The Unit as a Primitive for Machine Learning: A Formal Foundation for Learning from Unit-Linked Events

论证 spine

1. Introduction
2. The Unit as a Machine-Learning Primitive
3. Learning a Family of Unit-Conditioned Response Laws
4. Learner Access to the Unit
5. Unit Information: Predictive Value, Access, and Deployment
6. Recommendation as a Worked Setting
7. Relations to Established Learning Traditions
8. Empirical Implications and Evaluation
9. Discussion and Limitations
10. Conclusion

所需证据

The unit layer is scientifically useful only if preserving it changes a declared question, estimand, evaluation protocol, or falsifiable prediction. Proposed tests must separate unit-belief quality, fixed-unit response quality, marginalized prediction, and a matched unit-omitting baseline. They must use evidence/target separation, unit-disjoint evaluation where unseen-unit claims are made, unit-abduction settings where relevant, and negative controls such as grouping shuffles, label permutations, and no-persistence conditions.

No experiment has yet been run. If the unit-preserving formulation cannot be distinguished from an equally informed unit-omitting formulation on a requested or testable quantity, the simpler abstraction should be used.

Working abstract（未声称已在外部登记）

Machine learning is usually formalized through samples, while the persistent individual to which multiple observed or possible events refer often remains implicit. We propose the *unit* as an explicit primitive at the level of task semantics. A learning task first declares a population of persistent referents and a criterion for when observed or possible events concern the same one; the realized value $u$ denotes the selected referent. We develop supervised learning as the main formal specialization. Its learned object is a structured family of unit-conditioned response laws: homogeneity is the special case in which the laws coincide across units, while heterogeneity allows them to differ under shared restrictions. A sample-only conditional law is silent about this distinction because it may be either a homogeneous unit extension or the marginal projection of a heterogeneous family. Learning therefore requires separate statements about what varies across units and what structure permits information sharing among them. For many applied tasks, this makes stable individual variation available as learnable structure and inductive bias rather than leaving it only as residual error; it does not presume that every task is heterogeneous. Learner access is downstream of this declaration. A trusted resolver may provide direct unit access; when no resolver identifies the realized unit, *unit abduction* maps factual evidence to a belief over that already-realized unit and reuses the belief across response queries. Under response sufficiency, we separate oracle predictive value, value accessible from declared evidence, learned-pipeline approximation, and component identification. We also show that arbitrarily many unlinked single-row observations can fail to distinguish a heterogeneous unit world from a homogeneous pooled world, whereas trusted same-unit pairs separate a restricted witness. Practical corollaries clarify weighting and data splitting. The formulation organizes established repeated-measures, personalization, entity-resolution, latent-variable, and heterogeneous-model traditions around one unit contract without claiming their machinery as new. Its formal results concern the supervised predictive specialization; observational, causal, and other learning objects require their own additional commitments.

Exact current status

public semantic contract v0.12 is preserved. On 2026-07-30, the local canonical v0.15 source was grown so that the first-reading layer now explicitly answers which default machine-learning abstractions the unit primitive revises: a sample is an event rather than the persistent semantic subject; the unit precedes IDs and learned representations; a population may carry a structured family of unit-conditioned response laws rather than only one subject-free map; structured heterogeneity is a first-class model possibility for many applied tasks, with homogeneity retained as a special case; and which-unit attribution is separated from response inference. It also distinguishes referential identification from response-relevant structural localization, states the conditional duality between localization and information borrowing, and presents cross-field partial recovery as a research program rather than a reduction theorem. The existing value--access--approximation--identification theorem spine remains unchanged. The mutable 43-page working build compiles without manuscript warnings and has passed targeted visual inspection of the changed first-reading and conclusion surfaces, but it has not replaced the preserved 2026-07-28 all-page-reviewed preview and is not a frozen artifact. Experiments, theorem reprioritization, exact borrowing geometry, exhaustive historical-priority review, independent external review, freeze, and external synchronization remain open. The frozen v0.14 manuscript and supplement v0.9 remain the latest accepted artifacts.

Next writing gate

independently review the current unit-primitive logical chain, the value--access decomposition, the learned-pipeline component-error propagation, the single-row impossibility and repeated-linkage separation, the direct-access address/content boundary, the historical and DiscoSCM attribution boundaries, and the weighting/split diagnostics; then run the discriminating unit-preserving versus unit-erased evaluation. The 41-page direct-access/address-content PDF and same-basename SyncTeX artifact have been generated and internally verified (document QA plus focused internal semantic and mathematical audit), but remain unfrozen owner-review artifacts. Exhaustive priority and independent novelty review remain open. Do not treat working-source document QA, the local AAAI adaptation, or the frozen v0.14 artifact as public or externally synchronized.

Next evidence gate

freeze and run whole-user cold-start recommendation plus one non-isomorphic repeated-measure task with negative controls.

48h minimal experiment

implement a whole-user cold-start recommender split with $m\in\{0,1,3,5\}$ admissible prior interactions and a small synthetic negative control; compare sample-only prediction, observed-key PMF/property inference, evidence-abducted selector beliefs, deterministic point-summary ablations, Neural Process / Conditional Neural Process context inference, random-effects/grouped and established recommender baselines under matched information.

Closest SOTA opponents

entity/user/token embeddings; grouped latent-variable and Neural Process / amortized-inference models; hierarchical Bayes and random-effects models.

Strongest objection / kill signal

This is only entity embedding, hierarchical latent-variable learning, random effects or grouped representation learning with renamed notation.

downgrade the work to a perspective or tutorial if the Population/Individual distinction, the direct world conditional, and the two-source randomness contract add no falsifiable constraint, evaluation axis or algorithmic operation beyond established grouped or latent-variable practice.

Canonical provenance

highest-priority owner contract
papers/USL01-unit-as-a-primitive-for-machine-learning/hello_agent.md
v0.12 · sha256:1bd6a67c038b
local canonical source: v0.15
latest verified PDF: v0.14
latest verified supplement: v0.9
synchronized mirrors:
research-questions/USL01-unit-as-a-primitive-for-machine-learning/seed.md
papers/USL01-unit-as-a-primitive-for-machine-learning/paper.md

Registration boundary. This is the owner-approved working title. The external AAAI-27 record is still tracked under The Unit as a Primitive for Machine Learning: Foundations of Unit-Abductive Learning; a title update has not been verified.

Progress log