pdf_signature_extraction/paper/paper_a_conclusion_v3.md

# VI. Conclusion and Future Work

## Conclusion

We have presented an end-to-end AI pipeline for detecting non-hand-signed auditor signatures in financial audit reports at scale.
Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013--2023, our system extracted and analyzed 182,328 CPA signatures using a combination of VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-descriptor similarity verification, with threshold selection placed on a statistically principled footing through two methodologically distinct threshold estimators and a density-smoothness diagnostic applied at two analysis levels.

The seven numbered contributions listed in Section I can be grouped into four broader methodological themes, summarized below.

First, we argued that non-hand-signing detection is a distinct problem from signature forgery detection, requiring analytical tools focused on the upper tail of intra-signer similarity rather than inter-signer discriminability.

Second, we showed that combining cosine similarity of deep embeddings with difference hashing is essential for meaningful classification---among 71,656 documents with high feature-level similarity, the dual-descriptor framework revealed that only 41% exhibit converging structural evidence of non-hand-signing while 7% show no structural corroboration despite near-identical feature-level appearance, demonstrating that a single-descriptor approach conflates style consistency with image reproduction.

Third, we introduced a convergent threshold framework combining two methodologically distinct estimators---KDE antimode (with a Hartigan unimodality test) and an EM-fitted Beta mixture (with a logit-Gaussian robustness check)---together with a Burgstahler-Dichev / McCrary density-smoothness diagnostic.
Applied at both the signature and accountant levels, this framework surfaced an informative structural asymmetry: at the per-signature level the distribution is a continuous quality spectrum for which no two-mechanism mixture provides a good fit, whereas at the per-accountant level BIC cleanly selects a three-component mixture and the KDE antimode together with the Beta-mixture and logit-Gaussian estimators agree within $\sim 0.006$ at cosine $\approx 0.975$.
The Burgstahler-Dichev / McCrary test, by contrast, is largely null at the accountant level (no significant transition at two of three cosine bin widths and two of three dHash bin widths, with the one cosine transition sitting on the upper edge of the convergence band; Appendix A); at $N = 686$ accountants the test has limited power and cannot affirmatively establish smoothness, but its largely-null pattern is consistent with the smoothly-mixed cluster boundaries implied by the accountant-level GMM.
The substantive reading is therefore narrower than "discrete behavior": *pixel-level output quality* is continuous and heavy-tailed, and *accountant-level aggregate behavior* is clustered into three recognizable groups whose inter-cluster boundaries are gradual rather than sharp.

Fourth, we introduced a *replication-dominated* calibration methodology---explicitly distinguishing replication-dominated from replication-pure calibration anchors and validating classification against a byte-level pixel-identity anchor (310 byte-identical signatures) paired with a $\sim$50,000-pair inter-CPA negative anchor.
To document the within-firm sampling variance of using the calibration firm as its own validation reference, we split the firm's CPAs 70/30 at the CPA level and report capture rates on both folds with Wilson 95% confidence intervals; extreme rules agree across folds while rules in the operational 85-95% capture band differ by 1-5 percentage points, reflecting within-firm heterogeneity in replication intensity rather than generalization failure.
This framing is internally consistent with all available evidence: the visual-inspection observation of pixel-identical signatures across unrelated audit engagements for the majority of calibration-firm partners; the 92.5% / 7.5% split in signature-level cosine thresholds; and, among the 171 calibration-firm CPAs with enough signatures to enter the accountant-level GMM (of 180 registered CPAs; 178 after excluding two with disambiguation ties, Section IV-G.2), the 139 / 32 split between the high-replication and middle-band clusters.

An ablation study comparing ResNet-50, VGG-16 and EfficientNet-B0 confirmed that ResNet-50 offers the best balance of discriminative power, classification stability, and computational efficiency for this task.

## Future Work

Several directions merit further investigation.
Domain-adapted feature extractors, trained or fine-tuned on signature-specific datasets, may improve discriminative performance beyond the transferred ImageNet features used in this study.
Extending the accountant-level analysis to auditor-year units---using the same convergent threshold framework at finer temporal resolution---could reveal within-accountant transitions between hand-signing and non-hand-signing over the decade.
The pipeline's applicability to other jurisdictions and document types (e.g., corporate filings in other countries, legal documents, medical records) warrants exploration.
The replication-dominated calibration strategy and the pixel-identity anchor technique are both directly generalizable to settings in which (i) a reference subpopulation has a known dominant mechanism and (ii) the target mechanism leaves a byte-level signature in the artifact itself.
Finally, integration with regulatory monitoring systems and a larger negative-anchor study---for example drawing from inter-CPA pairs under explicit accountant-level blocking---would strengthen the practical deployment potential of this approach.