Fuzzy Relational Models: Convolution Techniques and Optimization
Why this work is in the frame
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Bibliographic record
Abstract
Convolutional operations have been one of the mechanisms of functional processing of neural networks, especially present as a part of convolutional neural networks. Fuzzy convolution (composition operation) has been widely explored. within the framework of fuzzy relational equations, its integration into computational architectures such as neural networks remains underexplored. This study introduces a framework that formally extends conventional convolution into the domain of fuzzy set theory through the development of fuzzy convolution operations. We formulate and solve an optimization problem aimed at fine-tuning fuzzy convolution kernels using established fuzzy relational structures, thereby enhancing the interpretability of neural processing. Several t-norms and t-conorms that implement convolution operators are examined within the framework of s-t and t-s convolutions (compositions) of fuzzy relations. A detailed derivation of the optimization schemes is presented. Several experiments on images are conducted, demonstrating that even with a data size reduction of up to 75%, the method can still effectively reconstruct images by optimizing the parameters of the relational architecture.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it