Approaching ORBIT: Examinations of Variant Agnostic Information Traversals in ML [2026_04_01-2026_09_23]

One endows the searcher with candidate representations that are then switched between due to local evidence and the experimentalist's utility. The most general claims (e.g., that all architectures have differently performant representations on arbitrary non-convex problems, or that instance-recoverability is always feasible) likely do not hold. So, this project examines those theoretical limits.</p><p dir="ltr"><br></p><p dir="ltr">Weaker hypotheses may nonetheless hold.

For example, given an unrestricted (locally reachable) representation class and fixed compute budget, a class of ORBIT algorithms may achieve lower regret than any strictly fixed representation (in hindsight). This project also examines those claims, building on the work of Chen et al. (2015), Liu et al. (2018), and Gavranovic et al. (2024).</p><p><br></p><p dir="ltr">Stages:</p><p dir="ltr"><br><b>1. Hylogisms</b><br>1.1 Matter-Config.

Quotient Smoothness<br>1.2 Full State-Config. Quotient Smoothness<br>1.3 Compositionality Principles and SVS Metric Projection<br>1.4 Discretisation/Lattice Formation<br>1.5 Extensions: Coordinate Agnosticism and Scale Renormalisation</p><p dir="ltr">1.6 Simple Empirical Example</p><p dir="ltr"><br><b>2. Information Space</b><br>2.1 Ontological Construction<br>2.2 Invariant Foundations<br>2.3 Minimal Variational Dynamics<br>2.4 Minimal Sufficient Formalism</p><p dir="ltr">2.5 Empirical Model Distinctions</p><p><br></p><p dir="ltr">Chen, T., Goodfellow, I. and Shlens, J. (2015) 'Net2Net: Accelerating learning via knowledge transfer', arXiv preprint arXiv:1511.05641.</p><p dir="ltr">Liu, C., Zoph, B., Neumann, M., Shlens, J., Hua, W., Li, L.J., Fei-Fei, L., Yuille, A., Huang, J. and Murphy, K. (2018) 'Progressive neural architecture search', in Proceedings of the European Conference on Computer Vision (ECCV), pp. 19-34.</p><p dir="ltr">Gavranović, B., 2024.

Fundamental Components of Deep Learning: A category-theoretic approach. arXiv preprint arXiv:2403.13001.</p>