Understanding Dilated Mathematical Relationship between Image Features and the Convolutional Neural Network’s Learnt Parameters

Deep learning, in general, was built on input data transformation and presentation, model training with parameter tuning, and recognition of new observations using the trained model. However, this came with a high computation cost due to the extensive input database and the length of time required in training. Despite the model learning its parameters from the transformed input data, no direct research has been conducted to investigate the mathematical relationship between the transformed information (i.e., features, excitation) and the model’s learnt parameters (i.e., weights). This research aims to explore a mathematical relationship between the input excitations and the weights of a trained convolutional neural network. The objective is to investigate three aspects of this assumed feature-weight relationship: (1) the mathematical relationship between the training input images’ features and the model’s learnt parameters, (2) the mathematical relationship between the images’ features of a separate test dataset and a trained model’s learnt parameters, and (3) the mathematical relationship between the difference of training and testing images’ features and the model’s learnt parameters with a separate test dataset. The paper empirically demonstrated the existence of this mathematical relationship between the test image features and the model’s learnt weights by the ANOVA analysis.     

Evaluating the Learning Procedure of CNNs through a Sequence of Prognostic Tests Utilising Information Theoretical Measures

Deep learning has proven to be an important element of modern data processing technology, which has found its application in many areas such as multimodal sensor data processing and understanding, data generation and anomaly detection. While the use of deep learning is booming in many real-world tasks, the internal processes of how it draws results is still uncertain. Understanding the data processing pathways within a deep neural network is important for transparency and better resource utilisation. In this paper, a method utilising information theoretic measures is used to reveal the typical learning patterns of convolutional neural networks, which are commonly used for image processing tasks. For this purpose, training samples, true labels and estimated labels are considered to be random variables. The mutual information and conditional entropy between these variables are then studied using information theoretical measures. This paper shows that more convolutional layers in the network improve its learning and unnecessarily higher numbers of convolutional layers do not improve the learning any further. The number of convolutional layers that need to be added to a neural network to gain the desired learning level can be determined with the help of theoretic information quantities including entropy, inequality and mutual information among the inputs to the network. The kernel size of convolutional layers only affects the learning speed of the network. This study also shows that where the dropout layer is applied to has no significant effects on the learning of networks with a lower dropout rate, and it is better placed immediately after the last convolutional layer with higher dropout rates.     

Synthesis of 3,5-diarylisoxazoles under solvent-free conditions using iodobenzene diacetate

A simple and efficient method has been developed for conversion of chalcone oximes to 3,5-diaryl isoxazoles in excellent yields under solvent-free conditions. The synthesized compounds were characterized by infrared spectroscopy, ^1H NMR, ^13C NMR and HRMS.     

Nonionic Micellar Catalyzed Oxidation of Vitamins by Chloramine-T in HClO4 Medium: A Kinetic Study

The kinetics of oxidation of vitamin B₁ (thiamine hydrochloride) and vitamin B₆ (pyridoxine hydrochloride) by chloramine-T (CAT) in perchloric acid medium and in presence of a non ionic surfactant (Triton x-100) have been investigated. A catalytic effect of the nonionic micelle on the rate of oxidation has been observed and rate is found to be proportional to 7lcub;k′ + k″ [Triton x-100]}, where k′ and k″ are the rate constants in absence and presence of surfactant, respectively. The rate shows a first-order, a fractional order and a zero order dependence on [Chloramine-T]_o, [Vitamin]_o and [H⁺]₀, respectively in absence as well as in presence of surfactant. A mechanism involving association/binding between the oxidant and the surfactant micelle, which is supported by spectrophotometric evidence has been proposed. The binding parameters have also been evaluated using a pseudo-phase kinetic model.