Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Schur's Positive-Definite Network: Deep Learning in the SPD cone with structure
Authors: Can Pouliquen, Mathurin Massias, Titouan Vayer
ICLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our experiments illustrate the versatility and relevance of Spod Net layers for such applications. We demonstrate the framework s relevance through applications in sparse precision matrix estimation. We highlight the limitations of other learning-based approaches and show how Spod Net addresses these issues. Our experiments validate Spod Net s effectiveness in jointly learning SPD-to-SPD and sparsity-inducing functions, yielding competitive results across various performance metrics. 5 EXPERIMENTS We now illustrate Spod Net s ability to learn SPD matrices with additional structure by using our three derived graph learning models (UBG, PNP and E2E) to learn sparse precision matrices, on both synthetic and real data. Additional details regarding the experimental setups can be found in Appendix A. Py Torch implementations can be found in our Git Hub repository2. |
| Researcher Affiliation | Academia | Can Pouliquen ENS de Lyon, Inria, CNRS, Université Claude Bernard Lyon 1, LIP, UMR 5668, 69342, Lyon cedex 07, France EMAIL Mathurin Massias Inria, ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, LIP, UMR 5668, 69342, Lyon cedex 07, France EMAIL Titouan Vayer Inria, ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, LIP, UMR 5668, 69342, Lyon cedex 07, France EMAIL |
| Pseudocode | Yes | Algorithm 1 The Spod Net layer 1: Input: Θin Sp ++ and Win = Θ 1 in 2: for column i {1, , p} do 3: Extract blocks: W11, w12, w22 4: Compute [Θ11] 1 = W11 1 w22 w12w 12 5: New column θ+ 12 = f(Θ) 6: New diagonal value θ+ 22 = g(Θ) + θ+ 12 [Θ11] 1θ+ 12 7: Update Θ = Θ+, W = W + as in Equations (2) and (3) 8: end for 9: Output: Θout Sp ++ and Wout = Θ 1 out |
| Open Source Code | Yes | Py Torch implementations can be found in our Git Hub repository2. 2https://github.com/Perceptronium/Spod Net |
| Open Datasets | Yes | We generate N sparse SPD p p matrices using sklearn s make_sparse_spd_matrix function (Pedregosa et al., 2011), of which we ensure proper conditioning by adding 0.1 Ip. We consider the Animals dataset (Lake and Tenenbaum, 2010), which comprises p = 33 animal species, each characterized by responses to n = 102 binary questions (e.g., "Has teeth?", "Is poisonous?"). |
| Dataset Splits | Yes | We generate Ntrain = 1000 different (S, Θtrue) couples for the training set and Ntest = 100 couples for the testing set on which we validate our models. Further details on the parameters used during the data generation are in Appendix A.1. |
| Hardware Specification | No | We would like to thank Badr Moufad (Ecole Polytechnique, France) for his help with the implementations, Paulo Gonçalves (Inria Lyon, France) for fruitful discussions as well as the Centre Blaise Pascal for computing ressources, which uses the SIDUS solution developed by Emmanuel Quemener (ENS Lyon, France) (Quemener and Corvellec, 2013). |
| Software Dependencies | No | Py Torch implementations can be found in our Git Hub repository2. We generate N sparse SPD p p matrices using sklearn s make_sparse_spd_matrix function (Pedregosa et al., 2011) |
| Experiment Setup | Yes | All three models are trained using ADAM with default hyperparameters (Kingma and Ba, 2014). For the weakly sparse settings, we use a learning rate of 10 3 for all three of our own models. For the strongly sparse settings, we use a learning rate of 10 2. GLAD s learning rate is set to 10 2 in all settings. All four models are trained on the same 1000 training matrices, using a batch-size of 10, with ADAM s default parameters. We generate 1000 training matrices and train the model for 100 epochs. |