Reasoning Models Are Accurate but Unsound on Identification

Arman Behnam; Binghui Wang

cs.AIOct 2, 2026

Reasoning Models Are Accurate but Unsound on Identification

Authors: Arman Behnam, Binghui Wang

Organizations: Department of Computer Science Illinois Institute of Technology Chicago, IL, USA

Abstract

A reasoning model asked whether a causal effect is recoverable from observational data can fail in two ways: it refuses an identifiable query or answers a nonidentifiable one. The latter is more consequential, as no observational data can validate the claimed formula. Measuring this failure requires queries that are provably non-identifiable, which prior evaluations lack, and grading that accepts correct formulas in any equivalent form, which string matching cannot provide. We build CERTID, a formal identification pipeline that addresses both limitations. CERTID uses the sound and complete causal identification algorithm ID to certify whether an effect is identifiable from a given graph and query, and verifies returned formulas against structural causal models whose interventional distributions are known exactly. CERTID further develops theoretical results to mitigate structural leakage, repair non-identifiable queries, and establish grading guarantees. We evaluate three frontier reasoning models (Gemini Flash, Gemini Pro, and GPT5.5) on 1,200 certified instances spanning 4 to 50 vertices. Accuracy proves a poor proxy for soundness: on identical instances, the false-claim rate on non-identifiable queries varies by seventeen-fold across models. We also find that models decide identifiability with 97-100% accuracy on graphs generated after the strongest model's training snapshot. Instances, the certification procedure, the verifier, and per-instance records are available at https://anonymous.4open.science/r/certid-D718.

Figures & tables

Benchmark	Ground truth	Unanswerable instances	Grading
cladder ( Jin et al., 2023 )	oracle-computed	—	string
noisycausal ( Xu and Fu, 2026 )	SCM-computed	—	string
qrdata ( Liu et al., 2024 )	data-computed	—	string
causalbench ( Wang, 2024 )	annotated	—	string
econcausal ( Lee et al., 2026 )	curated	underspecified	string
abstentionbench ( Kirichenko et al., 2026 )	annotated	annotated	string

Table 1: How ground truth and grading are established in causal reasoning benchmarks. In prior methods, every query is answerable when groundtruth is provided or unanswerable determined by human judgment. CertID is the only benchmark without ground truth or human judgment.

Panel of Figure 1 — Figure 1: (a) an error current evaluations cannot catch, (b) the two computations that let us catch it, and (c) what the resulting measurement separates.

Panel of Figure 2 — Figure 2: How CertID ’s one instance moves through the evaluation. (1) An instance is drawn from a family defined in Section 3.1 and certified by id (Definition 3 ). (2) The system sees the graph and query but not the label, and its reply is parsed into a response (Section 4.2 ). (3) The verdict is compared with the label (Definition 5 ); for a correct claim, the estimand is also verified on sampled SCMs (Section 4.3 ). The dashed row follows the confounded graph of Figure 1 (a): the system returns an estimand for a non-identifiable query, a false claim that no observational data can expose.

Model	Scored	Acc.	Id. rate	Ans. rate	False-claim rate
FLASH	600/600	0.983	0.500	0.513	0.030
PRO	589/600	0.978	0.506	0.511	0.028
GPT-5.5	600/600	0.998	0.500	0.498	0.000
	Accuracy			False-claim
Model	Rand. fam.	Pub. fam.		Rand. fam.	Pub. fam.
FLASH	0.981	0.992		0.033	0.017

Table 2: Verdict performance on the main pool: 600 instances, balanced between identifiable and non-identifiable queries. Random-family graphs sweep

|\mathbf{V}|\in\{5,7,9,11,13\}

Panel of Figure 3 — Figure 3: Accuracy and false-claim rate against graph size, three frontier models on identical instances and identical prompts. (a) Accuracy separates the models by about ten points and declines gently. (b) The false-claim rate separates them by a factor of 17 pooled.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

graphs and models
Symbol	Meaning	Introduced
$G$	acyclic directed mixed graph over $\mathbf{V}$	Sec. 2
$\mathbf{V}$	observed variables of $G$	Sec. 2
$\mathbf{X},\mathbf{Y}$	disjoint treatment and outcome sets	Sec. 2
$B(G)$	bi-directed edges of $G$	Sec. 2
$\mathrm{An}(\mathbf{Y})$	ancestors of $\mathbf{Y}$	Sec. 2

Appendix

Table 3: Symbols used in the paper, with the section in which each is introduced.

Feature	Definition	AUC
directed degree sum	$d(u)+d(v)$	0.574
directed degree min	$\min\{d(u),d(v)\}$	0.534
directed degree max	$\max\{d(u),d(v)\}$	0.580
bi-directed degree sum	$b(u)+b(v)$	0.442
bi-directed degree min	$\min\{b(u),b(v)\}$	0.410
bi-directed degree max	$\max\{b(u),b(v)\}$	0.480

Appendix

Table 4: The thirteen structural features, and their single-feature AUC on our construction (927 edges). Values outside

[0.45,0.55]

are in bold.

	uniform injection	our construction
common parents	0.266	0.472
directed degree min	0.321	0.534
bi-directed degree sum	0.299	0.442
bi-directed degree min	0.258	0.410
directed distance	0.585	0.637
pooled classifier	0.825	0.652

Appendix

Table 5: AUC under uniform injection and under our construction. Rows are single-feature AUCs; the last row is the held-out pooled classifier.

	main pool	scale grid
flash	2,421	4,114
pro	8,070	17,144
gpt-5.5	2,994	5,733

Appendix

Table 6: Mean reasoning tokens per reply.

Network	Domain	Source	Nodes	Edges
asia	lung-disease diagnosis	Lauritzen and Spiegelhalter [1988]	8	8
child	congenital heart disease	Spiegelhalter [1992]	20	25
insurance	car-insurance risk	Binder et al. [1997]	27	52
alarm	patient monitoring	Beinlich et al. [1989]	37	46
hepar2	liver-disorder diagnosis	Onisko [2003]	70	123

Appendix

Table 7: The five networks behind the published family (Definition 7 ).

false claims
		total	verdict line	estimand block	whole-text scan
flash	main	9	9	0	0
flash	scale	51	51	0	0
pro	main	8	4	2	2
pro	scale	22	16	6	0
gpt-5.5	main	0	0	0	0

Appendix

Table 8: How each verdict was read, by model, pool and label. Counts are of responses; the shipped metrics reproduce exactly from them.

pro	as shipped	truncated excluded
main-pool accuracy	0.9779 (589 scored)	0.9811 (583 scored)
main-pool false claims	8/291 = 0.0275	6/287 = 0.0209
scale-grid accuracy	0.9415	0.9430
scale-grid false claims	22/298 = 0.0738	21/297 = 0.0707
false claims at $n{=}50$	6/49 = 0.1224	5/48 = 0.1042

Appendix

Table 9: pro under the shipped treatment and with truncated responses excluded. flash and gpt-5.5 are unaffected, having none.

Scorer	published	scrambled	novel domains
Random	0.4953	0.4953	0.5342
Embedding similarity	0.5047	0.4115	0.5590
Structural (no names)	0.8210	0.8210	0.7487
0.5B	0.4405	0.4770	0.4529
1.5B	0.3586	0.4929	0.5363
3B	0.5181	0.4427	0.5100

Appendix

Table 10: Small open-weights models on the edge-classification task, against name-blind and lexical baselines. Values come from the uniform-injection construction of Appendix E ; the structural baseline is

0.821

under the original features and 0.825 under the permutation-invariant features of Table 4 .Values come from the superseded construction of Appendix E . Comparisons are valid within a column only : the published and scrambled columns are scored on the same 2,775 edge instances, the novel column on a separate set of 731, and none of these are comparable to the frontier-model results elsewhere in this paper. The 1.5B model discriminates in the wrong direction; scrambling variable names returns it to chance, so the inversion is name-driven.

	flash		pro		gpt-5.5
$n$	Acc.	False-claim	Acc.	False-claim	Acc.	False-claim
10	0.940	0.12	0.960	0.02	1.000	0.00
15	0.960	0.06	0.960	0.04	1.000	0.00
20	0.890	0.20	0.960	0.06	0.990	0.02
30	0.840	0.28	0.940	0.10	1.000	0.00
40	0.920	0.16	0.919	0.10	1.000	0.00

Appendix

Table 11: Verdict accuracy against graph size.

Model	Condition	Budget	Parse err.	Validity	Min. $\mid$ valid	Exact $\mathcal{F}$	Recall
flash	one-shot	8,192	0.007	0.9295	0.9675	0.8993	—
flash	asked-for-all	32,768	0.003	0.9264	0.9928	0.9197	0.9066
flash	oracle	8,192	0.053	1.0000	1.0000	1.0000	—
pro	one-shot	32,768	0.010	0.9697	0.9826	0.9529	—
pro	asked-for-all	32,768	0.030	0.9485	0.9746	0.9244	0.8704
pro	oracle	8,192	0.380	excluded: parse failure on 38% of instances

Appendix

Table 12: Repair and enumeration on the main pool.

$n$	Valid	Min. $\mid$ valid	Oracle valid	Oracle min.	$\mathcal{F}$ coverage	mean $\|\mathcal{F}\|$
10	0.880	0.9545	1.000	1.000	1.00	3.28
15	0.860	0.9535	1.000	1.000	1.00	3.73
20	0.860	0.8837	1.000	1.000	0.88	2.30
30	0.880	0.7500	1.000	1.000	0.10	1.40
40	0.920	0.8696	1.000	1.000	0.02	1.00
50	0.980	0.8163	1.000	1.000	0.00	—

Appendix

Table 13: Repair against graph size ( flash ).

Panel of Figure 4 — Figure 4: A certified instance, its frontier, and an invalid repair. Dashed edges are unobserved common causes.

$z_{2}$	$z_{3}$	$y$	truth	library	difference
0	0	0	0.068800	0.066377	$-0.002423$
0	0	1	0.087453	0.089876	$+0.002423$
0	1	0	0.073608	0.066449	$-0.007159$
0	1	1	0.083090	0.090249	$+0.007159$
1	0	0	0.028730	0.028270	$-0.000460$
1	0	1	0.039616	0.040076	$+0.000460$

Appendix

Table 14:

P(z_{1},z_{2},z_{3},y\mid\mathrm{do}(x{=}1))

under one seeded SCM. Ground truth by exact enumeration; the published estimand matches it to

5.6\times 10^{-17}

throughout and is omitted. Deviations cancel within each

(z_{1},z_{2},z_{3})

block.

Panel of Figure 5 — Figure 5: Our encoding of Figure 1 of Robins et al. [2000] . $A_{t}$ is zidovudine treatment at time $t$ , $L_{t}$ the measured risk factors, $Y$ the outcome, and $U_{t}$ the unmeasured risk factors (dashed, latent). (a) Projecting out $U_{0}$ and $U_{1}$ confounds every pair of observed variables, so the joint effect and both single effects are non-identifiable. (b) The authors’ assumption removes the three red edges, from unmeasured risk factors into treatments; only $L_{0}$ , $L_{1}$ and $Y$ stay confounded, and all three effects become identifiable. (c) For the effect of $A_{1}$ in (a), two minimal restoring sets have the same size and opposite meaning, so cardinality cannot choose between them. Two edges we could not read from the scan, $A_{0}\to Y$ and $L_{0}\to U_{1}$ , change neither projection and are omitted.

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Efficient Symbolic Computations for Identifying Causal Effects

Benjamin Hollering, Pratik Misra, Nils Sturma

Max Planck Institute for Mathematics in the Sciences, Germany · Binghamton University, USA · École Polytechnique Fédérale de Lausanne, Switzerland

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Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic computation. However, standard approaches based on Gröbner bases become computationally infeasible beyond small settings due to their doubly exponential complexity. In this work, we study how to practically use symbolic computation for deciding rational identifiability. In particular, we present an efficient algorithm that provably finds the lowest degree identifying formulas. For a causal effect of interest, if there exists an identification formula of a prespecified maximal degree, our algorithm returns such a formula in quasi-polynomial time.

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