Temporal Range: Concepts & Applications

• Temporal range is a fundamental concept defining the interval or window over which time-stamped data, events, or algorithmic dependencies are evaluated.
• It is implemented using specialized data structures and algorithms in databases, signal processing, and machine learning, balancing precision with computational cost.
• Its practical applications span neuroscience, video analysis, and physical sensing, enabling quantifiable improvements in performance and system robustness.

Temporal range is a foundational concept in the modeling, analysis, and processing of time-stamped data, signals, and high-dimensional temporal features. The term denotes either an explicit interval on the timeline, a window over past or future data points, or, more abstractly, the extent of temporal dependencies leveraged by algorithms or physical systems. Temporal range is central in diverse fields including temporal databases, signal processing, neuroscience, reinforcement learning, and computer vision, with distinct formalizations appropriate to each research domain.

1. Core Definitions and Formal Expression

Temporal range typically refers to either (a) a window or interval within the time domain, or (b) the set of timestamps over which an event, relation, or algorithm expresses sensitive dependence. In databases, it is operationalized as an interval $[t_s, t_e)$ over a discrete, totally-ordered set $\mathbb{T}$—the time domain. For a timestamped tuple $r$, one defines its interval attribute $r.T = [r.T_s, r.T_e)$ and its duration $|r.T| = r.T_e - r.T_s$ (Ceccarello et al., 2022). Temporal range also emerges as a parameter in models of uncertain time intervals, where it is described by both possible and reliable bounds, e.g.,

$$\text{UTI}\;w = \{ \hat{I} \mid w_p^b \leq \hat{I}^b \leq w_r^b \;\wedge\; w_r^e \leq \hat{I}^e \leq w_p^e \}$$

(Sekino, 2019), encoding the ambiguity of "when" an interval truly starts or ends.

In learning-based systems and analysis of memory or correlation, temporal range is quantified either as the index lag between useful timestamps, as in recurrent models or temporal convolutions (e.g., number of frames or steps $N$ to which a model is sensitive), or via influence measures such as the magnitude-weighted average lag $\hat\rho_T$ computed from policy Jacobians in RL (Lafuente-Mercado et al., 5 Dec 2025).

2. Data Structures and Algorithms Exploiting Temporal Range

Efficient exploitation of temporal range for querying or modeling requires tailored data structures and algorithms. In temporal databases, the RD-index (Ceccarello et al., 2022) provides a two-dimensional grid indexing intervals by $(\text{start\_time}, \text{duration})$, allowing range queries, duration queries, and their conjunction. Partitioning leverages quantile-based subdivision:

• Columns split by start time into $p \approx n / s^2$
• Cells within columns split by duration into $q \approx s$

Query algorithms perform binary search over these partitions and return all intervals $r$ with $r.T \cap t \neq \emptyset$ and $|r.T| \in [d_{\min}, d_{\max}]$, offering worst-case reporting bounds

$$O \left( \frac{n}{s^2} \log \frac{n}{s} + \frac{n}{s} + s^2 + k \right)$$

for $n$ intervals, page size $s$, and $k$ outputs.

For fuzzy or uncertain temporal ranges, retrieval reduces to boundary comparisons over all 13 Allen interval relations. Closed-form conditions for each relation (before, overlaps, contains, etc.) yield efficient match classification among reliable, impossible, or possible (Sekino, 2019). These are used for metadata systems and historical event modeling.

3. Temporal Range in Signal Processing and Neural Dynamics

Temporal range is reflected in the timescale of correlations in dynamical neural systems (Meisel et al., 2017, Mozaffarilegha et al., 2019). Quantification uses:

• Autocorrelation decay constant $\tau$ for exponential short-range ($R(\Delta t)\sim e^{-\Delta t/\tau}$)
• Power-law decay exponent $\alpha$ for long-range ($R(\Delta t)\sim\Delta t^{-\alpha}$)
• Hurst exponent $H$ for fractal signals ($H=h(2)-1$ via MFDMA (Mozaffarilegha et al., 2019))

Measured values for neural timescales show a dichotomy: long temporal range with large $\tau$ ($300$–$500$ ms) dominates awake and REM states, while short timescale $\tau\lesssim100$ ms typifies NREM sleep. In brainstem-evoked potentials, $H=0.77\pm0.12$ reflects robust long-range correlation even at subcortical levels, with multifractality ($h(q)$ varying with $q$) confirming broad temporal integration.

4. Temporal Range in Learning, Aggregation, and Memory

Optimally modeling or leveraging temporal range is crucial in learning-based video, RL, and spatio-temporal systems.

