Temporal Tokenization for Event Sequences

• Temporal tokenization is a method that discretizes continuous time data into tokens to facilitate event sequence modeling.
• Various strategies such as byte-level encoding, calendar decomposition, and RSQ quantization are tailored to address different data distributions and domain-specific needs.
• These techniques improve computational efficiency and precision, benefiting applications like event vision, biosensor analysis, and mobility modeling.

Temporal tokenization for event sequences refers to the process of discretizing and encoding temporal information—such as timestamps, temporal intervals, and cyclical structures—so that machine learning models can effectively ingest, represent, and reason over asynchronous, continuous-time event streams. This paradigm is central for temporal point process modeling, event-sequence learning, biosensor and event camera analysis, and LLM adaptation to event-driven domains. Temporal tokenization strategies must account for domain-specific characteristics, including asynchrony, sparsity, distributional skew, scale diversity, and multi-level cyclicity, to ensure both computational and sample efficiency in downstream architectures.

1. Foundational Principles and Formalization

The canonical event sequence is modeled as $\mathcal{S}=\{(t_i, k_i, m_i)\}_{i=1}^N$, where $t_i\in\mathbb{R}^+$ denotes the timestamp, $k_i$ the event type, and $m_i$ a (possibly optional) natural-language or structured description. The temporal component for each event is typically the inter-arrival interval $\Delta t_i = t_i - t_{i-1}$, with $t_0=0$ by convention. The central challenge is to map $\Delta t_i$ from a continuous domain to a discrete token or embedding that captures relevant temporal granularity, correlations, and patterns for the target backbone (e.g., RNN, Transformer, GNN).

Multiple representational axes are involved:

• Numeric/byte-level encoding: Direct numeric serialization or bit-level decomposition (e.g., IEEE float32 byte-tokens).
• Semantic time decomposition: Calendar fields, human-centric tokens (e.g., hours, days of week).
• Data-adaptive discretization: Histograms, uniform or non-uniform scale bins, vector quantization.
• Structural aggregation: Temporal windowing, patching, or segmenting (e.g., spiking patches, daily/weekly tokens).

2. Taxonomy of Temporal Tokenization Strategies

A broad taxonomy has emerged, motivated by the requirements of LLM integration and efficiency in modeling diverse event data distributions (Liu et al., 15 Dec 2025, Kong et al., 11 Feb 2025):

Strategy	Description	Token Cost
Numeric string	Encode $\Delta t_i$ as fixed-precision string	8–12 tokens
Float32 byte-level	4 specialized tokens representing bytes	4 tokens
Calendar decomposition	Tokens for (year, month, ...), absolute/rel.	2–6 tokens
Uniform binning	Linear/log bins over transformed intervals	1 token
Residual Scalar Quantization (RSQ)	Multi-stage K-means codebooks	$1$–$L$ tokens

Byte-level representations (as in Language-TPP (Kong et al., 11 Feb 2025), TPP-LLM (Liu et al., 15 Dec 2025)) transform each float32-valued interval to 4 tokenized bytes, enabling high-precision reconstruction, constant token length, and integration within standard LLM architectures. Calendar-based tokenization decomposes timestamps into human-meaningful segments (e.g., $\langle\mathrm{hour\_13}\rangle$), enhancing robustness for multi-modal or mixed-peak data. Scale binning and RSQ provide data-driven quantization, crucial for domains with heavy-tailed or log-normal interval statistics.

Patch-based or segmental approaches, such as daily/weekly tokens in RHYTHM (He et al., 27 Sep 2025) or spatial "spiking patches" in event vision (Øhrstrøm et al., 30 Oct 2025), further structure tokenization topologically or hierarchically, enabling multi-scale modeling.

3. Methodological Implementations

3.1 Byte-Level and Calendar Tokenization

• Float32 Byte Encoding: Given $v_i = \Delta t_i$, reinterpret its binary float32 as $v \in \{0, \dots, 2^{32}-1\}$; obtain bytes $b_k = \lfloor v / 2^{8k} \rfloor \bmod 256$; each $b_k$ mapped to a special LLM token (Liu et al., 15 Dec 2025, Kong et al., 11 Feb 2025).
• Calendar Decomposition: $t_i$ or $\Delta t_i$ expressed as multi-token fields at predefined granularities (e.g., $\langle\mathrm{year\_2025}\rangle$, $\langle\mathrm{day\_17}\rangle$).

3.2 Adaptive Quantization

• Uniform Binning: Transformed interval $v'_i = f(\Delta t_i)$ binned uniformly across $K$ levels, with $K$ calibrated to token budget or range.
• Residual Scalar Quantization (RSQ): $L$-stage K-means clustering on residuals, with token sequence $(q_1,\dots,q_L)$ indexing codebooks, supporting arbitrary adaptivity (Liu et al., 15 Dec 2025).

3.3 Structural Aggregation

• Spiking Patches for Event Cameras: The 2D event stream $\{(x_i, y_i, t_i, p_i)\}$ is partitioned into $(P\times P)$ grid patches, each acting as a leaky integrate-and-fire unit. Each patch emits a spike (token) when its potential exceeds threshold $\sigma$, recording events and entering a refractory period $T$. Tokens are embedded via stacked local histograms and positional encodings, then input to GNNs, PointNet++, or Vision Transformers (Øhrstrøm et al., 30 Oct 2025).
• Hierarchical Segmentation in Trajectories (RHYTHM): Sequences $\{e_t\}$ segmented into daily tokens $\{\mathbf{s}_i\}$, pooled via intra-segment attention, then grouped into weekly tokens $\{\mathbf{u}_j\}$ with higher-level inter-segment attention. Event embedding incorporates cyclical Day-of-Week and Time-of-Day fields, merged with semantic prompts into the LLM backbone (He et al., 27 Sep 2025).

3.4 Embedding for Sequence Models

• For LLM- and RNN-based methods, time representations are integrated as additional tokens or via time-modulated embeddings (mask or joint space) (Li et al., 2017).
• In graph and point cloud networks, tokens are embedded according to spatial, temporal, or joint spatio-temporal coordinates with per-token features (Øhrstrøm et al., 30 Oct 2025).

4. Empirical Performance and Comparative Analysis

Experimental studies demonstrate that:

• Alignment to data distribution is critical: Log-skewed or heavy-tailed intervals warrant log-scale binning or RSQ(Log); spiky or discrete modes favor calendar tokens; uniform domains are amenable to linear bins or single-stage RSQ (Liu et al., 15 Dec 2025).
• No single strategy is universally optimal: Prediction accuracy and RMSE for next-event times depend on tokenizer-data alignment; e.g., in NYC Taxi data, calendar tokens at second-level resolution achieved the lowest RMSE, while Stack Overflow and Chicago Crime data favor log-binning and RSQ(Log).
• Token efficiency and precision trade-offs: Byte and multi-level RSQ representations yield highest precision with 4+ tokens per value; single-token binning or RSQ offers strong performance when token budget is constrained (Liu et al., 15 Dec 2025).
• Inference time and sparsity preservation: Spiking Patches reduce inference times by up to $10.4\times$ relative to frame-based and $3.4\times$ to voxel-based vision tokens, while matching or exceeding accuracy due to preserved asynchrony and spatial sparsity (Øhrstrøm et al., 30 Oct 2025).
• Computational efficiency: Hierarchical temporal tokenization with local pooling (e.g., RHYTHM) produces substantial reductions in attention complexity (e.g., $1/2304$ of original cost with $L=48$) and overall training time (24.6% reduction) (He et al., 27 Sep 2025).

5. Applications Across Domains

Temporal tokenization has wide applicability:

• Event vision: Spiking Patches achieve high speed and accuracy for gesture recognition and object detection from event camera outputs (Øhrstrøm et al., 30 Oct 2025).
• Human mobility modeling: Hierarchical daily/weekly tokens with cyclical field embeddings enable trajectory reasoning with LLMs; this yields superior overall and weekend accuracy on real-world mobility datasets (He et al., 27 Sep 2025).
• General event sequence analysis: Tokenization strategies are essential for integrating temporal point processes with LLMs (Language-TPP, TPP-LLM), impacting next-event prediction, event description generation, and intensity estimation (Kong et al., 11 Feb 2025, Liu et al., 15 Dec 2025).
• Sequence segmentation: Frame-level embedding with dynamic graph construction supports temporal segmentation in image and motion sequences, outperforming prior unsupervised methods (Dimiccoli et al., 2019).

6. Generalization and Best-Practice Guidelines

Best-practice recommendations drawn from cross-domain benchmarks (Liu et al., 15 Dec 2025, Øhrstrøm et al., 30 Oct 2025, He et al., 27 Sep 2025, Kong et al., 11 Feb 2025):

• Align tokenization scheme with the data's temporal distribution: Use log-scale or RSQ quantization for skewed/intermittent domains; calendar-based or structural segmenting for periodic/human-centric data; byte-level or multi-level for maximal fidelity.
• Optimize token budget: Choose single-token strategies (scale bin, 1-stage RSQ) for minimal sequence length, byte/multi-stage RSQ when higher precision is mandated.
• Prompt and positional design: For LLMs, always position event type tokens before time tokens in input prompts; use positional encodings to maintain recoverability of original time and space information.
• Segmentation and hierarchy: When sequences exhibit multi-scale or cyclical behavior, adopt hierarchical tokenization and attention (break into local/global, day/week, patch/window structures).
• Downstream integration: Temporal tokens can be directly fed to LLMs, GNNs, PCNs, or transformers via embedding with built-in temporal structure.

A plausible implication is that future frameworks will increasingly employ adaptive, hierarchical, and sparsity-preserving tokenization methods to scale event modeling to longer, denser, and more heterogeneous streams across application domains.

7. Outstanding Challenges and Directions

No temporal tokenization scheme is universally optimal; strategies must be tuned for both token budget and statistical properties. Open challenges include bridging the gap between token efficiency and expressive capacity, adapting tokenization on the fly to evolving distributions, and unifying discrete, cyclic, and continuous temporal factors within editable prompt templates for LLM-based forecasting and causal modeling (Liu et al., 15 Dec 2025, He et al., 27 Sep 2025). Efficient, domain-adaptive, and compositional temporal tokenization remains a central area for further research and system design.