Remote Multilinear Compressive Learning with Adaptive Compression

Multilinear Compressive Learning (MCL) is an efficient signal acquisition and learning paradigm for multidimensional signals. The level of signal compression affects the detection or classification performance of a MCL model, with higher compression rates often associated with lower inference accuracy. However, higher compression rates are more amenable to a wider range of applications, especially those that require low operating bandwidth and minimal energy consumption such as Internet-of-Things (IoT) applications. Many communication protocols provide support for adaptive data transmission to maximize the throughput and minimize energy consumption. By developing compressive sensing and learning models that can operate with an adaptive compression rate, we can maximize the informational content throughput of the whole application. In this paper, we propose a novel optimization scheme that enables such a feature for MCL models. Our proposal enables practical implementation of adaptive compressive signal acquisition and inference systems. Experimental results demonstrated that the proposed approach can significantly reduce the amount of computations required during the training phase of remote learning systems but also improve the informational content throughput via adaptive-rate sensing.

Bilinear Input Normalization for Neural Networks in Financial Forecasting

Data normalization is one of the most important preprocessing steps when building a machine learning model, especially when the model of interest is a deep neural network. This is because deep neural network optimized with stochastic gradient descent is sensitive to the input variable range and prone to numerical issues. Different than other types of signals, financial time-series often exhibit unique characteristics such as high volatility, non-stationarity and multi-modality that make them challenging to work with, often requiring expert domain knowledge for devising a suitable processing pipeline. In this paper, we propose a novel data-driven normalization method for deep neural networks that handle high-frequency financial time-series. The proposed normalization scheme, which takes into account the bimodal characteristic of financial multivariate time-series, requires no expert knowledge to preprocess a financial time-series since this step is formulated as part of the end-to-end optimization process. Our experiments, conducted with state-of-the-arts neural networks and high-frequency data from two large-scale limit order books coming from the Nordic and US markets, show significant improvements over other normalization techniques in forecasting future stock price dynamics.

Graph-Embedded Subspace Support Vector Data Description

In this paper, we propose a novel subspace learning framework for one-class classification. The proposed framework presents the problem in the form of graph embedding. It includes the previously proposed subspace one-class techniques as its special cases and provides further insight on what these techniques actually optimize. The framework allows to incorporate other meaningful optimization goals via the graph preserving criterion and reveals spectral and spectral regression-based solutions as alternatives to the previously used gradient-based technique. We combine the subspace learning framework iteratively with Support Vector Data Description applied in the subspace to formulate Graph-Embedded Subspace Support Vector Data Description. We experimentally analyzed the performance of newly proposed different variants. We demonstrate improved performance against the baselines and the recently proposed subspace learning methods for one-class classification.

Knowledge Distillation By Sparse Representation Matching

Knowledge Distillation refers to a class of methods that transfers the knowledge from a teacher network to a student network. In this paper, we propose Sparse Representation Matching (SRM), a method to transfer intermediate knowledge obtained from one Convolutional Neural Network (CNN) to another by utilizing sparse representation learning. SRM first extracts sparse representations of the hidden features of the teacher CNN, which are then used to generate both pixel-level and image-level labels for training intermediate feature maps of the student network. We formulate SRM as a neural processing block, which can be efficiently optimized using stochastic gradient descent and integrated into any CNN in a plug-and-play manner. Our experiments demonstrate that SRM is robust to architectural differences between the teacher and student networks, and outperforms other KD techniques across several datasets.

Performance Indicator in Multilinear Compressive Learning

Recently, the Multilinear Compressive Learning (MCL) framework was proposed to efficiently optimize the sensing and learning steps when working with multidimensional signals, i.e. tensors. In Compressive Learning in general, and in MCL in particular, the number of compressed measurements captured by a compressive sensing device characterizes the storage requirement or the bandwidth requirement for transmission. This number, however, does not completely characterize the learning performance of a MCL system. In this paper, we analyze the relationship between the input signal resolution, the number of compressed measurements and the learning performance of MCL. Our empirical analysis shows that the reconstruction error obtained at the initialization step of MCL strongly correlates with the learning performance, thus can act as a good indicator to efficiently characterize learning performances obtained from different sensor configurations without optimizing the entire system.

Operational vs Convolutional Neural Networks for Image Denoising

Convolutional Neural Networks (CNNs) have recently become a favored technique for image denoising due to its adaptive learning ability, especially with a deep configuration. However, their efficacy is inherently limited owing to their homogenous network formation with the unique use of linear convolution. In this study, we propose a heterogeneous network model which allows greater flexibility for embedding additional non-linearity at the core of the data transformation. To this end, we propose the idea of an operational neuron or Operational Neural Networks (ONN), which enables a flexible non-linear and heterogeneous configuration employing both inter and intra-layer neuronal diversity. Furthermore, we propose a robust operator search strategy inspired by the Hebbian theory, called the Synaptic Plasticity Monitoring (SPM) which can make data-driven choices for non-linearities in any architecture. An extensive set of comparative evaluations of ONNs and CNNs over two severe image denoising problems yield conclusive evidence that ONNs enriched by non-linear operators can achieve a superior denoising performance against CNNs with both equivalent and well-known deep configurations.

