Neural FIM: Bridging Statistical Manifolds and Generative Modeling through Fisher Geometry
Bibliographic record
Abstract
While data diffusion-based embeddings are widely used in unsupervised learning to reveal the intrinsic geometry of data, they are fundamentally constrained by their discrete nature and inability to generalize beyond training points. This limitation obscures a key geometric property, the metric tensor, which encodes significant information about the intrinsic geometry of the data. To address this, we propose Neural FIM, a method that learns a continuous and differentiable representation of the data via Jensen-Shannon divergence, which enables the computation of the Fisher Information Metric (FIM). Neural FIM creates an extensible metric space from discrete point clouds, providing insights into various geometric characteristics such as volume and geodesics. Here, we introduce a new paradigm for computing geodesics via fast optimization of parametric curves, facilitating the interpolation of geodesic paths between points and geodesic flows between distributions. We demonstrate the utility of Neural FIM in selecting parameters for the PHATE visualization method and its ability to reveal local volume information, highlighting branching points in one toy dataset and two single-cell datasets involving IPSC reprogramming and embryoid body stem cell differentiation. Moreover, we show that the learned geodesics using neural FIM recover cell differentiation branches in the embryoid body data and outperforms state-of-the-art methods in single-cell population-level trajectory inference.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".