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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Learning (Approximately) Equivariant Networks via Constrained Optimization
Authors: Andrei Manolache, Luiz Chamon, Mathias Niepert
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conduct a systematic study across four representative domains to examine the impact of our algorithm on convergence, sample efficiency, and robustness to input degradation compared to strictly equivariant models and relaxed alternatives. |
| Researcher Affiliation | Collaboration | Andrei Manolache124 Luiz F.O. Chamon3 Mathias Niepert12 1Computer Science Department, University of Stuttgart, Germany 2International Max Planck Research School for Intelligent Systems, Germany 3Department of Applied Mathematics, École Polytechnique de Paris, France 4Bitdefender, Romania EMAIL EMAIL |
| Pseudocode | Yes | Algorithm 1 Strictly equivariant data 1: Inputs: ηp, ηd > 0, γ(0) = 1, λ(0) = 0 2: J(t) 0 = 1 n=1 ℓ0 fθ(t),γ(t)(xn), yn 3: θ(t+1) = θ(t) ηp θJ(t) 0 4: γ(t+1) i = γ(t) i ηp γi J(t) 0 + λ(t) i 5: λ(t+1) i = λ(t) i + ηdγ(t) i Algorithm 2 Partially equivariant data 1: Inputs: ηp, ηd > 0, γ(0) = 1, λ(0) = 0 2: J(t) 0 = 1 n=1 ℓ0 fθ(t),γ(t)(xn), yn 3: θ(t+1) = θ(t) ηp θJ(t) 0 4: γ(t+1) i = γ(t) i ηp γi J(t) 0 + λ(t) i 5: u(t+1) i = u(t) i + ηp(ρu(t) i λ(t) i ) 6: λ(t+1) i = h λ(t) i + ηd(|γ(t) i | u(t) i ) i |
| Open Source Code | Yes | The code and instructions on how to reproduce the experiments are publicly available at https: //github.com/andreimano/ACE. |
| Open Datasets | Yes | To address RQ1, we begin with the N-Body simulations dataset [63]. We evaluate on the QM9 dataset [64, 65] using the invariant Sch Net [12] and our ACE variant. On the Model Net40 classification benchmark [66], we apply ACE to the VN-DGCNN architecture [67, 45]. Next, we evaluate predictive performance on the CMU Motion Capture (Mo Cap) Run and Walk datasets [69] |
| Dataset Splits | Yes | For Sch Net, we shuffle the dataset obtained from Py Torch Geometric [73] and split the dataset with a 80%/10%/10% train/validation/test ratio. For SEGNN, we use the official splits from [44]. |
| Hardware Specification | Yes | All experiments were performed on a RTX A5000 GPU with an Intel i9-11900K CPU. All of the experiments were performed on internal clusters that contain a mix of Nvidia RTX A5000, RTX 4090, or A100 GPUs and Intel i9-11900K, AMD EPYC 7742, and AMD EPYC 7302 CPUs. |
| Software Dependencies | No | All experiments are implemented in Py Torch [72] using each model s official code base and default hyperparameters as a starting point. For Sch Net, we shuffle the dataset obtained from Py Torch Geometric [73] |
| Experiment Setup | Yes | The training splits, optimizer and hyperparameters follow previous literature. We detail the changes that we make in the Appendix. The code will be publicly released upon acceptance. All experiments are implemented in Py Torch [72] using each model s official code base and default hyperparameters as a starting point. Because several repositories employed learning rates that proved sub-optimal, we performed a grid search for both the primal optimizer and, when applicable, the dual optimizer in our constrained formulation. After selecting the best values, we re-ran every configuration with multiple random seeds. Table 5 lists the learning rates explored and the number of seeds per dataset. |