Learning with Exact Invariances in Polynomial Time
Authors: Ashkan Soleymani, Behrooz Tahmasebi, Stefanie Jegelka, Patrick Jaillet
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we provide complementary experiments to support our theoretical results. We first show that, in practice, Kernel Ridge Regression (KRR) is not a G-invariant estimator. Then, we demonstrate that our algorithm (Spec-Avg) achieves the same rate of population risk as KRR, while enjoying exact invariance properties. The results of the experiments are depicted in Figure 1 and Figure 2 in Appendix C. |
| Researcher Affiliation | Academia | 1MIT EECS and MIT LIDS 2MIT EECS and MIT CSAIL 3School of CIT, MCML, and MDSI, Technical University of Munich (TUM). |
| Pseudocode | Yes | Pseudocode for the method is presented in Algorithm 1. |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code or a link to a code repository. |
| Open Datasets | No | The paper describes a self-generated dataset based on a target function and uniform sampling from Td = [-1, 1)^d, but it does not refer to a publicly available or open dataset with access information (link, DOI, citation to a dataset paper). |
| Dataset Splits | No | The trained models are evaluated on a test dataset of size 100. Both the test and train datasets are generated uniformly from the interval [ -1, 1]d, independently and identically distributed. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as CPU, GPU models, or cloud computing instance types used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers. |
| Experiment Setup | Yes | We conduct our experiments for d = 10. The trained models are evaluated on a test dataset of size 100. Both the test and train datasets are generated uniformly from the interval [ -1, 1]d, independently and identically distributed. Each point in our plots represents an average over 10 different random seeds (from 1 to 10) to account for the randomness in the data generation process. ... In Figure 2 in Appendix C, we present the empirical excess population risk of KRR and Spec-Avg for different hyperparameters λ and D, respectively. ... It can be observed that Spec-Avg with D = 176 achieves the same order of performance as KRR with λ = 50. |