Writing study: Don’t Force the Fit: Bounded Log-Likelihood Loss for Enhanced Reasoning in Large Language Models

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← ICML 2026 oral writing corpus

Feng Zhao, Hong Zhang, Yu Yang, Ruilin Zhao, Guandong Xu · Official ICML 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: Training, objectives & optimization (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

23 physical pages

Before references / appendix

≈ 8.54 page-equivalents

Main figures / tables

4 / 3

Attached appendix figures / tables

4 / 5

Attached appendix span

≈ 11.91 page-equivalents

Before references / appendix: ≈ 37.13%References / intervening material: ≈ 11.09%Attached appendix: ≈ 51.78%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Source-bound correction: Source-checked physical-page text restores wrapped top-level heading labels on pp. 2, 4. Heading starts and measured positions are unchanged; this is label completeness, not a new section. Newly detected unnumbered impact/singular-acknowledgment statements are retained from the size-aware source extraction; authored heading corrections are unchanged.

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	≈ 0.99 pp.	4.3%
2. Empirical Diagnosis of SFT Optimization in Reasoning	2	≈ 2.09 pp.	9.09%
3. Method: Bounded Log-Likelihood Loss (BLL-Loss)	4	≈ 1.98 pp.	8.61%
4. Experiments	6	≈ 2.25 pp.	9.78%
5. Related Work	8	≈ 0.44 pp.	1.91%
6. Conclusion	9	≈ 0.12 pp.	0.52%
7. Limitations and Future Work	9	≈ 0.12 pp.	0.52%
Acknowledgments	9	≈ 0.07 pp.	0.3%
Impact Statement	9	≈ 0.14 pp.	0.61%
References	9	≈ 2.54 pp.	11.04%
A. Derivation of Log-Odds Decomposition	12	≈ 0.73 pp.	3.17%
B. Theoretical Analysis and Detailed Derivations	12	≈ 2.58 pp.	11.22%
C. Implementation Details	15	≈ 2.32 pp.	10.09%
D. Additional Experimental Results	17	≈ 4.13 pp.	17.96%
E. Case Studies	21	≈ 2.16 pp.	9.39%

All detected figure and table locations

Main text

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

Attached appendix

• Table 4 · p. 15
• Figure 5 · p. 18
• Table 5 · p. 19
• Table 6 · p. 19
• Table 7 · p. 20
• Table 8 · p. 21
• Figure 6 · p. 21
• Figure 7 · p. 22
• Figure 8 · p. 23

Argument and organization

1. Problem and contribution

   Distinguishes a genuine capability gap from a different valid realization and explicitly limits the goal to eliciting existing reasoning priors.

2. Argument sequence

   Empirical investigations precede loss design; two mathematical perspectives converge to one objective before ablations compare learning rate, clipping and training duration.

3. Evidence and verification

   Controls challenge simple smaller-step and longer-training explanations, while the appendix retains a zero-score out-of-distribution knowledge-injection failure.

Problem, claim and contribution

Distinguishes a genuine capability gap from a different valid realization and explicitly limits the goal to eliciting existing reasoning priors.

Section 2.2-2.3, pp. 2-3 · Main paper

Argument and section order

Empirical investigations precede loss design; two mathematical perspectives converge to one objective before ablations compare learning rate, clipping and training duration.

Sections 2-4, pp. 2-8 · Main paper

Figures, captions and visual explanation

Takeaway boxes sit beside probability/cumulative-tail plots. The results page separates optimization controls from cross-domain generalization and repeats the model-scale blocks.

Figure 1, p. 3; Tables 2-3, p. 8; both PNGs inspected · Main paper

Tables, comparisons and evidence

Controls challenge simple smaller-step and longer-training explanations, while the appendix retains a zero-score out-of-distribution knowledge-injection failure.

Table 2, p. 8; Appendix D.4, p. 19 · Main paper

Appendix and reproducibility

Full benchmark breakdowns and concurrent loss comparisons accompany derivations; failure analysis explicitly explains why essential novel tokens can be suppressed.

Appendices B-D, pp. 12-20 · Main paper

Clarity and writing conventions

Repeated motivation/setup/observation paragraphs aid the diagnosis, but broad domain-agnostic language is narrowed materially by the appendix's knowledge-acquisition boundary.

Section 2.3, p. 3; Section 4.5, p. 8; D.4, p. 19 · Main paper

What to reuse—and what not to infer

Transferable lesson: Make the hypothesis-to-intervention chain explicit and include a task where the intended inductive bias predictably fails.

Boundary: Low probability is not an intrinsic label for stylistic noise; a method that elicits prior capability can fail when the desired knowledge is absent.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-10-07

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Writing-focused distributed manuscript scan, not exhaustive technical/proof validation. Sections 1-6, pp. 1-9: token-fit diagnosis, masking tests, two loss derivations, gradient behavior, main comparisons, controls and transfer.

Appendix / supplement

Writing-focused appendix scan; code, data and external assets not executed. Appendices A-E, pp. 12-23: algebra/gradient derivations, implementation and evaluation, token analysis, concurrent comparisons, knowledge-injection failure and case studies.

Visually inspected PDF pages

3, 8

This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.

• Published ICML 2026 proceedings PDF, PMLR volume 306; retrieved 2026-10-07. Public OpenReview decision notes were not independently reverified. · 23 pages