Writing study: Path-dependent Discrete Amortized Inference

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← ICML 2026 oral writing corpus

Tiago Silva, Esmeralda S. Whitammer, Salem Lahlou · 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: Architecture & representation (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

26 physical pages

Before references / appendix

≈ 8.3 page-equivalents

Main figures / tables

7 / 2

Attached appendix figures / tables

7 / 3

Attached appendix span

≈ 12.91 page-equivalents

Before references / appendix: ≈ 31.92%References / intervening material: ≈ 18.42%Attached appendix: ≈ 49.65%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	≈ 1.36 pp.	5.23%
2. Preliminaries	2	≈ 0.43 pp.	1.65%
3. On the limitations of Markovian samplers	3	≈ 2.65 pp.	10.19%
4. Path-dependent Amortized Samplers	5	≈ 2.54 pp.	9.77%
5. Experiments	8	≈ 0.75 pp.	2.88%
6. Conclusions	9	≈ 0.15 pp.	0.58%
Impact statement	9	≈ 0.07 pp.	0.27%
Acknowledgements	9	≈ 0.04 pp.	0.15%
References	9	≈ 4.78 pp.	18.38%
A. Proofs	14	≈ 2.75 pp.	10.58%
B. Learning a recurrent flow	16	≈ 1.36 pp.	5.23%
C. Related works	18	≈ 0.41 pp.	1.58%
D. Stochastic latent dynamical system	18	≈ 3.95 pp.	15.19%
E. Distributed and Streaming Inference in Path-dependent Models	22	≈ 0.83 pp.	3.19%
F. Additional Experiments & Further Details	23	≈ 3.6 pp.	13.85%

All detected figure and table locations

Main text

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

Attached appendix

• Figure 8 · p. 17
• Figure 9 · p. 18
• Figure 10 · p. 24
• Figure 11 · p. 24
• Table 3 · p. 24
• Table 4 · p. 24
• Figure 12 · p. 25
• Figure 13 · p. 25
• Table 5 · p. 25
• Figure 14 · p. 26

Argument and organization

1. 1 Introduction; 2 Preliminaries; 3 Limitations

   Uses a running state graph to separate linear, GNN and empirical neural-policy aliasing cases.

2. 4 Path-dependent Amortized Samplers

   Defines the lifted state graph, chooses recurrent dynamics and extends balance criteria.

3. 5 Experiments; 6 Conclusions

   Tests distribution fit on compositional benchmarks and identifies stochastic latent dynamics as unfinished.

Problem, claim and contribution

The expressivity critique concerns specified parameterizations, not the nonexistence of any Markovian sampler for the target distribution.

Sections 3.1-3.2, pp.3-4; Proposition 4.8, p.8 · Main paper

Argument and section order

A single LINES example develops from a linear limitation to neural state aliasing before the lifted-DAG definition and recurrent implementation.

Sections 3-4.1, pp.3-6 · Main paper

Figures, captions and visual explanation

Compact matched heat strips visualize learned versus target mass, while the later page pairs policy-divergence curves, concise fit tables and matched grid-world heatmaps.

Figure 3, p.4; Figure 6, Tables 1-2 and Figure 7, p.8 · Main paper

Tables, comparisons and evidence

Balance conditions guarantee target marginals when satisfied; the implemented loss minimization and finite-subset FCS diagnostic do not establish exact global distribution matching after finite training.

Proposition 4.5 and Corollaries, p.7; experiment metric discussion, p.8 · Main paper

Appendix and reproducibility

Implementation details match parameter counts and disclose cubic latent-matrix rotation cost; separate ablations compare rotation, link functions and gated recurrent alternatives.

Appendix F.1, p.23; Appendix F.3, p.26 · Main paper

Clarity and writing conventions

The conclusion leaves stochastic latent dynamics open despite preliminary supplementary derivations, and the abstract uses often rather than an all-task convergence claim.

Abstract, p.1; Conclusion, p.9 · Main paper

What to reuse—and what not to infer

Transferable lesson: Connect each expressivity statement to a specific policy class, and separate ideal balance identities from finite-training fit and computational overhead.

Boundary: Path dependence can improve optimization even when the optimal unlifted policy is Markovian; improved iteration curves are not automatically end-to-end speedups or verified biological design outcomes.

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-oriented scan of the main argument through physical p.9, with focused physical-page text inspection on 1, 3, 4, 5, 6, 7, 8, 9. Framing, section progression, mechanism/proof explanation, displays, comparison conditions and conclusions were inspected. This is not exhaustive technical reading, proof verification or reproduction.

Appendix / supplement

Appendix organization and main-text pointers were checked; focused text inspection of physical pages 20, 23, 26. Remaining appendix proofs and details were not exhaustively read. No separately linked supplement inspected.

Visually inspected PDF pages

4, 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 proceedings PDF, PMLR volume 306, retrieved 2026-10-07 · 26 pages