Approximating Latent Manifolds in Neural Networks via Vanishing Ideals
Authors: Nico Pelleriti, Max Zimmer, Elias Samuel Wirth, Sebastian Pokutta
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments confirm the effectiveness and efficiency of the proposed approach. We perform extensive experiments that showcase that VI-Nets can achieve performance competitive to the pretrained baseline NNs while using much fewer parameters. Our experiments use a pretrained baseline neural network, leveraging only its latent outputs, and apply approximate vanishing ideal computations to these features. |
| Researcher Affiliation | Academia | 1Department for AI in Society, Science, and Technology, Zuse Institute Berlin, Germany 2Institute of Mathematics, Technische Universit at Berlin, Germany. All authors are affiliated with academic institutions. |
| Pseudocode | Yes | Algorithm 1 describes the VI-Net pipeline. It starts by training or using a pretrained network ϕ, truncating it at layer L , and extracting features Zk for each class k [K]. |
| Open Source Code | Yes | Our code is available at https://github.com/ZIB-IOL/approximating-neural-network-manifolds |
| Open Datasets | Yes | We evaluate classification on CIFAR-10/-100 (Krizhevsky, 2009) with Res Net models (He et al., 2015). |
| Dataset Splits | Yes | We apply truncations to a standard Res Net-18, retaining 512 training images per class for constructing approximate vanishing ideals. ... Throughput is measured on the test split (batch size 256), averaged across 5 random seeds with standard deviation indicated. ... We evaluate classification on CIFAR-10/-100 (Krizhevsky, 2009)... |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU/CPU models or processor types. It mentions 'throughput (measured in images per second)' but not the hardware on which this was measured. |
| Software Dependencies | No | All experiments use Py Torch (Paszke et al., 2019). No version number for PyTorch or any other library is specified. |
| Experiment Setup | Yes | Specifically, we (i) demonstrate that VI-Net achieves competitive accuracy, and (ii) examine the impact of network truncation and polynomial pruning on accuracy, parameter efficiency, and throughput (measured in images per second). ... vanishing tolerance ψ = 0.1 (cf. Definition 2.3), maximal polynomial degree d = 5, and feature reduction to 128 dimensions using PCA. Fine-tuning of the linear classifier and coefficient matrix uses SGD (learning rate 0.05, momentum 0.9) with standard data augmentations. |