Temporal Prompt Generation and Selection (Tenet)

• The paper presents a novel hybrid encoder–decoder architecture using transformer-based and memory-inspired techniques to integrate temporal cues for enhanced sequence modeling.
• Methodologies include prompt decomposition, temporal graph prompts, and auto prompt selection strategies that optimize time-dependent performance in various domains.
• Key applications span motion forecasting, video segmentation, and dynamic link prediction, showcasing scalable and temporally coherent system design.

Temporal prompt generation and selection refers to algorithmic strategies and architectural principles for integrating temporal information into prompt design, and for evaluating and selecting temporal prompts to improve model performance in time-dependent tasks. Under the label "Tenet," multiple research trajectories converge: representation learning in motion and sequence modeling, task-dependent prompt formulation, memory-inspired prompt fusion, efficient selection mechanisms for context-dependent adaptation, and foundational advances in scalable, temporally coherent systems for vision, language, and multimodal domains.

1. Principles of Temporal Prompt Generation

Temporal prompt generation encodes time-dependent cues—such as observed trajectories, timestamps, neighbor interactions, or semantic event ordering—into prompt representations for downstream tasks. Architectures deploy diverse mechanisms to exploit temporal structure:

• Transformer-based encoding: TENET introduces a hybrid encoder–decoder architecture integrating spatial agent–map features with temporal ordering through self-attention and cross-attention mechanisms. Predicted trajectory features $x_{pt}$ are formed by

$$x_{pt} = \text{SelfAtt}_K(\text{CrossAtt}_{K,M}(x_k, x_m))$$

where $x_k$ are learnable tokens and $x_m$ are agent–map scene embeddings (Wang et al., 2022).

• Prompt decomposition in time series: TEMPO leverages statistical decomposition of input $X$ into trend $X_t$, seasonal $X_s$, and residual $X_r$ components, segmenting each into tokens and concatenating them with task-specific or adapted prompt vectors (semi-soft, hard, or pool-based) (Cao et al., 2023).
• Temporal graph prompts: TIGPrompt formulates a "Temporal Prompt Generator" which, in transformer mode, combines recent neighbor embeddings, edge features, and time-encoded differences to produce temporally aware tokens:

$$t_u = z_v \,\|\, z_u \,\|\, p_u \,\|\, e_{uv} \,\|\, f_\omega(t-t_{uv})$$

where $z_*$ are node embeddings, $p_u$ is a position embedding, $e_{uv}$ is an interaction feature, and $f_\omega$ is a time encoder (Chen et al., 9 Feb 2024).

• Time-varying prompt embedding: In STP4D, textual prompts are encoded and mapped—via MLP—to frame-specific prompt embeddings, which are integrated into Gaussian splatting via cross-attention (Deng et al., 25 Apr 2025).

2. Temporal Flow Headers, Closed-Loop Regression, and Architectural Extensions

Enhancing temporal consistency is critical in sequential decision tasks, such as motion prediction and video segmentation:

• Temporal Flow Header (TENET): An auxiliary module enforces coherence between predicted futures and historical trajectories by regressing backward. Future timestamps $x_f$ extracted from $x_{pt}$ are processed with a Feature Pyramid Network (FPN) and an MLP:

$h_{pred} = \text{MLP}(\text{FPN}(x_f))$

This closed-loop regression encourages the model to learn consistent dynamics by mapping predicted futures to plausible historical patterns, mitigating long-range errors (Wang et al., 2022).

• Temporal Extension Deformation (TED, STP4D): TED "deforms" anchor frame representations via cross-attention to generate temporally interpolated content:

$G^{STP} = \text{C-ATT}(P_G, G^{SP}, G^{SP})$

where $P_G$ is a learnable weight pool and $G^{SP}$ are geometrically enhanced features (Deng et al., 25 Apr 2025).

• Temporal event reasoning: TemPrompt uses masked LLMing over event triggers to focus PLM attention on event-centric cues, with a cross-entropy loss:

$$L_{ter} = -\frac{1}{2} \left\{ \sum \log P(s_j^m|S_{prompt}) \right\}$$

(Yang et al., 21 Jun 2024)

3. Prompt Selection Strategies: Evaluation, Preference Learning, and Optimization

Temporal prompt selection addresses the challenge of identifying prompts that maximize downstream utility (accuracy, coherence, consistency):

• Ensemble methods and clustering: TENET employs multi-model K-means clustering on candidate trajectories, using endpoint distance for grouping and confidence score aggregation to form a robust multi-modal ensemble (Wang et al., 2022).
• Prompt Preference Learning: In RVOS, temporal prompt candidates (tracks generated via object detection and tracking) are evaluated via a transformer-based classifier that processes image and text features $(f^c_i, f^r, f^t)$ for each candidate, optimizing a binary cross-entropy loss on prompt "quality":

$$L_{\mathrm{bce}} = -\sum_{i} \left[ y_{i} \log \sigma(s_{i}) + (1-y_{i}) \log (1-\sigma(s_{i})) \right]$$

with $y_i$ determined by box-level mIoU against the reference (Lin et al., 8 Oct 2025).