• Action recognition and detection: Structured state-space models (MambaTAD) and temporal adapters (LoSA) fuse features over short and long temporal ranges in video backbones (Lu et al., 22 Nov 2025, Gupta et al., 2024). Bidirectional scans, diagonal masking, and gated fusion aggregate both fine-grained and global cues, enhancing temporal action detection and localization. Temporal pyramids (spanning/recent banks) and max-pooling aggregate context for next-action anticipation and segmentation (Sener et al., 2020).
• Video super-resolution/compression: Recurrent architectures exploit long-range hidden states and temporal priors to enable inference over $\gg10$ frames. Training strategies such as truncated backpropagation allow models to use temporal propagation features over long clips with low memory cost (Zhou et al., 4 May 2025). In learned video compression, hierarchical temporal prior buffers and multi-scale motion compensation jointly encode both long- and short-range dependencies, leading to large rate–distortion gains (Wang et al., 2022).
• Traffic forecasting and dynamic texture synthesis: Multi-filter convolutions, Transformer masking, and multi-range aggregation modules allow learning systems to zoom in on fine-grained cycles while integrating trends over tens to hundreds of steps (Zou et al., 2023). Sampling motion at multiple frame intervals and matching long-range spatial correlations extend the model’s temporal receptive field for dynamic textures (Zhang et al., 2021).

Explicit metrics for temporal range, such as $\hat\rho_T$ computed from RL policy Jacobians (Lafuente-Mercado et al., 5 Dec 2025), enable quantitative comparison of memory usage and inform model design (e.g., optimal window sizes).

5. Trade-Offs, Limits, and Practical Guidelines

Optimal exploitation of temporal range entails trade-offs:

• Capacity versus computational cost: Attention-based schemes scale quadratically with the size of the temporal window in memory banks, limiting the practical range. Low-rank memory bases via incremental SVD (MeMSVD) reduce both complexity and memory by an order of magnitude while sustaining accuracy for minute-long contexts (Ntinou et al., 2024).
• Model stability versus generality: Overly long ranges may introduce noise or temporal mis-alignment, especially for fast-evolving patterns, while too short ranges lead to loss of global coherence.
• Aggregation granularity: Multi-range modules (video dehazing, traffic prediction) empirically show best performance with three temporal ranges (e.g., $t-1$, $t-2$, $t-3$ (Xu et al., 2023)), balancing local accuracy and global stability.

Quantitative gains from extending temporal range are evident in several domains: improved phenotype prediction from fMRI (sex classification $+6.2\%$, fluid intelligence correlation $+0.18$ (Dahan et al., 2021)), action localization (LoSA: $+3.1\%$ mAP THUMOS-14 (Gupta et al., 2024)), compression rate savings (LSTVC: $-35.9\%$ BD-rate PSNR (Wang et al., 2022)), and robustness across RL context ablations (TR-guided window selection retains $>95\%$ return (Lafuente-Mercado et al., 5 Dec 2025)).

6. Advanced Extensions and Physical Interpretation

In radar and physical sensing, temporal range is manipulated using engineered phase modulations. By imposing artificial Doppler-phase profiles on backscattered signals, scatterers can induce range errors proportional to the rate of phase change:

$\Delta R = \frac{c}{2K} \frac{d\varphi}{dt}$

with $K$ the chirp rate, $c$ the speed of light (Kozlov et al., 2022). Range–Doppler coupling signals permit semi-passive deception, whereas conjugate-symmetric waveforms enforce ambiguity-mitigating constraints.

Physiologically, long-range correlation (large $\tau$, $H>0.5$) is associated with critical brain states allowing extended temporal integration, signal accumulation, and enhanced cognitive performance (wake/REM) (Meisel et al., 2017). Breakdown to short-range correlation (NREM sleep) marks functional shifts and network reorganization.

7. Ontologies, Abstraction, and Cross-Domain Relevance

Ontological frameworks such as the HuTime Ontology codify uncertain temporal ranges as recursively defined objects within RDF/OWL standards, supporting complex queries, reliable/possible/impossible match logic, and linkage to calendar resources (Sekino, 2019).

More broadly, temporal range spans pure timestamp intervals, algorithmic sensitivity profiles, spectral/correlational regimes, and windowed data structures (grid partitions, hierarchical convolutional filters, SVD bases). Its explicit modeling and measurement enable rigorous cross-domain applications—from high-frequency signal deception and time-series database indexing to scalable attention in long-term video analysis, memory quantification in RL, and robust spatio-temporal prediction.

References:

(Ceccarello et al., 2022, Sekino, 2019, Lu et al., 22 Nov 2025, Dahan et al., 2021, Meisel et al., 2017, Zhang et al., 2021, Sener et al., 2020, Zhou et al., 4 May 2025, Lafuente-Mercado et al., 5 Dec 2025, Gupta et al., 2024, Wang et al., 2022, Mozaffarilegha et al., 2019, Xu et al., 2023, Zou et al., 2023, Ntinou et al., 2024, Kozlov et al., 2022)