Model Merging Process Ontology

FLOW ALGEBRA v1.0 — MODEL MERGING PROCESS ONTOLOGY
SEMANTIC LIBRARY | AI CORE | ENTITY GRAPH | TRAINING PROCESS ENTITIES

AUTHORS: Mark Anthony Higgins — Sky Recursive AI
SOURCE: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/model-merging-process-ontology.html
STATUS: Topic-based formalisation; original page content not verified.
DATE: 2026-10-29
PURPOSE: Represent the entities, relationships, constraints and executable reasoning pathways involved in combining AI model parameters, adapters or outputs.

01. ONTOLOGY IDENTITY
ontology_id: AI.TrainingProcess.ModelMerging
entity_type: TrainingProcess
parent: AI.TrainingProcess
related: ModelCheckpoint, FineTuning, TransferLearning, ModelEvaluation, ModelDeployment
scope: Parameter-space merging, task-vector merging, adapter merging and output-level ensembles (distinguished explicitly).

02. STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t: candidate checkpoints, architectures, parameter tensors, adapters and evaluation data
R_t: merge relationships, provenance, compatibility and task similarity
B_t: hard limits on memory, licensing, safety, architecture and deployment
K_t: merging algorithms, validation knowledge and previous measurements
E_t = expand(I_t, R_t)
V_t = {x in E_t | compatible(x) and permitted(x) and constraints(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, evaluation(x*_t))
NOTE: P is a decision score or probabilistic ranking only when calibrated; it is not a guarantee of model quality.

03. ENTITY DEFINITIONS
BaseModel: reference architecture and starting checkpoint
SourceModel: candidate model to combine
Checkpoint: immutable, versioned tensor snapshot
ParameterTensor: named numerical array with shape and dtype
ArchitectureSignature: layers, tensor names, tokenizer and configuration
Tokenizer: text-to-token mapping with vocabulary and special tokens
TaskVector: delta(theta_task, theta_base)
Adapter: parameter-efficient update, e.g. LoRA factors
MergePolicy: selected algorithm and its configuration
MergeWeight: contribution coefficient assigned to a source
MergeCandidate: constructed parameter or adapter artefact
ValidationSet: held-out, provenance-checked evaluation examples
Metric: accuracy, loss, calibration, robustness, latency or memory
SafetyTest: evaluation of unwanted behaviour and regressions
ProvenanceRecord: sources, licences, hashes and transformation history
DeploymentArtifact: validated output and runtime configuration

04. RELATIONSHIP GRAPH
SourceModel --hasCheckpoint--> Checkpoint
Checkpoint --implements--> ArchitectureSignature
Checkpoint --uses--> Tokenizer
SourceModel --derivedFrom--> BaseModel
TaskVector --computedFrom--> SourceModel + BaseModel
MergePolicy --selects--> SourceModel
MergePolicy --assigns--> MergeWeight
MergePolicy --produces--> MergeCandidate
MergeCandidate --evaluatedOn--> ValidationSet
ValidationSet --reports--> Metric
MergeCandidate --subjectTo--> SafetyTest
MergeCandidate --records--> ProvenanceRecord
DeploymentArtifact --createdFrom--> MergeCandidate

05. FORMAL MERGING OPERATORS
Let theta_i be aligned parameter vectors and w_i merge weights.
Weighted averaging: theta_merge = sum_i w_i * theta_i, where w_i >= 0 and sum_i w_i = 1.
Task-vector merge: theta_merge = theta_base + sum_i alpha_i * (theta_i - theta_base).
Interpolation (two checkpoints): theta_merge = (1-lambda)*theta_A + lambda*theta_B, 0 <= lambda <= 1.
Mask-based merge: theta_merge[j] = select(theta_1[j],...,theta_n[j]; mask[j]).
Adapter merge: combine compatible low-rank updates or their realised deltas; verify rank and scaling conventions.
Output ensemble: p_merge(y|x) = sum_i w_i * p_i(y|x); this combines predictions, NOT model parameters.
NOTE: Tensor alignment is a necessary technical condition, not evidence that parameter averaging preserves capability.

06. PRECONDITIONS
PRE-01: Verify rights and licences for every source and derived artefact.
PRE-02: Confirm tensor shapes, layer mappings, dtypes and architecture compatibility.
PRE-03: Confirm tokenizer and embedding compatibility; do not silently average mismatched vocabularies.
PRE-04: For task vectors, verify a shared reference base and aligned parameters.
PRE-05: Record merge weights, random seeds, source hashes and software versions.
PRE-06: Prepare representative, held-out tests and baseline comparisons.
PRE-07: Set compute, memory, accuracy, safety and latency constraints.

