Explorations in Self-Supervised Learning: Dataset Composition Testing for Object Classification
Raynor Kirkson E. Chavez, Kyle Gabriel M. Reynoso
TL;DR
This work develops a variational duality framework to establish the existence and nontriviality of $T$-periodic orbits for convex Hamiltonians that are subquadratic at infinity. By formulating the boundary-value problem $\dot{x}=JH'(t,x)$ with $x(0)=x(T)$ as a minimization problem for a dual action $\psi$, the authors derive explicit spectral conditions, notably $\lambda+\gamma<0$, under which at least one nontrivial $T$-periodic solution exists. For autonomous Hamiltonians with $(A_{\infty},B_{\infty})$-subquadratic growth, they obtain nonconstant periodic solutions and discuss minimal-period implications via index considerations and corollaries. Together, these results advance the variational theory of periodic orbits in Hamiltonian dynamics and provide a robust toolkit for proving subharmonics under convex subquadratic growth.
Abstract
This paper investigates the impact of sampling and pretraining using datasets with different image characteristics on the performance of self-supervised learning (SSL) models for object classification. To do this, we sample two apartment datasets from the Omnidata platform based on modality, luminosity, image size, and camera field of view and use them to pretrain a SimCLR model. The encodings generated from the pretrained model are then transferred to a supervised Resnet-50 model for object classification. Through A/B testing, we find that depth pretrained models are more effective on low resolution images, while RGB pretrained models perform better on higher resolution images. We also discover that increasing the luminosity of training images can improve the performance of models on low resolution images without negatively affecting their performance on higher resolution images.