An algebraic generalization for graph and tensor-based neural networks
Bibliographic record
Abstract
Despite significant effort, there is currently no formal or de facto standard framework or format for constructing, representing, or manipulating general neural networks. In computational neuroscience, there have been some attempts to formalize connectionist notations and generative operations for neural networks, including Connection Set Algebra, but none are truly formal or general. In computational intelligence (CI), though the use of linear algebra and tensor-based models are widespread, graph-based frameworks are also popular and there is a lack of tools supporting the transfer of information between systems. To address these gaps, we exploited existing results about the connection between linear and relation algebras to define a concise, formal algebraic framework that generalizes graph and tensor-based neural networks. For simplicity and compatibility, this framework is purposefully defined as a minimal extension to linear algebra. We demonstrate the merits of this approach first by defining new operations for network composition along with proofs of their most important properties. An implementation of the algebraic framework is presented and applied to create an instance of an artificial neural network that is compatible with both graph and tensor based CI frameworks. The result is an algebraic framework for neural networks that generalizes the formats used in at least two systems, together with an example implementation.
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 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".