C-Softmax: Contextual Softmax Operator Incorporating Row and Column Priorities
Bibliographic record
Abstract
This study proposes a novel operator, C-Softmax, which enables the direct integration of contextual information into probability normalization. By overcoming the limitation of traditional softmax functions that produce decisions solely based on intrinsic scores, C-Softmax directly incorporates external contextual information into the output distribution. Such context can be modeled through structures like class priorities, user preferences, or system-inherent biases, thereby enhancing flexibility, interpretability, and controllability in decision-making processes. In this work, the mathematical definition of the C-Softmax operator, its affine invariance, gradient properties, limit behavior, and entropy-temperature relationship are rigorously analyzed, with all theorems fully supported by proofs. Theoretical analyses demonstrate that the operator satisfies desirable properties such as affine invariance, Lipschitz continuity, and entropy-controlled decision-making. The results indicate that C-Softmax provides a solid theoretical foundation for contextual decision-making systems, personalized modeling, and controllable artificial intelligence frameworks.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".