Q-ROAR: RoPE-Aware Quantized LLM Enhancement

• Q-ROAR is a rescaling procedure that stabilizes rotary position embeddings in quantized LLMs by mitigating failure modes during position interpolation.
• It employs diagnostics like Interpolation Pressure and Tail Inflation Ratio to guide a bandwise, weight-only rescaling algorithm without requiring retraining.
• Empirical results show that Q-ROAR recovers up to 0.7 accuracy points and reduces perplexity by 13% at extended contexts while maintaining base performance.

Q-ROAR

Q-ROAR refers to a RoPE-aware, outlier-aware rescaling procedure designed to stabilize rotary position embedding (RoPE) position interpolation (PI) in quantized long-context LLMs by mitigating several failure modes that arise when post-training quantization (PTQ) and PI are combined. The method introduces diagnostics and a targeted, bandwise, weight-only rescaling to improve long-context accuracy and perplexity while maintaining compatibility with existing inference stacks and without necessitating retraining or architectural changes (Qiao et al., 17 Sep 2025).

1. Failure Modes of Position Interpolation under Quantization

Extending the context window of LLMs using RoPE-based position interpolation has enabled processing much longer sequences than training-time limits. However, when these RoPE-PI techniques (such as YaRN or frequency-aware scaling) are deployed on models that have been subjected to post-training quantization (PTQ) for efficient inference, they trigger sharp degradation in long-context accuracy and perplexity. The root causes are four coupled effects:

• Long-context aliasing: High-frequency RoPE dimensions, when interpolated beyond the training regime, can have their periodic phases exceed $2\pi$ and begin to alias into lower-frequency regions, causing systematic misalignments in the relative attention pattern.
• Dynamic-range dilation: Increased phase scaling under PI inflates the dynamic range in the corresponding frequency bands, pushing more values into the quantization tails. This breaks the representational calibration established by PTQ and leads to higher quantizer noise and distorted outlier handling.
• Axis-grid anisotropy: RoPE is a geometric rotation in 2D subspaces, preserving $\ell_2$ norm, but scalar quantizers operate axis-wise. As the rotation angles experience PI-induced warping, axis alignment is lost, and certain axes accumulate disproportionate quantization error, leading to anisotropic grid effects.
• Outlier shifting: Outliers in attention logit activations, which largely determine quantizer scaling, shift in both magnitude and frequency under PI. The PTQ quantizer, calibrated on short-context statistics, either over-clips or saturates these shifted outliers at long context, further increasing logit uncertainty.

Collectively, these effects induce position-dependent attention logit bias and variance, undermining model reliability for long-context applications (Qiao et al., 17 Sep 2025).

2. Diagnostic Metrics: Interpolation Pressure and Tail Inflation Ratio

Q-ROAR introduces two diagnostics that quantify the vulnerability of different RoPE frequency bands under PI+PTQ:

• Interpolation Pressure (IP): For RoPE dimension $i$, the phase under scaling is written as

$$\phi_i^{\mathrm{scaled}}(m) = \omega_i\,\frac{f(m)}{s_i},\quad s_i>0,$$

where $\omega_i$ is the base frequency, $f(m)$ is the PI warp, and $s_i$ is the PI scaling. The sensitivity of phase error to $s_i$ ("pressure") is

$IP_i = \omega_i \frac{f(D)}{s_i^2},$

where $D$ is the maximal extrapolation. High $IP$ in a band indicates high fragility and warrants more conservative rescaling.

• Tail Inflation Ratio (TIR): To estimate how quantization tails expand from short to long context,

$$TIR_i^W = \frac{Q_{|w_i^\top h|,\;\text{long}}(1-\varepsilon)}{Q_{|w_i^\top h|,\;\text{short}}(1-\varepsilon)},$$

where $Q_{X,q}$ denotes the $q$-quantile. Large $TIR$ indicates that clipping/noise associated with PTQ will grow, suggesting scale reduction for robustness.

Diagnosing $IP$ and $TIR$ for each frequency band enables targeted mitigation without retraining (Qiao et al., 17 Sep 2025).

