Strategy/projects/files/splitting_status_2026-04-10.md
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splitting_status_2026-04-10

Splitting Paper — Status Brief

Date: 2026-04-10
Paper: “Stochastic gradient algorithms from ODE splitting perspective”
Authors: Daniil Merkulov, Ivan Oseledets
Primary target: JCAM (Journal of Computational and Applied Mathematics, Elsevier, IF ~2.4)
Secondary track: ЖВММФ (pending Oselodets OK for parallel submission)

Current State (April 2026)

JCAM Draft — Ready for April meeting

File: Strategy/projects/files/splitting/split-sgd/main_jcam.tex
Status: 26 pages, elsarticle format, compiles clean

Done:
- ✅ Full paper structure: SGD as first-order ODE splitting, LLS/Logreg/Softmax/Kaczmarz applications
- ✅ Theorem A (LT / ISTA zero bias): rigorous proof (4 steps: descent lemma, prox optimality, one-step bound, telescoping). Matches Beck & Teboulle 2009.
- ✅ Theorem D (Strang-ISTA bias bound): proof sketch (4 steps present, Steps 3-4 approximations)
- ✅ C_D formula: C_D = ‖A·sign(θ*)‖²/8 stated in theorem; numerical verification C_D ≈ 0.769 (scripts/article3_cd_estimation.py). Analytic value explains 80% of empirical 0.959.
- ✅ Related work: Blanes/Casas/Murua Acta Numerica 2024, DOSnet (JCP 2023), Kaczmarz literature
- ✅ JCAM elsarticle template (\documentclass[preprint,12pt]{elsarticle})
- ✅ All figures generated:
- lasso_convergence.pdf, lasso_bias_floor.pdf, lasso_fixed_point_shift.pdf (from scripts/article3_lasso_figures.py)
- lasso_support_expansion.pdf, lasso_dual_variables.pdf (from scripts/article3_support_expansion.py)
- All LLS/Logreg/Softmax/upper_bound figures copied from phd/thesis_real/Figures/

Missing (discuss with Oselodets):
- ⬜ Theorem D rigorous proof — Steps 3-4 approximations need exact tracking; waiting for C_D formula confirmation
- ⬜ Verify C_D = ‖A·sign(θ*)‖²/8 analytically — key agenda item for April meeting
- ⬜ Oselodets confirmation as co-author for journal version
- ⬜ arxiv preprint (not posted yet — local only)

April Oselodets Meeting Agenda (KEY BLOCKER)

  1. C_D formula correctness: C_D = ‖A·sign(θ*)‖²/8? Support expansion shows: Strang activates j iff dual_j > λ/2 (vs λ for LT) — this is the core mechanism.
  2. Rigorous proof strategy for Theorem D (Lyapunov? Descent lemma?)
  3. JCAM vs COAP — journal choice + connections?
  4. Parallel submission JCAM + ЖВММФ — need explicit OK
  5. Co-authorship confirmation

ЖВММФ Track (separate, 19pp skeleton)

File: Strategy/phd/zhvmmf_article3_skeleton.tex
Status: Draft complete, BLOCKED on Oselodets OK for parallel submission
Review item: /review/inbox/zhvmmf_submit.md — P1, 28+ days overdue
Note: ЖВММФ is a ВАК-listed journal → counts as PhD qualification publication

Connection to Other Projects

PhD Defense (P1)

  • ЖВММФ version, if published, = 4th qualification publication (3 already: Empirical 2019 Scopus, Lyapunov ЖВММФ 2024, Труды МФТИ 2020)
  • JCAM: Q2, not ВАК — counts for résumé, not PhD requirements

RNF Grant (LabMMO, Gasnikov)

  • RNF 23-11-00229-П needs 14 more papers
  • Splitting paper is a candidate contribution

OPTIMA 2026 Conference

  • Sep 22-26, Petrovac
  • CFP expected ~May 2026
  • Splitting paper (or JCAM version) could be submitted as conference paper

Next Steps (Priority Order)

  1. Immediate (ask-level): Get Oselodets meeting date (April → confirm specific date)
  2. Before meeting: Nothing blocking — draft is ready
  3. After meeting:
    - Rigorous Theorem D proof → finalize JCAM manuscript
    - If OK for parallel: submit ЖВММФ version (script ready: scripts/submit_zhvmmf_patchright.py)
    - arxiv preprint post
  4. Target: JCAM submission Q3 2026 (after PhD defense process starts)

Generated by Feanor worker, 2026-04-10 02:10 MSK

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