TimeRep: Temporal Representations Across Domains

• TimeRep is a diverse concept that formalizes temporal structure through methods like waiting-time analysis, temporal graphs, and learned embeddings.
• It supports applications from quantum network rate control and natural language event sequencing to time series modeling in recommendations and anomaly detection.
• Structured temporal representations in TimeRep capture relational and periodic dynamics, outperforming simple scalar timestamp approaches in various domains.

Searching arXiv for "TimeRep" to ground the article in current arXiv metadata and disambiguate usage across papers. TimeRep is not a single universally standardized construct across arXiv literature; rather, it appears as a field-dependent shorthand for formalizing, exploiting, or measuring temporal structure. In different research areas, the term denotes an average waiting-time formalism for probabilistic imperfect memories in quantum repeaters (Praxmeyer, 2013), a temporal graph representation of events and time expressions in natural language processing (Ning et al., 2019), an intermediate-representation memory mechanism for anomaly detection with time series foundation models (Han et al., 16 Sep 2025), and a broader class of time-aware representations in recommendation, sequence modeling, and evaluation (Zhu et al., 2024, Fraikin et al., 2023, Ng et al., 15 Apr 2026). Across these usages, a common theme is the elevation of temporal structure from auxiliary metadata to a first-class representational object.

1. Terminological scope and recurring themes

The term “TimeRep” is used in the literature to denote temporal representation at different abstraction levels. In probabilistic quantum-network analysis, it refers to “the time required to ‘reposition’ the system in a state where all segments are ready,” captured by an exact waiting-time expression under finite memory lifetimes (Praxmeyer, 2013). In NLP, it denotes a document-level temporal representation built from normalized time expressions, event nodes, and temporal relations, yielding a temporal graph and derived timeline (Ning et al., 2019). In recommendation and time-series learning, it refers to user- or timestep-level time-aware embeddings that encode periodicity, temporal drift, or fine-grained temporal dependencies (Zhu et al., 2024, Fraikin et al., 2023). In anomaly detection with time series foundation models, TimeRep is a method that represents normality through selected intermediate TSFM patch embeddings stored in a compact reference collection (Han et al., 16 Sep 2025).

This heterogeneity suggests that TimeRep is best understood as a family resemblance term rather than a single formalism. A plausible implication is that the literature converges on a shared design principle: temporal information is most useful when represented structurally rather than treated as a scalar timestamp alone.

2. TimeRep as waiting-time representation in probabilistic memories

In “Reposition time in probabilistic imperfect memories” (Praxmeyer, 2013), TimeRep is the waiting-time formalism governing protocols with $N$ identical finite time memories whose success events are geometric and whose imperfections are modeled by a step-function cutoff. Each memory is a two-state bit, $|0)$ or $|1)$, and each attempt flips $|0)$ to $|1)$ with probability $p$, with $q=1-p$ (Praxmeyer, 2013). In the imperfect-memory setting, entanglement is stored perfectly for a fixed time $T$, after which the earliest success is “completely and irreversibly lost,” and the full system is reset if all $N$ successes have not been obtained within $T$ steps after the first success (Praxmeyer, 2013).

The central quantity is the average number of steps until one successful round occurs, denoted $|0)$0, with main formula

$|0)$1

This yields the average waiting time to obtain $|0)$2 successes within a memory window $|0)$3, including all resets (Praxmeyer, 2013). The limiting cases recover $|0)$4 at $|0)$5 and the perfect-memory result

$|0)$6

as $|0)$7 (Praxmeyer, 2013).

In quantum repeater analysis, this TimeRep quantity determines the rate bottleneck for simultaneously preparing all elementary links. With synchronized attempts of duration $|0)$8, the entanglement-generation rate is approximately

$|0)$9

so finite $|1)$0 directly constrains achievable repeater throughput (Praxmeyer, 2013). The paper emphasizes that the reset rule is pessimistic and therefore yields conservative rate estimates (Praxmeyer, 2013).

3. TimeRep as temporal graph representation in natural language processing

In “CogCompTime: A Tool for Understanding Time in Natural Language Text” (Ning et al., 2019), TimeRep is a document-level temporal representation that combines explicit time expressions with implicit temporal relations. The representation contains nodes for events and timexes, edges for temporal relations, and supports both graph and timeline visualization (Ning et al., 2019).

