Continual Learning Process Ontology

FLOW ALGEBRA — CONTINUAL LEARNING PROCESS ONTOLOGY
Version: 1.0 | Language: en-GB | Date: 2026-10-29
Authors: Mark Anthony Higgins — Sky Recursive AI
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/continual-learning-process-ontology.html
Status: Topic-based formalisation; source page could not be retrieved for verification.

01. PURPOSE
Represent continual learning as an explicit, bounded, auditable sequence of model updates across changing tasks and data distributions, balancing adaptation, retention and safety.

02. ENTITY MODEL
E = {Learner, Model, Parameters, Task, TaskSequence, Dataset, Sample, Label, Stream, Distribution, MemoryBuffer, ReplaySample, Optimiser, Loss, Gradient, Regulariser, ParameterMask, Adapter, Checkpoint, Evaluator, Metric, DriftSignal, UpdateEvent, Constraint, Version, AuditRecord}.
Relations:
  receives(Learner, Stream)
  contains(Stream, Sample)
  belongs_to(Sample, Task)
  updates(Optimiser, Parameters)
  stores(MemoryBuffer, ReplaySample)
  evaluates(Evaluator, Model)
  precedes(Task_i, Task_j)
  derives_from(Version_t+1, Version_t)
  records(AuditRecord, UpdateEvent)

03. STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t = incoming task/data stream, observations and evaluation evidence.
R_t = update, replay, consolidation, drift detection and rollback rules.
B_t = constraints on memory, compute, privacy, safety and retention.
K_t = model parameters, learned representations, task history and checkpoints.
Expanded candidates: E_t = expand(I_t, R_t).
Valid updates: V_t = {x in E_t | satisfies(x, B_t)}.
Decision: x*_t = argmax_{x in V_t} P(x | I_t, R_t, B_t, K_t).
Transition: S_{t+1} = Update(S_t, x*_t, evaluation_t).
If V_t is empty, defer update and retain the previous validated version.

04. MATHEMATICAL FORMALISATION
Task sequence T_1, T_2, ..., T_n with data distributions D_1, D_2, ..., D_n.
Model f_{theta_t} is updated at step t using current data and permitted history.
L_total(theta) = L_current(theta; D_t) + lambda_r L_replay(theta; M_t)
               + lambda_c L_consolidation(theta, theta_{t-1}) + lambda_s L_safety(theta).
Parameter update: theta_{t+1} = theta_t - eta_t * grad_theta L_total(theta_t).
Replay term is zero when replay is disallowed or unavailable.
Retention score R_t = mean_{i < t} performance(f_{theta_t}, T_i), where evaluations exist.
Forgetting on task i: F_i(t) = max_{k < t} score_i(k) - score_i(t).
Average forgetting: F_avg(t) = mean_i F_i(t), over previously evaluated tasks.
Backward transfer BWT = mean_{i < t} [score_i(t) - score_i(i)], when comparable.
Forward transfer is measured against a declared baseline on unseen/future tasks.
Plasticity and stability are competing objectives, not universal guarantees.

05. PATHWAYS
P1 Data arrival -> validate provenance -> identify task/distribution -> queue samples.
P2 Detect distribution shift -> quantify uncertainty -> choose adaptation strategy.
P3 Select replay, regularisation, architectural expansion or parameter isolation.
P4 Train candidate -> validate current-task improvement -> test retained tasks.
P5 Check safety/privacy/resource boundaries -> approve or reject candidate.
P6 Publish checkpoint and audit record -> monitor -> repeat on next event.
P7 On unacceptable regression -> rollback to validated checkpoint.

06. MINI RECURSION ENGINE
function continual_step(S_t, batch_t):
    I_t <- validate(batch_t)
    drift <- estimate_drift(I_t, K_t)
    strategies <- expand(I_t, R_t, drift)
    candidates <- filter(strategies, B_t)
    if candidates is empty: return (S_t, 'defer')
    candidate <- choose(candidates, retention_and_adaptation_objective)
    theta_prime <- train(K_t.parameters, I_t, candidate)
    evidence <- evaluate(theta_prime, current_and_previous_tasks)
    if not passes(evidence, B_t): return (S_t, 'reject_or_rollback')
    K_next <- checkpoint(theta_prime, evidence, K_t)
    return (Update(S_t, K_next), 'accepted')

07. INFERENCE RULES
IF incoming distribution differs materially from baseline THEN flag potential drift.
IF current-task gain coincides with old-task regression THEN flag possible forgetting.
IF memory budget is exhausted THEN apply a bounded selection or non-replay strategy.
IF evaluation coverage is insufficient THEN mark retention unknown, not preserved.
IF a candidate violates privacy or safety constraints THEN reject candidate.
IF performance drops beyond approved tolerance THEN restore prior checkpoint.
IF evidence is sufficient and constraints pass THEN permit a versioned update.

