Research map / Learning theory and algorithms / Prediction and decision losses
Metric and ordinal embedding
Learn distance-preserving embeddings from metric or ordinal information.
47 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Prediction and decision losses, keyword cluster “ranking · nearest · neighbor”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
10 papers in 2023–24 and 10 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 1.9% to 1.7%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Finite Sample Prediction and Recovery Bounds for Ordinal Embedding (NeurIPS 2016 · 52 citations)
- 2017 · Joint Dimensionality Reduction and Metric Learning: A Geometric Take (ICML 2017 · 47 citations)
- 2018 · Representation Tradeoffs for Hyperbolic Embeddings (ICML 2018 · 190 citations)
- 2019 · TensorFuzz: Debugging Neural Networks with Coverage-Guided Fuzzing (ICML 2019 · 134 citations)
- 2020 · Revisiting Saliency Metrics: Farthest-Neighbor Area Under Curve (CVPR 2020 · 7 citations)
- 2021 · Margin-Independent Online Multiclass Learning via Convex Geometry (NeurIPS 2021 · 0 citations)
- 2022 · Optimally Controllable Perceptual Lossy Compression (ICML 2022 · 3 citations)
- 2023 · Neural Bregman Divergences for Distance Learning (ICLR 2023 · 2 citations)
- 2024 · The Linear Representation Hypothesis and the Geometry of Large Language Models (ICML 2024 · 10 citations)
- 2025 · Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embedding (CVPR 2025 · 3 citations)
- 2026 · Magnitude Distance: A Geometric Measure of Dataset Similarity (ICML 2026 · 0 citations)
Earliest papers here
- Finite Sample Prediction and Recovery Bounds for Ordinal Embedding (NeurIPS 2016 · 52 citations)
- Nearly Isometric Embedding by Relaxation (NeurIPS 2016 · 17 citations)
- Spatially Binned ROC: A Comprehensive Saliency Metric (CVPR 2016 · 9 citations)
What has been tried
40 papers here report 316 measured changes (a component added, removed or swapped, compared with a baseline): helped 59%, no clear effect 12%, hurt 22%, mixed 8%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Increase embedding dimension from 80 to the ESD dimension 140 | DNA storage test · AE_h | 0.48±0.01 -> 0.47±0.00 | Helped | Levenshtein Distance Embedding with Poisson Regression for DNA Storage (AAAI 2024 · 2 citations) |
| replace importance sampling with uniform sampling | Real datasets without outliers · relative error | No clear effect | Fully Dynamic Algorithms for Chamfer Distance (NeurIPS 2025 · 0 citations) |
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 20 papers; from OpenAlex and the papers' affiliations).
- Columbia University · 2 papers
- Google · 2 papers
- Universität Vienna · 2 papers
- Peking University · 2 papers
Use it
Download BibTeX of 35 key papersOpen the topic in the interactive map
Get alerts. Describe your idea in scime atlas and save it (free scime account): you get a weekly email when new preprints land close to it.
Related approaches
Same keyword cluster
- Ranking models from comparisons (127 papers)
- Approximate nearest neighbor indexing (58 papers)
- Locality-sensitive hashing (30 papers)
Elsewhere in the topic
- Adaptive testing and experiments (201 papers)
- Active learning and subset selection (199 papers)
- Distributionally robust optimization (184 papers)
- Data attribution and recourse (160 papers)
- Theory of neural network sensitivity (143 papers)
- Determinantal point process inference (122 papers)
- Conformal prediction sets (116 papers)
- Provable post-hoc explanations (92 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).