Temporal Fingerprinting

• Temporal Fingerprinting is a method that converts time-series data into discriminative signatures by preserving unique temporal patterns for identity and parameter inference.
• It employs diverse representation forms, including embeddings, histograms, and low-rank factors, tailored to different domains like EEG, MRI, audio, and web traffic.
• Method robustness relies on careful segmentation, alignment, and adaptive matching rules, balancing performance gains with privacy and synchronization challenges.

Searching arXiv for papers on temporal fingerprinting across domains. Searching for exact and closely related temporal fingerprinting papers. Temporal fingerprinting denotes a family of methods that represent time-varying observations as signatures used for identification, retrieval, authentication, or parameter inference. In recent work, these signatures have appeared as empirical distributions of inter-event times for cross-domain identity matching (Somin et al., 2024), inter-token times and packet timing patterns for large-language-model identification (Alhazbi et al., 27 Feb 2025), connectivity vectors extracted from windowed EEG for biometrics (Didaci et al., 2023), transient voxel trajectories in Magnetic Resonance Fingerprinting (MRF) (Chen et al., 2019), variable-length audio embeddings for retrieval (Chen et al., 25 Mar 2026), and compact, discrete motion signatures for dance retrieval in DANCEMATCH (Kharlamova et al., 1 Apr 2026). Across these settings, the defining feature is that temporal organization is not treated as incidental metadata but as the primary source of discriminative structure.

1. Conceptual basis

At a high level, temporal fingerprinting maps a sequence, stream, or temporally ordered event set to a signature that remains informative under comparison. The mathematical form varies by domain. In VLAFP, the objective is an embedding map $f : a \mapsto \mathbf{z} \in \mathbb{R}^d$ for variable-length audio (Chen et al., 25 Mar 2026). In cross-domain identity matching on Ethereum, the fingerprint is the empirical cumulative distribution function of inter-event times,

$$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$

where $S^{u_d}_{\tau}$ is the inter-event sequence for profile $u_d$ on day $\tau$ (Somin et al., 2024). In EEG biometrics, a 60 s recording is segmented into fixed-length windows and each window yields a connectivity-based feature vector derived from the upper triangular part of a $64 \times 64$ PLV or PLI matrix, producing a 2016-dimensional template (Didaci et al., 2023).

Taken together, these formulations suggest a common abstraction: temporal fingerprinting begins with a temporally indexed object, constructs a representation that preserves class- or identity-specific temporal structure, and then applies a similarity, retrieval, or inference rule. The representation may be a sequence, a histogram, an embedding, a low-rank factor, a distance profile, or a discrete token vocabulary, but the operative assumption is the same: temporal evolution contains stable information not recoverable from static summaries alone.

2. Representation forms across domains

The representation layer is the main point of divergence among temporal fingerprinting methods. Some systems preserve explicit temporal trajectories. In MRF, each voxel is associated with a temporal signal driven by a varying acquisition schedule, and that temporal evolution is treated as a fingerprint of $[T_1, T_2, \mathrm{PD}]$ or related parameter sets (Chen et al., 2019). FLOR models these voxel fingerprints as rows of a space-time matrix $\mathbf{X} \in \mathbb{C}^{N \times L}$ and exploits low rank together with a dictionary subspace derived from Bloch simulations (Mazor et al., 2017). A temporal multiscale variant later approximated the Bloch dynamics on temporal grids $S_N(\delta)$, replacing exact full-length gradients with coarse-to-fine updates on subsampled time indices (Cortinhas et al., 2020).

Other methods convert temporal structure into compact descriptors. EEG biometrics compute PLV or PLI over time windows and flatten the resulting connectivity matrix into a template vector (Didaci et al., 2023). The Ethereum identity-matching method discards absolute time and retains only the distribution of inter-event gaps, arguing that bursty and heavy-tailed activity patterns are sufficiently individual to enable linkage across domains (Somin et al., 2024). LLM fingerprinting uses packet inter-arrival times and packet sizes, from which it derives a 36-dimensional feature vector per window before classification with an attention-based BiLSTM (Alhazbi et al., 27 Feb 2025).

A third class learns signatures directly from sequences. Fingerprint spoof detection uses ten color frames captured on a touch-based reader, extracts minutiae-centered local patch sequences, and processes them with a time-distributed MobileNet-v1 followed by a bi-directional LSTM (Chugh et al., 2019). VLAFP processes variable-length spectrogram sequences with inter-frame self-attention and frame-to-segment cross-attention, producing an $L_2$-normalized embedding (Chen et al., 25 Mar 2026). DANCEMATCH, as described in its abstract, constructs compact, discrete motion signatures by integrating Skeleton Motion Quantisation with Spatio-Temporal Transformers, and retrieves semantically similar choreographies through a DANCE RETRIEVAL ENGINE (Kharlamova et al., 1 Apr 2026).

