Writing study: Understanding and Enforcing Weight Disentanglement in Task Arithmetic

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← CVPR 2026 oral writing corpus

Shangge Liu, Yuehan Yin, Lei Wang, Qi Fan, Yinghuan Shi, Wenbin Li, Yang Gao, Dacheng Tao · Official CVPR 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: Theory & formal analysis (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

10 physical pages

Before references / appendix

≈ 8.11 page-equivalents

Main figures / tables

6 / 2

Attached appendix figures / tables

0 / 0

Attached appendix span

Separate file recorded below; not in this PDF total

Before references / appendix: ≈ 81.1%References / intervening material: ≈ 18.9%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

Extraction notes: No attached appendix boundary detected. Zero means no recognized caption, not independently verified absence.

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	≈ 1.3 pp.	13%
2. Related Work	2	≈ 0.39 pp.	3.9%
3. Preliminaries and Problem Formulation	3	≈ 0.56 pp.	5.6%
4. The Proposed Framework	3	≈ 3.15 pp.	31.5%
5. Experiments	6	≈ 2.06 pp.	20.6%
6. Conclusion	8	≈ 0.25 pp.	2.5%
References	9	≈ 1.89 pp.	18.9%

All detected figure and table locations

Main text

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

Attached appendix

No recognized caption labels.

Separate source files—excluded from canonical-PDF totals

A separate author version may repeat main text and references. Whole-file lengths and counts are not extra appendix material and are never added to the canonical PDF totals. Read the study's source scope for which sections received substantive reading versus layout inspection.

Additional source 1

Separate PDF (or ZIP containing it): whole-file layout of 20 physical pages; 5 detected figures and 4 tables. These may include overlapping main-text material.

Located appendix only: starts on physical p.1; ≈ 19.94 page-equivalents, 5 figure labels and 4 table labels. This interval is distinct from the whole file.

Detected heading	PDF page	Estimated span
Supplementary Material	1	≈ 0.02 pp.
A. Note on the Scope of Analysis: Why Focus	1	≈ 0.22 pp.
B. Justification for Two-Task Simplification	1	≈ 0.45 pp.
C. Proof of Lemma 1	1	≈ 0.46 pp.
D. Detailed Proof of Theorem 1	2	≈ 1.6 pp.
E. Proof of Corollary 1	3	≈ 1.88 pp.
F. Bayesian Analysis of the Relationship be-	5	≈ 1.11 pp.
G. Detailed Proof of Theorem 2	6	≈ 4.91 pp.
H. Comparative Analysis with TTA	11	≈ 4.52 pp.
I. Experiments Details	16	≈ 0.17 pp.
J. More Experimental Results	16	≈ 3.16 pp.
References	19	≈ 1.45 pp.

• Table 1 · p. 12
• Figure 1 · p. 13
• Figure 2 · p. 14
• Table 2 · p. 15
• Table 3 · p. 15
• Figure 3 · p. 17
• Figure 4 · p. 17
• Figure 5 · p. 18
• Table 4 · p. 18

Argument and organization

1. Conditions before intervention

   Define weight disentanglement and linearization, then state feature specialization as a sufficient condition.

2. Ideal structure to regularization

   Explain realistic feature overlap, propose OrthoReg and test addition, negation and orthogonality diagnostics.

Problem, claim and contribution

The introduction separates explaining successful task arithmetic from constructing better task vectors, giving theory and intervention distinct roles.

Introduction and Figure 1 · Main paper · Additional source 2

Argument and section order

Definitions, assumptions and the sufficient-condition theorem are adjacent before the practical regularizer, preventing an empirical orthogonality observation from silently becoming a guarantee.

Section 4.2, PDF p. 4 · Main paper · Additional source 2

Figures, captions and visual explanation

Weight-angle histograms show the geometric clue, while per-task radar panels complement aggregate addition accuracy with task-specific effects.

Figure 2, PDF p. 4; Figure 4, p. 7 · Main paper · Additional source 2

Tables, comparisons and evidence

The negation table reports target accuracy subject to a stated control-task retention threshold and shows deltas for baseline-plus-regularizer pairs.

Table 2, PDF p. 7 · Main paper · Additional source 2

Appendix and reproducibility

Proofs and comparison assumptions are separated from compute, alternative retention thresholds and full per-layer/module analyses.

Supplement Sections A–J, pp. 1–20 · Main paper · Additional source 2

Clarity and writing conventions

The prose labels orthogonality a clue in the ideal analysis before discussing imperfect feature overlap, an important distinction for theory-motivated methods.

Sections 4.2.4–4.3.1 · Main paper · Additional source 2

What to reuse—and what not to infer

Transferable lesson: Keep assumptions beside the theorem, then state precisely what the practical regularizer encourages rather than claiming it enforces every ideal condition.

Boundary: Weight orthogonality alone is not the full sufficient condition. The supplement reports an MLP-only exception, so consistent improvement must be qualified by configuration.

Apply this lesson using the argument and evidence worksheet.

Inspection record and sources

Checked

2026-09-26

Reading status

Writing-focused manuscript scan + selected visuals inspected

Main text

Manuscript-wide writing scan of main PDF pp. 1–8: framing, section structure, method exposition, figure/table captions, evaluation organization and conclusions; not an exhaustive technical proof audit or reproduction.

Appendix / supplement

Separate supplement pp. 1–20 scanned: scope assumptions, proofs, Bayesian argument, TTA comparison, compute, all-layer diagnostics, alternative forgetting thresholds and module ablations.

Visually inspected PDF pages

4, 7

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.

• Official CVPR 2026 CVF proceedings PDF; retrieved 2026-09-26 · 10 pages
• Official CVPR 2026 separate supplementary PDF; retrieved 2026-09-26 · 20 pages