Retained theories compared with retained traces under resource limits

Type: notes/types/theory-proposal.md

This theory proposal would add three terms for resource comparisons: trace strategy, effective context, and derived state. It separates conditions that require intermediate or reusable state from the conjecture that retaining theories supplies that state efficiently. The terms remain unadopted. The research arrangement already states the persistence conjecture without depending on them.

Adoption would be justified if a comparison needs to distinguish these resource conditions repeatedly and ordinary descriptions no longer suffice. It would commit the KB to defining the terms, stating how effective context is assessed, and maintaining their use across comparison notes and articles. No current experiment requires that import. The proposal does not authorize changes to experiment protocols.

What each resource limit establishes

Unlimited replay can substitute for retained computation

Assume deterministic machinery, access to its initial state, and a complete record of external inputs and interventions. With unlimited computation and storage, the system can replay its history to regenerate a retained state. Under those assumptions, retaining an assembled theory rather than regenerating it adds no in-principle capability. It can change cost and stability for consumers. Missing inputs, unrecoverable state, or stochastic choices invalidate exact replay unless the information needed to reproduce them is also available.

Replay is not the same as asking a model to synthesize a theory afresh from outcomes. The replay argument establishes no quality ordering between fresh synthesis and revising an existing theory. Neither incremental revision nor reconstruction is defined by a preference for small edits. A local-search limit in a particular classical algorithm cannot establish a limit for all criticism-guided revision.

Some decisions need synthesis across contexts

The proposed effective context is the amount of loaded material a model uses adequately for a specified task and reliability criterion. It need not equal the nominal context window or remain constant across tasks. A history larger than that capacity creates no problem when the next decision needs only a retrievable part.

The proposed trace strategy retains records of past work and consults them when needed. Its simplest form loads a selection of intact records into one context. That form cannot support a decision when no such selection contains enough evidence and the decision requires combining more material than the model can use adequately in one call.

The proposed derived state is a result of processing history that stands in for some of it during later processing. Summaries, aggregates, intermediate syntheses, and theories can supply it. Multiple passes or computation outside the model can therefore combine evidence across contexts. Such a strategy may discard its intermediate results after each decision. Bounded context under the stated synthesis demand requires some way of carrying results between steps; it does not require retaining an assembled theory between decisions. A retrieval index can lower the cost of finding evidence without itself supplying the required synthesis.

Consulting records when needed also requires detecting that need. A theory on the decision path may supply the trigger; a retrieval strategy may instead use learned triggers or routine lookups. Comparisons must allow and price those mechanisms.

Some decision budgets require reuse

Suppose the minimum cost of reconstructing information needed for a decision exceeds its computation budget at the required reliability. The decision then needs reusable state that avoids that reconstruction, or a change to the budget or task requirement. Retention alone is insufficient: maintaining, retrieving, and using that state must also fit the budget.

The limits differ: more computation can be bought, making the computation budget an economic constraint. For a fixed model, buying more calls does not enlarge its context window; synthesis across calls must carry intermediate results. The context limit is architectural under that fixed-model condition.

Growing history does not establish this condition. A bounded lookup or a fixed recent window may remain adequate. Nor does average cost settle a strict budget for each decision. Periodically rebuilding at history sizes 1, 2, 4, 8, and so on can bound average work per arriving record when each rebuild is linear in history size; an individual rebuild can still exceed the decision budget. Incorporating new evidence between rebuilds also costs work, or requires accepting delayed use of that evidence.

Condition Supported conclusion
Deterministic, fully recorded replay with unlimited resources Retention is unnecessary for reproducing computed state
Required synthesis exceeds what one context can support Information must be combined across processing steps
Required reconstruction exceeds the decision budget Continued performance needs reuse or a changed constraint
Any of these conditions The best retained form remains a separate question

Why theories might earn their costs

A theory can retain an explanation synthesized from many episodes. Later work may use its consequences without repeating that synthesis. A criticism can identify what to reconsider; addressability can make particular assumptions or parts available for inspection. Neither property guarantees a correct diagnosis, a small edit, or preservation of untested behavior.

The conjecture is that, for some demands, explanatory content preserves more of what later decisions need per unit of total cost than competing retained forms. Structured shifts may favor reusable explanations when relevant relations survive while other features change. Mistaken abstractions can instead cause negative transfer. An aggregate may preserve the information needed for a task exactly; derived state need not be lossy or smaller than its inputs. No general superiority follows from calling theories compression.

Records remain evidence from which a theory can be challenged or rebuilt; retaining episode evidence serves that purpose. Retaining more records and more theory also adds retrieval, interpretation, maintenance, and consistency costs.

Separate the two reconstruction comparisons

The storage container does not decide whether a system is a theory builder. Indexed traces can expose theories and their criticisms as retained, addressable knowledge. A theory can also be reconstructed from retained criticism without retaining the assembled theory. Both arrangements meet the builder's iteration condition, and both keep criticism's results across problems. They differ in how much of that work persists. Whether either learns, in the sense of improving capacity for future action, is a separate question.

The two reconstruction comparisons therefore compare persistence grades and ask different questions:

  • Assembled theory and testing record versus retained criticisms. This asks what keeping the assembled theory buys over reconstructing it from criticism already done. Both arms are theory builders.
  • Assembled theory and testing record versus inputs and outcomes only. This asks what keeping the work of conjecture and criticism buys over doing that work again. What the second arm retains holds no stated theory or criticism, so nothing criticism produced persists across runs: this arm is the baseline for the persistence conjecture. Its active machinery may still formulate and use criticisms, and a storage contrast cannot establish their absence. A reconstructor that states, criticizes, and revises within a run is a builder at that run's grade, and it may still learn in the ordinary sense.

Full reasoning traces may contain theories and criticism. Treating all traces as raw observations would change what the comparison varies. Generic or learned retrieval, reconstruction, and direct use can be combined in any arrangement if their roles and costs are declared. The useful contrast is the work retained and consumed, not whether it sits in a file called a theory. Supplying the same model weights also does not hold processing fixed when the inputs change.

Records with a maintained retrieval index are a stronger rival than records with generic retrieval alone. After the first comparison, a further arm should test that rival while declaring which content the records retain and counting index construction and maintenance. This is a deferred comparison, not an addition to the currently commissioned protocol.

Comparisons should count initial construction, retrieval, reconstruction, testing, and maintenance, and report cost at comparable quality or quality under matched budgets. Content interventions can strengthen attribution to what a theory says. A result establishes only the contrast actually run, not a universal boundary between learning and nonlearning arrangements.

Open questions

  • Can effective context be measured reliably enough for this vocabulary to improve comparisons over direct descriptions of tasks and supplied text?
  • Which decisions require combining evidence across contexts rather than retrieving a small sufficient subset?
  • When is retaining an assembled theory cheaper than reconstructing it from criticism at comparable quality, including maintenance and stale-theory failures?
  • Can retained criticisms be kept usefully distinct from a compressed or partially assembled theory in an actual implementation?
  • Which costs or failures should cause a system to revise, reconstruct, or combine the two? Either strategy meets the builder's iteration condition; neither is required.
  • When does a learned index itself expose an addressable theory, rather than only route access to records? Retention or editability alone does not decide.
  • How should replay be compared when stochastic choices cannot be reproduced and reconstruction yields a distribution of states rather than the same state?
  • When a prior theory is supplied, what evidence distinguishes revision that uses it from independent reconstruction? Output alone may not distinguish them; a decision-point citation and an intervention removing the prior theory are candidate checks.

Relevant Notes: