Large language models are increasingly used to answer questions over financial filings, where an unfaithful answer can mislead investment, compliance, or client decisions. Hallucination detectors are a common safeguard, but they are usually evaluated with a single binary score that reveals neither which kinds of errors analysesed nor why. This paper studies hallucination detection on PHANTOM, a long-context benchmark built from SEC filings, at the level of hallucination type. We first analyze 15,443 paired hallucinated and faithful answers without any detector and find that hallucinated answers are more than twice as long as faithful ones, and that lexical grounding separates the two classes only because faithful answers are bimodal. We then generate hallucinations in nine financially motivated categories, confirm each with a separate verification pass, and diagnose an LLM-based detector on 4,086 usable examples. Generation success varies from 66.3% to 100% across categories. The detector reaches 80.2% binary accuracy but only 44.7% subtype accuracy, never assigns two of the nine categories, and misses between 5.3% and 46.8% of hallucinations depending on category; these misses are unrelated to input length but rise with how far an answer departs from the correct one. Guided by this diagnosis, we propose a two-stage hierarchical detector that first decides whether an answer is hallucinated and then assigns a subtype, raising binary accuracy to 95.6% and subtype accuracy to 56.1%. The results show that type-level evaluation exposes detector weaknesses that aggregate metrics conceal.
Figures & tables
Label
Count
Mean
Std
Min
25%
50%
75%
Hallucination
15,443
76.5
36.9
28
55
67
88
Not hallucination
15,443
35.0
39.8
1
2
25
55
Table 1: Answer length (word count) by ground-truth label, over 15,443 pairs.
Label
Count
Mean
Std
25%
50%
75%
Max
Hallucination
15,443
0.356
0.156
0.241
0.338
0.453
0.923
Not hallucination
15,443
0.521
0.376
0.150
0.545
0.908
1.000
Table 2: Answer grounding score (word 3-gram recall against the source context) by ground-truth label, over 15,443 pairs.
Metric
Result
Total evaluated samples
4,086
Binary classification accuracy
0.956
Subtype classification accuracy
0.561
Table 3: Overall performance of the hallucination detector, measured by binary classification accuracy and subtype classification accuracy.
Hallucination Type
Original Accuracy
Enhanced Accuracy
entity_hallucination
72.90%
92.29%
instruction_drift
88.60%
96.92%
numerical_hallucination
93.20%
98.90%
reasoning_errors
68.30%
94.71%
reasoning_hallucination
76.10%
96.04%
regulatory_hallucination
89.70%
99.34%
Table 4: Comparison of binary hallucination detection accuracy between the original and enhanced detectors across hallucination categories.
Figure 1: A figure caption is always placed below the illustration. Please note that short captions are centered, while long ones are justified by the macro package automatically.
Category
Support
Predicted
TP
Precision
Recall
F1-score
unsupported_inference
454
1072
336
0.3134
0.7401
0.4404
reasoning_hallucination
453
484
205
0.4236
0.4525
0.4376
regulatory_hallucination
452
474
446
0.9409
0.9867
0.9633
temporal_hallucination
441
432
340
0.7870
0.7710
0.7789
numerical_hallucination
400
610
345
0.5656
0.8625
0.6832
reasoning_errors
400
89
64
0.7191
0.1600
0.2618
Table 5: Hallucination subtype classification performance, including the number of ground-truth examples (support), predicted instances, true positives (TP), precision, recall, and F1-score for each category.
Category
Attempted
Landed
Landing rate
default_phantom
454
301
66.3%
entity_hallucination
453
357
78.8%
instruction_drift
454
396
87.2%
numerical_hallucination
454
400
88.1%
reasoning_errors
454
400
88.1%
temporal_hallucination
454
441
97.1%
Table 6: Landing rate by attempted hallucination category: the fraction of generation attempts that verification confirmed as genuine hallucinations, and, among those, the fraction that matched the intended category.
True category
Predicted as
Share
instruction_drift ( n=396 )
non_hallucination
28.5%
numerical_hallucination
24.0%
temporal_hallucination
18.9%
reasoning_hallucination ( n=453 )
unsupported_inference
66.2%
non_hallucination
23.6%
regulatory_hallucination
6.0%
Table 7: Where verified hallucinations of the two "missing" categories get reassigned by the detector (share of that category’s landed hallucinations; top three destinations shown).
Figure 2: Subtype confusion matrix: true attempted category (rows) vs. detector-predicted category (columns), restricted to verified hallucinations. The all-zero diagonal cells for instruction_drift and reasoning_hallucination are visible as the two rows with no diagonal mass.
Category
Miss rate
Top predictor of a miss
p
default_phantom
46.8%
context grounding (lower)
0.045
reasoning_errors
38.2%
edit distance from correct (higher) †
< 0.001
instruction_drift
28.5%
edit distance from correct (higher) †
< 0.001
unsupported_inference
26.4%
context grounding (lower) †
< 0.001
reasoning_hallucination
23.6%
correct-answer overlap (lower) †
< 0.001
entity_hallucination
17.6%
number overlap (lower)
0.028
Table 8: Detector miss rate by category (share of verified hallucinations labeled non_hallucination ), and the single feature most predictive of a miss within that category (Mann-Whitney U test, Bonferroni-corrected α=0.01/9≈0.0011 across the nine candidate features). † denotes significance surviving correction.
