Simplicial Hopfield networks
Authors: Thomas F Burns, Tomoki Fukai
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We empirically show improved performance under parameter constraints. By restricting the total number of connections to that of pairwise Hopfield networks with a mixture of pairwise and setwise connections, we show simplicial Hopfield networks retain a surprising amount of improved performance over pairwise networks but with fewer parameters, and are robust to topological variability. We tested the performance of our simplicial Hopfield networks by embedding data from the MNIST (Le Cun et al., 2010), CIFAR-10 (Krizhevsky & Hinton, 2009), and Tiny Image Net (Le & Yang, 2015) datasets as memories. |
| Researcher Affiliation | Academia | Thomas F. Burns Neural Coding and Brain Computing Unit OIST Graduate University, Okinawa, Japan thomas.burns@oist.jp Tomoki Fukai Neural Coding and Brain Computing Unit OIST Graduate University, Okinawa, Japan tomoki.fukai@oist.jp |
| Pseudocode | No | The paper provides mathematical equations for energy and update rules, but no explicit pseudocode or algorithm blocks are included. |
| Open Source Code | Yes | To reproduce our results in the main text and appendices, we provide our Python code as supplementary material at https://github.com/tfburns/simplicial-hopfield-networks. |
| Open Datasets | Yes | We tested the performance of our simplicial Hopfield networks by embedding data from the MNIST (Le Cun et al., 2010), CIFAR-10 (Krizhevsky & Hinton, 2009), and Tiny Image Net (Le & Yang, 2015) datasets as memories. |
| Dataset Splits | No | The paper mentions using MNIST, CIFAR-10, and Tiny Image Net datasets. However, it does not explicitly specify train/validation/test splits in terms of percentages or sample counts. It describes embedding memories and testing recall, but not in the typical supervised learning split context. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the experiments, such as GPU or CPU models. It only mentions running "numerical simulations." |
| Software Dependencies | No | The paper states that Python code is provided for reproducibility but does not list specific versions for Python or any key libraries or software dependencies used in the experiments (e.g., NumPy, PyTorch, etc.). |
| Experiment Setup | Yes | In our numerical simulations, we perform updates synchronously until E is non-decreasing or until a maximum number of steps is reached, whichever comes first. In all tests, we used T 1 = 100. We initialise S as one of the memory patterns corrupted by Gaussian noise with variance 0.5. To inspect changes in the energy landscapes of different network conditions, we set N = 10 and P = 10 random patterns. Correct recall was defined as a sum of the squared difference being < 50. |