Incremental Fingerprinting Approach

• Incremental Fingerprinting Approach is a dynamic paradigm that incrementally builds and refines fingerprint models by integrating new data and adapting existing protocols.
• It leverages techniques like active automata learning, adaptive separating sequences, and pseudo-feature rehearsal to handle open-world scenarios and prevent catastrophic forgetting.
• The approach has demonstrated efficiency and robustness in applications such as protocol identification, device recognition, biometric spoof detection, and neural network fingerprinting.

Incremental fingerprinting refers to algorithmic frameworks and learning-based protocols that iteratively construct, update, or refine fingerprint models or matching structures as new data, subjects, or implementations become available. Unlike closed-world fingerprinting—where the set of candidate identities or reference models is fixed and complete—incremental approaches handle dynamically expanding universes, continuously incorporating previously unseen instances without global retraining. Key instantiations arise in protocol identification (Kruger et al., 29 Jan 2026), class-incremental device recognition (Jiang et al., 6 Jan 2026), browser script detection (Durey et al., 2021), adaptive ensemble learning for biometrics (Agarwal et al., 2020), open-world neural network fingerprinting (Maho et al., 2022), and scalable dictionary inference in magnetic resonance fingerprinting (Oudoumanessah et al., 2024).

1. Formal Problem Statements and Model-Theoretic Foundations

In incremental protocol fingerprinting, each implementation is modeled as a deterministic, input-complete, data-less finite state machine (FSM) $M = (Q, q_0, \delta, \lambda)$, operating under finite alphabets $I$ (inputs) and $O$ (outputs) (Kruger et al., 29 Jan 2026). Behavioral equivalence $M_1 \sim M_2$ is defined by equality of output sequences for all input words. A "fingerprint" is a set of separating sequences $L \subseteq I^*$ such that for all distinct $M_1, M_2$ in a collection $\mathcal{M}$, there exists $\sigma \in L$ distinguishing them.

Closed-world matching presumes a fixed reference set $\mathcal{M}_0$, mapping each black-box $U$ to a unique $M \in \mathcal{M}_0$ such that $U \sim M$. The incremental (open-world) variant seeks to construct both (1) an expanding reference set $\mathcal{M}$ and (2) a consistent assignment $\mu: \mathcal{U} \to \mathcal{M}$, with $\mu(U)=M$ iff $U \sim M$, as implementations arrive.

In biometric or classification settings, incremental learning frameworks fit new class instance distributions (e.g., GMMs of device features (Jiang et al., 6 Jan 2026), clustering-driven ensembles on streaming fingerprint data (Agarwal et al., 2020)), integrating them with prior models to preserve historical accuracy while adapting rapidly to novel inputs.

2. Algorithmic Mechanisms and Incremental Workflows

The archetypal incremental protocol fingerprinting algorithm (“Infernal” (Kruger et al., 29 Jan 2026)) interleaves closed-world fingerprinting, conformance checking, and active automata learning (AAL):

• For each new “unknown” implementation $U$:
  • If reference set $\mathcal{M}$ is empty, $U$ is learned from scratch.
  • Otherwise, fingerprint $U$ against current $\mathcal{M}$ using adaptive separating sequences (ADG or SepSeq).
  • If $U$ matches exactly one candidate, verify with conformance queries (Wp$_k$, RandomWp).
  • If all checks fail, trigger adaptive AAL leveraging traces and model structure to generate a new FSM $M^*$, expanding $\mathcal{M}$.

In class-incremental device recognition (Jiang et al., 6 Jan 2026), each round fits per-class diagonal GMMs to “twin-difference” features. Pseudo-feature rehearsal mitigates forgetting, while lightweight Adapter modules enable stage-specific feature modulation. Adapters are merged into a student via multi-teacher distillation, producing a single inference path regardless of class provenance.

Browser fingerprinting script detection (Durey et al., 2021) utilizes a process where feature overlaps (API-call signatures) with a growing set of known scripts bootstrap new automatic and manual labels, iteratively expanding both “fingerprinter” and “non-fingerprinter” sets until convergence.

Adaptive classification ensembles (AILearn (Agarwal et al., 2020)) generate cluster-specialized base classifiers in each phase, prune by validation accuracy, and merge new survivors with historical ensembles. No previous raw data are revisited, ensuring stability despite streaming concept drift.

Neural network fingerprinting (“FBI” (Maho et al., 2022)) incrementally augments model families and input pools, deploying mutual information or greedy query selection to distinguish new variants with minimal queries.

Scalable MRF dictionary inference (Oudoumanessah et al., 2024) employs incremental (online) EM algorithms to learn high-dimensional elliptical mixtures, updating subspace, location, and variance parameters on each new batch of signals, effectively compressing representation and enabling tractable matching in gigantic search spaces.

3. Structure Exploitation, Complexity Gains, and Empirical Performance

Incremental approaches exploit existing model structure for efficiency. In open-world FSM fingerprinting (Kruger et al., 29 Jan 2026), pre-existing models yield significant reductions in output- and equivalence-query complexity; adaptive AAL initialized from prior structure achieves $O(m(k n^2 + n\log l) + i m^2)$ output queries and $m n + i$ equivalence queries, as opposed to naive repeated learning ($O(i(k n^2 + n\log l))$ and $i n$ respectively).

Class-incremental RFF recognition (Jiang et al., 6 Jan 2026) achieves >2% higher mean accuracy and reduces catastrophic forgetting by >10% compared to regularization or replay-based methods, at <30 KB per incremental stage. Adapter-based pipelines maintain decision boundaries efficiently.

Browser script workflows (Durey et al., 2021) guarantee full convergence after at most $|S|$ manual steps, with bootstrapping minimizing human effort and eliminating retraining burdens.

