Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Factorization and finite-endpoint warnings
Remark
The learned sampler assumes conditional independence across positions at each reverse update. Forward masking is independent across positions only after conditioning on the clean sequence; marginalizing a dependent clean-sequence law can make the true reverse coordinates dependent, so a normalized learned sampler need not be the exact reverse law. The counterexample on the companion page gives a finite witness. The identities here concern a fixed finite grid only; they assert no continuous-time or zero-mesh limit, which would require separate convergence hypotheses. The weighted-cross-entropy ELBO identity uses the exact clean and all-mask endpoints and their matching decoder and prior; approximate endpoints retain their reconstruction and terminal-prior terms. Sahoo et al. label their zero-masking and carry-over substitutions as “RB techniques” and call the simplified objective “Rao–Blackwellized”; this finite identity makes no variance-reduction claim, because no estimator and conditioning comparison are specified here.
Remark references
A factorized reverse kernel fails for correlated tokens ↗: a two-token finite witness where the true reverse posterior is dependent but the learned reverse draw is a product.
Negative expected finite masked-diffusion ELBO is weighted cross-entropy: the exact-endpoint finite ELBO identity and the support condition for its finite proof.
Sahoo et al., §3.3 and Appendix B.1: the paper's objective simplifications using zero-masking and carry-over substitutions, termed “RB techniques.”
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
20 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Subham Sekhar Sahoo et al., Simple and Effective Masked Diffusion Language Models, arXiv v1 (standard reference, not scraped)