Discovering Numerous Strassen’s Equivalent Equations Using a Simple Micro Multimodal GA: Evolution in Action
Bibliographic record
Abstract
Solving real-world complex optimization problems using simple metaheuristic algorithms is a challenging but attractive task. Making matrix multiplication efficient is one of the interesting problems. This time-consuming algebric operation is required in many applications in science and engineering, thus reducing its complexity targets more efficient computation. In fact, many of practical and theatrical complicated calculations can be modeled efficiently as matrix-based operations, therefore matrix multiplication is computationally expansive operator among all others. In this paper, a simple metaheuristic method based on Micro Genetic Algorithm is proposed to find Strassen's equivalent solutions which is an algebraic method to compute the product of two matrices with minimal number of multiplications. Since there are numerous optimal solutions, the modeled problem is a large-scale and highly multi-modal optimization problem. The proposed method could find more than 160, 000 valid solutions with same complexity as Strassen's in a large-scale search space. Among all discovered solutions found using the proposed method, there are 701 distinct solutions which is the maximum number of discovered Strassen's equivalent solutions to the best of our knowledge. The proposed algorithm is simple but very efficient to find more and more solutions, in fact, that is a great demonstration of “evolution in action” to tackle real-world complex problems like the current one, which just one set of its equations has been discovered by the Germen mathematicians and has remained mysterious for more than 50 years.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| 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".