The Gradient Wall: Why Scaling Cannot Cross the Shannon-Kolmogorov Barrier

Key Points

• To explore the transformer gradient wall phenomenon and its implications for scaling in AI models.
• Introduced the Void Framework to analyze the gradient wall phenomena.
• Utilized concepts like the Fantasia Bound to predict the existence of the wall.
• Applied K-Factorization for understanding scale invariance among models.
• Examined the gradient signal necessary for effective learning through the shape function.
• Confirmed the existence of a gradient wall that restricts scaling.
• Demonstrated that scaling beyond certain limits leads to diminishing returns in performance.
• Provided theoretical support for the importance of gradient signal in the training process.