Super Level Sets and Exponential Decay: A Synergistic Approach to Stable Neural Network Training

The objective of this paper is to enhance the optimization process for neural networks by developing a dynamic learning rate algorithm that effectively integrates exponential decay and advanced anti-overfitting strategies. Our primary contribution is the establishment of a theoretical framework where we demonstrate that the optimization landscape, under the influence of our algorithm, exhibits unique stability characteristics defined by Lyapunov stability principles. Specifically, we prove that the superlevel sets of the loss function, as influenced by our adaptive learning rate, are always connected, ensuring consistent training dynamics. Furthermore, we establish the "equiconnectedness" property of these superlevel sets, which maintains uniform stability across varying training conditions and epochs. This paper contributes to the theoretical understanding of dynamic learning rate mechanisms in neural networks and also pave the way for the development of more efficient and reliable neural optimization techniques. This study intends to formalize and validate the equiconnectedness of loss function as superlevel sets in the context of neural network training, opening newer avenues for future research in adaptive machine learning algorithms. We leverage previous theoretical discoveries to propose training mechanisms that can effectively handle complex and high-dimensional data landscapes, particularly in applications requiring high precision and reliability.

Cross-Vendor Reproducibility of Radiomics-based Machine Learning Models for Computer-aided Diagnosis

Background: The reproducibility of machine-learning models in prostate cancer detection across different MRI vendors remains a significant challenge. Methods: This study investigates Support Vector Machines (SVM) and Random Forest (RF) models trained on radiomic features extracted from T2-weighted MRI images using Pyradiomics and MRCradiomics libraries. Feature selection was performed using the maximum relevance minimum redundancy (MRMR) technique. We aimed to enhance clinical decision support through multimodal learning and feature fusion. Results: Our SVM model, utilizing combined features from Pyradiomics and MRCradiomics, achieved an AUC of 0.74 on the Multi-Improd dataset (Siemens scanner) but decreased to 0.60 on the Philips test set. The RF model showed similar trends, with notable robustness for models using Pyradiomics features alone (AUC of 0.78 on Philips). Conclusions: These findings demonstrate the potential of multimodal feature integration to improve the robustness and generalizability of machine-learning models for clinical decision support in prostate cancer detection. This study marks a significant step towards developing reliable AI-driven diagnostic tools that maintain efficacy across various imaging platforms.