Feature
H
p
Edit distance from correct answer
1633.2
< 0.001
Entity-token overlap w/ correct
1336.1
< 0.001
Number-token overlap w/ correct
997.0
< 0.001
Jaccard overlap w/ correct answer
545.2
< 0.001
Generated answer length
478.0
< 0.001
Sentence-count delta
473.3
< 0.001
Table 9: Kruskal-Wallis test for whether each feature’s distribution differs across the nine attempted hallucination categories.
Figure 3: Distribution of six candidate features, split by category and by whether the detector caught (blue) or missed (red) the verified hallucination.
Large language models (LLMs) in financial applications fail most consequentially when they are confidently wrong. Hedged, uncertain answers invite scrutiny, whereas confident errors silently degrade downstream decisions without warning. We ask how reliably such confidently wrong answers, or confident hallucinations, can be detected from a model's internal activations, and whether those activations carry information beyond its output-level confidence signals. We train linear probes on the residual stream and evaluate them on two established numerical question-answering (QA) benchmarks built from real filings, FinQA and TAT-QA. Behavioral confidence is measured as the agreement among eight resampled answers to the same question, and probe effectiveness is compared against baselines, such as token log-probabilities and the model's own True/False self-assessment of its answer. Our findings show that among confident answers, those for which all eight resamples agree, 15-23% are wrong on FinQA. There the probes have a significant advantage over output-level baselines in detecting hallucinations, holding 0.68-0.77 AUROC while the best baselines fall to 0.55-0.63, across Qwen3-8B, Llama-3.1-8B, and Gemma-2-9B. Our results suggest that probing can be a cost-effective triage mechanism for routing LLM answers to human review and quality control procedures in high-stakes financial applications. Code and data are available at https://github.com/richardzhewang/confidently-wrong.
As organizations increasingly integrate AI-powered question-answering systems into financial information systems for compliance, risk assessment, and decision support, ensuring the factual accuracy of AI-generated outputs becomes a critical engineering challenge. Current Knowledge Graph (KG)-augmented QA systems lack systematic mechanisms to detect hallucinations - factually incorrect outputs that undermine reliability and user trust. We introduce FinBench-QA-Hallucination, a benchmark for evaluating hallucination detection methods in KG-augmented financial QA over SEC 10-K filings. The dataset contains 755 annotated examples from 300 pages, each labeled for groundedness using a conservative evidence-linkage protocol requiring support from both textual chunks and extracted relational triplets. We evaluate six detection approaches - LLM judges, fine-tuned classifiers, Natural Language Inference (NLI) models, span detectors, and embedding-based methods under two conditions: with and without KG triplets. Results show that LLM-based judges and embedding approaches achieve the highest performance (F1: 0.82-0.86) under clean conditions. However, most methods degrade significantly when noisy triplets are introduced, with Matthews Correlation Coefficient (MCC) dropping 44-84 percent, while embedding methods remain relatively robust with only 9 percent degradation. Statistical tests (Cochran's Q and McNemar) confirm significant performance differences (p < 0.001). Our findings highlight vulnerabilities in current KG-augmented systems and provide insights for building reliable financial information systems, where hallucinations can lead to regulatory violations and flawed decisions. The benchmark also offers a framework for integrating AI reliability evaluation into information system design across other high-stakes domains such as healthcare, legal, and government.
Financial AI systems must produce answers grounded in specific regulatory filings, yet current LLMs fabricate metrics, invent citations, and miscalculate derived quantities. These errors carry direct regulatory consequences as the EU AI Act's high-risk enforcement deadline approaches (August 2026). Existing hallucination detectors treat all claims uniformly, missing 43% of computational errors that require arithmetic re-verification against structured tables. We present FinGround, a three-stage verify-then-ground pipeline for financial document QA. Stage 1 performs finance-aware hybrid retrieval over text and tables. Stage 2 decomposes answers into atomic claims classified by a six-type financial taxonomy and verified with type-routed strategies including formula reconstruction. Stage 3 rewrites unsupported claims with paragraph- and table-cell-level citations. To cleanly isolate verification value from retrieval quality, we propose retrieval-equalized evaluation as standard methodology for RAG verification research: when all systems receive identical retrieval, FinGround still reduces hallucination rates by 68% over the strongest baseline (p<0.01). The full pipeline achieves a 78% reduction relative to GPT-4o. An 8B distilled detector retains 91.4% F1 at 18x lower per-claim latency, enabling $0.003/query deployment, supported by qualitative signals from a four-week analyst pilot.
Dongxin Guo, Jikun Wu, Siu Ming Yiu
1The University of Hong Kong · 2Stellaris AI Limited