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.

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Object recognition is an essential element of machine intelligence tasks. However, one model cannot practically be trained to identify all the possible objects it encounters. An ensemble of models may be needed to cater to a broader range of objects. Building a mathematical understanding of the relationship between various objects that share comparable outlined features is envisaged as an effective method of improving the model ensemble through a pre-processing stage, where these objects' features are grouped under a broader classification umbrella. This paper proposes a mechanism to train an ensemble of recognition models coupled with a model selection scheme to scale-up object recognition in a multi-model system. An algorithmic relationship between the learnt parameters of a trained classification model and the features of input images is presented in the paper for the system to learn the model selection scheme. The multiple models are built with a CNN structure, whereas the image features are extracted using a CNN/VGG16 architecture. Based on the models' excitation weights, a neural network model selection algorithm, which links a new object with the models and decides how close the features of the object are to the trained models for selecting a particular model for object recognition is developed and tested on a five-model neural network platform. The experiment results show the proposed model selection scheme is highly effective and accurate in selecting an appropriate model for a network of multiple models.