# The Role of Minimal Complexity Functions in Unsupervised Learning of Semantic Mappings

arXiv: https://arxiv.org/abs/1709.00074 · HTML: https://mlsanity.com/paper/1709.00074/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2017.

## Built on by (most cited first, 4 of 4)

- [Towards Identifiable Unsupervised Domain Translation: A Diversified Distribution Matching Approach](https://mlsanity.com/paper/2401.09671/) (2024)
- [Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures](https://mlsanity.com/paper/2409.19422/) (2024)
- [Weakly Supervised Recovery of Semantic Attributes](https://mlsanity.com/paper/2103.11888/) (2021)
- [Domain Transfer Becomes Identifiable via a Single Alignment](https://mlsanity.com/paper/2605.17918/) (2026)

## Abstract (arXiv)

We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any definition of the semantic information, the problem might seem ill-posed. Specifically, in typical cases, it seems possible to build infinitely many alternative mappings from every target mapping. This apparent ambiguity stands in sharp contrast to the recent empirical success in solving this problem. We identify the abstract notion of aligning two domains in a semantic way with concrete terms of minimal relative complexity. A theoretical framework for measuring the complexity of compositions of functions is developed in order to show that it is reasonable to expect the minimal complexity mapping to be unique. The measured complexity used is directly related to the depth of the neural networks being learned and a semantically aligned mapping could then be captured simply by learning using architectures that are not much bigger than the minimal architecture. Various predictions are made based on the hypothesis that semantic alignment can be captured by the minimal mapping. These are verified extensively. In addition, a new mapping algorithm is proposed and shown to lead to better mapping results.