AILearn exhibits a $49.57\%$ mean improvement in accuracy for new fake biometric materials with minimal degradation ($<6\%$) on previously known materials (Agarwal et al., 2020).

FBI requires 1–3 benign queries for 95% detection (closed world) and $>$90% identification rates with 100–500 queries (open world), robust to model perturbations (Maho et al., 2022).

Incremental elliptical mixture modeling in MRF (Oudoumanessah et al., 2024) reduces dictionary size by $7$–$10\times$, yields $<3\%$ RMSE reconstruction error, and accelerates matching by $6\times$ with clinically acceptable parameter estimation accuracy.

4. Critical Subcomponents, Ablations, and Robustness Factors

Algorithmic subcomponents are frequently ablated for performance trade-off analysis:

• In Infernal (Kruger et al., 29 Jan 2026), adaptive distinguishing graphs (ADG) outperform static SepSeqs for fingerprinting; RandomWp100 balances conformance accuracy and symbol expense; AL$_\mathsf{ref}$ boosts model fidelity over vanilla AAL.
• Class-incremental RFF (Jiang et al., 6 Jan 2026) shows pseudo-feature rehearsal prevents catastrophic forgetting, Adapters yield 2% higher final accuracy, and random-masking boosts robustness, particularly for few-shot classes. Adapter distillation streamlines inference, avoiding runtime and memory “blow-up.”
• For AILearn (Agarwal et al., 2020), clustering-based diversity and validation-driven pruning underpin stability-plasticity trade-offs. Feature extraction choices (BSIF, LPQ, ResNet-50) modulate incrementality effects according to sensor type.
• FBI (Maho et al., 2022) demonstrates that top-$k$ output requests halve query budgets; empirical mutual information is resilient to compression, input transformations, and adversarial training.

5. Limitations, Assumptions, and Prospective Enhancements

Incremental fingerprinting approaches are subject to context-dependent constraints:

• Infernal (Kruger et al., 29 Jan 2026) assumes deterministic, input-complete FSMs and exact reset capabilities; imperfections in conformance oracles introduce residual misclassification; hardware nondeterminism is abstracted.
• Class-incremental RFF (Jiang et al., 6 Jan 2026) acknowledges that diagonal GMMs omit inter-feature correlations (future extensions could use sparse/low-rank covariances, VAEs, or normalizing flows); pipeline performance depends on absence of severe domain shifts.
• Browser script workflows (Durey et al., 2021) observe API signatures only on the client; ambiguities or new fingerprinting APIs complicate labeling accuracy. Manual curation remains a bottleneck for ambiguous/novel scripts.
• AILearn's ensemble-based update (parameter threshold, cluster count per phase) controls adaptation speed versus stability, with minimum ensemble diversity required for robust new spoof detection (Agarwal et al., 2020).
• FBI’s accuracy declines with restrictive APIs (e.g., top-1 only) or highly similar variants; misidentification between variant types (e.g., quantization level) may require more queries (Maho et al., 2022).
• HD-MED for MRF (Oudoumanessah et al., 2024) requires selection of subspace dimensions and initialization on fit-size subsets; run-time depends heavily on mixture size $K$ and per-component subspace ranks $d_k$.

6. Representative Application Domains and Benchmark Studies

Incremental fingerprinting has demonstrated practical utility in diverse technology sectors:

• Protocol implementation for TLS, SSH, BLE, BLEDiff, MQTT suites, with up to 596 real-world implementations and ground-truth FSM sets ($6$–$66$ states per model) (Kruger et al., 29 Jan 2026).
• Radio-frequency device authentication, validated on ADS-B datasets totaling 2,175 pretraining and 669 incremental classes, against established baselines (iCaRL, DER, EWC, PASS) (Jiang et al., 6 Jan 2026).
• Browser script detection, sharing open-source workflows and ground-truth bootstraps from Disconnect (Durey et al., 2021).
• Biometric spoof detection, with LivDet 2011/2013/2015 datasets and rigorous phase partitioning to test new vs. known spoof material accuracy (Agarwal et al., 2020).
• Neural network family and variant identification, with >1000 networks and 20,000 natural images on ImageNet (Maho et al., 2022).
• Magnetic resonance fingerprinting, compressing high-dimensional dictionaries (up to $4 \times 10^{8}$ signals of dimension $260$), yielding clinical parameter accuracy and $6\times$ matching speedup (Oudoumanessah et al., 2024).

7. Future Directions and Emerging Research Challenges

Key avenues for advancement include:

• Gray-box incremental fingerprinting with integration of side information (e.g., source code, telemetry) into membership and conformance verification (Kruger et al., 29 Jan 2026).
• Extension to non-deterministic and data-rich FSMs or complex automata structures, accommodating richer behavioral landscapes.
• Adapter and mixture modeling innovations in class-incremental learning (low-rank mixtures, domain-adaptive augmentations, end-to-end distillation) (Jiang et al., 6 Jan 2026).
• Multimodal and semantic corpus generation for model ownership verification, robust to scaling and cross-lingual transfer (Xu et al., 19 Jan 2026).
• Incorporation of dynamic taint-tracking, network-flow analysis, or refined similarity computation in script labeling workflows (Durey et al., 2021).
• Theoretical bounds on mutual information separation and query-complexity for model identification, especially in high-variance or sparse-data regimes (Maho et al., 2022).
• Efficient Bayesian mixture refinement and high-dimensional subspace learning to further compress fingerprint dictionaries for large-scale biomedical or physical systems (Oudoumanessah et al., 2024).

Incremental fingerprinting thereby presents a mathematically rigorous, versatile, and empirically validated paradigm for dynamic identification and model construction across open-set environments, yielding substantial improvements in accuracy, computational scalability, and adaptability to novel classes or protocols.