Training Example Ontology

FLOW ALGEBRA — TRAINING EXAMPLE ONTOLOGY
Semantic Library | AI Core | Entity Graph | Training Process Entities
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/training-example-ontology.html
Authors (source attribution): Mark Anthony Higgins — Sky Recursive AI
Companion formalisation; the embedded page specification was not retrievable.
Version: 1.0 | 2026-10-29 | UTF-8

01 PURPOSE
Define a training example as an individually identifiable, provenance-bearing unit of data used to compute or support a learning objective. Preserve distinctions between examples, batches, datasets, labels, targets, and model predictions.

02 STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t: observed example and processing context
R_t: typed relations among entities
B_t: boundaries, permissions and validation constraints
K_t: schema, task definition and model knowledge
E_t = expand(I_t, R_t)
V_t = {x in E_t | satisfies(x, B_t)}
x*_t = argmax_{x in V_t} P(x | I_t, R_t, B_t, K_t)
I_(t+1) = update(I_t, x*_t, evidence_t)
Note: argmax is a selection convention, not a guarantee of calibrated probabilities.

03 ENTITY TYPES
TrainingExample: {example_id, dataset_id, modality, input, target?, metadata, split, provenance}
Input: text | image | audio | video | code | structured | multimodal
Target: class | scalar | sequence | mask | preference | reward | none
Annotation: {annotator_id?, guideline_version?, timestamp?, confidence?}
Prediction: {model_id, checkpoint_id, output, timestamp}
LossRecord: {objective_id, value, reduction, weighting}
Dataset: {dataset_id, version, partition_policy}
Batch: ordered or indexed collection of training examples
Transform: {operation, version, parameters, randomness_seed?}
Provenance: {origin, licence?, consent_basis?, collection_time?, transformations}

04 RELATIONSHIPS
TrainingExample --member_of--> Dataset
TrainingExample --has_input--> Input
TrainingExample --has_target--> Target (optional)
TrainingExample --annotated_by--> Annotation (optional)
TrainingExample --transformed_by--> Transform (zero or more)
TrainingExample --included_in--> Batch (zero or more)
Model --predicts_for--> TrainingExample
Prediction --compared_with--> Target
Comparison --evaluated_by--> LossRecord
TrainingExample --derived_from--> Provenance

05 MATHEMATICAL DEFINITIONS
Supervised example: e_i = (x_i, y_i, m_i)
Unlabelled example: e_i = (x_i, m_i)
Dataset: D = {e_i}_{i=1}^N
Mini-batch: B_t subseteq D_train
Model output: yhat_i = f_theta(x_i)
Per-example loss: ell_i = L(yhat_i, y_i)
Weighted batch objective: J_B(theta) = [sum_{i in B} w_i ell_i] / [sum_{i in B} w_i], when denominator > 0
Gradient: g_t = grad_theta J_B(theta_t)
SGD illustration: theta_(t+1) = theta_t - eta_t g_t
Self-supervised target: y_i = T(x_i, seed_i), with task-specific transformation T
Data augmentation: x'_i = A(x_i; phi_i), preserving task-required target semantics
These equations are illustrative; training objectives and optimisers vary.

06 VALIDATION RULES
R01: Every example MUST have a unique identifier within its dataset version.
R02: Input MUST conform to the declared modality and schema.
R03: Supervised objectives MUST have an available, valid target or an explicit masking rule.
R04: Dataset split membership MUST follow a recorded partition policy.
R05: Grouped or near-duplicate samples SHOULD remain in the same split to prevent leakage.
R06: Transformations MUST preserve or update targets as required by task semantics.
R07: Unknown labels MUST NOT be silently converted into ground truth.
R08: Provenance and usage permissions MUST be checked before training inclusion.
R09: Invalid or quarantined examples MUST NOT enter active batches.
R10: Example weights MUST be finite and non-negative; their batch sum MUST be positive for weighted means.
R11: Missing values MUST be represented explicitly rather than fabricated.
R12: Evaluation examples MUST NOT be used for gradient updates unless a new documented split protocol authorises it.

07 INFERENCE RULES
IF example has input and valid target THEN eligible_for(supervised_loss).
IF example has input and no target THEN eligible_for(unlabelled_objective) only when objective supports it.
IF provenance is insufficient THEN status = review_required.
IF near_duplicate spans training and evaluation splits THEN flag = leakage_risk.
IF annotation conflicts exist THEN flag = adjudication_required.
IF transform changes label semantics THEN recompute_or_reject(target).
IF schema and permission checks pass THEN candidate_for_batch = true.

08 RECURSIVE ENGINE
step(e, state):
  inspect schema, modality, target, provenance and split
  expand relevant relationships and permitted transformations
  filter invalid, unlicensed or leakage-prone candidates
  select task-compatible representation and loss pathway
  record decision, evidence, version and transformation lineage
  return updated state and audit record
Repeat only when new evidence or transformations warrant another pass.
Termination: stable validated record, explicit rejection or review_required.

09 TRI-MAPPING
Entity layer: TrainingExample -> Input, Target, Annotation, Provenance
Relationship layer: member_of, has_target, derived_from, included_in
Execution layer: ingest -> validate -> partition -> transform -> batch -> compute_loss -> audit

10 TEXT DIAGRAM
[Raw Sample] -> [Provenance / Permission Check] -> [Schema Validation]
                                            | invalid -> [Quarantine]
                                            v
                                    [Split Assignment]
                                            v
                                    [Task Transformation]
                                            v
                                       [Training Example]
                                            v
                                          [Batch]
                                            v
                                [Prediction + Objective]
                                            v
                                   [Gradient / Update]

11 EXECUTION GUARANTEES AND LIMITS
Guarantee G1: Given valid inputs, deterministic transformations and fixed seeds, the validation path is reproducible within a specified software environment.
Guarantee G2: Each accepted example retains its dataset version and transformation lineage.
Guarantee G3: Rejected examples do not contribute to the training objective under the defined workflow.
Non-guarantee: Correct labels, unbiased sampling, privacy, model generalisation or scientific validity cannot be inferred solely from schema compliance.

12 AI SEARCH FLOW
QUERY: What is a training example?
PATH: TrainingExample -> Dataset -> Input -> OptionalTarget -> TaskObjective
ANSWER: An individual data unit used in a model-learning workflow, optionally with labels or other supervision.
QUERY: How is a training example validated?
PATH: Schema -> Provenance -> Permission -> Split -> LabelQuality -> TransformConsistency
ANSWER: Verify structure, source rights, split integrity, target suitability and transformation lineage.
QUERY: How does an example affect training?
PATH: Example -> Batch -> ModelPrediction -> Loss -> Gradient -> OptimiserUpdate
ANSWER: Its contribution depends on the objective, weighting, masking and batch reduction.

13 SOURCE AND CITATION
Source page: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/training-example-ontology.html
Attribution: Mark Anthony Higgins — Sky Recursive AI, Kireth Research.
This companion text is an independent formalisation based on established ML principles; it is not a verbatim extraction of the inaccessible embedded page specification.
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