QSBMs: Lightweight Quantized Simulated Bifurcation Ising Machines
Bibliographic record
Abstract
Ising machines have shown great potential as efficient domain-specific accelerators for solving combinatorial optimization problems (COPs). Derived from quantum mechanics, simulated bifurcation (SB) achieves massive parallelism in updating the spin states in an Ising machine. Although SB speeds up the search for a solution compared to traditional simulated annealing, it requires more hardware resources since continuous variables are used for the positions of oscillators to obtain discrete spin states. In this article, lightweight quantized SB Ising machines (QSBMs) are developed to achieve a better tradeoff between search performance and hardware efficiency. In various quantization schemes, ternary and multiple-value quantized SB (qSB) algorithms discretize the position variables for the multiply-and-accumulate (MAC) operations in SB. The ternary qSB with dynamic threshold settings converts the MAC into addition, while uniform and logarithmic quantization schemes improve precision in the number representation when solving large-scale COPs. Three hardware-efficient QSBMs are subsequently designed with a fully connected topology. Synthesized on a Xilinx Virtex UltraScale+ field-programmable gate array (FPGA), the costly multiplication is implemented by using simple logic operators. Fully connected 2048-spin QSBMs use up to 50.8% fewer lookup tables and up to 82.5% fewer flip-flops than conventional FPGA-based SB machines. The QSBMs are superior in both long and short searches, respectively reaching 99. 1% and 98.5% of the best known solution in 1.46 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ms$</tex-math></inline-formula> and 0.73 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ms$</tex-math></inline-formula> on solving 2000-spin Ising problems.
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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 | 0.001 | 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) | 0.000 | 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".