AI Algorithm
AI generated Algorithm
Prompt
Role: Principal AI Research Scientist in Machine Learning & Optimizations. Task: Propose a mathematically rigorous, novel training algorithm that serves as an alternative to Standard Backpropagation for Deep Neural Networks, eliminating the need to store intermediate activation states for the backward pass. Requirements: Mathematical Formulation: Define the layer-wise energy function, objective equations, and update rule using formal LaTeX math. Convergence & Complexity: Provide formal proofs or rigorous derivations for convergence and prove space complexity is reduced to O(1) relative to depth L. Production PyTorch Code: Write a self-contained, working PyTorch implementation showing a 3-layer MLP training on a mock dataset without calling loss.backward(). Theoretical Benchmarks: A structured comparison table mapping your algorithm against Standard Backprop, Forward-Forward Algorithm (Hinton), and Target Propagation.