Domain	Temporal object	Signature form
EEG biometrics	Windowed EEG connectivity	Upper-triangular PLV/PLI vector, 2016 dimensions (Didaci et al., 2023)
MRF/qMRI	Voxel time course across $$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$0 excitations	Dictionary/subspace fingerprint or low-rank temporal factor (Chen et al., 2019)
Audio retrieval	Variable-length spectrogram sequence	$$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$1-normalized embedding $$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$2 (Chen et al., 25 Mar 2026)
Dance retrieval	Pose sequence from raw video	Compact, discrete motion signatures (Kharlamova et al., 1 Apr 2026)
Cross-domain identity matching	Inter-event gaps	Empirical CDF $$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$3 (Somin et al., 2024)
Encrypted traffic / model ID	Packet timings and sizes	Windowed feature sequences for temporal classification (Alhazbi et al., 27 Feb 2025)

3. Segmentation, alignment, and temporal invariance

Temporal fingerprinting depends strongly on how the time axis is partitioned or aligned. In the EEG study, each 60 s recording is segmented into fixed-length, non-overlapping windows from 0.5 s to 12 s in 0.5 s steps, with the number of epochs given by

$$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$4

The authors report that biometric performance improves markedly as the window increases and reaches very high performance with windows of order 10 s; specifically, for PLV in gamma band, eyes-open, they report $$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$5 with a minimum window length of at least 10.5 s (Didaci et al., 2023).

Other systems make segmentation adaptive. Holmes, a website-fingerprinting attack for early-stage traffic, derives per-site effective loading ranges from cumulative SHAP importance distributions and then samples truncation points from those ranges to synthesize early-stage traces (Deng et al., 2024). VLAFP uses spectral-entropy-based variable-length segmentation with $$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$6 s and $$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$7 s, explicitly rejecting fixed 1 s fingerprinting as too rigid for temporal distortions and segmentation variability (Chen et al., 25 Mar 2026). TSA-WF treats a trace almost literally as a time series and uses a sliding window equal to prototype length to scan for the best subsequence match within a longer trace (Wrana et al., 20 May 2025).

Alignment mechanisms are equally central. ZK-SERIES supports Dynamic Time Warping and Time Warp Edit Distance as series distances for temporal biometric authentication, with the decision rule

$$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$8

where $$Q^{u_d}_{\tau}(\Delta t) = \frac{\left|\{\delta \in S^{u_d}_{\tau} : \delta \le \Delta t\}\right|}{m},$$9 is derived from distances between enrolled and fresh time series (Reijsbergen et al., 24 Jun 2025). In delay-based fingerprint embedding for secure media distribution, cropping and time shifting alter the absolute delay used as the user identifier; the proposed remedy is a synchronization fingerprint and recovery by relative delay,

$S^{u_d}_{\tau}$0

which restores the original offset after desynchronization (0801.0625).

A plausible implication is that segmentation and alignment are not preprocessing details but integral components of the fingerprint itself. Fixed windows, adaptive truncation, warping-based matching, and relative-delay correction all determine which temporal structure is preserved and which is treated as nuisance variation.

4. Matching, retrieval, and inference rules

Once a signature has been constructed, temporal fingerprinting requires a comparison rule. In EEG biometrics, pairwise matching uses Euclidean distance between 2016-dimensional connectivity vectors,

$S^{u_d}_{\tau}$1

which is converted to similarity by

$S^{u_d}_{\tau}$2

Genuine and impostor score distributions are then summarized through EER and AUC (Didaci et al., 2023).

For inter-event fingerprints on Ethereum, matching is driven by the Kolmogorov–Smirnov statistic

$S^{u_d}_{\tau}$3

with profile pairs ranked by goodness-of-fit and KS distance (Somin et al., 2024). Holmes instead maps traces into an embedding space and assigns each monitored site a centroid $S^{u_d}_{\tau}$4 and a radius $S^{u_d}_{\tau}$5 computed from median absolute deviation; an early-stage trace is associated with a site through cosine distance to these centroids, and detection proceeds incrementally as more traffic arrives (Deng et al., 2024).

MRF retains the classical paradigm of dictionary matching. In both conventional dictionary-based MRF and low-rank variants such as FLOR, parameter estimation selects the dictionary atom whose temporal evolution maximizes normalized inner product with the reconstructed voxel fingerprint, and then reads $S^{u_d}_{\tau}$6 from a lookup table (Mazor et al., 2017). MRF-FCNN and HYDRA replace or relax this step with learned regression from temporal fingerprints to continuous-valued parameter maps, thereby reducing storage and matching complexity while maintaining the temporal fingerprinting logic (Chen et al., 2019, Song et al., 2019).

Retrieval-oriented systems combine similarity with indexing. DANCEMATCH uses a histogram-based index followed by re-ranking for sub-linear motion retrieval (Kharlamova et al., 1 Apr 2026). TSA-WF computes STUMPY, Euclidean, weighted Euclidean, compression-based distance, and DTW between site prototypes and observed traces, then uses XGBoost over the resulting distance vector to infer the most likely website; because the full trace is preserved as a time series, the minimum-distance location also gives the approximate instant of a visit inside a multi-tab trace (Wrana et al., 20 May 2025).

