The Compression of Knowledge: From Explicit Graphs to Latent Representations

ConceptConcept maps, language models, distributed agents, and the problem of trust

To say that a system "knows" something can refer to very different architectural conditions. The system may hold an explicit statement that can be retrieved directly. It may hold a graph of entities and named relations. It may place related concepts near one another in a vector space. It may embody a statistical regularity spread across billions of learned parameters. Or it may know how to obtain an answer from another agent without holding the answer locally at all.

These are not equivalent forms of knowledge. They preserve different features, support different operations, and fail in different ways. A knowledge graph makes relations inspectable, but only those its schema permits. An embedding preserves useful similarities while obscuring their explanation. A language model can reconstruct plausible propositions across a large domain, but reconstruction is not the same as retrieving a stored claim that carries its provenance. The question is therefore not only whether knowledge is present. It is how that knowledge has been compressed, where it resides, how it can be reconstructed, and what justifies trusting the result.compression is lossy. what is discarded matters.

This page takes up that question across four bodies of work: concept mapping and conceptual navigation, symbolic and connectionist representation, agentic and distributed systems, and the calculus of trust. The unifying idea is that knowledge representation determines what can be recovered, and trust determines what may be done with the recovery.

1. Five Kinds of Compression FoundationalKnowledge that endures for decades — core principles

LevelLevel of compression" is a useful phrase, but it can hide several separate processes. At least five are involved:

1. Structural compression reduces a richly connected domain to selected entities and relations.
2. Dimensional compression projects representations from many dimensions into fewer, as when a high-dimensional space is drawn as a two-dimensional concept map.
3. Statistical compression captures recurring patterns in learned parameters or embedding coordinates.
4. Linguistic compression expresses a larger conceptual structure in a word, label, summary, or proposition.
5. Social and architectural compression lets one agent, service, or repository stand in for knowledge that another component does not hold locally.

These processes are related but not identical. A knowledge graph can be highly compressed relative to the world and still be fully explicit. A language model can contain an enormous amount of learned regularity while leaving individual claims implicit. A concept map can reduce dimensionality sharply while preserving neighbourhood and navigational relations. The useful question is therefore not simply whether something is more or less compressed. It is what has been preserved, what has been discarded, what can be recovered, at what cost, with what confidence, and by whom.

2. Explicitness Is Compression Made Inspectable FoundationalKnowledge that endures for decades — core principles

EveryEvery knowledge representation is selective. The world contains more detail than any model can hold, so each representation has to decide which entities, differences, relations, temporal boundaries, contexts, uncertainties, histories, and sources matter. Even an explicit ontology or knowledge graph is already compressed. Suppose a university knowledge graph records that a lecturer teaches a module, that the module contains a topic, and that the topic has a resource. It omits how the teaching happens, whether the relation holds this year, whether the lecturer designed the module or only delivers it, how strongly the resource relates to the topic, who disputes the classification, whether students use the resource, and how the topic has changed.Ontologies are choices, not mirrors of reality.

Explicit representation therefore does not remove compression. It makes the chosen compression inspectable. Explicitness is compression whose selected distinctions remain available for inspection. That distinction carries through the rest of the page.

3. A Spectrum of Representations Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

FormsForms of representation can be arranged roughly from explicit and inspectable to distributed and reconstructive:

Text description of the diagram

Six boxes in a vertical chain: documents and observations; concept maps and taxonomies; ontologies and knowledge graphs; embeddings and semantic spaces; learned model parameters; generated reconstruction. Downward arrows link each stage to the next.

The chain should not be read as a progression in which each stage is more advanced. Information moves in both directions. Explicit triples can be used in training to shape latent parameters. Latent parameters can be decoded into explicit propositions. Documents can be extracted into a knowledge graph, and a knowledge graph can be verbalised back into documents. Embeddings can be projected into a concept map, and agent output can be validated into an explicit record. Each transformation preserves some properties and discards others.

4. Explicit Knowledge Graphs Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

AnAn explicit knowledge graph represents knowledge through identifiable nodes and typed edges. Knowledge graphs are studied as a formal data model in their own right[4]. They give several properties that other representations lack:

Addressability

A claim can be located and queried.

Compositionality

Relations can be followed across several nodes.

Inspectability

A person or system can see which entities and relations support an inference.

