Bibliographic record
Abstract
Developed from the Ising model, Ising machines are promising to be efficient domain-specific accelerators for solving combinatorial optimization problems (COPs). A simulated bifurcation (SB) algorithm enables an Ising machine to achieve massive parallelism in the simulation of Hamiltonian dynamics. Although SB significantly accelerates the search, more resources are required due to the use of continuous variables for the position of oscillators to obtain discrete spin states, compared to conventional simulated annealing. This article proposes ternary and multiple-value quantized SB (qSB) algorithms by discretizing the position variables used for the hardware-consuming multiply-accumulate (MAC) operations in SB. These quantization schemes do not only reduce the computational complexity, but also improve the solution quality for COPs. Specifically, the ternary qSB with dynamic threshold settings converts the MAC into addition and subtraction. To improve the precision in number representation when solving large-scale COPs, a uniform quantization scheme is applied to provide multiple-valued quantization. Alternatively, a logarithmic qSB leverages the evolution characteristics of position variables and implements multiplication by using simple shift operations. We demonstrate that using the proposed qSB improves the solution quality in a long search and accelerates energy convergence in a short search for solving COPs tackled by up to 2000 fully connected spins.
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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 | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".