The system is organized into three components: a Timex Component, an Event Extraction Component, and a Temporal Relation (TempRel) Component (Ning et al., 2019). Timex extraction is formulated as BIO chunking, using a retrained TemporalChunker with a sparse averaged perceptron, followed by rule-based normalization to TIMEX3-style values such as dates, durations, and sets, often relative to the Document Creation Time (Ning et al., 2019). Events are defined using MATRES as main-axis events and extracted by token-level binary classification with a sparse averaged perceptron over lexical, POS, SRL, and related features (Ning et al., 2019).

The core TimeRep structure is a temporal graph. Event–event edges are labeled from $|1)$1, while event–timex edges use $|1)$2 (Ning et al., 2019). Local TempRel scores are computed as

$|1)$3

and then globally reconciled through an ILP with decision variables $|1)$4, objective

$|1)$5

single-label constraints, and consistency constraints such as anti-symmetry and transitivity (Ning et al., 2019).

This yields a globally coherent temporal graph rather than a collection of locally predicted pairwise relations. The derived timeline is linearized from the partial order, resolving VAGUE relations by appearance order in text for visualization purposes (Ning et al., 2019). On TempEval3 “Platinum,” CogCompTime reports Timex extraction $|1)$6, $|1)$7, $|1)$8, normalization accuracy $|1)$9, end-to-end F1 $|0)$0, and runtime $|0)$1 seconds (Ning et al., 2019). On MATRES-based data with gold extraction, Event–Event TempRel performance is $|0)$2, $|0)$3, $|0)$4, with relaxed Event–Event F1 $|0)$5, and Event–Timex F1 $|0)$6 (Ning et al., 2019).

A closely related formalization appears in “Predicting Event Time by Classifying Sub-Level Temporal Relations Induced from a Unified Representation of Time Anchors” (Cheng et al., 2020), where TimeRep is explicitly a unified event-time anchor representation

$|0)$7

encoding earliest/latest possible begin and end days for events (Cheng et al., 2020). This representation unifies Single-Day/Multi-Day and Certain/Uncertain event times and induces four sub-level temporal relations $|0)$8–$|0)$9, each labeled $|1)$0 (Cheng et al., 2020). The paper reports 43.2% event time accuracy on TBET versus 41.6% for the decision tree baseline, and 24.6% combined E-D+E-T accuracy on TE3-Test for the proposed attention-based SR classifier (Cheng et al., 2020).

A broader temporal-graph pretraining perspective is given by “Once Upon a $|1)$1 in $|1)$2: Relative-Time Pretraining for Complex Temporal Reasoning” (Yang et al., 2023), which constructs a graph over temporally-scoped sentences and classifies pairwise relations as Earlier, Later, or Contemporary (Yang et al., 2023). The TRC loss is

$|1)$3

optimized jointly with the T5 denoising objective (Yang et al., 2023). This suggests a second recurrent theme in TimeRep research: relative temporal structure is often more useful for reasoning than absolute timestamps alone.

4. TimeRep as learned temporal representation in recommendation and time series

In “Interest Clock: Time Perception in Real-Time Streaming Recommendation System” (Zhu et al., 2024), TimeRep is instantiated as a personalized daily preference clock. A day is partitioned into 24 buckets; for each user and hour, past 30 days of interactions are aggregated over genre, mood, and language using

$|1)$4

and the top 3 feature values per type are embedded (Zhu et al., 2024). The final interest clock embedding is a Gaussian-weighted sum over hourly preference vectors: $|1)$5 with $|1)$6 and $|1)$7 (Zhu et al., 2024). On Douyin Music, online A/B tests reported +0.509% on Active Days and +0.758% on Duration, while offline results showed AUC/UAUC of 0.6695/0.6069 for Gaussian Clock versus 0.6631/0.6007 for the baseline (Zhu et al., 2024).

