ArticleProceedings of the National Academy of Sciences of the United States of America2024
The training process of many deep networks explores the same low-dimensional manifold.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
4 citing papers in PubMed.
- Contrastive learning to fine-tune feature extraction models for the visual cortex.PLoS computational biology · 2026Article
- Artificial intelligence as a surrogate brain: bridging neural dynamical models and data.National science review · 2026Review
- Searching for physical principles of morphogenesis.Development (Cambridge, England) · 2025Review
- Dimensional reduction and adaptation-development-evolution relation in evolved biological systems.Biophysical reviews · 2024Review
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
8 authors.
Funding
Abstract
We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an effectively low-dimensional manifold. Networks with a wide range of architectures, sizes, trained using different optimization methods, regularization techniques, data augmentation techniques, and weight initializations lie on the same manifold in the prediction space. We study the details of this manifold to find that networks with different architectures follow distinguishable trajectories, but other factors have a minimal influence; larger networks train along a similar manifold as that of smaller networks, just faster; and networks initialized at very different parts of the prediction space converge to the solution along a similar manifold.
Indexed as
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.