3. Q-ROAR Bandwise Weight-Only Rescaling Algorithm

Q-ROAR applies a bandwise, diagnostics-guided rescaling directly to the query and key weights $W_Q,W_K$ associated with RoPE frequency bands. The procedure is as follows:

1. Partition RoPE dimensions: Split the $2d_{\mathrm{RoPE}}$ coordinates into $B$ log-spaced frequency bands $\{\mathcal{B}_b\}$ (e.g., $B=6$ or $B=8$), pairing adjacent coordinates of similar frequency.
2. Compute per-band diagnostics: For each band $b$, compute $IP_b$ and $TIR_b^W$ from empirical activations under both short-context and PI long-context runs.
3. Define scaling window per band: For each $b$, define allowed scale interval $\mathcal{G}_b = [g_b^{\min},\,g_b^{\max}]$ with

$$g_b^{\max} = 1 + \frac{\tau}{1 + \log (\omega_{b,\mathrm{med}}/\omega_{\min})}, \quad g_b^{\min} = \kappa / TIR_b^W,$$

where $\tau,\kappa$ are hyperparameters.

1. Grid search for optimal scale: On a small long-context dev set, conduct a grid search over candidate $\{g_b\}_{b=1}^B$ in each band/window, targeting minimum perplexity (or other relevant objective) at maximal context length.
2. Projection update: Apply learned $g_b$ to $W_Q^{(b)}$ and $W_K^{(b)}$. Either shared mode ($$W_Q^{(b)}\to g_b W_Q^{(b)}, W_K^{(b)}\to g_b W_K^{(b)}$$) or symmetric mode ($W_K^{(b)}\to g_b^{-1} W_K^{(b)}$) can be used; symmetric mode preserves logit scale exactly.

Q-ROAR does not require any backward gradient or fine-tuning pass and is fully compatible with weight-only PTQ workflows.

4. Empirical Performance and Quantitative Impact

Extensive evaluation on the LLaMA-2-7B architecture and standard long-context benchmarks demonstrates that Q-ROAR:

• Recovers up to 0.7 points of zero-shot accuracy on standard tasks lost under PI + PTQ.
• Reduces GovReport perplexity at 32K context by 13% relative to the RTN W4 baseline.
• Improves WikiText2 perplexity by 0.2 while keeping 4K context accuracy unchanged (ensuring base-context performance is preserved).
• Performs in a fully quantizer-agnostic fashion, supporting RTN, AWQ, and other weight-only PTQ stacks.

The resource demands are modest: diagnostic collection and grid search take 4 GPU hours with two NVIDIA RTX 4090 cards. Only a small dev set of ≈10 documents longer than 60K tokens is needed for tuning (Qiao et al., 17 Sep 2025).

Table: Example Results from Q-ROAR Experiments

Setting	2K	4K	8K	16K	32K
FP16	4.437	4.359	4.329	4.175	6.069
RTN W4	4.544	4.485	4.470	4.485	6.713
AWQ W4	4.489	4.421	4.405	4.414	6.302
Q-ROAR W4	4.444	4.393	4.321	4.181	5.833

At 32K context, Q-ROAR yields a 13% perplexity reduction relative to RTN W4 (Qiao et al., 17 Sep 2025).

5. Integration and Operational Guidelines

Q-ROAR is deployed as a single, weight-only patch at model load time:

• No changes to inference kernel, activations, tokenization, or model architecture.
• Rescaling is applied by a loader script that multiplies $W_Q^{(b)}$ and $W_K^{(b)}$ by the precomputed $g_b$ for each band, as serialized in model metadata.
• Mode selection: If symmetric mode is stable (as determined by grid search), it is preferred for softmax and logit calibration; otherwise, shared mode is used.
• Q-ROAR is fully compatible with any quantizer and does not affect model behavior at short context (since $g_b=1$ when no PI is active).

6. Scope, Limitations, and Broader Context

Q-ROAR addresses the emergent degradation encountered when deploying RoPE-PI with weight-only quantized LLMs in long-context settings, providing a low-friction, robust, and quantizer-agnostic mitigation that systematically targets the most fragile RoPE frequency bands. Principal limitations are inherent to PI/quantization: if sequencing or tokenization patterns produce out-of-distribution activation statistics, no fixed rescaling fully resolves all logit pathologies. The method hinges on good diagnostics coverage of problematic frequency bands, but in practice, a small diverse set of long documents suffices.

Q-ROAR can be seen as a bridge enabling practical long-context inference for quantized LLMs without the prohibitive computational costs of retraining, thereby facilitating domain-specific or resource-constrained deployments of state-of-the-art LLMs (Qiao et al., 17 Sep 2025).