Temporal Event Representation

• Temporal event representation is the systematic process of encoding, learning, and inferring evolving events using mathematically grounded and algorithmic frameworks.
• It integrates diverse methodologies including temporal point and interval models, spatio-temporal graphs, and neural as well as logical approaches to capture event dynamics.
• The field balances high temporal resolution, structural fidelity, and computational tractability to support applications in vision, NLP, and predictive analytics.

Temporal event representation encompasses the mathematical, algorithmic, and symbolic methodologies for encoding, learning, and inferring properties of events as they evolve in time across a range of problem domains, including event stream processing, temporal knowledge graphs, temporal reasoning, event-based vision, and temporal relation extraction. Effective representations must balance temporal granularity, structural fidelity, computational tractability, and compatibility with task-specific downstream architectures. This article synthesizes the landscape of temporal event representations, integrating core techniques from event-based neural modeling, logic and knowledge graphs, spatio-temporal embedding frameworks, and temporal relation learning systems.

1. Foundations: Formalisms for Temporal Event Representation

The basis of any temporal event representation is the formal definition of "event" within its application context and the method by which temporal information (points, intervals, distributions) is associated to those events. Key paradigms include:

• Temporal Point Representation: Events are encoded as tuples $e = (x, y, t, p)$, where $x, y$ are spatial coordinates (optional), $t$ is the timestamp (continuous or discrete), and $p$ may encode polarity or type. This formalism underpins event-based cameras, spatio-temporal point clouds, and streaming data (Innocenti et al., 2020, Lin et al., 2023, Lin et al., 2024).
• Interval Representation: Durative events or states are characterized as pairs $[t_b, t_e]$, denoting the start and end times. Both certain and uncertain (open/closed, bounded/unbounded) intervals are modeled, often as quadruples $((b_e, b_l), (e_e, e_l))$ denoting earliest/latest start and end (Cheng et al., 2020).
• Graphical Models and Knowledge Graphs: Events may instantiate nodes in temporal graphs with labeled edges encoding temporal/causal relations, or as entities in temporal knowledge graphs, with time-stamped properties (begin/end) (Mellor, 2017, Gottschalk et al., 2018, Gottschalk et al., 2019).
• Temporal Logic and Algebraic Relations: Symbolic frameworks draw on interval and point algebra (e.g., Allen's relations: before, meets, overlaps), allowing formal expression and querying over event patterns, intervals, and complex phenomena (Pitsikalis et al., 2021).

These formalisms are often layered, with explicit conversion or fusion between point, interval, and graph representations depending on task requirements.

2. Discretization, Granularity, and Lossless Encoding Methods

Temporal event systems must address the tension between high temporal resolution (microsecond-scale) and computational tractability. Discretization strategies transform raw asynchronous event streams into representations amenable to neural processing, statistical reasoning, or symbolic inference:

• Binary Sub-frame and Temporal Binary Representation (TBR): Temporal windows are partitioned into fixed-duration bins (Δt), in which events are aggregated into binary images. N such sub-frames are compacted via binary-to-decimal encoding, yielding lossless, pixel-aligned encodings that preserve temporal ordering up to Δt (Innocenti et al., 2020). Notably, TBR supports efficient conversion of event streams to CNN-suitable images, with high temporal granularity controlled by Δt and N.
• Spike-TBR and Neuromorphic Noise Filtering: To mitigate noise sensitivity in frame-based representations, per-pixel spiking neuron layers (LIF/RecLIF/LRLIF/PLIF) are interposed, emulating biological temporal integration and noise rejection. Only temporally coherent events elicit spikes, and the final TBR-like representation is robust to sensor noise while remaining compact (Magrini et al., 5 Jun 2025).
• Multi-Temporal Granularity Fusion: Hybrid frameworks combine coarse voxel-based grids (dense in space, coarse in time) and fine-grained point cloud encodings (sparse in space, continuous in time), with fusion networks aligning and diffusing features across granularities to preserve both spatial detail and microsecond-level temporal cues (Lin et al., 2024).
• Attention and Token Selection: Temporal-wise attention modules reweight, score, and prune event frames based on informativeness, compensating for variable framewise signal-to-noise ratio and enabling progressive token selection over spatio-temporal patches for computational efficiency (Yao et al., 2021, Zhao et al., 26 Sep 2025).

