Distillation Process Ontology

FLOW ALGEBRA — DISTILLATION PROCESS ONTOLOGY
Version: 1.0
Date: 2026-10-29
Authors: Mark Anthony Higgins — Sky Recursive AI
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/distillation-process-ontology.html
Status: Topic-based formalisation; source-page text not verified.
Domain: AI / Training Process Entities / Knowledge Distillation

1. PURPOSE
Formalise knowledge distillation as a directed, constrained training process in which a student model learns from signals produced by a teacher model, potentially combined with ground-truth labels. This is AI model distillation, not physical distillation.

2. ENTITY SET
TeacherModel T; StudentModel S; TrainingDataset D; InputSample x; GroundTruthLabel y; TeacherLogits z_T; StudentLogits z_S; Temperature tau; SoftTargets q_T; StudentProbabilities q_S; HardLabelLoss L_hard; DistillationLoss L_soft; FeatureLoss L_feat; Optimiser O; EvaluationSet E; TrainingCheckpoint C; DeploymentTarget P.

3. RELATIONSHIPS
T produces z_T for x.
S produces z_S for x.
softmax(z_T / tau) defines q_T.
softmax(z_S / tau) defines q_S.
q_T supervises S via L_soft.
y supervises S via L_hard when labels exist.
O updates S parameters using a combined loss.
E evaluates S against explicit quality and resource criteria.

4. STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t = current training inputs, teacher outputs, labels and student predictions.
R_t = training rules, objective terms, optimiser and scheduling policy.
B_t = limits on data access, compute, memory, latency and acceptable error.
K_t = student parameters, learned representations and validated training history.

5. FORMAL MATHEMATICS
q_T(i|x,tau) = exp(z_T,i(x)/tau) / sum_j exp(z_T,j(x)/tau)
q_S(i|x,tau) = exp(z_S,i(x)/tau) / sum_j exp(z_S,j(x)/tau)
L_soft = tau^2 * KL(q_T || q_S)
L_hard = CrossEntropy(y, softmax(z_S))
L_total = alpha * L_hard + beta * L_soft + gamma * L_feat
alpha,beta,gamma >= 0; terms included only where corresponding supervision is available.
theta_S(t+1) = OptimiserStep(theta_S(t), gradient_theta_S L_total)
Note: The tau^2 factor is a common gradient-scaling convention, not a universal requirement.

6. FLOW ALGEBRA
Et = expand(It, Rt)
Vt = {e in Et : satisfies(e, Bt) and valid(e, Kt)}
a_t = argmax_{e in Vt} P(e | It, Rt, Bt, Kt)
It+1 = update(It, a_t, observations_t)
Kt+1 = learn(Kt, a_t, evaluated_outcomes_t)
If Vt is empty, halt or request revised constraints; do not assert a successful update.

7. PROCESS PATHWAY
START -> validate teacher, student, dataset and permissions
-> select distillation targets (logits, probabilities, features or sequences)
-> produce teacher targets under the defined inference protocol
-> run student forward pass
-> calculate applicable supervised and distillation losses
-> check finite loss and gradient constraints
-> update student parameters
-> evaluate held-out metrics and resource budget
-> checkpoint or adjust configuration
-> repeat until stopping rule
-> document evaluation and deploy only if acceptance criteria hold.

8. MINI-RECURSION ENGINE
function DISTILL(state):
  if invalid_inputs(state): return HALT_INVALID
  targets = teacher_inference(state.inputs)
  predictions = student_inference(state.inputs)
  loss = weighted_objective(targets, predictions, state.labels)
  if not finite(loss): return HALT_NUMERIC
  candidate = optimiser_update(state.student, loss)
  metrics = evaluate(candidate, state.validation)
  if violates_hard_bounds(metrics): return REVISE_OR_REJECT
  state.student = candidate
  state.history.append(metrics)
  if stopping_rule(metrics, state.budget): return STOP_WITH_REPORT
  return DISTILL(next_batch(state))

9. INFERENCE RULES
IF teacher output is unavailable THEN omit teacher-dependent loss or stop.
IF labels are unavailable THEN hard-label loss cannot be computed.
IF teacher and student vocabularies differ THEN define an explicit output alignment map.
IF teacher targets are unreliable or biased THEN flag possible error transfer.
IF student meets quality threshold and resource limits THEN mark eligible for deployment review.
IF evaluation deteriorates THEN investigate overfitting, distribution shift or objective weights.

10. INVARIANTS
Temperature tau > 0.
All probability vectors are non-negative and sum to one within tolerance.
Loss weights are non-negative.
No train/validation leakage.
Student updates must use gradients defined for the chosen objective.
Data use and model access must respect applicable permissions and policy.
A smaller student is a design objective, not an automatic outcome or guarantee.

11. TRI-MAPPING
Entity: TeacherModel -> Relation: supplies supervision -> Process: teacher inference.
Entity: StudentModel -> Relation: approximates teacher behaviour -> Process: parameter optimisation.
Entity: Dataset -> Relation: provides inputs -> Process: sampling and preprocessing.
Entity: EvaluationSet -> Relation: tests generalisation -> Process: validation.
Entity: DeploymentTarget -> Relation: constrains resources -> Process: acceptance testing.

12. MAPPING TABLE
Input sample | teacher targets | distillation objective | student update
Ground-truth label | reference target | supervised objective | student update
Held-out example | prediction and metrics | acceptance criterion | checkpoint decision
Resource profile | memory/latency/size | hard constraint | deployment decision

13. EXECUTION GUARANTEE (CONDITIONAL)
Given valid inputs, finite differentiable objectives, supported optimisation operations and bounded execution, the procedure defines a reproducible sequence of attempted student updates. It does NOT guarantee convergence, improved accuracy, preservation of teacher capability, safety, fairness or successful deployment. Those claims require independent evaluation.

14. AI SEARCH FLOW
FLOW_ID: AI-TRAINING-DISTILLATION-PROCESS-ONTOLOGY
ENTITY_TYPE: TrainingProcess
PREFERRED_LABEL: Knowledge Distillation Process
ALTERNATE_LABELS: Model Distillation; Teacher-Student Training; AI Distillation
PARENT: AI Training Process Entities
INPUTS: TeacherModel, StudentModel, Dataset, Objective, Constraints
OUTPUTS: TrainedStudent, EvaluationReport, Checkpoints
RELATED: TransferLearning, FineTuning, SupervisedTraining, ModelCompression
SEARCH_INTENTS: what is model distillation; teacher student training; distillation loss; temperature scaling; knowledge transfer
CONFIDENCE: Conditional on source validation and evaluation results
SOURCE_URL: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/distillation-process-ontology.html
CITATION: Mark Anthony Higgins — Sky Recursive AI, Kireth Research Semantic Library.
UPDATE_MODEL: Revise when source ontology or validated process specification changes.

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