Expressive Power of Implicit Models: Rich Equilibria and Test-Time Scaling

Researchers provide mathematical proof that implicit models can achieve greater expressive power through increased test-time computation, explaining how these memory-efficient architectures can match larger explicit networks. The study validates this scaling property across image reconstruction, scientific computing, operations research, and LLM reasoning domains.

• →Implicit models use constant memory by iterating a single parameter block to fixed points, significantly reducing memory requirements compared to explicit models.
• →Mathematical analysis proves that simple implicit operators can express increasingly complex mappings through iteration.
• →Test-time compute scaling allows implicit models to match the performance of much larger explicit networks.
• →Validation across four domains shows that increased iterations improve both solution quality and stability.
• →The research provides theoretical foundation for understanding why compact implicit models can outperform larger traditional architectures.