Nebula: Network Enhanced Boltzmann Machine With Universal Local Search Architecture
Bibliographic record
Abstract
We propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nebula</i> , a computational method for combinatorial optimization and stochastic sampling. The proposed method is designed for a generic local search engine utilized for digital annealing in an optimization system for multidimensional binary variables, and it can handle a variety of cost functions of multidimensional binary variables with multi-body interactions in a unified manner. In addition to optimization, the method can be used to perform sampling to reproduce the Boltzmann distribution. To achieve this, we extend the network of conventional Boltzmann machines or Ising machines to include dependent variables mediating various interactions. The extended network enables fast operation by predicting the total energy change due to state transitions in all one-flip neighborhoods. The energy function, which is limited to the quadratic form in conventional Ising machines, is extended here to represent inequality constraints and higher-order products. The ability to handle higher-order spin products enables the implementation of arbitrary energy functions with k-body interactions based on the Walsh transform. We conducted numerical experiments to demonstrate the concept of our proposed method and show that it can solve problems with inequality constraints and higher order terms, which are difficult to solve with conventional Ising machines. The numerical experiments also show that our method can exploit the expansion of the energy landscape by the Walsh function and reproduce the Boltzmann distribution by sampling.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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".