3. Spatio-Temporal Graphs and Point Cloud Embeddings

Representing the dynamical evolution of events in structured domains (e.g., networks, sensory surfaces, spatio-temporal scenes) requires models that capture both event-wise individuality and collective node or network-level dynamics:

• Temporal Graph Representations (TREND): Temporal graphs are defined as $G=(V,E,T,X)$, with events as triplets $(i,j,t)$. Representation learning is performed via temporal GNNs that inductively embed node histories using time-decayed neighbor message passing (exponential kernel) (Wen et al., 2022). Event intensities are parameterized by Hawkes processes, integrating base intensities, decaying excitation from historical events, and event-conditioned transfer functions.
• Temporal Event Graph (TEG): For event interaction networks, the TEG is a static, lossless, unique DAG whose nodes are events and whose directed edges encode Δt-adjacency. Edges are labeled by inter-event time and motif classes (six possible two-event motifs), which enables motif-distributional, entropy, and behavioral analysis. Lossless inversion ensures that all temporal and structural information is represented without aggregation loss (Mellor, 2017).
• Spatio-Temporal Point Cloud to Grid Transformation: In high-dimensional event data (vision, registration), events are mapped from sparse 3D point clouds (x, y, t) into dense 2D or 3D tensors via local aggregation (spatial-/temporal-first neighbor selection), MLP-based embedding, gated residual fusion, and rasterization. Learned weighting and specialized pooling reconcile the inhomogeneity of spatial versus temporal dimensions (Lin et al., 2023, Yan et al., 3 Aug 2025).
• Space-Filling Curve Aggregation (OmniEvent): Scalable batch-wise event processing exploits space-filling curve mappings (Hilbert, Z-order) to efficiently group neighbors in spatial, temporal, or spatio-temporal domains, enabling hierarchical receptive field growth and locality preservation in grid tensorization, without manually-tuned S-T distance weighting (Yan et al., 3 Aug 2025).

4. Temporal Relation Extraction, Classification, and Temporal Knowledge Graphs

Natural language processing and structured knowledge approaches require temporal event representations that support fine-grained relation classification, uncertainty modeling, and global consistency:

• Dynamic Event Representations for Temporal Relation Extraction: Event mentions are embedded (e.g., via BERT), then dynamically updated as recurrent neural networks walk chains of temporal links. Per-TLINK representations concatenate updated source embeddings with target, and classifier heads for event–event, event–time, and event–DCT categories are trained in multi-task fashion (Cheng et al., 2023).
• Joint Event–Relation Extraction via Structured Prediction: Shared context encoders (e.g., BiLSTM-BERT) feed both event unary and relation pair scorers; global ILP inference over event and relation variables, enforcing event–relation consistency and temporal transitivity constraints via structured SVM loss, achieves consistent, error-propagation-resistant predictions (Han et al., 2019).
• Unified Quadruple for Time Anchors: Events are temporally anchored as quadruples: $((b_e, b_l), (e_e, e_l))$ (earliest/latest start and end), subsuming single-day/multi-day and certain/uncertain cases. Temporal relations decompose into four sub-level endpoint relations, each classified via mention-attention LSTMs and grouped cross-entropy loss for multi-label output (Cheng et al., 2020).
• Temporal Knowledge Graphs (EventKG): Events/entities constitute nodes with time intervals, and temporal relations are reified as n-ary nodes with subject, object, and time span, leveraging semantic web ontologies (SEM, RDF, OWL) for canonical, cross-source, multi-lingual representation. Temporal queries, timeline extraction, and provenance-driven biographical timeline synthesis are built on fused, interlinked temporal facts (Gottschalk et al., 2019, Gottschalk et al., 2018).

