Fuzzy Relational Models: Convolution Techniques and Optimization
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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".