Provenance

The graph can record who asserted a claim, when, and on what evidence.

Revisability

A single node or edge can be changed without retraining anything.

Constraint

An ontology can limit which statements count as well formed.

Explicitness has costs as well. Construction is expensive, schemas are selective, ambiguous cases resist crisp representation, changing domains cause maintenance problems, unanticipated relations stay invisible, and formal consistency can mask questionable assumptions. A graph preserves named relations well, but only where someone has decided to name them.the map is not the territory

5. Concept Maps as Compressions for Navigability Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

AA concept map sits between a formal graph and an embedding space. It can preserve proximity, neighbourhood, clusters, bridges, boundaries, routes, overlapping memberships, and landmarks. It need not say exactly what each spatial relation means. If two pages sit close together on a concept map, their proximity might reflect shared vocabulary, shared references, embedding similarity, membership in overlapping conceptual subspaces, common links, human categorisation, or some combination of these. The map preserves navigational usefulness without translating every proximity into an explicit proposition.

The site's concept mapping work, together with the graph traversal and pathways page, treats conceptual exploration as wayfinding: helping a reader work out where they are, what lies nearby, and which routes connect distant regions. It also shows that different projection mechanisms produce different conceptual territories. A self-organising map projects high-dimensional document vectors onto a two-dimensional topology. The k-blade approach, described in the algorithm-not-metric paper, was extended in a follow-up paper to overlapping conceptual membership, where a page can belong to more than one territory.

A concept map is therefore not simply a picture of knowledge. It is a compression chosen to preserve navigability, in the way a road map preserves the features needed to find a route and omits most of a city.the map is a tool, not a mirror

6. Embeddings as Compressed Relational Histories Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

AnAn embedding represents an item as a vector \(\mathbf{v}_x \in \mathbb{R}^n\). That vector does not usually contain a list of propositions about the item. Its position encodes learned relations within a larger space. Early work on learning such representations from large text corpora showed that simple geometric operations on the vectors could recover analogical relations[3].

An embedding can preserve similarity, co-occurrence, substitutability, thematic association, patterns useful for prediction, and contextual relations present in its training data. It usually does not preserve directly a human-readable account of why two items are similar, the source of a particular association, named logical relations, reliable temporal scope, explicit disagreement, or a clear separation between correlation and implication. That makes embeddings useful for different operations rather than inferior ones:no causal logic, just stats

Knowledge graph:
  Lecturer ──writesAbout──> Activity Theory

Embedding:
  vector(lecturer's page) lies near vectors associated with
  mediation, tools, activity, cognition, and meaning

The graph answers an explicit relational query. The embedding supports similarity, retrieval, clustering, and analogy. A graph stores selected relations as statements. An embedding stores the statistical consequences of many relations as position.

7. The LLM as Distributed Knowledge Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

ItIt is tempting to say that a language model is a database compressed into its weights. The metaphor is useful up to a point and misleading beyond it. An LLM does not generally hold one identifiable location for each fact. Learned regularities are spread across token representations, attention mechanisms, intermediate features, parameter interactions, and layer-specific transformations, and a prompt activates and recombines them. Probing studies have tested how much factual material such models can produce when queried directly, and they treat that as a question for empirical measurement rather than something to assume[1].probing reveals structure, but does not prove storage

The generated answer is therefore usually reconstructed through the model's learned conditional patterns rather than retrieved from a fact-shaped slot. That gives the model real strengths: broad generalisation, tolerance of varied phrasing, analogical transfer, synthesis across domains, fluent reconstruction, and the ability to respond where no exact stored statement exists. It also brings characteristic weaknesses. Provenance is usually unavailable, precise updating is difficult, contradictory patterns can coexist, temporal boundaries blur, confidence may not track accuracy, and fluent reconstruction can produce unsupported claims.

A knowledge graph retrieves what has been explicitly asserted. An LLM reconstructs what its learned structure makes probable in the present context. That is not an absolute boundary. Knowledge graphs can infer new claims, and models can memorise particular strings. The distinction captures the architectural difference without pretending the line is perfectly clean.

