Optimal evaluation of symmetry-adapted <i>n</i>-correlations via recursive contraction of sparse symmetric tensors
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract We present a comprehensive analysis of an algorithm for evaluating high-dimensional polynomials that are invariant (or equi-variant) under permutations and rotations. This task arises in the evaluation of linear models as well as equivariant neural network models of many-particle systems. The theoretical bottleneck is the contraction of a high-dimensional symmetric and sparse tensor with a specific sparsity pattern that is directly related to the symmetries imposed on the polynomial. The sparsity of this tensor makes it challenging to construct a highly efficient evaluation scheme. Bachmayr et al. (“Polynomial approximation of symmetric functions,” Math. Comp. , vol. 93, pp. 811–839, 2024) and Lysogorskiy et al. (“Performant implementation of the atomic cluster expansion (pace): application to copper and silicon,” npj Comput. Mater. , vol. 7, Art. no. 97, 2021) introduced a recursive evaluation strategy that relied on a number of heuristics, but performed well in tests. In the present work, we propose an explicit construction of such a recursive evaluation strategy and show that it is in fact optimal in the limit of infinite polynomial degree.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.005 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it