Writing study: RAIN-Merging: A Gradient-Free Method to Enhance Instruction Following in Large Reasoning Models with Preserved Thinking Format

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← ICLR 2026 oral writing corpus

Zhehao Huang, Yuhang Liu, Baijiong Lin, Yixin Lou, Zhengbao He, Hanling Tian, Tao Li, Xiaolin Huang · Official ICLR 2026 oral record

Observed writing choices, not acceptance rules. This study examines the inspected manuscript version. It does not establish why the paper was accepted or that its presentation choices should be copied unchanged.

Figure, table and section ledger

Editorial contribution type: Learning & optimization algorithms (primary).

Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.

Canonical PDF

41 physical pages

Before references / appendix

≈ 10.25 page-equivalents

Main figures / tables

6 / 6

Attached appendix figures / tables

7 / 10

Attached appendix span

≈ 24.89 page-equivalents

Before references / appendix: ≈ 25%References / intervening material: ≈ 14.29%Attached appendix: ≈ 60.71%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: RAIN-Merging: restore Figure 2 on physical page 3, whose label is split across same-baseline Poppler lines, and Table 3 on page 9, whose label is a standalone line beside Table 4. Both are real captions verified in the rendered pages.

Section-by-section lengths and source pages

The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.

Top-level heading	Starts on PDF page	Estimated span	Share of entire PDF
1 INTRODUCTION	1	≈ 1.49 pp.	3.63%
2 PRELIMINARY AND OBSERVATIONS	3	≈ 0.52 pp.	1.27%
3 OUR RAIN-MERGING METHOD	3	≈ 3.8 pp.	9.27%
4 EXPERIMENTS	7	≈ 3.26 pp.	7.95%
5 CONCLUSION	10	≈ 0.31 pp.	0.76%
ACKNOWLEDGMENTS	11	≈ 0.14 pp.	0.34%
REFERENCES	11	≈ 5.85 pp.	14.27%
APPENDIX	17	≈ 0.03 pp.	0.07%
A ETHICS STATEMENT	17	≈ 0.27 pp.	0.66%
B REPRODUCIBILITY STATEMENT	17	≈ 0.12 pp.	0.29%
C LLM USAGE STATEMENT	17	≈ 0.24 pp.	0.59%
D RELATED WORK	17	≈ 1.55 pp.	3.78%
E PROOF	19	≈ 3.28 pp.	8%
F ALGORITHM	22	≈ 0.08 pp.	0.2%
G METHOD IMPLEMENTATION DETAILS	22	≈ 0.69 pp.	1.68%
H CALIBRATION SET CONSTRUCTION	23	≈ 1.84 pp.	4.49%
I DETAILED EXPERIMENTAL SETUP	25	≈ 2.51 pp.	6.12%
J ADDITIONAL EXPERIMENTS	27	≈ 13.38 pp.	32.63%
K IMPLICATIONS	41	≈ 0.33 pp.	0.8%
L LIMITATIONS AND FUTURE WORK	41	≈ 0.56 pp.	1.37%

All detected figure and table locations

Main text

• Figure 1 · p. 2
• Figure 2 · p. 3
• Figure 3 · p. 5
• Table 1 · p. 7
• Table 2 · p. 8
• Table 4 · p. 9
• Table 3 · p. 9
• Figure 4 · p. 9
• Figure 5 · p. 9
• Figure 6 · p. 9
• Table 5 · p. 10
• Table 6 · p. 10

Attached appendix

• Figure A1 · p. 19
• Figure A2 · p. 19
• Table A1 · p. 23
• Figure A3 · p. 24
• Table A2 · p. 24
• Table A3 · p. 25
• Table A4 · p. 27
• Table A5 · p. 27
• Table A6 · p. 28
• Table A7 · p. 28
• Figure A4 · p. 29
• Figure A5 · p. 29
• Figure A6 · p. 30
• Table A8 · p. 30
• Table A9 · p. 31
• Figure A7 · p. 31
• Table A10 · p. 32

Argument and organization

1. Parameter-space observation followed by its limitation

   Uses task-vector near-orthogonality to motivate merging, then shows why output-format preservation needs a separate constraint.

2. Two-stage method and research-question-led evaluation

   Pairs projection and attention-guided scaling with separate component diagnostics and joint reasoning/instruction tests.

Problem, claim and contribution

The motivating failure is concrete: a correct reasoning answer can still violate a requested format. The paper distinguishes parameter compatibility from behavioral compatibility.

Sections 1–2, pages 1–3. · Main paper

Argument and section order

Stage headings, a final merged-parameter equation and numbered research questions keep the mathematical derivation connected to evaluation.

Section 3 and research questions, pages 4–7. · Main paper

Figures, captions and visual explanation

Figure 3 combines a before/after projection example with colored instruction/response spans and an attention map; the two panels correspond directly to the two method stages.

Figure 3, page 5. · Main paper

Tables, comparisons and evidence

Table 1 separates data-free and calibrated merging and includes runtime. Figure 5 measures missing closing markers as well as KL shift, while MathIF evaluates correct answers and satisfied constraints jointly.

Table 1, page 7; Figure 5 and Table 5, pages 9–10. · Main paper

Appendix and reproducibility

Calibration sample counts, span extraction, numerical precision and per-benchmark metrics are documented separately, enabling readers to identify the actual data dependencies of a gradient-free method.

Appendices G–I, pages 23–27. · Main paper

Clarity and writing conventions

The paper explicitly calls its attention-coefficient derivation an engineering approximation rather than silently equating measured attention with exact derivatives.

Equation 14 and surrounding explanation, page 6. · Main paper

What to reuse—and what not to infer

Transferable lesson: When preserving one capability while adding another, report both task success and the specific failure mechanism the preservation component is intended to prevent.

Boundary: Gradient-free does not mean data-free: calibration uses generated responses and selected spans, including IFEval-derived prompts. Format preservation is not a safety guarantee. The appendix needs independent mathematical checking (including its softmax Hessian bound), and Table A9 repeats EIFBench scores as averages; do not propagate these unchecked claims.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-09-19

Reading status

Full text + selected visuals inspected

Main text

Pages 1–10, Sections 1–5; acknowledgments and references on pages 11–16.

Appendix / supplement

Pages 17–41, Appendices A–L, including proofs, full algorithm, calibration construction, benchmark settings, all ablations/cases, implications and limitations.

Visually inspected PDF pages

5, 7

• ICLR 2026 official proceedings PDF, retrieved 2026-09-19 · 41 pages