08. INVARIANTS
I1: Every accepted update has an identifiable parent checkpoint.
I2: Evaluation scores are linked to task, dataset version and metric definition.
I3: No update bypasses declared privacy and safety boundaries.
I4: Memory and compute use remain within configured budgets.
I5: Unknown retention is not reported as successful retention.
I6: Rejected updates do not overwrite the last validated checkpoint.
I7: Provenance and update decisions remain auditable.

09. TRI-MAPPING
Ontology entity -> algebra state -> execution component
Task / Stream -> I_t -> ingestion and task identification
Rules / Strategy -> R_t -> training strategy selector
Constraints -> B_t -> policy and resource gate
Model / Memory -> K_t -> parameters, replay store, checkpoints
Evaluation -> evidence_t -> validation and monitoring
UpdateEvent -> S_t to S_t+1 -> versioned deployment or rollback

10. MAPPING TABLE
Concept | Input | Transformation | Output
New task | task data | validation and classification | accepted task batch
Drift | observed features | statistical comparison | drift signal
Replay | bounded historical examples | sampling | replay batch
Consolidation | previous parameters | regularised optimisation | candidate parameters
Evaluation | candidate + test suites | scoring | retention/adaptation report
Deployment | approved candidate | version promotion | active checkpoint
Rollback | failed threshold | checkpoint restore | prior validated model

11. HOW TO READ
Read S_t as the current learner state. Incoming experiences expand the set of possible updates; rules and boundaries eliminate invalid updates. An optimisation step proposes a candidate model. Explicit evaluation decides whether to accept it. The process repeats as new tasks or distributions arrive.

12. EXECUTION GUARANTEE (CONDITIONAL)
The flow guarantees a traceable decision path and preservation of the last validated checkpoint only if validation, atomic checkpointing, audit logging and rollback are implemented correctly. It does NOT guarantee convergence, zero catastrophic forgetting, generalisation, or perpetual improvement. Empirical outcomes depend on data, optimisation, capacity, evaluation and environmental drift.

13. AI SEARCH FLOW
flow "ContinualLearningProcessOntology" v1.0
AUTHORS: ["Mark Anthony Higgins", "Sky Recursive AI"]
SOURCE: "https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/continual-learning-process-ontology.html"
CITATION_BACKLINK: SOURCE
PURPOSE: "Describe continual adaptation with retention checks and bounded updates."
STATE_MODEL: "S_t=(I_t,R_t,B_t,K_t)"
ENTITIES: [Task, Stream, Model, MemoryBuffer, Checkpoint, Evaluator, UpdateEvent]
PATHWAYS: [Ingest, DetectDrift, SelectStrategy, Train, Evaluate, Gate, CommitOrRollback]
MINI_RECURSION_ENGINE: "S_{t+1}=Update(S_t,SelectValid(expand(I_t,R_t),B_t))"
INFERENCE_RULES: [DetectForgetting, EnforceConstraints, RequireEvidence, RollbackOnRegression]
CONFIDENCE: "Conditional on observed data and declared evaluation coverage"
SEMANTIC_EQUIVALENCE: ["continual learning", "lifelong learning", "incremental learning (context-dependent)"]
UPDATE_MODEL: "Versioned checkpoints with retention monitoring and rollback"
FLOW_HASH: "Compute SHA-256 from canonical UTF-8 text at publication; not pre-populated"

14. LIMITATIONS AND CITATION
This file is an original formal interpretation of the named topic. The source page was not accessible at generation time; do not treat its wording or ontology structure as a verified transcription. Scientific claims require independent empirical validation. Preserve the source URL and author attribution when redistributing.