Self-Organized Operational Neural Networks for Severe Image Restoration Problems

Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and has outperformed the traditional non-local class of methods. However, the top-performing networks are generally composed of many convolutional layers and hundreds of neurons, with trainable parameters in excess of several millions. We claim that this is due to the inherent linear nature of convolution-based transformation, which is inadequate for handling severe restoration problems. Recently, a non-linear generalization of CNNs, called the operational neural networks (ONN), has been shown to outperform CNN on AWGN denoising. However, its formulation is burdened by a fixed collection of well-known nonlinear operators and an exhaustive search to find the best possible configuration for a given architecture, whose efficacy is further limited by a fixed output layer operator assignment. In this study, we leverage the Taylor series-based function approximation to propose a self-organizing variant of ONNs, Self-ONNs, for image restoration, which synthesizes novel nodal transformations onthe-fly as part of the learning process, thus eliminating the need for redundant training runs for operator search. In addition, it enables a finer level of operator heterogeneity by diversifying individual connections of the receptive fields and weights. We perform a series of extensive ablation experiments across three severe image restoration tasks. Even when a strict equivalence of learnable parameters is imposed, Self-ONNs surpass CNNs by a considerable margin across all problems, improving the generalization performance by up to 3 dB in terms of PSNR.

FastONN -- Python based open-source GPU implementation for Operational Neural Networks

Operational Neural Networks (ONNs) have recently been proposed as a special class of artificial neural networks for grid structured data. They enable heterogenous non-linear operations to generalize the widely adopted convolution-based neuron model. This work introduces a fast GPU-enabled library for training operational neural networks, FastONN, which is based on a novel vectorized formulation of the operational neurons. Leveraging on automatic reverse-mode differentiation for backpropagation, FastONN enables increased flexibility with the incorporation of new operator sets and customized gradient flows. Additionally, bundled auxiliary modules offer interfaces for performance tracking and checkpointing across different data partitions and customized metrics.

Data Normalization for Bilinear Structures in High-Frequency Financial Time-series

Financial time-series analysis and forecasting have been extensively studied over the past decades, yet still remain as a very challenging research topic. Since the financial market is inherently noisy and stochastic, a majority of financial time-series of interests are non-stationary, and often obtained from different modalities. This property presents great challenges and can significantly affect the performance of the subsequent analysis/forecasting steps. Recently, the Temporal Attention augmented Bilinear Layer (TABL) has shown great performances in tackling financial forecasting problems. In this paper, by taking into account the nature of bilinear projections in TABL networks, we propose Bilinear Normalization (BiN), a simple, yet efficient normalization layer to be incorporated into TABL networks to tackle potential problems posed by non-stationarity and multimodalities in the input series. Our experiments using a large scale Limit Order Book (LOB) consisting of more than 4 million order events show that BiN-TABL outperforms TABL networks using other state-of-the-arts normalization schemes by a large margin.

Multilinear Compressive Learning with Prior Knowledge

The recently proposed Multilinear Compressive Learning (MCL) framework combines Multilinear Compressive Sensing and Machine Learning into an end-to-end system that takes into account the multidimensional structure of the signals when designing the sensing and feature synthesis components. The key idea behind MCL is the assumption of the existence of a tensor subspace which can capture the essential features from the signal for the downstream learning task. Thus, the ability to find such a discriminative tensor subspace and optimize the system to project the signals onto that data manifold plays an important role in Multilinear Compressive Learning. In this paper, we propose a novel solution to address both of the aforementioned requirements, i.e., How to find those tensor subspaces in which the signals of interest are highly separable? and How to optimize the sensing and feature synthesis components to transform the original signals to the data manifold found in the first question? In our proposal, the discovery of a high-quality data manifold is conducted by training a nonlinear compressive learning system on the inference task. Its knowledge of the data manifold of interest is then progressively transferred to the MCL components via multi-stage supervised training with the supervisory information encoding how the compressed measurements, the synthesized features, and the predictions should be like. The proposed knowledge transfer algorithm also comes with a semi-supervised adaption that enables compressive learning models to utilize unlabeled data effectively. Extensive experiments demonstrate that the proposed knowledge transfer method can effectively train MCL models to compressively sense and synthesize better features for the learning tasks with improved performances, especially when the complexity of the learning task increases.