Mutual Information-Based Generalisation Gap Analysis Using Deep Learning Model

Most deep learning models face difficulties in analysing image information due to the concept of information bottlenecks and their corresponding methodologies. But, the information bottleneck is used for discarding redundant data and trying to maximise in favour of data directly relevant to the task-oriented information. However, managing information bottlenecks is challenging in the learning model process. Although convolutional neural networks are designed for small-scale processing, their inductive bias makes it difficult to learn contextual features. Thus, we have considered the theoretical learning model to justify the advantages of information bottleneck in deep learning model. We tried to use a fundamental information bottleneck in the vision transformer model. The channel density module cleans up task-related data, while the collected image representations are encouraged to be diverse through local connections in cumulative local transformer blocks. We considered the encoder and decoder methods that analyse the information bottleneck techniques in the deep learning model. This paper presents a rigorous learning theory that mathematically links information bottlenecks for generalisation errors, demonstrating the usefulness of information bottlenecks in deep learning. Our approach suggests that limiting information bottlenecks is crucial for managing errors in deep learning techniques. We conducted experiments across various mathematical models and learning environments to test the validity of our new mathematical insights. In many cases, generalisation errors correspond to unwanted information at hidden levels. We have considered boundary approaches using various scaling parameters and dimensions for the degree of information bottleneck. As per the estimation loss and error by different correlation approaches using generalisation gap methods, we found Spearman correlation having loss (0.86) and error (0.758), whereas Pearson correlation having loss (0.85) and error (0.76), respectively. We also considered outputs for model compression metrics and analysed them through comparative performance.