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LIT-375: Structural Learning Theory: A Metric-Topology Factorization Approach

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StatusProposed — read in full 2026-10-01 (NOTE-324); >- Promising and unproven. It is the programme's fullest and most careful formal statement, and it carries the learning theory of LIT-374 §3 with the assumptions in the body. Its routine results hold, and its bouquet slip is repairable. What would settle it: - a theorem that the CS count for a learned predictor equals w(P; γ, δ), not w_G(P); - a K-sweep on benchmarks of known width, showing the floor at K < w for routed learners, and testing whether a capacity-matched monolithic model shows it; - the decoupled-versus-joint training comparison it motivates but does not run.
Version2
Tagslearning-theory, representation-learning, mathematics
Cited as “paper” byNOTE-324 — Structural Learning Theory: A Metric-Topology Factorization Approach
Cited as “source” byTHEORY-574 — The structural width of Xin Li's learning programme is a covering number of the margin-safe region by local pieces: its lower bounds come from metric confinement through a wedge point, not from topology, labels enter only through the margin, and the error floor below width binds only learners assembled from local experts, so it does not entail routing, nor training routing apart from the task loss

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Li (2026), ‘arXiv preprint, cs.LG. v2 (2026-05-06) is the version read and the first appearance of this work. v1 (2026-02-08) under the same identifier is a different paper, “Beyond Optimization: Intelligence as Metric-Topology Factorization under Geometric Incompleteness”. Typeset in a JMLR template with placeholder publication data; not published in JMLR.’ — arXiv:2602.07974

Standing in the record

Filed on 2026-10-01 at the owner’s request. published: is the first appearance (ADR-002). Here that is 2026-05-06, the date of arXiv v2: v1 (2026-02-08) under the same number is a different paper, “Beyond Optimization”, a Morse-theory argument. Read together with LIT-373 and LIT-374 as one research programme (curation entry of 2026-10-01); this is its fullest formal statement. Its JMLR-style header is template residue: it is an unrefereed preprint.

It was filed Deferred, unread. NOTE-324 is the close reading of 2026-10-01, and it placed the work: Proposed — >- Promising and unproven. It is the programme’s fullest and most careful formal statement, and it carries the learning theory of LIT-374 §3 with the assumptions in the body. Its routine results hold, and its bouquet slip is repairable. What would settle it: - a theorem that the CS count for a learned predictor equals w(P; γ, δ), not w_G(P); - a K-sweep on benchmarks of known width, showing the floor at K < w for routed learners, and testing whether a capacity-matched monolithic model shows it; - the decoupled-versus-joint training comparison it motivates but does not run.

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