Splitting Project Status — 2026-04-09

Paper: “Stochastic gradient algorithms from ODE splitting perspective”
Authors: Daniil Merkulov, Ivan Oseledets
Target: JCAM (Journal of Computational and Applied Mathematics, IF 2.4)
Timeline: Q3 2026 submission (after PhD defense phase begins)

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Current Paper State

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Blockers (in priority order)

1. April meeting with Оселедец (primary blocker)
   - Agenda item 1: Verify C_D = ‖A·sign(θ*)‖²/8 analytically
   - Agenda item 2: Strategy for rigorous Theorem D proof
   - Agenda item 3: JCAM vs COAP — which journal?
   - Agenda item 4: Confirm co-authorship for journal version
   - Agenda item 5: Confirm OK for parallel ЖВММФ + JCAM publication

2. ЖВММФ parallel publication approval
   - ЖВММФ submission has been waiting 28+ days for Оселедец OK
   - ЖВММФ skeleton ready: Strategy/phd/zhvmmf_article3_skeleton.tex
   - Review item: /review/inbox/zhvmmf_submit.md (P1!)
   - This unblocks a required PhD qualification publication

3. Rigorous Theorem D proof
   - Steps 3-4 of sketch need exact coefficient tracking
   - C_D formula analytically: C_D = ‖A·sign(θ*)‖²/8 (needs verification)
   - Support expansion analysis: Strang activates j iff dual_j > λ/2

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Strategic Context

For PhD defense: Splitting paper = 3rd qualified publication (needed for defense).
- ЖВММФ (ВАК journal) = fastest path to getting paper counted
- JCAM = higher impact, but 3-4 month review

For РНФ grant (LabMMO): РНФ 23-11-00229-П needs 14 more papers.
- Гасников confirmed Splitting paper as candidate (2026-04-02)
- Timeline: submit ЖВММФ ASAP (unblocked after Оселедец call)

Literature positioning: Main USP — SGD-splitting connection is under-explored.
Key citation: Blanes/Casas/Murua (Acta Numerica 2024) = PDE focus, not ML optimization.
Our angle: ML optimization / stochastic analysis of splitting bias.

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Next Actions (priority order)

1. [ask] Get ЖВММФ submission OK from Оселедец — email/call ASAP (28+ days waiting)
2. [ask] Schedule April Оселедец meeting for C_D + Theorem D discussion
3. [auto] After meeting: write rigorous Theorem D proof → finalize main_jcam.tex
4. [auto] Prune arxiv-preprint figures to final quality before JCAM submission
5. [auto] Submit to ЖВММФ (via Patchright script: scripts/submit_zhvmmf_patchright.py)

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Key Files