A graph-based compression approach showed a sharp accuracy drop in each of three tested neural networks when the allowed error reached a reported range of 0.35 to 0.5. At smaller error settings, network size fell while test accuracy changed little. The experiments were carried out after training, so the pattern is a result from those three networks rather than evidence of a universal compression threshold.
The document is arXiv:2608.25598v1, an arXiv version 1 preprint dated 26 August 2026. Its stated aim is to provide a general theoretical framework for fibrations on graphs labelled by a commutative monoid and apply that framework to compression of arbitrary neural networks, including convolutional networks.
The three tests
The experiments covered a LeNet-300-100 multilayer perceptron, or MLP, and a LeNet-5 convolutional neural network, or CNN, both using MNIST, as well as a VGG16-BN network using CIFAR-10. In each case, the trained network was converted after training into an M-graph, processed with the ε-approximate M-fibration algorithm, converted back into a neural network and evaluated on a test set.
For the MNIST MLP, ε=0.4 left 305 surviving units, equal to 76% of the original, and 210k parameters, or 79%, while test accuracy was 97.53%. With ε=0.5, the compressed network retained 169 units, or 42%, and 121k parameters, or 45%; accuracy was 79.6%.
The MNIST CNN retained 166 units, or 94%, and 74.7k parameters, or 93%, at ε=0.4, with 98.89% accuracy. At ε=0.5, it retained 18 units, or 10%, and 2.1k parameters, or 2.6%, while accuracy was 14.7%.
VGG16-BN showed three reported settings. At ε=0.30, it retained 3,610 units, or 69%, and 8.38 million parameters, or 55%, with 91.53% accuracy. At ε=0.35, the figures were 3,233 units, or 62%, and 6.75 million parameters, or 44%, with 90.18% accuracy. At ε=0.40, 2,493 units, or 48%, and 4.32 million parameters, or 28%, remained, while accuracy was 10.0%.
The mathematical frame
The framework works with graphs whose labels come from a commutative monoid, a label system in which the order of combining values does not matter. It defines an ε-approximate M-fibration through a global error bound and introduces fibration distance, written fd(G,H), and βG(ε) to express compression at a chosen error level.
For exact fibrations, the paper proves that every M-graph has a minimal M-fibration. Its base is unique up to isomorphism, and the fibration is unique up to composition with an isomorphism of that base. The minimum base can be computed constructively by refining a partition of the graph's nodes until the partition stabilizes.
The paper gives a related invariance result. If G maps to H by an epimorphic M-fibration, H maps epimorphically by an M-fibration to G's minimum base, and the two minimum bases are isomorphic.
Approximate compression has a separate limitation. For positive ε, the paper states that there is generally no single coarsest ε-approximate M-equitable partition. The greedy algorithm guarantees a radius of at most ε for every class, but it may not produce the minimum number of classes.
A worked example called H makes the trade-off visible. The coordinatewise-mean version of the algorithm produced four nodes for ε in [0,1), three for [1,13.5), and one for ε≥13.5. The minimum function βH(ε) was four on [0,1), three on [1,12), and one from ε≥12. The mean-based algorithm was therefore not optimal on [12,13.5), while the exact ℓ1 Chebyshev-center rule reached βH(ε) for every ε.
A narrow result, with code reported
The experimental evidence remains narrow: only three trained networks were evaluated in post-training compression experiments, and no uncertainty estimates were reported. The results therefore do not establish that the same transition is universal or that it extends beyond the three reported cases.
The author interprets the pattern as a sharp accuracy-versus-compression transition under the framework's global error bound. That interpretation is tied to the three reported cases and does not establish a universal law.
The paper reports a self-contained Python library implementing the algorithms, along with an ONNX script that accepts a network, compresses it, tests accuracy and reports the results. The listed repository is https://github.com/boldip/mfib.
Paper data and sources
Original title: M-Fibration Theory with Applications to Neural Network Compression
Authors: Paolo Boldi
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text