COLLAGE-BASED INVERSE PROBLEMS FOR IFSM WITH ENTROPY MAXIMIZATION AND SPARSITY CONSTRAINTS
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Bibliographic record
Abstract
We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its invariant fixed point f is sufficiently close to f in the Lp distance. In this paper, we extend the collage-based method developed by Forte and Vrscay (1995) along two different directions. We first search for a set of mappings that not only minimizes the collage error but also maximizes the entropy of the dynamical system. We then include an extra term in the minimization process which takes into account the sparsity of the set of mappings. In this new formulation, the minimization of collage error is treated as multi-criteria problem: we consider three different and conflicting criteria i.e., collage error, entropy and sparsity. To solve this multi-criteria program we proceed by scalarization and we reduce the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented. Numerical studies indicate that a maximum entropy principle exists for this approximation problem, i.e., that the suboptimal solutions produced by collage coding can be improved at least slightly by adding a maximum entropy criterion.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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