5. Probabilistic and Logical Temporal Reasoning

Temporal event representations underpin advanced temporal reasoning in both probabilistic and logical frameworks:

• Continuous-Time Probabilistic Graphical Models: Causal Probabilistic Networks encode event occurrence times either as sequences of (state, sojourn-time) variables (semi-Markov) or as real-valued date nodes, with causal/inhibitory/competitive influences mediated by delay kernels and auxiliary ("instrumental") nodes. Joint distributions are factored via inter-event kernels, and both representation and learning (MLE, EM) handle multiple time scales and structured delay relations (1304.1493).
• Logic-Based Complex Event Processing and Interval Algebra: Temporal event specification languages (e.g., Phenesthe) admit (i) instantaneous event predicates, (ii) state predicates (on maximal intervals), and (iii) dynamic interval phenomena with full Allen's interval algebra (before, overlaps, meets, starts, finishes, contains, equals). Declarative semantics over time-points and intervals, formal EBNF syntax, and single-pass CEP execution enable efficient monitoring of complex temporal patterns (Pitsikalis et al., 2021).

6. Cross-Domain Applications and Impact

Temporal event representation models are foundational across domains:

• Event-Based Vision: Frame-based deep networks process event streams via compact, information-rich representations (TBR, Spike-TBR, MET) that bridge asynchronous, sparse inputs and dense, synchronous architectures for action recognition, semantic segmentation, motion deblurring, and 2D–3D registration (Innocenti et al., 2020, Magrini et al., 5 Jun 2025, Yao et al., 2 May 2025, Lin et al., 2024, Lin et al., 2023).
• Temporal Knowledge Synthesis and Timeline Generation: Fused temporal KGs with provenance, coverage-driven fusion, and distant supervision enable reliable extraction, ranking, and biographical timeline construction from noisy, heterogeneous sources (Gottschalk et al., 2019).
• Event Stream Sparsification and Efficiency: Plug-and-play modules (PSTTS) exploiting spatio-temporal event density and continuity prune redundant tokens, yielding substantial computational savings with minimal loss of accuracy, scaling to contemporary transformer, SSM, and vision-language architectures (Zhao et al., 26 Sep 2025).
• Prediction in Clinical, Financial, and Social Contexts: Deep temporal point process models for event sets leverage contextual embeddings, position/time encodings, and Transformer-based joint modeling of "what/when" for accurate, scalable prediction in settings where multiple events occur simultaneously in continuous time (Dutta et al., 2023).

7. Comparative Summary of Methods and Trade-offs

Representation	Temporal Resolution	Type	Structural Support	Losslessness	Task/Domain
TBR / Spike-TBR	μs–ms (Δt, N)	Frame-based	Pixels/patches	Yes (≤Δt)	Vision, gesture
Voxel/Point Fusion	MS/μs (hybrid)	Grid + points	2D grids, point clouds	Partial	Deblurring
Temporal GNN (TREND)	Event-level	Node/Edge graph	Dynamic graphs	Parametric	Inductive graph learn
TEG	Event/Δt-adjacent	DAG	Events/motifs	Yes	Network science
EventKG (TKG/SEM)	Time intervals	RDF graph	Entities/relations, n-ary	Yes	KGs, QA, timeline
Mention-attn LSTM	Textual mentions	Seq/classifier	Document events/timexes	Statistical	NLP/IE
PSTTS, TA-SNN	Token/frame-level	Accel. sparse	Patches/tokens	Adaptive	Efficient vision
Probabilistic Graph	Continuous	CPN, TPP	Causal dependency	Stochastic	Reasoning/prediction
Logical (CEP/Allen)	Point/interval	Predicate logic	Events, states, intervals	Declarative	CEP, monitoring

Each approach reflects trade-offs among temporal precision, scalability, structural richness, and the feasibility of recovering event timing, provenance, and interactions. Lossless methods (TBR, TEG, KGs with full intervals) guarantee precise recovery up to binning scale, while others (deep event embeddings, attention-based neural models) prioritize semantic and predictive adequacy in data-rich domains.

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Temporal event representation has matured into a multidimensional discipline, anchored in precise mathematical foundations and informed by advances in neural, logical, and knowledge-based methods. Its centrality is underscored by the proliferation of high-bandwidth event sources and the growing demand for temporally-aware learning, inference, and decision support across scientific and engineering fields.