• DOI:10.48550/arXiv.2212.07934
• Corpus ID: 254685535

Extending Universal Approximation Guarantees: A Theoretical Justification for the Continuity of Real-World Learning Tasks

@article{Durvasula2022ExtendingUA,
  title={Extending Universal Approximation Guarantees: A Theoretical Justification for the Continuity of Real-World Learning Tasks},
  author={Naveen Durvasula},
  journal={ArXiv},
  year={2022},
  volume={abs/2212.07934}
}

• Naveen Durvasula
• Published 6 December 2022
• Computer Science
• ArXiv

Universal Approximation Theorems establish the density of various classes of neural network function approximators in C ( K, R m ) , where K ⊂ R n is compact. In this paper, we aim to extend these guarantees by establishing conditions on learning tasks that guarantee their continuity. We consider learning tasks given by conditional expectations x (cid:55)→ E [ Y | X = x ] , where the learning target Y = f ◦ L is a potentially pathological transformation of some underlying data-generating process L . Under a factorization L = T ◦ W for the data-generating process where T is thought of as a deterministic map acting on some random input W , we establish conditions (that might be easily verified using knowledge of T alone) that guarantee the continuity of practically any derived learning task x (cid:55)→ E [ f ◦ L | X = x ] . We motivate the realism of our conditions using the example of randomized stable matching, thus providing a theoretical justification for the continuity of real-world learning tasks.