In “T-Rep: Representation Learning for Time Series using Time-Embeddings” (Fraikin et al., 2023), TimeRep denotes timestep-level self-supervised representation learning with explicit learned time-embeddings. Given $|1)$8, the encoder produces $|1)$9, so that each timestep has its own representation (Fraikin et al., 2023). Time embeddings $p$0 are probability vectors derived from a learnable map $p$1, and are concatenated with the projected signal before a TCN encoder (Fraikin et al., 2023). Two time-aware pretext tasks supplement TS2Vec-style contrastive losses: a time-embedding divergence prediction objective using $p$2, and a time-embedding-conditioned forecasting objective (Fraikin et al., 2023).

The combined objective is

$p$3

where $p$4 are instance-wise and temporal contrasting losses, and $p$5 are the new time-aware pretexts (Fraikin et al., 2023). T-Rep reports F1 $p$6 on Yahoo anomaly detection versus 0.733 for TS2Vec, F1 $p$7 on Sepsis versus 0.619 for TS2Vec, average classification accuracy 0.706 across 30 UEA datasets, and average forecasting MSE/MAE $p$8, outperforming TS2Vec, Informer, TCN, and a linear baseline on aggregated ETT results (Fraikin et al., 2023).

These works frame TimeRep as a learned latent variable system in which temporal structure is encoded directly in features or auxiliary objectives rather than inferred post hoc.

5. TimeRep as evaluation and anomaly-scoring infrastructure

A further usage of TimeRep appears in evaluation frameworks and anomaly-detection systems. “RecNextEval: A Reference Implementation for Temporal Next-Batch Recommendation Evaluation” (Ng et al., 15 Apr 2026) treats time as a first-class axis in evaluation rather than representation learning. It partitions timestamped interactions into an initial training window and sequential test windows, enforcing a global timeline and a test-then-train loop that mimics production behavior (Ng et al., 15 Apr 2026). Metrics are aggregated per window and across windows, for example

$p$9

with analogous micro aggregation (Ng et al., 15 Apr 2026). This suggests a complementary interpretation of TimeRep: not only how time is encoded in a model, but also how temporal order constrains valid evaluation.

In “Leveraging Intermediate Representations of Time Series Foundation Models for Anomaly Detection” (Han et al., 16 Sep 2025), TimeRep is a memory-based anomaly detector operating on intermediate TSFM patch representations. Using a pre-trained TSFM such as MOMENT-Large, TimeRep selects an intermediate layer $q=1-p$0 and patch token $q=1-p$1, builds a reference memory from training embeddings, compresses it with a greedy k-Center core-set, and scores test windows by nearest-neighbor distance (Han et al., 16 Sep 2025). The coreset solves

$q=1-p$2

and the anomaly score is

$q=1-p$3

with $q=1-p$4 under the default Euclidean metric (Han et al., 16 Sep 2025). A test-time adaptive memory bank adds representations whose nearest-neighbor distance exceeds the 80th percentile of training NN distances, thereby adapting to concept drift without updating model parameters (Han et al., 16 Sep 2025).

On the UCR Anomaly Archive, TimeRep reports Top-1 accuracy 72.8 for last-aligned and 77.6 for center-aligned representations, exceeding DAMP at 63.2, TimeVQVAE-AD at 66.8, and foundation-model baselines using final-layer heads such as MOMENT fine-tuning at 32.8 and Timer fine-tuning at 36.0 (Han et al., 16 Sep 2025). Layer-wise analysis identified layer 16 as best for MOMENT-Large, and center patch selection improved Top-1 from 70.8 to 75.6 before adaptive memory updates (Han et al., 16 Sep 2025).

This use of TimeRep departs from explicit symbolic temporal reasoning and instead treats temporal structure as a latent manifold whose geometry defines normality.

6. TimeRep in physical timing and time-sensitive control

Several papers use closely related “time representation” ideas in physical systems, although not always under the exact TimeRep label. In “Scalable Time-Tagged Data Acquisition for Entanglement Distribution in Quantum Networks” (Amlou et al., 17 May 2025), time representation is built from 1-second White Rabbit PPS blocks with calibrated relative timestamps: $q=1-p$5 and reconstructed absolute time

$q=1-p$6

The system achieved synchronized coincidence detection at 25,000 counts/s, with raw tags reduced from 14.32 bytes/tag to 3.80 bytes/tag, a 73.5% reduction (Amlou et al., 17 May 2025).

