Temporal Redundancy Scoring

• Temporal Redundancy Scoring is a suite of methods that quantifies repetition in sequential data by assigning scores based on incremental information gain relative to previous segments.
• It employs both explicit approaches (e.g., n-gram overlap and cosine similarity) and implicit, adaptive strategies (e.g., dynamic programming and reinforcement learning) to penalize redundancy.
• This methodology has key applications in summarization, video/speech processing, time-series analysis, and dataset curation, driving improved computational efficiency and content clarity.

Temporal redundancy scoring refers to the suite of principled methods for quantifying, penalizing, and adaptively controlling the repetition or lack of novelty in data or model outputs across the temporal dimension. This concept is central to domains such as extractive summarization, video and speech processing, knowledge retrieval, and active dataset curation. The primary objective is to distinguish between necessary information—such as core updates or salient events—and information that is repeated, superfluous, or already accounted for in prior temporal segments. State-of-the-art approaches leverage explicit surface feature overlap (e.g., n-grams), information-theoretic functionals (e.g., transfer entropy), statistical or deep feature similarity, and optimization-driven policies to measure and manipulate redundancy over time, enabling improved efficiency, informativeness, and clarity of output.

1. Core Principles and Definitions

Temporal redundancy scoring is grounded in the observation that sequential data often contains high degrees of repetitiveness due to process-inherent dynamics (e.g., static video frames, repeated sentences, or steady-state audio). Redundancy can be formally quantified either at the syntactic/lexical level (n-gram, token, patch similarity) or at the semantic/information-theoretic level (e.g., mutual information, transfer entropy across time). The central task is to assign each candidate data item, model output, or feature a scalar “redundancy score” representing its incremental information gain relative to previously processed temporal segments.

Explicit approaches often use measures such as

• N-gram overlap: $$f_{n\text{-}gram}(s_i) = \frac{|n\text{-}gram(selected) \cap n\text{-}gram(s_i)|}{|n\text{-}gram(s_i)|}$$
• Semantic similarity: $$f_{sem}(s_i) = \max_{s_j \in selected} \operatorname{cosine}(emb(s_i), emb(s_j))$$

Causal and information-theoretic formulations—prevalent in time-series analysis—utilize transfer entropy (TE): $$\mathrm{TE}(X \rightarrow Z) = I(X^{n-1}; Z_n | Z^{n-1})$$ to quantify the predictive contribution of a source signal $X$ to a target $Z$ in the presence of temporal structure (Østergaard, 1 May 2024).

2. Methodologies for Redundancy Scoring

Redundancy scoring methodologies can be categorized along several axes:

A. Implicit vs. Explicit Scoring:

• Implicit scoring integrates redundancy into the model objective by using the model’s internal state or context, as in ARedSum-Seq, which trains a decoder to select sentences by optimizing marginal ROUGE gain (Bi et al., 2020).
• Explicit scoring employs dedicated features (n-gram overlap, cosine similarity) as in ARedSum-Ctx (Bi et al., 2020) or direct penalization of similar candidate pairs in the loss function (Xiao et al., 2020).

B. Position in the Pipeline:

• During scoring: Sentence or feature importance is penalized if similarity to already selected elements is high (e.g., RdLoss: $$L_{rd} = \sum_{i,j} P(y_i)P(y_j)\operatorname{Sim}(s_i, s_j)$$ (Xiao et al., 2020)).
• During selection: Maximal Marginal Relevance (MMR) or variants select the element with the best tradeoff between informativeness and non-redundancy (Xiao et al., 2020).

C. Adaptive and Temporal Policies:

Policy-driven methods adapt the threshold for redundancy dynamically—e.g., VA-RED² leverages a soft-modulation gate to select which temporal (and channel) features to compute or reconstruct per input video (Pan et al., 2021). Eventful Transformers compute per-token errors across frames, only reprocessing those tokens with significant change and thus scoring temporal redundancy at the token level (Dutson et al., 2023).

D. Optimization and Dynamic Programming:

In speech codecs (CodecSlime), ScheDFR formulates redundancy scoring as a segmentation optimization problem, merging frames where intra-segment feature L₂ distance is minimal (Wang et al., 26 Jun 2025). Dynamic programming solves for optimal downsampling that balances information preservation and redundancy elimination.

3. Redundancy Scoring in Key Application Domains

Domain	Redundancy Scoring Approach	Impact/Objective
Summarization	N-gram/semantic overlap; marginal gain via ROUGE	Informative, non-repetitive summaries
Video/Speech	Patch/feature similarity, token gating, dynamic segmentation	Reduced FLOPs, real-time inference
Time Series	Transfer entropy, minimal sufficient statistics, durability	Identification of persistent, unique events
Dataset Pruning	Temporal dual-depth scoring of per-example contributions	Better data subset for generalization
Retrieval QA	Time-anchored entities, temporal subgraph decomposition	Non-redundant, temporally accurate answers

For example, in video models, VA-RED² reduces computation by reconstructing temporally redundant features with linear operations, achieving 20–40% FLOP reductions without accuracy loss (Pan et al., 2021). In neural speech coding, dynamic frame rate merging reduces wasted tokens on steady-state regions, improving both word error rate and bitrate efficiency (Wang et al., 26 Jun 2025).

