Learning Polynomial Problems with $SL(2, \mathbb{R})$-Equivariance
Authors: Hannah Lawrence, Mitchell Tong Harris
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this work, we demonstrate for the first time that neural networks can effectively solve such problems in a data-driven fashion, achieving tenfold speedups while retaining high accuracy. In our experiments, we compare several instantiations of equivariant learning. Timing Comparison: Trained Network vs Solver |
| Researcher Affiliation | Academia | Hannah Lawrence & Mitchell Tong Harris Massachusetts Institute of Technology |
| Pseudocode | Yes | Algorithm 1 SL(2, R)-equivariant architecture |
| Open Source Code | Yes | We have released all data generation (as well as training) code, so that future research may build on these preliminary benchmarks. can be found in the code at github.com/harris-mit/poly SL2equiv. |
| Open Datasets | No | The paper generates its own synthetic datasets based on described distributions and mathematical constructs (e.g., 'Random, rotationally symmetric' and 'Delsarte spherical code bounds') rather than utilizing an existing, pre-published public dataset. While the data generation code is provided, the datasets themselves are not described as pre-existing public resources with direct access information (e.g., a specific download link for the generated data). |
| Dataset Splits | Yes | We used 5, 000 training examples, 500 validation examples, and 500 test examples. |
| Hardware Specification | Yes | All experiments were run on Nvidia Volta V100 GPUs |
| Software Dependencies | No | The paper mentions software like the Ada M optimizer, Mosek, and SCS, but does not provide specific version numbers for these or other key software dependencies (e.g., Python, PyTorch, CUDA versions) necessary for replication. |
| Experiment Setup | Yes | All experiments were run on Nvidia Volta V100 GPUs, using the Ada M optimizer with learning rate 3 10 4. Experiments were trained for 700 epochs across 4 random seeds. We used the hyperparameters shown in Tables 3 and 4... |