In fiber-optic time synchronization, “Time Reversal Enabled Fiber-Optic Time Synchronization” (Chen et al., 2023) derives clock offset from a time-reversed waveform without a data layer: $q=1-p$7 up to calibrated hardware and asymmetry constants (Chen et al., 2023). Over 230 km, the method achieved TDEV $q=1-p$8 at $q=1-p$9 and $T$0 at $T$1, with multiple-access nodes reaching $T$2 at $T$3 and $T$4 at $T$5 (Chen et al., 2023). A different repeater-based timing architecture using OEO stations over BTDM-SFSW achieved time deviations of less than 80 ps/s and 11 ps/$T$6 s over 13,200 km, with combined standard uncertainties of less than 70 ps (Zhang et al., 2017).

In reinforcement learning, “About Time: Model-free Reinforcement Learning with Timed Reward Machines” (Majumdar et al., 19 Dec 2025) embeds time into non-Markovian reward structure באמצעות timed reward machines

$T$7

where transitions are labeled by propositions, clock guards, resets, and next automaton states (Majumdar et al., 19 Dec 2025). A trajectory with explicit delays yields discounted return

$T$8

with separate digital-time and real-time semantics, finite cross-product MDPs or corner abstractions, and counterfactual-imagining heuristics for timed exploration (Majumdar et al., 19 Dec 2025). This work broadens the TimeRep theme from descriptive temporal encoding to executable reward logic.

7. Conceptual synthesis, misconceptions, and research directions

A common misconception would be to treat TimeRep as a single algorithm or benchmark. The literature instead shows multiple incompatible but conceptually related meanings. In symbolic settings, TimeRep is a graph, anchor tuple, or automaton that explicitly encodes temporal relations (Ning et al., 2019, Cheng et al., 2020, Yang et al., 2023, Majumdar et al., 19 Dec 2025). In statistical and representation-learning settings, it is a learned embedding or latent manifold constrained by temporal objectives or intermediate-model geometry (Zhu et al., 2024, Fraikin et al., 2023, Han et al., 16 Sep 2025). In systems and networking, it is a synchronization-safe timestamping or waiting-time formalism that makes temporal constraints analyzable and operational (Praxmeyer, 2013, Amlou et al., 17 May 2025, Chen et al., 2023, Zhang et al., 2017).

Another misconception would be to equate temporal representation with absolute time-stamping. Several papers explicitly argue that absolute timestamps alone are insufficient when downstream behavior depends on relative ordering, synchronization windows, or temporal consistency across entities (Yang et al., 2023, Praxmeyer, 2013, Ning et al., 2019). This suggests that successful TimeRep designs often combine anchoring with relational structure.

A plausible implication is that the field is converging toward hybrid temporal representations with three layers: a calibrated or normalized absolute anchor, a relational structure over entities or intervals, and a learned latent space that captures smooth temporal variation. Such an overview is only partially realized in current work. Symbolic systems offer interpretability and logical consistency (Ning et al., 2019, Cheng et al., 2020, Yang et al., 2023), while learned systems offer robustness, scalability, and transfer (Fraikin et al., 2023, Han et al., 16 Sep 2025). Physical timing systems add requirements of synchronization, bounded drift, and efficient storage (Amlou et al., 17 May 2025, Chen et al., 2023).

The most consistent open problems across these usages are also shared. The step-function memory model in quantum repeaters is an idealization of smooth decoherence (Praxmeyer, 2013). NLP temporal graph systems still under-handle nominal events, event coreference, and multi-axis time (Ning et al., 2019). Unified event-time anchors remain coarse and largely local, with room for finer-grained or globally constrained reasoning (Cheng et al., 2020). Recommendation and time-series models need stronger handling of sparse users, irregular temporal structure, and multi-scale cycles (Zhu et al., 2024, Fraikin et al., 2023). Memory-based anomaly scoring depends on TSFM quality and can be affected by contamination under drift (Han et al., 16 Sep 2025). Timed reward machines face state-space explosion and currently target tabular rather than deep RL (Majumdar et al., 19 Dec 2025).

Taken together, TimeRep designates a broad research program: making temporal structure explicit enough to reason over, efficient enough to compute with, and flexible enough to adapt across domains.