8. Compression and Decompression Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

AnAn LLM's output can be read as a provisional decompression: latent, distributed structure is turned, under the influence of a prompt and its context, into an explicit sequence of tokens, which is then interpreted and validated as a candidate claim, explanation, or action. Decompression is never neutral. The prompt influences which patterns are activated, which level of abstraction is used, which terminology is chosen, which relations are foregrounded, which uncertainties are stated, and which plausible continuation wins. The same latent model can produce a simple explanation, a technical account, a metaphor, a false but plausible answer, a structured graph, or a tool call. The context acts as an instruction for decompression.

This extends the earlier argument about context engineering: it is partly the design of the conditions under which latent knowledge will be decompressed into a usable form. Retrieval-augmented generation then becomes a hybrid process. Latent model knowledge, explicit retrieved material, and instructions with tool schemas combine into a single context-conditioned reconstruction[2].tools turn output into action, not just text

9. What Each Representation Preserves Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

RatherRather than placing representations on one scale of compression, it helps to compare what each preserves.

What each representation keeps relatively explicit, and what it keeps relatively compressed or implicit

Representation	Relatively explicit	Relatively compressed or implicit
Document	Authored wording and local context	Cross-document structure
Taxonomy	Broader and narrower categories	Rich relation types
Knowledge graph	Entities and named relations	Unmodelled context and tacit knowledge
Formal ontology	Classes, constraints, and permissible inference	Messy exceptions and evolving practice
Concept map	Proximity, pathways, and regions	The exact semantics of proximity
Embedding	Statistical and relational geometry	Provenance and named relations
LLM parameters	Broad learned regularities	Individual claims, sources, and update paths
Distributed agent network	Specialised capabilities and access paths	Global state and a unified explanation

The aim is not to pick a universally best representation. It is to match the representation to the purpose and to the risk.

10. Knowing Where, Whom, and How Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

DistributedDistributed systems add a further kind of compression. An individual node does not need to hold all the relevant knowledge. It needs an address, a protocol, a routing mechanism, a service description, a trust relationship, and a way to validate responses. This parallels a familiar distinction in human knowledge: knowing that, knowing how, knowing where, and knowing who. An agent may not know the current weather, an account balance, an institutional policy, or the status of a shipment. It may know which service can supply that information:

Agent A
  ├── knows task state
  ├── knows Agent B handles policy
  ├── knows Service C provides live data
  └── knows how to combine their responses

Knowledge is then partly represented as a structure of delegation. The location of knowledge can be compressed into a route, a capability description, or a trust relationship. The multi-agent systems page distinguishes direct signalling from coordination through shared environments, and the distributed-systems page treats partitioning and replication as ways of making many machines behave as one service. Both bear on this point: communication in distributed systems is not one uniform mechanism, and the knowledge held across a system depends on how it is coordinated.delegation compresses the map, not the territory

11. Agentic Design as Translation Between Representations Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

AgenticAgentic architecture is often drawn as orchestration of tasks: an orchestrator delegates research and analysis, requests validation, and assembles a response. It is equally a choreography among forms of knowledge. A user request is interpreted by a model, turned into an explicit plan, used to query a vector index, checked against document evidence and a knowledge graph, extended by a specialist agent, grounded by a tool-derived observation, and finally synthesised into a response. At each stage the information is re-represented. Natural language becomes a task representation, the task becomes a query, the query becomes vector coordinates or graph patterns, results become model context, context becomes an explanation or a tool call, and execution results become episodic memory. Repeated episodes may later become semantic memory or policy.

Agentic design is therefore partly the design of translation boundaries between representations. The system has to decide when to rely on latent reconstruction, retrieve explicit evidence, query a graph, delegate to a specialist, invoke a real-world tool, ask a person, or preserve a new explicit record.

Each of those translations has a loss profile. Turning documents into embeddings may preserve semantic proximity while losing wording and provenance. Turning experience into a knowledge graph may preserve selected entities and relations while losing ambiguity and embodied context. Summarising a multi-agent discussion may keep the conclusions while losing dissent, uncertainty, and minority interpretations. Turning model output into a tool action may keep the operational intent while discarding the explanation. The design questions become: what information may safely be lost, what must be preserved, and what must remain recoverable? A brainstorming system can tolerate considerable lossy reconstruction. A system affecting finance, assessment, healthcare, access, or legal rights may need explicit sources, audit records, and reversible decisions.

