Temporal RoPE Interpolation Techniques

• Temporal RoPE Interpolation is a set of methods that extend rotary positional encoding to support arbitrary, non-integer, and out-of-distribution temporal positions.
• It employs techniques such as linear scaling and frequency-aware adjustments (e.g., Resonance RoPE) to mitigate phase misalignment and maintain stable attention in long-context models.
• Applications span language models, video generation, and temporal knowledge graphs, enhancing performance metrics like perplexity, fidelity, and retrieval accuracy.

Temporal RoPE Interpolation is a collection of methodologies and theoretical formulations designed to extend, refine, or generalize the temporal positional encoding capacity of large-scale neural sequence models—especially those based on Rotary Position Embedding (RoPE)—to effectively interpolate and extrapolate temporal positions. The concept applies not only to LLMing in long-context LLMs but also to structured data such as video and temporal knowledge graphs. The core principle involves adapting or interpolating positional encoding structures so that models can represent or generate sequence elements at arbitrary or out-of-distribution (OOD) temporal positions, often beyond the regime on which models were originally trained.

1. Fundamental Principles of Temporal RoPE Interpolation

Rotary Position Embedding (RoPE) encodes absolute or relative positions using complex-valued rotations in each 2-dimensional subspace of the embedding dimension. For position $m$ and subspace frequency $\theta_j$, RoPE assigns a position-dependent rotation: $\exp(i m \theta_j)$. In its original design, RoPE ties feature phases to integer-valued position indices, producing well-aligned features only for in-distribution (ID) positions. Dependencies between phases, sequence length, and model generalization capacity become especially apparent in “train-short-test-long” (TSTL) scenarios.

Temporal RoPE Interpolation specifically addresses two mathematical and practical concerns:

• For long-context extrapolation, as $m$ increases past the maximum value $L$ seen at training, standard RoPE features become misaligned and phase-wrapped, producing sharp interpolation gaps for non-integer or OOD positions.
• For applications demanding arbitrary, non-integer, or continuous temporal positions (as in generative video interpolation or flexible video conditioning), the conventional integer-based positional rotation lacks sufficient granularity and adaptability.

Interpolative strategies can involve: (i) compressing or scaling position indices, (ii) warping or rounding frequencies, or (iii) explicitly encoding fractional or timestamp-based positions in RoPE. These methods allow models to produce robust temporal features, maintain stable attention score magnitudes, and enable flexible conditioning or frame synthesis in unseen or undersampled temporal regimes.

2. RoPE Interpolation Methods in LLMs

A key driver for temporal RoPE interpolation research is the effective extension of context windows in LLMs without additional retraining. Standard RoPE-based attention mechanisms degrade when exposed to sequence lengths exceeding those encountered during training. Two major methodologies address this:

• Linear Position Interpolation: When sequences at inference are longer than the training context ($L' > L$), positions $p$ in $[0, L' - 1]$ are “compressed” or scaled by $p' = p \cdot (L / L')$. This keeps the input to the rotary phase computation within the same operational regime, mitigating attention instability by avoiding excessive phase wrapping. For Attention with Linear Biases (ALiBi), the analogous process is to dynamically scale the per-head attention slope: $m'_j = m_j (L / L')$ for $L' > L$, which maintains the relative impact of each token as the sequence stretches. This method substantially improves perplexity and retrieval/ROUGE scores for LLMing, summarization, and long-context retrieval, enabling effective extrapolation to 2$\times$ the original context length without retraining (Al-Khateeb et al., 2023).
• Frequency-Aware and “Snapped” Interpolation (Resonance RoPE): Classic RoPE frequencies correspond to non-integer wavelengths, introducing an alignment discontinuity (interpolation gap) at OOD token positions. Resonance RoPE refines all subspace frequencies by rounding each wavelength $\lambda_j = 2\pi / \theta_j$ to its nearest integer, then recomputing the angular frequency as $\tilde{\theta}_j = 2\pi / \text{round}(\lambda_j)$. This ensures exact feature repetition for pre-critical (stable) dimensions across both ID and OOD positions, thus fully bridging the interpolation gap for positions longer than seen at training. The method’s offline implementation guarantees no runtime cost, and empirical measurements indicate lower long-sequence perplexity and improved OOD accuracy for models across LLMing and long-text tasks (Wang et al., 29 Feb 2024).

The following table summarizes the principal RoPE Interpolation formulations:

Formulation	Key Operation	Effect on Extrapolation
Linear PI	$p' = p \cdot (L / L')$	Compresses positions for stable handling at long context
Resonance RoPE	$\theta_j \leftarrow 2\pi/\text{round}(\lambda_j)$	Eliminates phase misalignment at OOD positions
Frequency-aware scaling	Band-wise $f(p)$ adaptation	Reduces aliasing and phase sensitivity in high-ω bands

3. Temporal RoPE Interpolation in Video and Multimodal Models

Temporal RoPE Interpolation extends beyond text to video, where frames are indexed over one or more spatial and temporal axes. Challenges unique to video include spatiotemporal structure retention, positional bias mitigation, and seamless cross-modal token alignment.