• Automatic Prompt Selection (APS): Inputs are clustered, candidate prompts generated per cluster, and a preference-based evaluator trained to rank prompt–input pairs using a Bradley-Terry style loss:

$$\mathcal{L} = -\sum_{(q, c)} \sum_{(\text{good}, \text{bad})} \log \left( E_{\theta}(q, c, p_{good}) - E_{\theta}(q, c, p_{bad}) + \epsilon \right)$$

At inference, prompts are ranked and the best is selected (Do et al., 3 Apr 2024).

• Thompson sampling and bandit-based selection: EvoPrompt-OPTS explicitly manages prompt design strategies with multi-armed bandit algorithms; each strategy is associated with a reward distribution, updated via:

$r = \mathbb{I}[s > \max(\tilde{s})]$

where $s$ measures performance improvement over parent prompts (Ashizawa et al., 3 Mar 2025).

4. Temporal Consistency and Theoretical Guarantees

Temporal consistency—robustness of predictions or segmentations across time—remains a central concern:

• TiARA applies Discrete Short-Time Fourier Transform (DSTFT) to attention maps. A motion intensity metric is defined:

$$\rho_i = \frac{\sum_{k=\phi_1}^{\phi_2-1} |\mathrm{DSTFT}(A_i, \psi, i, k)|^2} {\sum_{k=0}^{\phi_2-1} |\mathrm{DSTFT}(A_i, \psi, i, k)|^2}$$

Diagonal attention reweighting then adapts based on $\rho_i$, with the theoretical guarantee that for target ratio $\eta$, a reweighting parameter $\alpha$ can always be found such that:

$$\limsup_{n\to\infty} E(y, \tau)/E(x, \tau) \leq \eta$$

ensuring bounded high-frequency inconsistency (Li et al., 23 Dec 2024).

• Simulation optimization for dynamic prompt selection: Surrogate models for prompt score are updated sequentially, and acquisition functions guide prompt evaluation. Consistency is proven in the limit of infinite simulation budget (Zhang et al., 12 Apr 2024).

5. Applications Across Modalities and Tasks

Temporal prompt generation and selection methods have demonstrated efficacy in a variety of domains:

Domain	Application	Key Techniques
Autonomous driving	Motion forecasting, trajectory prediction	Transformer encoding, Temporal Flow Header, Ensemble (Wang et al., 2022)
Sequential text	Data-to-text, zero-shot QA, summarization	Textual/linear prompts, automatic prompt selection (Cao et al., 2022, Do et al., 3 Apr 2024)
Time series	Electricity, weather, multimodal prediction	Decomposition, prompt pools, zero-shot transfer (Cao et al., 2023)
Multimodal fusion	Video, text–image classification	Memory-inspired temporal prompt interaction (Yu et al., 26 Jan 2024)
Temporal graphs	Dynamic link prediction, node classification	Temporal prompt generation, fine-tuning paradigm (Chen et al., 9 Feb 2024)
Crowdsourcing TRE	Event extraction, relation reasoning	Cloze prompt construction, auxiliary MLM task (Yang et al., 21 Jun 2024)
Video generation	Scene consistency, prompt blending	DSTFT-based reweighting, prompt alignment (Li et al., 23 Dec 2024, Deng et al., 25 Apr 2025)
Video segmentation	RVOS, referred object segmentation	Temporal prompt candidates, preference learning (Lin et al., 8 Oct 2025)

Efficient adaptation, improved forecasting, enhanced temporal coherence, and scalable transfer to new distributional regimes are notable impacts.

6. Future Directions and Challenges

Persistent challenges and open avenues include:

• Adaptive hybrid prompt schemes: Combining textual and numerical encoding, adaptive selection based on modality and downstream temporal requirements (Cao et al., 2022).
• Robust evaluation metrics: Developing automated and objective metrics for temporal factuality in generative text, segmentations, and dynamics (Cao et al., 2022, Li et al., 23 Dec 2024).
• Memory-inspired approaches: Extending prompt fusion and activation mechanisms to richer hierarchical representations (Yu et al., 26 Jan 2024).
• Online and dynamic prompt updating: Simulation optimization and bandit-style strategy selection offer flexible frameworks for evolving temporal contexts (Zhang et al., 12 Apr 2024, Ashizawa et al., 3 Mar 2025).
• Integration with foundation models: Leveraging powerful pre-trained models via temporal prompt adaptation—especially critical for domains with complex, multimodal, or dynamic input (Lin et al., 8 Oct 2025).

A plausible implication is that future research will integrate temporally adaptive prompt generation and selection into streaming or online learning systems, foundational vision–LLMs, and temporal reasoning in collaborative environments, supported by rigorous analytical guarantees and empirical validation across modalities.