12. Trust as the Price of Compression Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

TheThe less directly inspectable a representation is, the more the receiving system has to rely on other grounds for accepting its output. A graph edge may be trusted because it has provenance. A document may be trusted because of its author and publication process. A sensor value may be trusted because the device is calibrated. An agent's answer may be trusted because of its prior performance in that context. A language model's output may receive only provisional trust until it is checked against an external source. A distributed result may be trusted because several independent routes converge.

Trust, on this view, compensates for representational opacity, incomplete verification, and distributed dependence. It is not a substitute for evidence. It is the mechanism by which an actor decides whether the available evidence and assurances are sufficient for a particular action. The idea that trust is relational rather than a single property of an entity has a long history in computing. Marsh's 1994 formalisation treated trust as a computational concept that an agent could use in making decisions[5]. The calculus of trust on this site takes the relational view further, representing each pairwise relationship as an experiential embedding, as set out in the calculus-of-trust page.

A trust judgement follows a sequence: a representation produces a claim, its provenance and context are checked, the prior relationship with its source is considered, the risk of the task is assessed, and a threshold is applied. The outcome is to accept, verify, delegate, qualify, or reject.

13. Trust Governs Action, Not Truth Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

AA trust score should not be read as "this proposition is 82 per cent true". It is closer to a statement that, given this source, this context, this history, this task, and this potential consequence, the system has sufficient grounds to rely on the claim to a given degree. Trust is relational and sensitive to the action at stake. The same claim may be adequate for generating search terms or drafting an outline, and inadequate for assigning a grade, transferring money, changing a medical record, revoking access, or making an irreversible public statement. Trust depends on the trustor, source, context, history, evidence, risk, and proposed action, which can be written schematically as:

\[ T = f(\text{trustor}, \text{source}, \text{context}, \text{history}, \text{evidence}, \text{risk}, \text{action}) \]

Trust therefore determines the permitted consequence of a knowledge representation. An opaque, highly compressed representation can support a low-consequence use with little verification. As consequence rises, the architecture should demand less compressed evidence: from a latent suggestion, to retrieved supporting text, to an explicit claim with provenance, to independent corroboration, to an auditable decision record.

14. Triangulation and Source Independence Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

TheThe site's concept-navigation work uses triangulation as a metaphor. A reader locates an idea by its relation to several landmarks rather than by one hierarchical address, and the triangulation page develops this in detail. The same pattern can apply to distributed knowledge. An agent can raise its confidence by triangulating an LLM reconstruction, a knowledge-graph assertion, a retrieved document, a live tool result, another specialist agent, and a historical record.

Agreement does not guarantee truth, because several components may inherit the same error. The architecture should distinguish independent corroboration, repeated propagation of one source, genuinely diverse evidence, multiple agents running the same underlying model, and multiple summaries of a single document. Five agents repeating the same model's unsupported reconstruction are not five independent confirmations. Provenance and trust have to work together here, because provenance is what reveals whether two apparent sources share an origin.

15. Provenance as Decompression History Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

AA knowledge item's provenance can be understood as a record of its transformations. A claim may begin as an original document, be extracted by an entity-relation extractor, validated in a knowledge graph, retrieved by a research agent, summarised by a language model, and reviewed by a person or a verification agent. Attaching a source link only at the final stage loses most of that history. Provenance models of this kind are standardised, and the W3C's PROV-O recommendation expresses provenance as entities, activities, and agents, so that the chain of production can be recorded and queried[6].

A system should ideally record the original source, who or what performed each transformation, which model or rule set was used, when it occurred, what confidence was assigned, what was omitted, whether a person checked it, and which later claims depend on it. Provenance is in this sense the history of compression, transmission, and reconstruction.

16. Commitments Rather Than Claimed Internal States Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

AA system cannot usually inspect whether another agent genuinely believes a message. It can inspect what was asserted, under which preconditions, what action was promised, whether the protocol was followed, and whether the expected outcome occurred. The contract-BDD messaging page argues for grounding inter-agent exchange in checkable commitments and protocols rather than in unverifiable claims about private internal states. That fits the compression argument. When internal knowledge is opaque, trust should attach less to what an agent is said to know or believe, and more to externally checkable evidence, commitments, provenance, and performance. That avoids attributing mental states to agents while still giving coordination a practical basis.

