Generalization of Gradient Descent in Over-Parameterized ReLU Networks: Insights from Minima Stability and Large Learning Rates

Title: Generalization of Gradient Descent in Over-Parameterized ReLU Networks: Practical Insights and AI Solutions Neural networks trained with gradient descent can effectively work in overparameterized settings with random weight initialization, often finding global optimum solutions despite the non-convex nature of the problem. These solutions, achieving zero training error, surprisingly do not overfit in many cases, a phenomenon known as “benign overfitting.” However, for ReLU networks, interpolating solutions can lead to overfitting. Practical training often stops before reaching full interpolation to avoid entering unstable regions or spiky, non-robust solutions. Key Insights: - Gradient descent with a fixed learning rate converges to local minima representing smooth, sparsely linear functions, avoiding overfitting and achieving near-optimal mean squared error (MSE) rates. - Large learning rates induce implicit sparsity and ReLU networks can generalize well even without explicit regularization or early stopping. - Gradient descent induces an implicit bias resembling L1-regularization, achieving optimal rates in nonparametric regression without weight decay. Practical AI Solutions: 1. Identify Automation Opportunities: Find key customer interaction points that can benefit from AI. 2. Define KPIs: Ensure your AI endeavors have measurable impacts on business outcomes. 3. Select an AI Solution: Choose tools that align with your needs and provide customization. 4. Implement Gradually: Start with a pilot, gather data, and expand AI usage judiciously. Consider the AI Sales Bot from itinai.com/aisalesbot designed to automate customer engagement 24/7 and manage interactions across all customer journey stages. If you want to evolve your company with AI, stay competitive, and use the insights from the Generalization of Gradient Descent in Over-Parameterized ReLU Networks, connect with us at hello@itinai.com. For continuous insights into leveraging AI, stay tuned on our Telegram or Twitter. List of Useful Links: AI Lab in Telegram @itinai – free consultation Twitter – @itinaicom