similarly to attention-based models. In this paper, we seek to enable $\mathcal O(1)$ compute and memory cost per token in any pre-trained long convolution architecture to reduce memory footprint and increase throughput during generation. Concretely, our methods consist in extracting low-dimensional linear state-space models from each convolution layer, building upon rational interpolation and model-order reduction techniques. We further introduce architectural improvements to convolution-based layers such as Hyena: by weight-tying the filters across channels into heads, we achieve higher pre-training quality and reduce the number of filters to be distilled. The resulting model achieves 10x higher throughput than Transformers and 1.5x higher than Hyena at 1.3B parameters, without any loss in quality after distillation

Adaptive spatial image steganography and steganalysis using perceptual modelling and machine learning

Image steganography is a method for communicating secret messages under the cover images. A sender will embed the secret messages into the cover images according to an algorithm, and then the resulting image will be sent to the receiver. The receiver can extract the secret messages with the predefined algorithm. To counter this kind of technique, image steganalysis is proposed to detect the presence of secret messages. After many years of development, current image steganography uses the adaptive algorithm for embedding the secrets, which automatically finds the complex area in the cover source to avoid being noticed. Meanwhile, image steganalysis has also been advanced to universal steganalysis, which does not require the knowledge of the steganographic algorithm. With the development of the computational hardware, i.e., Graphical Processing Units (GPUs), some computational expensive techniques are now available, i.e., Convolutional Neural Networks (CNNs), which bring a large improvement in the detection tasks in image steganalysis. To defend against the attacks, new techniques are also being developed to improve the security of image steganography, these include designing more scientific cost functions, the key in adaptive steganography, and generating stego images from the knowledge of the CNNs. Several contributions are made for both image steganography and steganalysis in this thesis. Firstly, inspired by the Ranking Priority Profile (RPP), a new cost function for adaptive image steganography is proposed, which uses the two-dimensional Singular Spectrum Analysis (2D-SSA) and Weighted Median Filter (WMF) in the design. The RPP mainly includes three rules, i.e., the Complexity-First rule, the Clustering rule and the Spreading rule, to design a cost function. The 2D-SSA is employed in selecting the key components and clustering the embedding positions, which follows the Complexity-First rule and the Clustering rule. Also, the Spreading rule is followed to smooth the resulting image produced by 2D-SSA with WMF. The proposed algorithm has improved performance over four benchmarking approaches against non-shared selection channel attacks. It also provides comparable performance in selection-channel-aware scenarios, where the best results are observed when the relative payload is 0.3 bpp or larger. The approach is much faster than other model-based methods. Secondly, for image steganalysis, to tackle more complex datasets that are close to the real scenarios and to push image steganalysis further to real-life applications, an Enhanced Residual Network with self-attention ability, i.e., ERANet, is proposed. By employing a more mathematically sophisticated way to extract more effective features in the images and the global self-Attention technique, the ERANet can further capture the stego signal in the deeper layers, hence it is suitable for the more complex situations in the new datasets. The proposed Enhanced Low-Level Feature Representation Module can be easily mounted on other CNNs in selecting the most representative features. Although it comes with a slightly extra computational cost, comprehensive experiments on the BOSSbase and ALASKA#2 datasets have demonstrated the effectiveness of the proposed methodology. Lastly, for image steganography, with the knowledge from the CNNs, a novel postcost-optimization algorithm is proposed. Without modifying the original stego image and the original cost function of the steganography, and no need for training a Generative Adversarial Network (GAN), the proposed method mainly uses the gradient maps from a well-trained CNN to represent the cost, where the original cost map of the steganography is adopted to indicate the embedding positions. This method will smooth the gradient maps before adjusting the cost, which solves the boundary problem of the CNNs having multiple subnets. Extensive experiments have been carried out to validate the effectiveness of the proposed method, which provides state-of-the-art performance. In addition, compared to existing work, the proposed method is effcient in computing time as well. In short, this thesis has made three major contributions to image steganography and steganalysis by using perceptual modelling and machine learning. A novel cost function and a post-cost-optimization function have been proposed for adaptive spatial image steganography, which helps protect the secret messages. For image steganalysis, a new CNN architecture has also been proposed, which utilizes multiple techniques for providing state of-the-art performance. Future directions are also discussed for indicating potential research.Image steganography is a method for communicating secret messages under the cover images. A sender will embed the secret messages into the cover images according to an algorithm, and then the resulting image will be sent to the receiver. The receiver can extract the secret messages with the predefined algorithm. To counter this kind of technique, image steganalysis is proposed to detect the presence of secret messages. After many years of development, current image steganography uses the adaptive algorithm for embedding the secrets, which automatically finds the complex area in the cover source to avoid being noticed. Meanwhile, image steganalysis has also been advanced to universal steganalysis, which does not require the knowledge of the steganographic algorithm. With the development of the computational hardware, i.e., Graphical Processing Units (GPUs), some computational expensive techniques are now available, i.e., Convolutional Neural Networks (CNNs), which bring a large improvement in the detection tasks in image steganalysis. To defend against the attacks, new techniques are also being developed to improve the security of image steganography, these include designing more scientific cost functions, the key in adaptive steganography, and generating stego images from the knowledge of the CNNs. Several contributions are made for both image steganography and steganalysis in this thesis. Firstly, inspired by the Ranking Priority Profile (RPP), a new cost function for adaptive image steganography is proposed, which uses the two-dimensional Singular Spectrum Analysis (2D-SSA) and Weighted Median Filter (WMF) in the design. The RPP mainly includes three rules, i.e., the Complexity-First rule, the Clustering rule and the Spreading rule, to design a cost function. The 2D-SSA is employed in selecting the key components and clustering the embedding positions, which follows the Complexity-First rule and the Clustering rule. Also, the Spreading rule is followed to smooth the resulting image produced by 2D-SSA with WMF. The proposed algorithm has improved performance over four benchmarking approaches against non-shared selection channel attacks. It also provides comparable performance in selection-channel-aware scenarios, where the best results are observed when the relative payload is 0.3 bpp or larger. The approach is much faster than other model-based methods. Secondly, for image steganalysis, to tackle more complex datasets that are close to the real scenarios and to push image steganalysis further to real-life applications, an Enhanced Residual Network with self-attention ability, i.e., ERANet, is proposed. By employing a more mathematically sophisticated way to extract more effective features in the images and the global self-Attention technique, the ERANet can further capture the stego signal in the deeper layers, hence it is suitable for the more complex situations in the new datasets. The proposed Enhanced Low-Level Feature Representation Module can be easily mounted on other CNNs in selecting the most representative features. Although it comes with a slightly extra computational cost, comprehensive experiments on the BOSSbase and ALASKA#2 datasets have demonstrated the effectiveness of the proposed methodology. Lastly, for image steganography, with the knowledge from the CNNs, a novel postcost-optimization algorithm is proposed. Without modifying the original stego image and the original cost function of the steganography, and no need for training a Generative Adversarial Network (GAN), the proposed method mainly uses the gradient maps from a well-trained CNN to represent the cost, where the original cost map of the steganography is adopted to indicate the embedding positions. This method will smooth the gradient maps before adjusting the cost, which solves the boundary problem of the CNNs having multiple subnets. Extensive experiments have been carried out to validate the effectiveness of the proposed method, which provides state-of-the-art performance. In addition, compared to existing work, the proposed method is effcient in computing time as well. In short, this thesis has made three major contributions to image steganography and steganalysis by using perceptual modelling and machine learning. A novel cost function and a post-cost-optimization function have been proposed for adaptive spatial image steganography, which helps protect the secret messages. For image steganalysis, a new CNN architecture has also been proposed, which utilizes multiple techniques for providing state of-the-art performance. Future directions are also discussed for indicating potential research