4. Algorithmic and Optimization Frameworks

Algorithmic strategies for temporal redundancy scoring exploit temporal structure for efficiency and informativeness.

• Dynamic Programming for Segmentation: CodecSlime defines a surrogate score $$\mathcal{J}_h(h, s) = -\sum_{i=1}^{T'} L(\sigma_i, s_i)$$ where $L(j,s)$ measures segment internal dispersion (Wang et al., 26 Jun 2025). Backtracking the DP table identifies which temporal segments can be merged.
• Durability Queries: In rank-oriented time series scoring, durable top-$k$ queries use sliding or adaptive windowing to retain records with persistent prominence over time, with worst-case complexity $O((|S| + k\lceil I/\tau \rceil) (q(n) + k)\log n)$ (Gao et al., 2021).
• Redundancy-Penalized Losses: Summarization systems incorporate penalties for high-similarity pairs, and RL-based reward structures compute differences in ROUGE or other metrics between baseline and redundancy-managed outputs (Xiao et al., 2020).
• Token Gating and Sparse Attention: Eventful Transformers select tokens for update via thresholding per-token change magnitudes, and perform delta-based attention updates for efficiency (Dutson et al., 2023).

5. Empirical Evaluation and Metrics

Metrics for evaluating temporal redundancy include:

• ROUGE and Unique n-gram ratio: Quantifies redundancy in extractive summarization. Higher unique n-gram ratio, lower normalized inverse diversity (NID), and higher ROUGE scores are indicative of improved redundancy handling (Xiao et al., 2020).
• FLOPs/Inference Time: Measures total computation in video/audio models before and after temporal redundancy reduction (Pan et al., 2021).
• Word Error Rate (WER), STOI, PESQ: Speech codec quality under varying frame rate compression (Wang et al., 26 Jun 2025).
• Durability Window Coverage: Expected size $E[|S|] = kI/(\tau+1)$ for durable top-$k$ time series records; output-sensitivity validated experimentally (Gao et al., 2021).
• Human Judgments/Bespoke Conciseness/Redundancy Metrics: In walking assistants, Temporal Redundancy F1 (TRF) and GPT-based scorers are deployed (Li et al., 22 Aug 2025).

Strong empirical findings include 20-40% compute reductions in VA-RED² without loss in video recognition accuracy (Pan et al., 2021), 46% reduction in speech codec reconstruction WER at constant bitrates (Wang et al., 26 Jun 2025), and more concise, contextually relevant outputs in Walking Assistant VLMs (improved TRF, ROUGE, and GPT Score) (Li et al., 22 Aug 2025).

6. Extensions to Causal, Multi-Source, and Knowledge-Intensive Contexts

Advanced approaches extend redundancy scoring from heuristics and direct overlaps to general causal and multi-source frameworks. The notion of “directed redundancy” in time series is formalized by bounding redundant information transfer using transfer entropy and minimal sufficient statistics—a strategy that generalizes to multiple, partially overlapping sources by introducing a hidden redundancy process to explain common information (Østergaard, 1 May 2024). Similarly, knowledge-intensive retrieval-augmented systems decompose temporal queries and assemble time-specific subgraphs to mitigate the risk of aggregating stale or repeated information (Li et al., 3 Aug 2025).

ReTaKe’s dual-module approach combines inter-frame distance-peak keyframe selection and adaptive KV cache pruning in LLM-based video understanding, targeting both low- and high-level temporal redundancy to allow long video processing with minimal accuracy drop and significantly reduced latency (Wang et al., 29 Dec 2024).

7. Practical Implications and Future Challenges

Effective temporal redundancy scoring enables:

• Summarization systems that flexibly balance informativeness and non-redundancy across evolving document streams or news events (Bi et al., 2020, Xiao et al., 2020).
• Efficient video and speech models achieving real-time operation on resource-constrained devices, by adapting computation to content dynamics (Pan et al., 2021, Wang et al., 26 Jun 2025, Dutson et al., 2023).
• Reliable extraction of temporally persistent records or facts in time series and knowledge graphs, with utility in scientific, financial, and knowledge-intensive applications (Gao et al., 2021, Li et al., 3 Aug 2025).
• Robustness and generalization in active dataset selection and pruning, through temporal dual-depth scoring of training dynamics (Zhang et al., 2023).

Key challenges include scaling memory for long-range sequence tracking, adaptively tuning trade-offs between novelty and coverage, and generalizing redundancy scoring across data modalities and application domains. Some papers suggest unified frameworks for redundancy detection and adaptive model architectures as promising directions (Huang et al., 2022, Wang et al., 26 Jun 2025). The field continues to evolve toward methods that embed temporal signals directly into learning and retrieval pipelines, balancing efficiency with completeness and preserving critical information amid highly redundant sequential inputs.