17. Matching Decompression to Consequence Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

TheThe page proposes a design principle: use the most compressed representation adequate to the task, but decompress before the consequences exceed the representation's assurance. At low consequence, embedding similarity or an LLM reconstruction can suggest related reading. At moderate consequence, supporting documents should be retrieved and their sources exposed. At significant consequence, the claim should be converted into an explicit, provenance-bearing structure and independently verified. At high consequence, auditable rules, accountable human review, and evidence whose transformation history can be inspected should be required.

This is not simply a rule about human oversight. It is a theory of when knowledge must move from latent, approximate forms into explicit, accountable ones. High-consequence actions need not avoid embeddings or language models altogether. They should not rely on opaque reconstruction alone.

18. A Unifying Picture Applied / MethodologicalKnowledge with a 5–10 year half-life — stable practice

TheThe argument can be drawn as a single flow:

                    WORLD / ACTIVITY
                           │
                observation and inscription
                           ▼
              DOCUMENTS, EVENTS AND RECORDS
                           │
              extraction, indexing, abstraction
          ┌────────────────┼────────────────┐
          ▼                ▼                ▼
   KNOWLEDGE GRAPH     EMBEDDINGS      CONCEPT MAP
    explicit claims    latent space    navigable space
          └────────────────┼────────────────┘
                           ▼
                 AGENTIC ORCHESTRATION
           retrieval, reasoning, delegation,
                 tool use and synthesis
                           │
                           ▼
                GENERATED REPRESENTATION
                           │
            provenance, triangulation and trust
                           ▼
                     ACTION THRESHOLD
                           │
                           ▼
                    WORLD / ACTIVITY

Text description of the flow

Observation and inscription produce documents, events, and records. Extraction, indexing, and abstraction then feed three parallel forms: a knowledge graph of explicit claims, an embedding space of latent relations, and a concept map of navigable space. The three converge on agentic orchestration, which handles retrieval, reasoning, delegation, tool use, and synthesis. That produces a generated representation, which is checked through provenance, triangulation, and trust before it reaches an action threshold and returns to the world. Feedback runs from action to new experience, from experience to trust, from trust to routing, from new evidence to graphs and stores, and from failures to revision of the ontology or architecture.

19. Conclusion FoundationalKnowledge that endures for decades — core principles

KnowledgeKnowledge does not move through an intelligent system unchanged. It is selected, encoded, projected, embedded, retrieved, generated, summarised, transmitted, and acted upon, and at each boundary some structure is preserved while some is lost. An explicit graph preserves named relations and excludes what its ontology cannot express. A concept map preserves neighbourhood and navigability while leaving many relations unnamed. An embedding preserves statistical geometry while obscuring sources and explanations. A language model compresses broad regularities into distributed parameters from which propositions can be reconstructed, but not necessarily traced, updated, or trusted as stored facts.

Distributed and agentic systems add a further possibility: the system may not hold the relevant knowledge at all, but may know where to find it, which agent can supply it, which protocol governs the exchange, and how much confidence to place in the result. Trust is therefore not an optional layer added after knowledge has been produced. It is part of the mechanism by which compressed, reconstructed, and distributed representations become grounds for action.

The question to ask of a system is not simply whether it knows something. It is in what form it knows, what was lost in producing that form, and what degree of action that representation can safely support. In short: knowledge representation determines what can be recovered, and trust determines what may be done with the recovery.

Related Topics and Continuations

• Symbolic and Connectionist Reasoning — the technical contrast between explicit and distributed representation that sections 4 to 7 build on.
• Multi-Agent Systems: Coordination, Communication, and Strategic Interaction — coordination among agents, which section 10 relates to distributed knowledge.
• Designing Auditable, Robust Agentic Systems — the engineering side of the provenance and assurance questions in sections 15 and 17.
• Big Data and Distributed Systems — partitioning, replication, and coherent service across machines.
• A Distributed Embedding Calculus of Trust — the relational account of trust that section 12 applies.
• Triangulating in Complex Concept Spaces — triangulation as a navigational method, used in section 14.

References

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5. S. P. Marsh, Formalising Trust as a Computational Concept, PhD thesis, University of Stirling, 1994.
6. W3C, PROV-O: The PROV Ontology, W3C Recommendation, 30 April 2013. https://www.w3.org/TR/2013/REC-prov-o-20130430/