INSTABILITIES AND OSCILLATION IN THE DETERMINISTIC BOLTZMANN MACHINE
Bibliographic record
Abstract
Simulations indicate that the deterministic Boltzmann machine, unlike the stochastic Boltzmann machine from which it is derived, exhibits unstable behavior during contrastive Hebbian learning of nonlinear problems, including oscillation in the learning algorithm and extreme sensitivity to small weight perturbations. Although careful choice of the initial weight magnitudes, the learning rate, and the annealing schedule will produce convergence in most cases, the stability of the resulting solution depends on the parameters in a complex and generally indiscernible way. We show that this unstable behavior is the result of over parameterization (excessive freedom in the weights), which leads to continuous rather than isolated optimal weight solution sets. This allows the weights to drift without correction by the learning algorithm until the free energy landscape changes in such a way that the settling procedure employed finds a different minimum of the free energy function than it did previously and a gross output error occurs. Because all the weight sets in a continuous optimal solution set produce exactly the same network outputs, we define reliability, a measure of the robustness of the network, as a new performance criterion.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".