5. Learning architectures and system design

Recent temporal fingerprinting methods increasingly rely on learned encoders tailored to temporal structure. MRF-FCNN first applies PCA to compress each voxel fingerprint, then feeds the reduced temporal channels into a fully convolutional network that outputs $S^{u_d}_{\tau}$7, $S^{u_d}_{\tau}$8, and $S^{u_d}_{\tau}$9, avoiding explicit dictionary search (Chen et al., 2019). HYDRA uses a two-stage design: low-rank signature restoration in k-space followed by a 1D nonlocal residual CNN for parameter restoration, with the nonlocal block implementing self-attention over time (Song et al., 2019). A later generative-subspace MRF method combines a fixed temporal subspace from simulated magnetization evolutions with an untrained convolutional generator that regularizes the spatial coefficients of the low-rank model (Lu et al., 2023).

Outside MRI, CNN–RNN hybrids remain common when temporal evolution is local and short. Fingerprint spoof detection processes ten-frame patch sequences with a time-distributed MobileNet-v1 and a bi-directional LSTM, improving cross-material performance from TDR of 81.65% to 86.20% at $u_d$0 (Chugh et al., 2019). ADL-ID for wireless device fingerprinting factorizes features into a device-specific latent and a domain-specific latent, using a Gradient Reversal Layer and orthogonality constraints to address temporal domain adaptation in RF fingerprinting; it reports about 24% improvement in accuracy on short-term temporal adaptation and up to 9% on long-term temporal adaptation (Elmaghbub et al., 2023).

Transformer-style temporal encoders are increasingly prominent where sequence length varies or long-range dependencies matter. VLAFP uses inter-frame self-attention, frame-to-segment cross-attention, and supervised contrastive learning to fingerprint audio of variable length, and reports that it outperforms existing state-of-the-arts in live audio identification and audio retrieval across three real-world datasets (Chen et al., 25 Mar 2026). Holmes couples a convolutional Encoder with supervised contrastive learning so that early-stage and complete traces of the same website cluster together in embedding space (Deng et al., 2024). DANCEMATCH adopts Spatio-Temporal Transformers over quantized motion representations (Kharlamova et al., 1 Apr 2026). LLM fingerprinting by “rhythm” uses an attention-based BiLSTM over sequences of packet-timing features to identify both open-source SLMs and proprietary LLMs across local host, LAN, remote network, and VPN scenarios (Alhazbi et al., 27 Feb 2025).

These systems indicate a shift from handcrafted temporal descriptors toward architectures that explicitly model sequence structure, yet the temporal fingerprint remains operationally meaningful only when the learned embedding is linked to a clear matching rule, retrieval mechanism, or inference objective.

6. Robustness, privacy, and open issues

Temporal fingerprinting is valuable precisely because timing and temporal order are often hard to fake, but the same property creates both robustness and privacy risk. In EEG biometrics, increasing the time window reduces estimator variance for PLV/PLI and sharply improves discriminability, but extending the window size beyond a certain maximum does not improve performance (Didaci et al., 2023). In website fingerprinting, Holmes successfully identifies dark web websites when the ratio of page loading on average is only 21.71%, and reports an average precision improvement of 169.36% over existing WF attacks in that replay setting (Deng et al., 2024). In privacy-preserving authentication, ZK-SERIES shows that the privacy-preserving authentication protocol can be completed within 1.3 seconds on older devices while supporting time-series distances such as DTW and TWED (Reijsbergen et al., 24 Jun 2025).

The privacy implications are equally direct. The Ethereum study concludes that simply knowing when an individual is active, even if information about who they talk to and what they discuss is lacking, poses risks to users’ privacy (Somin et al., 2024). The LLM “rhythm” study shows that inter-token times remain effective even under encrypted network traffic and across different deployment scenarios, making model identification possible without access to model weights or plaintext output (Alhazbi et al., 27 Feb 2025). Delay-based media fingerprinting shows the converse: when temporal synchronization is weak, cropping and time shifting can break identification unless a synchronization fingerprint or relative delay is introduced (0801.0625).

A plausible implication is that robust temporal fingerprinting requires joint treatment of three variables: duration, alignment, and deployment drift. Duration governs how much temporal evidence is available; alignment determines whether equivalent events are compared to one another; deployment drift changes the generating process itself, as in wireless RF fingerprinting across time or LLM timing under different network conditions (Elmaghbub et al., 2023, Alhazbi et al., 27 Feb 2025). The literature therefore converges on a common design tension: the more faithfully a system preserves temporal structure, the more discriminative it becomes, but the more sensitive it also becomes to synchronization, environmental shift, and privacy leakage.