Manifold embedding underpins most data‑visualisation techniques, yet the dominant methods (t‑SNE, UMAP, PaCMAP) are handcrafted for fixed objectives and cannot be easily steered toward user‑specified structural priorities. AutoManifold introduces a fully autonomous algorithm‑generation pipeline that decomposes the embedding process into three primitive families—affinity, cost, and optimisation—and orchestrates them with a multi‑agent large language model (LLM). Users express structural preferences (e.g., local neighbourhood preservation, global topology, class separation) through a simple interface. In each iteration the system:
- Lets the LLM propose a candidate configuration of primitives conditioned on the user’s priority;
- Evaluates the candidate using predefined metrics such as K‑NN fidelity, global‑structure preservation, and class separability;
- Feeds the metric feedback back to the LLM to refine the next configuration. The loop repeats until the metrics meet the user‑defined thresholds or converge. Experiments on a suite of real‑world datasets—spanning low‑dimensional, noisy, and imbalanced regimes—show that the AutoManifold‑generated algorithms consistently outperform the three most widely used SOTA methods under identical evaluation pipelines, achieving higher scores on the user‑directed structural metrics while preserving the intrinsic data geometry. The implementation is publicly available at https://github.com/buraksusam/AutoManifold_NeurIPS2026.
Review: AutoManifold demonstrates that LLMs can move beyond hyper‑parameter tuning to actual algorithm synthesis, offering a practical route to user‑driven visualisation methods and expanding the toolbox for interactive data analysis.