arXiv:2511.12398v2 Announce Type: replace Abstract: Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry. In this paper, we construct symmetric deep neural networks to approximate symmetric Korobov functions and prove that both the convergence rate and the constant prefactor scale at most polynomially with respect to the ambient dimension. This represents a substantial improvement over prior approximation guarantees that suffer from the curse of dimensionality. Building on these approximation bound
This paper represents a significant step in overcoming a long-standing theoretical limitation in deep neural network application, building on recent advances in AI architecture and mathematical tools.
Improved approximation capabilities for symmetric functions could unlock new efficiencies and performance gains in AI systems dealing with complex physical simulations or structured data, reducing computational burden and improving accuracy.
The ability to handle the 'curse of dimensionality' for symmetric Korobov functions in deep neural networks means AI can more efficiently model certain types of complex, high-dimensional data, expanding its practical application space.
- · AI researchers
- · Deep learning practitioners
- · Computational science
- · Physics simulations
- · Traditional approximation methods
- · Brute-force computational approaches
More efficient and accurate deep learning models for problems with inherent symmetry.
Accelerated development and deployment of AI in fields requiring high-dimensional symmetry modeling, such as materials science or quantum chemistry.
These algorithmic improvements could contribute to the overall efficiency and scalability of AI systems, indirectly impacting the compute supply chain by allowing more complex models to run on existing infrastructure.
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Read at arXiv cs.LG