# On the Parameter Combinations That Matter and on Those That do Not

arXiv: https://arxiv.org/abs/2110.06717 · HTML: https://mlsanity.com/paper/2110.06717/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 58 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 5 of 5)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Emergence of Invariance and Disentanglement in Deep Representations](https://mlsanity.com/paper/1706.01350/) (2017)
- [Latent common manifold learning with alternating diffusion: analysis and applications](https://mlsanity.com/paper/1602.00078/) (2016)
- [Spectral Discovery of Jointly Smooth Features for Multimodal Data](https://mlsanity.com/paper/2004.04386/) (2020)

## Built on by (most cited first, 12 of 12)

- [Dimensionless machine learning: Imposing exact units equivariance](https://mlsanity.com/paper/2204.00887/) (2022)
- [Integrating supervised and unsupervised learning approaches to unveil critical process inputs](https://mlsanity.com/paper/2405.07751/) (2024)
- [Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling](https://mlsanity.com/paper/2311.00797/) (2023)
- [Identifiability of Differential-Algebraic Systems](https://mlsanity.com/paper/2405.13818/) (2024)
- [Conformal Disentanglement and Latent-Space Curation: A Neural Framework for Perspective Synthesis, Differentiation and Targeted Generation](https://mlsanity.com/paper/2408.15344/) (2024)
- [Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example](https://mlsanity.com/paper/2310.19039/) (2023)
- [Nonlinear Manifold Learning Determines Microgel Size from Raman Spectroscopy](https://mlsanity.com/paper/2403.08376/) (2024)
- [Thinner Latent Spaces: Detecting Dimension and Imposing Invariance with Conformal Autoencoders](https://mlsanity.com/paper/2408.16138/) (2024)
- [Hierarchical Dimensionless Learning (Hi-π): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations](https://mlsanity.com/paper/2507.18332/) (2025)
- [On Some Tunable Multi-fidelity Bayesian Optimization Frameworks](https://mlsanity.com/paper/2508.01013/) (2025)
- [RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservation](https://mlsanity.com/paper/2601.14794/) (2026)
- [The Degeneracy Distillery](https://mlsanity.com/paper/2606.23838/) (2026)

## Abstract (arXiv)

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically.