Reasoning structures (e.g., chains and graphs) are increasingly used for probabilistic inference, factuality verification, and uncertainty estimation, but their structural reliability is rarely evaluated directly. We test whether this reliability holds through a proposed two-stage diagnostic evaluation in open-ended multi-hop QA. Stage 1 tests different capabilities required to construct reasoning graphs, showing that graph reliability varies with topology, prompt design, and model family. Stage 2 uses uncertainty estimation as a downstream test case. Generated-edge experiments show that graph-based computation is sensitive to upstream graph errors, with performance dropping relative to the gold-graph setting. Gold-graph experiments further show that graph structure provides little benefit when used only as prompt context, but improves the separation of correct from incorrect answers by confidence score and enables node-level diagnostics.
Figures & tables
Set.
Given to model
Predicted
Purpose
A
Gold sub-questions, answers, paragraphs
Edges
Dependency wiring
B
Gold sub-questions, paragraphs
Answers, evidence IDs, edges
Local node grounding
C
Question, paragraphs
Full graph
End-to-end generation
Table 1: Three controlled diagnostic settings. Difficulty increases from A to C as gold scaffolding is progressively removed.
Setting A
Setting B
Setting C
Model
Family
Params
Edge F1
Exact Edge
Edge F1
Ans F1
Attr F1
HPS
Step F1
Edge HPS
Attr F1
Llama-3.1-8B
Llama
8B
0.797 †
0.388 †
0.803
0.386
0.567
0.688
0.679
0.344
0.676
Qwen3-8B
Qwen
8B
0.809 †
0.444 †
0.970
0.504
0.706
0.735
0.777
0.533
0.786
Qwen3-14B
Qwen
14B
0.963
0.913
0.957
0.465
0.763
0.801
0.837
0.567
0.812
Qwen3-32B
Qwen
32B
0.985
0.961
0.970
0.419
0.795
0.863
0.857
0.705
0.831
Qwen3-32B-Reasoning
Qwen
32B
0.992
0.976
0.973
0.579
0.821
0.878
0.894
0.745
0.850
Table 2: Stage 1 results on MuSiQue full dev. Bold marks the best completed value in each column. † Subject to schema-example artifact in the edge-only setting; see Appendix C.1 . ‡ DeepSeek V4-Flash is a mixture-of-experts model with 284B total parameters and 13B activated parameters.
Slice
N
Llama-3.1-70B
Qwen3-32B
Claude Sonnet 4.5
HPS
Edge HPS
Δ Step
HPS
Edge HPS
Δ Step
HPS
Edge HPS
Δ Step
2-hop
1252
0.918
0.780
0.049
0.921
0.820
0.133
0.973
0.920
0.159
3-hop
760
0.716
0.480
-0.622
0.842
0.638
-0.041
0.962
0.882
0.217
4-hop
405
0.590
0.340
-1.062
0.721
0.478
-0.397
0.917
0.814
0.165
simple_tree
1820
0.855
0.698
-0.162
0.897
0.780
0.069
0.968
0.910
0.169
v_structure
351
0.683
0.350
-0.723
0.792
0.454
-0.108
0.957
0.836
0.393
Table 3: Setting C end-to-end graph generation performance stratified by hop count and topology slices.
Tag
Description
Setting A:edge wiring failures
miss. terminal
Gold dependency into qfinal is omitted.
shortcut repl.
Gold dependency replaced by a shortcut edge, often into qfinal .
broad mixed
Multiple answers, evidence, and edge failures with no dominant cause.
Setting B:local grounding failures
ans.+evid.
Both generated answer and evidence attribution fail at a fixed node.
Table 4: Error tags appearing in Table 5 .
Model
Setting A
Setting B
Setting C
Llama-3.1-8B
miss. terminal 45.7%
broad mixed 35.0%
struct. gap 37.9%
Qwen3-8B
miss. terminal 46.5%
ans.+evid. 40.7%
under-decomp. 38.6%
Qwen3-14B
shortcut repl. 7.1%
ans.+evid. 34.0%
under-decomp. 33.7%
Qwen3-32B
shortcut repl. 3.2%
ans.+evid. 30.2%
struct. gap 19.5%
Qwen3-32B-Reasoning
shortcut repl. 1.8%
ans.+evid. 25.9%
under-decomp. 20.7%
Llama-3.1-70B
shortcut repl. 19.2%
ans.+evid. 23.7%
under-decomp. 34.7%
Table 5: Top non-aligned error type and rate per model per diagnostic setting (MuSiQue full dev set). Each entry is the most frequent error category excluding fully_aligned .
Method
EM ↑
F1 ↑
AUROC ↑
ECE ↓
Brier ↓
Direct-SC
0.462
0.569
0.718
0.325
0.319
CoT-Conf
0.487
0.593
0.686
0.271
0.297
CoT-SC
0.572
0.680
0.766
0.161
0.220
Decomp-SC
0.550
0.659
0.770
0.234
0.247
Graph-CoT-SC
0.562
0.671
0.764
0.238
0.251
vPGM-Style
0.439
0.550
0.622
0.235
0.295
Table 6: Stage 2 confidence estimation on MuSiQue full dev set.
Method
N
EM
F1
AUROC
ECE ↓
Brier ↓
Gen
Gold
Δ
Gen
Gold
Δ
Gen
Gold
Δ
Gen
Gold
Δ
Gen
Gold
Δ
Graph-CoT-SC
446
0.476
0.469
+0.007
0.620
0.622
-0.002
0.689
0.714
-0.025
0.313
0.324
-0.011
0.326
0.322
+0.004
Sampled BN
446
0.459
0.493
-0.034
0.599
0.657
-0.058
0.738
0.755
-0.017
0.300
0.283
+0.017
0.300
0.285
+0.015
Table 7: Generated-edge stress test on valid non-exact Setting A graphs (446 examples). Gen: performance under Llama-3.1-70B generated edges. Gold: performance using gold edges on the same examples. Δ = Gen − Gold.
Figure 1: Confidence distributions for CoT-SC, vPGM-Style, and Sampled BN, separated by final-answer correctness.
Slice
F1
AUROC
CoT-SC
Sampled BN
CoT-SC
Sampled BN
2-hop
0.717
0.742
0.753
0.795
3-hop
0.673
0.706
0.770
0.816
4-hop
0.577
0.499
0.780
0.752
simple_tree
0.713
0.737
0.761
0.789
v_structure
0.519
0.555
0.761
0.790
Table 8: Structure-stratified F1 and AUROC for CoT-SC and Sampled BN. Bold marks the higher value per row.
Appendix figures & tables24 assets
Supplementary material from the paper’s appendix.
Appendix
Model
Setting
Parse OK
Schema OK
Llama-3.1-8B
A
1.000
1.000
B
0.998
0.998
C
0.990
0.990
Llama-3.1-70B
A
1.000
1.000
B
0.996
0.996
C
0.995
0.995
Appendix
Table 9: Parse and schema validity across models and settings (2,417 examples per run).
Model
Var.
N
Parse OK
Schema OK
Disconn.
Edge F1
Exact Edge
Shortcut
Qwen3-8B
E1
2417
0.998
0.998
0.472
0.809
0.444
0.058
E2
2417
0.998
0.998
0.260
0.856
0.611
0.097
E3
2417
0.998
0.998
0.013
0.909
0.793
0.153
E4
2417
0.998
0.998
0.008
0.902
0.785
0.169
E5
2417
0.998
0.998
0.281
0.836
0.550
0.126
Qwen3-32B
E1
2417
0.999
0.999
0.003
0.985
0.961
0.028
Appendix
Table 10: Full Setting A schema-example ablation across model families on MuSiQue full development set (2,417 examples per model/variant). Variants differ only in the output-schema example; all other prompt text, dataset, metrics, and inference code are unchanged. E1 is the variant used in main experiments (Table 2 ).
Decoding
Edge F1
Exact Edge
Shortcut
Non-thinking (main)
0.985
0.961
0.028
Thinking-on
0.992
0.976
0.018
Appendix
Table 11: Qwen3-32B thinking-on vs. non-thinking under Setting A (2,417 examples). Thinking mode yields a further 0.7 pp Edge F1 gain and 1 pp shortcut reduction.
Model
Edge HPS
Strict Edge HPS
Llama-3.1-70B
0.612
0.597
Qwen3-32B
0.705
0.672
Claude Sonnet 4.5
0.890
0.841
Appendix
Table 12: Setting C Edge HPS under the main reachability-based criterion and a strict direct-edge criterion on the MuSiQue full development set.
Backbone
τ=0.75
τ=0.85
τ=0.90
τ=0.95
e5-large-v2
0.913
0.836
0.714
0.504
MiniLM-L6-v2
0.703
0.523
0.378
0.176
BGE-large-v1.5
0.787
0.621
0.474
0.230
Appendix
Table 13: Mean Setting C HPS across the nine main-table models under different semantic-alignment thresholds and embedding backbones.
Figure 2: Schematic error modes across diagnostic settings. Red solid edges indicate incorrect dependencies, red dashed edges or nodes indicate missing structure, and shaded nodes indicate incorrect local payloads.
Tag
Operational Detection Criterion
fully_aligned
Predicted nodes, edges, answers, and evidence all match the gold graph under the setting-specific evaluator.
shortcut_replacement
A gold dependency is missing and a direct or transitive shortcut edge connects an earlier prerequisite to a later node, often q_final .
spurious_final_shortcut
A non-parent node has an extra direct edge into q_final .
spurious_internal_shortcut
A non-parent node has an extra shortcut edge into an internal node.
mixed_shortcut
Final and internal shortcut behavior appear in the same fixed-node output.
missing_terminal_edge
A gold dependency into q_final is omitted.
Appendix
Table 14: Stage 1 diagnostic failure taxonomy. Tags are automatic labels over the evaluated graph outputs, intended to localize failure modes within each diagnostic setting.
Model
Full
Shortcut repl.
Missing term.
Missing gold
Other edge
Final shortcut
Internal shortcut
Mixed shortcut
Parse fail.
Claude Sonnet 4.5
2382
32
0
2
0
1
0
0
0
DeepSeek V4 Flash
2372
45
0
0
0
0
0
0
0
GPT-5 Chat
2337
67
0
0
2
10
0
1
0
Llama-3.1-70B
1880
465
3
48
8
9
4
0
0
Llama-3.1-8B
937
89
1105
23
245
5
0
13
0
Qwen3-8B
1071
173
1123
11
20
7
0
6
6
Appendix
Table 15: Full-dev Setting A error counts by model (2,417 examples). Full denotes fully_aligned . Rates are reported in the source analysis; this table gives counts to avoid rounding ambiguity.
Model
Full
Ans+Ev
Ev only
Ans only
Interm. ans
Edge only
Broad
Ans+Edge
Edge+Ev
Subq drift
Final synth
Final+Ev
Final+Edge
Final mixed
Parse
Schema
Claude Sonnet 4.5
1195
449
390
145
142
21
9
8
5
36
7
6
4
0
0
0
DeepSeek V4 Flash
1018
591
371
170
168
24
21
25
9
4
7
4
3
0
2
0
GPT-5 Chat
839
584
498
177
172
28
29
28
12
0
23
19
6
2
0
0
Llama-3.1-70B
756
572
290
160
108
152
157
101
38
54
3
6
10
1
9
0
Llama-3.1-8B
54
630
60
37
58
210
847
175
144
168
6
12
9
2
5
0
Qwen3-8B
543
983
317
183
130
15
111
42
9
51
7
4
2
1
16
3
Appendix
Table 16: Full-dev Setting B error counts by model (2,417 examples). Full denotes fully_aligned ; Ans+Ev denotes answer_and_evidence ; Interm. ans denotes intermediate_answer_only_recovered_final .
Model
Full
Under
Structure gap
Evidence gap
Over
Extra benign
Minor mixed
Parse fail.
Schema fail.
Claude Sonnet 4.5
1172
99
228
452
221
226
18
1
0
DeepSeek V4 Flash
900
506
393
306
164
91
19
9
29
GPT-5 Chat
873
153
423
421
291
221
21
0
14
Llama-3.1-70B
701
838
454
278
72
30
33
11
0
Llama-3.1-8B
134
639
917
203
408
62
31
23
0
Qwen3-8B
602
932
424
354
30
11
39
22
3
Appendix
Table 17: Full-dev Setting C error counts by model (2,417 examples). Full denotes fully_aligned ; Under and Over denote under_decompose and over_decompose .
Model
Hop
Topology
N
HPS
Edge HPS
Evidence HPS
Δ Step
Llama-3.1-70B
3
simple_tree
568
0.715
0.517
0.667
-0.626
Llama-3.1-70B
3
v_structure
192
0.717
0.370
0.568
-0.609
Llama-3.1-70B
4
v_structure
159
0.642
0.326
0.566
-0.861
Llama-3.1-70B
4
complex_tree
246
0.556
0.349
0.535
-1.193
Qwen3-32B
3
simple_tree
568
0.842
0.692
0.742
-0.073
Qwen3-32B
3
v_structure
192
0.842
0.477
0.696
0.052
Appendix
Table 18: Within-hop Setting C graph generation performance by topology on MuSiQue. MuSiQue does not contain all hop–topology combinations: 2-hop examples are all simple_tree, 3-hop examples compare simple_tree and v_structure, and 4-hop examples compare v_structure and complex_tree. Δ Step is predicted minus gold node count; negative values indicate under-decomposition.
Setting A
Setting B
Setting C
Model
Family
Params
Edge F1
Exact Edge
Edge F1
Ans F1
Attr F1
HPS
Step F1
Edge HPS
Attr F1
Llama-3.1-8B
Llama
8B
0.803
0.402
0.863
0.665
0.643
0.818
0.727
0.361
0.769
Qwen3-8B
Qwen
8B
0.923
0.774
0.863
0.807
0.724
0.866
0.903
0.722
0.901
Qwen3-14B
Qwen
14B
0.972
0.952
0.799
0.723
0.756
0.956
0.960
0.784
0.920
Qwen3-32B
Qwen
32B
0.988
0.976
0.932
0.691
0.765
0.981
0.967
0.923
0.939
Llama-3.1-70B
Llama
70B
0.823
0.573
0.748
0.859
0.707
0.848
0.862
0.641
0.797
Appendix
Table 19: 2WikiMultiHopQA Stage 1 diagnostics on 498 stratified development examples, five models, all three settings. Bold marks the best value per column. Ans F1 in Setting B is token-level F1 over intermediate sub-answers under the fixed-decomposition interface. Metric names follow the main Stage 1 table (Table 2 ).
Question Type
N
Edge HPS ↑
inference †
80
0.634
compositional †
80
0.634
comparison
170
0.976
bridge_comparison
168
0.308
Appendix
Table 20: 2WikiMultiHopQA Stage 1 Setting C Edge HPS by official question type (498 examples, Llama-3.1-70B). Bold marks the highest. † Inference and compositional are both chain-shaped types; the Edge HPS value is reported for both combined. Comparison questions involve two independent fact retrievals merged at a comparison step and reach near-ceiling. Bridge_comparison questions require 4-step parallel chain merging and produce the lowest Edge HPS.
Method
Calls / example
Completions / example
Full-dev calls
Direct-SC
1
10
2,417
CoT-SC
1
10
2,417
Decomp-SC
1
10
2,417
Graph-CoT-SC
1
10
2,417
vPGM-Style
1
10
2,417
CoT-Conf
1
1
2,417
Appendix
Table 21: API call budget for Stage 2 methods on MuSiQue full development set (2,417 examples). SC-family runners use batch sampling ( K=10 per request); Sampled BN cost scales with graph structure.
Model
Mean
Median
Max
Qwen3-32B
3.568
3
71
Llama-3.1-70B
4.098
3
54
Appendix
Table 22: Sampled BN API calls per example on MuSiQue full dev.
Model
2-hop
3-hop
4-hop
Qwen3-32B
2.280
3.974
6.788
Llama-3.1-70B
2.568
4.546
7.990
Appendix
Table 23: Mean Sampled BN API calls per example by hop count.
Figure 3: Selective prediction curves for Stage 2 methods.
CoT-SC Correct
CoT-SC Wrong
Sampled BN Correct
1117 (46.2%)
255 (10.5%)
Sampled BN Wrong
266 (11.0%)
779 (32.2%)
Appendix
Table 24: Pairwise correctness contingency between Sampled BN and CoT-SC on MuSiQue full development set (2,417 examples; κ=0.560 ). The near-symmetric one-method-only split (10.5% BN-only correct vs. 11.0% CoT-SC-only correct) indicates complementary rather than redundant error patterns.
α
EM
F1
AUROC
ECE ↓
Brier ↓
High-conf. wrong ↓
0.0
0.568
0.691
0.795
0.206
0.225
11.0%
0.1
0.568
0.690
0.795
0.194
0.221
8.0%
0.5
0.569
0.692
0.790
0.168
0.212
7.3%
1.0
0.568
0.690
0.790
0.147
0.207
7.0%
Appendix
Table 25: Sensitivity of Sampled BN to additive CPT smoothing on the Llama-3.1-70B MuSiQue gold-graph setting. High-conf. wrong denotes examples with an incorrect final prediction and confidence ≥0.9 .
Comparison
Metric
Difference
p -value
Decomp-SC vs. CoT-SC
AUROC
+0.004
0.79
Graph-CoT-SC vs. CoT-SC
AUROC
−0.002
0.82
Sampled BN vs. CoT-SC
AUROC
+0.029
0.017
Sampled BN vs. CoT-SC
F1
+0.011
0.16
Sampled BN vs. CoT-SC, 4-hop
F1
−7.7 pp
<0.001
Sampled BN vs. CoT-SC, complex_tree
F1
−12.3 pp
<0.001
Appendix
Table 26: Paired bootstrap significance tests for the main comparative claims in Stage 2. Differences are computed as the first condition minus the second.
Method
Hop
N
Ans. EM ↑
Ans. F1 ↑
AUROC ↑
Direct-SC
2
1252
0.491
0.602
0.717
CoT-Conf
2
1252
0.522
0.636
0.688
CoT-SC
2
1252
0.611
0.717
0.753
Decomp-SC
2
1252
0.601
0.713
0.763
Graph-CoT-SC
2
1252
0.617
0.727
0.762
vPGM-Style
2
1252
0.466
0.587
0.608
Appendix
Table 27: Hop-stratified performance on MuSiQue full development set (2,417 examples, Llama-3.1-70B, K=10 ). Bold marks per-hop per-column best. Sampled BN leads on 2-hop and 3-hop but drops to 0.393 EM on 4-hop, where CoT-SC retains 0.504 EM.
Method
Topology
N
Ans. EM ↑
Ans. F1 ↑
AUROC ↑
ECE ↓
Brier ↓
Direct-SC
simple_tree
1820
0.491
0.599
0.718
0.305
0.306
CoT-Conf
simple_tree
1820
0.518
0.628
0.671
0.257
0.289
CoT-SC
simple_tree
1820
0.597
0.713
0.761
0.160
0.220
Decomp-SC
simple_tree
1820
0.587
0.697
0.752
0.221
0.245
Graph-CoT-SC
simple_tree
1820
0.599
0.711
0.757
0.224
0.242
vPGM-Style
simple_tree
1820
0.465
0.577
0.609
0.233
0.298
Appendix
Table 28: Topology-stratified Answer EM, F1, and EM-based calibration metrics on MuSiQue full dev. Bold marks per-topology per-column best. Sampled BN leads on simple_tree and v_structure for answer quality, while CoT-SC remains strongest on complex_tree .
Qwen3-32B
Llama-3.1-70B
Method
EM ↑
F1 ↑
AUROC ↑
ECE ↓
EM ↑
F1 ↑
AUROC ↑
ECE ↓
Direct-SC
0.425
0.540
0.678
0.429
0.462
0.569
0.718
0.325
CoT-SC
0.537
0.654
0.776
0.176
0.572
0.680
0.766
0.161
CoT-Conf
0.386
0.507
0.672
0.432
0.487
0.593
0.686
0.271
Decomp-SC
0.534
0.653
0.722
0.327
0.550
0.659
0.770
0.234
Graph-CoT-SC
0.536
0.656
0.717
0.331
0.562
0.671
0.764
0.238
Appendix
Table 29: Cross-model Stage 2 comparison on MuSiQue full dev ( K=10 , temperature 0.7; CoT-Conf uses one temperature-0 call). Bold marks per-model per-column best.
Llama-3.1-70B
Qwen3-32B
Method
EM ↑
F1 ↑
AUROC ↑
ECE ↓
EM ↑
F1 ↑
AUROC ↑
ECE ↓
Direct-SC
0.647
0.698
0.668
0.244
0.582
0.653
0.619
0.359
CoT-SC
0.843
0.894
0.715
0.076
0.821
0.883
0.723
0.118
CoT-Conf
0.801
0.854
0.721
0.134
0.769
0.854
0.636
0.165
Decomp-SC
0.799
0.853
0.715
0.139
0.803
0.859
0.627
0.172
Graph-CoT-SC
0.805
0.857
0.730
0.133
0.797
0.851
0.621
0.183
Appendix
Table 30: 2WikiMultiHopQA Stage 2 diagnostic on the same 498-example stratified sample used in Stage 1 evaluation. Bold marks per-model best values.
Reliable uncertainty estimation is essential for deploying large language models in high-stakes reasoning tasks, yet most existing approaches rely on expensive sampling strategies or shallow token-level signals that ignore the internal logical structure of model outputs. We introduce Argument Graph Uncertainty, a post-hoc framework for multiple choice question tasks, that estimates model confidence directly from the logical structure of a single chain-of-thought reasoning trace. Our method uses either a lightweight instruction-tuned model or a simple deterministic rule to segment the reasoning chain into propositional units, then applies a NLI model to infer relational edges and construct two complementary argument graphs over these segments. The resulting edge scores are aggregated into a Dirichlet posterior over answer options, whose concentration yields calibrated uncertainty estimates reflecting both local step-to-step coherence and global logical consistency across the reasoning trace. Evaluated on GPQA, MMLU-Pro and TruthfulQA, our method consistently surpasses token-based and consistency-based uncertainty baselines across multiple reasoning models. We further demonstrate through extensive combination analyses that argument graph uncertainty captures an orthogonal signal to existing approaches, making it a complementary component in uncertainty ensembles. Crucially, our framework requires no additional calls to the evaluated model and relies entirely on small, efficient auxiliary models, producing fully interpretable, per-node uncertainty attributions at low computational cost.
Large-Language Models (LLMs) can be prone to flawed and unfaithful reasoning that decoding strategies like Self-Consistency (SC) fail to detect as they evaluate only final-answer agreement while ignoring the logical validity of intermediate steps. This raises three fundamental questions: How can we reliably quantify uncertainty in LLM reasoning? Can semantic, structural, and causal awareness select more faithful reasoning compared to naïve majority voting? and How robust is reasoning topology under adversarial conditions? To address these questions, we introduce GRAPHEVAL, a graph-based reasoning framework that re-frames uncertainty quantification (UQ) as a holistic reasoning fidelity problem. We propose a novel UQ metric, Graph Reasoning Coherence Score (GRCS), that quantifies semantic-structural consensus of the reasoning space and captures pathological mode collapse and confident hallucinations. We find that GRCS is the only metric that is consistently negatively correlated with reasoning faithfulness across both more capable and smaller models. Additionally, we introduce Graph Self-Consistency (GSC), a medoid-based decoding strategy that trades nominal accuracy for reasoning fidelity, exposing the degree to which SC is inflated by unfaithful lucky guesses in smaller models, while preserving or improving accuracy in more capable ones. Finally, through adversarial medoid ablation, we demonstrate that the GSC-selected path acts as a "load-bearing path" and forcing models away from it degrades reasoning faithfulness and, in targeted cases, causes drops in accuracy.
Riccardo Revalor, Jalees Rehman, Debjit Pal
¶Department of Electrical and Computer Engineering · ‡Department of Biochemistry and Molecular Genetics
Large Reasoning Models produce Long Chains-of-Thought (LCoTs) which involve breaking down the problem into smaller reasoning steps before reaching the conclusion. However, these steps often contain contradictions, unsupported inferences, or irrelevant steps, even when the final answer is correct. We propose Long Chain-of-Thought Graph Verifier (LCoT-GV), a graph-based framework that represents LCoTs as reasoning graphs. Each node in the graph represents a reasoning step and the edges encode semantic and logical relations. A Graph Attention Network is then trained to predict chain-of-thought correctness from the reasoning graph. We construct a new graph-oriented verification dataset from multiple reasoning benchmarks for question answering in various domains. The results show that our method is competitive with the most similar approaches.
Bérénice Jaulmes, Mehwish Alam
1T´el´ecom Paris, Institut Polytechnique de Paris, France · 2BNP Paribas, IT Group, France