AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity
Authors: Silviu-Marian Udrescu, Andrew Tan, Jiahai Feng, Orisvaldo Neto, Tailin Wu, Max Tegmark
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We describe our symbolic regression algorithm (which is publicly available1) in Section 2 and test it with numerical experiments in Section 3. We now turn to quantifying the performance of our method with numerical experiments, comparing it with that of [25] which recently exceded the previous state of-the-art performance of [10]. |
| Researcher Affiliation | Collaboration | Silviu-Marian Udrescu1, Andrew Tan1, Jiahai Feng1, Orisvaldo Neto1, Tailin Wu2 & Max Tegmark1,3 1MIT Dept. of Physics and Institute for AI & Fundamental Interactions, Cambridge, MA, USA 2Stanford Dept. of Computer Science, Palo Alto, CA, USA 3Theiss Research, La Jolla, CA, USA |
| Pseudocode | No | The paper describes its algorithms and methods using prose and diagrams (e.g., Figure 2, Figure 3), but it does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our code is can be installed by typing pip install aifeynman and is also available at https://ai-feynman. readthedocs.io. |
| Open Datasets | Yes | As seen in Table 3, our method solves 73 of 100 baseline problems from the Feynman Symbolic Regression Database [25] with r = 1, and is typically 1-3 orders of magnitude more robust than that of [25]. |
| Dataset Splits | Yes | We used 80% of the available data the training and the rest for validation. |
| Hardware Specification | No | The paper mentions 'The flows trained in about 20 minutes on one CPU', but it does not provide specific details about the CPU model, GPU, or any other hardware specifications used for running the experiments. |
| Software Dependencies | No | The paper states that its code can be installed via 'pip install aifeynman' and mentions using the Adam optimizer and 'RQ-NSF' (rational-quadratic neural spline flows), but it does not list specific software dependencies with their version numbers (e.g., Python 3.x, PyTorch 1.x). |
| Experiment Setup | Yes | Our neural network approximation f NN of the mystery function f is fully-connected, feed-forward neural network with 4 hidden layers of 128, 128, 64 and 64 neurons, respectively, all with tanh activation function. We used 80% of the available data the training and the rest for validation. We used the r.m.s. error loss function and the Adam optimizer with β-parameters of 0.9 and 0.999. The learning rate was initialized to 0.01 and reduced by a factor of 10 whenever the validation loss failed to improve for more than 20 epoch, until it reached 10 5. Specifically, we used three steps of the RQ-NSF with RQ-NSF (C) coupling layers as described in [34], parametrized by three 16-neuron softplus layers, trained for 50, 000 epochs with the Adam optimizer. The learning rate was initialized to 3 10 4 and halved every time the test loss failed to improve for 2500 epochs. |