Notable advances include:

• VRoPE (Video Rotary Position Embedding): VRoPE generalizes RoPE for video by mapping spatial $(w, h)$ indices through a spatial rotation, then generating symmetric coordinate pairs $(u_+, u_-, v_+, v_-)$ for robust, bias-mitigated attention. Tokens are assigned temporal and spatial indices that preserve both locality and smooth transition across modalities (e.g., video → text). This structure supports robust temporal reasoning, enhances understanding at long temporal spans (up to 1216 frames), and provides smooth cross-modal interpolation (Liu et al., 17 Feb 2025).
• Timestamp-aware RoPE (TaRoPE) for Arbitrary Video Interpolation: For generative video interpolation, models such as ArbInterp redefine temporal RoPE to operate over continuous, normalized timestamps: for an inter-frame interpolation at position $t$, set $t = (k-1)/(N-1)$ for $k$ out of $N$ total frames, replacing integer $k$ directly in the RoPE angular computation. This allows generation at arbitrary intermediate positions and supports fine-grained temporal control, segment-based synthesis, and hierarchical multi-step interpolation for very long sequences (Zhang et al., 1 Oct 2025).
• Temporal RoPE Interpolation in VideoCanvas: Highly flexible video completion as formulated in VideoCanvas demands the alignment of arbitrary user-provided patches or frames at any possible timestamp with the latent representation processed by the model. Here, each conditional token is assigned a fractional temporal RoPE position according to $pos_t(z_{\text{cond},i}) = t_i / N$ (where $N$ is the VAE stride). Applied in their 3D RoPE DiT backbone, this mechanism delivers segment-level, pixel-frame temporal alignment and leads to superior per-frame fidelity and dynamics (Cai et al., 9 Oct 2025).

4. RoPE Interpolation Under Quantization and Practical Deployment

Applying RoPE-based interpolation (PI) in combination with post-training quantization (PTQ) for real-time or resource-limited deployment introduces complex interactions, manifesting as aliasing, dynamic range dilation, anisotropic axis grid distortions, and outlier shifting in the representation space. These effects collectively produce position-dependent logit noise and degrade accuracy.

Q-ROAR addresses these failure modes by:

• Grouping RoPE dimensions into a small number of frequency bands.
• Optimizing per-band rescaling factors $g_b$ for the $W_Q, W_K$ projections using diagnostics based on Interpolation Pressure and Tail Inflation Ratios—metrics directly measuring phase scaling sensitivity and distributional tail inflation from short to long contexts, respectively.
• Employing either “shared” or “symmetric” rescaling (the latter to maintain logit scale).

A lightweight grid search using a tiny development set suffices to recover up to 0.7% accuracy and reduce perplexity by more than 10% on long-range tasks, while requiring no retraining or changes to existing inference kernels or quantization schemes (Qiao et al., 17 Sep 2025).

5. Applications in Temporal Knowledge Graphs and Symbolic Reasoning

While rotary-based methods remain less common in temporal knowledge graph (TKG) interpolation, the general challenge—interpolating missing facts (edges) at arbitrary timestamps—parallels temporal RoPE interpolation in sequence models. The Temporal PAth-based Reasoning (TPAR) model proposes a recursive, neural-symbolic path-aggregation methodology, where temporal evidence is fused using flexible, periodic, and non-periodic relative time encodings. This allows for robust inference of missing (interpolated) edges even with ambiguous timestamps and enables downstream extrapolation after initial history completion (Chen et al., 28 May 2024).

6. Benchmarks and Empirical Impact

Multiple synthetic and real-world benchmarks are used to evaluate the effectiveness of temporal RoPE interpolation strategies:

• PosGen Benchmark (Resonance RoPE): Designed to isolate the influence of OOD position recognition from the inherent difficulty of long-context token generation, PosGen includes recursive, chain-of-thought, and semi-recursive tasks. Resonance RoPE achieves strong and robust OOD accuracy, narrowing the TSTL generalization gap without additional computational cost (Wang et al., 29 Feb 2024).
• MultiInterpBench (ArbInterp): Tests arbitrary-length video interpolation scenarios (2$\times$–32$\times$), quantifying fidelity (FID, LPIPS, CLIP), subject consistency, and temporal smoothness. Timestamp-aware RoPE consistently outperforms fixed-index and integer-only strategies, delivering improved consistency and dynamism (Zhang et al., 1 Oct 2025).
• VideoCanvasBench: Evaluates arbitrary spatiotemporal completion scenarios, tracking per-frame PSNR and dynamic degree for various temporal conditioning strategies. Temporal RoPE Interpolation delivers the highest peak PSNR at target frames and preserves motion, in contrast to alternatives that produce motion collapse or misalign temporal peaks (Cai et al., 9 Oct 2025).
• Long-Context Language/Document Tasks: For LLMs, Position Interpolation in RoPE and ALiBi extends stable perplexity and improves question answering retrievability well beyond baseline capacities, sometimes nearly doubling summary ROUGE scores in long-context summarization (Al-Khateeb et al., 2023).

7. Implications, Limitations, and Future Directions

Temporal RoPE Interpolation radically expands the practical expressivity and generalization of position-encoding-based models across modalities and contexts. By enabling both interpolation (precise frame generation, patch-based conditioning) and extrapolation (long-range language and retrieval tasks), these methods eliminate several bottlenecks of fixed-index encodings.

Key implications and future directions include:

• The extension to other modalities with complex temporal or spatiotemporal structure (audio, 3D/4D data).
• Theoretical refinement of interpolation strategies, such as incorporating learned, non-linear, or probabilistic position mappings.
• Robust handling of edge-cases such as extreme quantization or rapidly-changing context adaptation.
• Further integration of temporal interpolation with downstream applications, such as streaming, video editing, and knowledge graph completion—potentially even without further learning.

Ongoing challenges include managing phase aliasing and feature collapse in extreme long-context regimes, aligning compositional spatiotemporal encodings in cross-modal tasks, and ensuring efficient and robust implementation under various hardware and deployment constraints. The methodological toolkit provided by recent advances in temporal RoPE interpolation is now foundational to modern long-context neural sequence processing and generative modeling.