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.