Writing study: Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers

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← ICLR 2026 oral writing corpus

Panagiotis D. Grontas, Antonio Terpin, Efe Balta, Raffaello D'Andrea, John Lygeros · 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: Architecture & representation design (primary) · Learning & optimization algorithms · Theory & formal foundations.

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

47 physical pages

Before references / appendix

≈ 9.82 page-equivalents

Main figures / tables

4 / 0

Attached appendix figures / tables

18 / 6

Attached appendix span

≈ 28.89 page-equivalents

Before references / appendix: ≈ 20.89%References / intervening material: ≈ 17.64%Attached appendix: ≈ 61.47%Estimated layout envelopes, not text/artwork area. Unresolved appendix boundaries remain within the undivided post-body material.

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	≈ 1.77 pp.	3.77%
2 TRAINING HARD-CONSTRAINED NEURAL NETWORKS	3	≈ 3.27 pp.	6.96%
3 NUMERICAL EXPERIMENTS	6	≈ 3.59 pp.	7.64%
4 CONCLUSIONS	10	≈ 0.46 pp.	0.98%
REFERENCES	10	≈ 8.28 pp.	17.62%
A TOY VISUAL EXAMPLE	19	≈ 1.35 pp.	2.87%
B ADDITIONAL RESULTS	20	≈ 12.65 pp.	26.91%
C THE SHARP BITS	33	≈ 8 pp.	17.02%
D DERIVATION DETAILS	41	≈ 3 pp.	6.38%
E MORE EXAMPLES OF CONSTRAINT SETS	44	≈ 2 pp.	4.26%
F ON THE DIFFERENTIABILITY OF THE PROJECTION LAYER AND THE	46	≈ 1.89 pp.	4.02%

All detected figure and table locations

Main text

• Figure 1 · p. 1
• Figure 2 · p. 7
• Figure 3 · p. 8
• Figure 4 · p. 9

Attached appendix

• Table 1 · p. 20
• Figure 5 · p. 20
• Table 2 · p. 21
• Table 3 · p. 21
• Figure 6 · p. 22
• Figure 7 · p. 23
• Figure 8 · p. 24
• Figure 9 · p. 24
• Table 4 · p. 25
• Figure 10 · p. 26
• Figure 11 · p. 27
• Figure 12 · p. 28
• Figure 13 · p. 29
• Figure 14 · p. 31
• Table 5 · p. 31
• Figure 15 · p. 32
• Figure 16 · p. 36
• Figure 17 · p. 36
• Table 6 · p. 36
• Figure 18 · p. 37
• Figure 19 · p. 38
• Figure 20 · p. 38
• Figure 21 · p. 42
• Figure 22 · p. 47

Argument and organization

1. Projection-layer construction

   Define the constrained problem, derive forward splitting and implicit backward computation, then separate architecture and numerical tuning.

2. Benchmarks and motion planning

   Evaluate objective quality, feasibility and time separately, followed by an application with non-convex preferences but convex constraints.

Problem, claim and contribution

The contribution is carefully positioned as a specialized implicit layer, not the invention of implicit differentiation; exploiting projection structure explains the practical novelty.

Contribution box, page 3; Appendix C.5, pages 39–40. · Main paper

Argument and section order

A short numerical-details subsection routes readers to matrix equilibration, automatic tuning and their ablations, making implementation engineering a named contribution rather than an undocumented trick.

Section 2.4, page 6; Appendix C.1–C.3, pages 33–38. · Main paper

Figures, captions and visual explanation

The first-page diagram uses three shaded regions for backbone, geometric projection and constrained objective, with backward arrows above. It communicates both inference and training without listing every numerical step.

Figure 1, page 1. · Main paper

Tables, comparisons and evidence

Figure 2 plots constraint violation against relative suboptimality per test instance with explicit acceptance boundaries; separating the two axes prevents a low objective obtained through infeasibility from looking successful.

Figure 2 and metrics, page 7. · Main paper

Appendix and reproducibility

The detailed contents plus lists of figures/tables support a long supplement containing toy counterexamples, expanded solver comparisons, projection derivations and gradient checks.

Pages 15–18; Appendices A–F. · Main paper

Clarity and writing conventions

The main method acknowledges that finite iterations need not satisfy every constraint exactly and that the backward linear solve is heuristic when singular. Those qualifications should accompany the abstract's feasible-by-design language.

Sections 2.1.1–2.1.2, page 5; Appendix F, pages 46–47. · Main paper

What to reuse—and what not to infer

Transferable lesson: For optimization layers, visually separate feasibility, objective quality and runtime, and expose numerical stabilization choices as part of the method.

Boundary: Finite-step projection is approximate, constraints must be convex, and the motion-planning example does not guarantee collision avoidance. Appendix C.4's displayed minimizer signs are reversed relative to its plotted linear objective; proof examples still need independent checking.

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 1–4, all method and experiment text.

Appendix / supplement

Pages 15–47: contents, Appendices A–F, numerical examples, algorithms, derivations and differentiability discussion.

Visually inspected PDF pages

1, 7

• ICLR 2026 final proceedings · 47 pages