07. EXECUTION PATHWAYS
PATH A: CHECKPOINT AVERAGING
A1 ingest sources -> A2 verify alignment -> A3 select coefficients -> A4 merge tensors -> A5 save candidate -> A6 evaluate -> A7 accept or reject.
PATH B: TASK-VECTOR MERGING
B1 identify common base -> B2 compute deltas -> B3 resolve conflicting updates -> B4 scale and sum -> B5 reconstruct checkpoint -> B6 evaluate.
PATH C: ADAPTER MERGING
C1 validate adapter/base compatibility -> C2 map updates -> C3 combine deltas -> C4 optionally compress -> C5 evaluate.
PATH D: ENSEMBLING
D1 preserve individual models -> D2 align output semantics -> D3 aggregate predictions -> D4 measure runtime overhead and quality.

08. MINI-RECURSION ENGINE
input: sources, merge_policies, candidate_weights, constraints, validation_sets
initialise best = NONE
for policy in merge_policies:
  if not preconditions(policy, sources): continue
  for weights in candidate_weights(policy):
    candidate = merge(sources, policy, weights)
    results = evaluate(candidate, validation_sets)
    if violates_hard_constraints(results): reject(candidate); continue
    if best is NONE or score(results) > score(best.results):
      best = (candidate, policy, weights, results)
return best if best is not NONE else FAILURE_WITH_REASONS
Termination: finite policies/weights or a fixed evaluation budget.

09. INFERENCE RULES
IF architecture signatures mismatch AND no verified mapping exists THEN parameter_merge = INADMISSIBLE.
IF token embeddings differ in meaning THEN naive embedding average = INADMISSIBLE.
IF sources share a base AND deltas are aligned THEN task_vector_merge = CANDIDATE.
IF validation quality falls below baseline threshold THEN candidate = REJECT.
IF safety regression exceeds permitted bound THEN candidate = REJECT.
IF evaluation passes AND licences permit distribution THEN candidate = ELIGIBLE_FOR_RELEASE.
IF provenance is incomplete THEN release_status = HOLD.
IF model outputs are combined without modifying parameters THEN process = ENSEMBLING.

10. INVARIANTS
INV-01: Source checkpoint bytes remain unchanged.
INV-02: Every output is traceable to source hashes and merge configuration.
INV-03: Shape and semantic compatibility must be checked before tensor operations.
INV-04: Evaluation is conducted on data not used to optimise the reported final comparison.
INV-05: A merged model is not assumed better than any input model.
INV-06: Licence, safety and deployment constraints are never relaxed by ranking scores.

11. TRI-MAPPING
ONTOLOGY: Model, Checkpoint, TaskVector, MergePolicy, MergeCandidate, Metric.
FLOW: validate -> align -> combine -> test -> compare -> publish or reject.
EVIDENCE: source hashes, configuration, tensor checks, evaluation results, safety report.

12. MAPPING TABLE
Ontology entity | Flow operation | Observable evidence
SourceModel | ingest | checkpoint hash
ArchitectureSignature | validate | compatibility report
TaskVector | derive | delta tensor manifest
MergePolicy | configure | algorithm + coefficients
MergeCandidate | construct | output checkpoint hash
ValidationSet | evaluate | dataset manifest
Metric | compare | per-task scores and uncertainty
ProvenanceRecord | audit | source and licence record
DeploymentArtifact | release | tested runtime package

13. CONDITIONAL EXECUTION GUARANTEE
Given valid compatible inputs, a deterministic merge operator, fixed numerical environment and sufficient resources, the merge procedure can produce a reproducible candidate artefact within specified numerical tolerances.
No unconditional guarantee is made for accuracy, safety, generalisation, convergence or improvement. These require empirical validation.

14. AI SEARCH FLOW
flow_id: AI_SEARCH_MODEL_MERGING_PROCESS_V1
intent: explain or evaluate model merging approaches
entities: [SourceModel, Checkpoint, TaskVector, Adapter, MergePolicy, MergeCandidate, Metric]
query_expansion: [model merging, checkpoint averaging, model soup, task arithmetic, adapter fusion, weight interpolation, ensemble]
pathway: identify_intent -> retrieve_entities -> check_method_distinction -> enforce_constraints -> provide_formalisation -> cite_source
confidence: evidence-dependent; distinguish verified page content from topic-based derivation
citation_backlink: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/model-merging-process-ontology.html
update_model: versioned revisions with source and test provenance

15. HOW TO READ
Entities identify what participates; relationships identify connections; pathways identify operations; equations describe permitted numerical combinations; invariants and evaluation gates prevent unsupported claims.

16. OPEN RESEARCH ATTRIBUTION
Research attribution: Mark Anthony Higgins — Sky Recursive AI.
Original ontology URL is retained for citation and discovery.
This TXT is an independently composed, topic-based Flow Algebra representation, not a verified extraction of the webpage.
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