Spatial dissection of a soundfield using spherical harmonic decomposition

A real-world soundfield is often contributed by multiple desired and undesired sound sources. The performance of many acoustic systems such as automatic speech recognition, audio surveillance, and teleconference relies on its ability to extract the desired sound components in such a mixed environment. The existing solutions to the above problem are constrained by various fundamental limitations and require to enforce different priors depending on the acoustic condition such as reverberation and spatial distribution of sound sources. With the growing emphasis and integration of audio applications in diverse technologies such as smart home and virtual reality appliances, it is imperative to advance the source separation technology in order to overcome the limitations of the traditional approaches. To that end, we exploit the harmonic decomposition model to dissect a mixed soundfield into its underlying desired and undesired components based on source and signal characteristics. By analysing the spatial projection of a soundfield, we achieve multiple outcomes such as (i) soundfield separation with respect to distinct source regions, (ii) source separation in a mixed soundfield using modal coherence model, and (iii) direction of arrival (DOA) estimation of multiple overlapping sound sources through pattern recognition of the modal coherence of a soundfield. We first employ an array of higher order microphones for soundfield separation in order to reduce hardware requirement and implementation complexity. Subsequently, we develop novel mathematical models for modal coherence of noisy and reverberant soundfields that facilitate convenient ways for estimating DOA and power spectral densities leading to robust source separation algorithms. The modal domain approach to the soundfield/source separation allows us to circumvent several practical limitations of the existing techniques and enhance the performance and robustness of the system. The proposed methods are presented with several practical applications and performance evaluations using simulated and real-life dataset

Proceedings of the 3rd Annual Conference on Aerospace Computational Control, volume 1

Conference topics included definition of tool requirements, advanced multibody component representation descriptions, model reduction, parallel computation, real time simulation, control design and analysis software, user interface issues, testing and verification, and applications to spacecraft, robotics, and aircraft

Reduced order modeling of convection-dominated flows, dimensionality reduction and stabilization

We present methodologies for reduced order modeling of convection dominated flows. Accordingly, three main problems are addressed. Firstly, an optimal manifold is realized to enhance reducibility of convection dominated flows. We design a low-rank auto-encoder to specifically reduce the dimensionality of solution arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to reduce the dimensionality of data characterized by large Kolmogorov n-width, they typically lack a straightforward mapping from the latent space to the high-dimensional physical space. Also, considering that the latent variables are often hard to interpret, many of these methods are dismissed in the reduced order modeling of dynamical systems governed by partial differential equations (PDEs). This deficiency is of importance to the extent that linear methods, such as principle component analysis (PCA) and Koopman operators, are still prevalent. Accordingly, we propose an interpretable nonlinear dimensionality reduction algorithm. An unsupervised learning problem is constructed that learns a diffeomorphic spatio-temporal grid which registers the output sequence of the PDEs on a non-uniform time-varying grid. The Kolmogorov n-width of the mapped data on the learned grid is minimized. Secondly, the reduced order models are constructed on the realized manifolds. We project the high fidelity models on the learned manifold, leading to a time-varying system of equations. Moreover, as a data-driven model free architecture, recurrent neural networks on the learned manifold are trained, showing versatility of the proposed framework. Finally, a stabilization method is developed to maintain stability and accuracy of the projection based ROMs on the learned manifold a posteriori. We extend the eigenvalue reassignment method of stabilization of linear time-invariant ROMs, to the more general case of linear time-varying systems. Through a post-processing step, the ROMs are controlled using a constrained nonlinear lease-square minimization problem. The controller and the input signals are defined at the algebraic level, using left and right singular vectors of the reduced system matrices. The proposed stabilization method is general and applicable to a large variety of linear time-varying ROMs