Phase-Aware Quantization Scheme

• Phase-aware quantization schemes are techniques that assign quantization parameters based on detected operational phases or the phase component of signals.
• They use methods like integer linear programming and adaptive codebooks to dynamically optimize bitwidth and improve throughput while reducing memory usage.
• Practical implementations in LLM pipelines and MIMO systems demonstrate up to 2.88× speedup and near-optimal error rates, maintaining accuracy with ultra-low bitwidth models.

Phase-aware quantization schemes encompass algorithmic and representational mechanisms that explicitly leverage the structure or runtime stages (“phases”) of model operation, or exploit the phase (angle) component in signal and weight representations for advanced quantization. Emerging in both large-scale model inference pipelines and signal processing architectures, phase-aware quantization provides tailored bitwidth assignments, optimized codebooks, and dynamic adaptation across operational or spatial domains, yielding significant gains in throughput, memory efficiency, and accuracy retention compared to uniform quantization strategies.

1. Principle and Formal Definition

Phase-aware quantization refers to schemes that assign quantization parameters or discrete values based on explicit detection or modeling of distinct functional phases of operation (e.g., prompt prefill vs. token decode in LLM inference), or according to the phase (in the mathematical sense) of complex-valued weights and signals. Schemes in this family employ phase detection, ordered codebooks, and adaptive allocation of precision or quantization intervals per phase or axis, often via integer linear programming or grouped heuristics.

In distributed LLM serving, phase-aware partitioning distinguishes compute-bound prefill from memory-bound decode stages, allowing mixed-precision quantization per phase to respect latency and memory constraints (Zhao et al., 2024). In signal processing, phase-aware quantization encodes the angle component of complex symbols using tailored bins or roots of unity, with amplitude quantization adaptively grouped by magnitude (Kim et al., 18 Feb 2025, Wang et al., 2 Dec 2025).

2. Pipeline Phase-Aware Quantization for LLMs

Recent advances deploy phase-aware quantization for efficient serving of LLMs on heterogeneous GPU clusters, exploiting the bi-phasic nature of decoder-only inference:

• Prefill (“prompt processing”): Aggregates computation-heavy tasks, storing key/value caches. Latency scales with prompt length, benefiting from higher-precision layers (FP16/INT8) to minimize compute bottlenecks.
• Decode (“token generation”): Marked by repeated, memory-intensive accesses as each token is generated. Here, lower-precision kernels (INT4/INT3) are sufficient, facilitating memory savings and increased throughput without substantial quality loss.

LLM-PQ assigns bitwidths, devices, and micro-batch sizes separately for Prefill and Decode, using a microbatch manager to flag and control operational phases. The partitioning is solved as a mixed-integer program with constraints on layer assignment, device memory, and accuracy (controlled by a scalar $\theta$) (Zhao et al., 2024):

$$\min_{z}\ T_\text{pre} + T_\text{dec} + \theta \sum_{i,b} \omega_{i,b} \sum_j z_{i,j,b}$$

Imposing separate scheduling and cost modeling on phases enables efficient allocation, yielding up to 2.88$\times$ (average 2.26$\times$) throughput improvements and maintaining perplexity within 0.2 of FP16 across OPT/BLOOM models in production clusters.

3. Signal-Level Phase-Aware Quantization and Hybrid Schemes

In multi-antenna relay and MIMO systems, phase-aware quantization exploits the phase and amplitude components of complex baseband signals (Kim et al., 18 Feb 2025, Wang et al., 2 Dec 2025):

• Uniform Phase Quantization (U-PQ): Discretizes the phase $\angle y_i$ into $2^{b_P}$ bins, typically losing amplitude information and saturating performance.
• Uniform Amplitude-Phase Quantization (U-APQ): Spreads bits over both phase and amplitude uniformly but can be memory-inefficient if amplitude distributions are nonuniform.
• Hybrid Amplitude-Phase Quantization (H-APQ): Groups amplitudes by ordering, assigning them to adaptive bins, while phase is quantized uniformly. Trade-off parameter $m$ gives control over amplitude resolution and total bit requirement:

$N_b^{\mathrm{H-APQ}} = b_P N_{\mathrm{R}} + b_A$

H-APQ achieves near-optimal BER at significantly reduced relay memory, with performance saturation of U-PQ eliminated due to preserved amplitude diversity. This mechanism is “phase-aware” in adapting amplitude quantization according to instantaneous envelope rank post phase discretization (Kim et al., 18 Feb 2025).

4. Phase-Aware Quantization-Aware Training (QAT) Workflows

Modern quantization-aware training (QAT), particularly for ultra-low-bit LLM regimes, utilizes phase-aware, multi-stage workflows:

• EfficientQAT (Chen et al., 2024): Employs two consecutive training phases:
  • Block-AP: Block-wise all-parameter QAT; each transformer block is independently optimized for its weights and quantizer, massively expanding the solution space for low-bit quantization.
  • E2E-QP: End-to-end tuning of quantization parameters (step sizes), globally adjusting scale factors across all blocks to harmonize quantization effects and minimize downstream task loss.
• QKD (Kim et al., 2019): Orchestrates three phase-aware stages for quantization-plus-distillation:
  • Self-studying (SS): Pre-distillation warmup of the quantized model alone.
  • Co-studying (CS): Joint adaptation of teacher and student, enhancing teacher quantization-friendliness.
  • Tutoring (TU): Final distillation, fixing teacher and refining student performance.

Phase structuring prevents poor minima, improves feature alignment, and enables ultra-low-bit quantized models (e.g., W3A3) to match or surpass full-precision accuracy (Kim et al., 2019, Chen et al., 2024).

5. Phase-Aware Quantization in Complex-Valued and Widely-Linear Networks

FAIRY2I (Wang et al., 2 Dec 2025) extends phase-aware quantization into complex-valued networks, transforming pretrained real-valued layers via widely-linear reparameterization. Each transformed layer $y = Ux + W\overline{x}$ is quantized using a codebook of fourth roots of unity ($\{1, i, -1, -i\}$), encoding the phase of each complex weight:

• Phase-Quant Function: Projects the phase of $w$ to the nearest codeword, then applies axis-wise scaling for dequantization:

$$Q_{\mathrm{phase}}(w) = s_{\mathrm{re}} \Re[b(w)] + i\,s_{\mathrm{im}} \Im[b(w)]$$

• Recursive Residual Quantization: Decomposes weights as sums of multiple phase-quantized terms to reduce error—enabling multiplication-free inference by representing weights with integer phase codes and two scaling factors per group.

Key results on LLaMA-2 7B show that 2-bit phase-aware quantization matches or outperforms all real-valued 2-bit and ternary/binary baselines, closing most of the gap with FP16 in both perplexity and zero-shot accuracy. Implementation requires only code index and scale storage per group, with forward passes relying on adds and sign flips rather than multiplies (Wang et al., 2 Dec 2025).

6. Practical Impact and Experimental Results

Phase-aware quantization yields measurable improvements in efficiency and accuracy for both model serving and signal processing:

Scheme/Model	Throughput/Accuracy Gain	Memory Benefit	Benchmark Domains
LLM-PQ (OPT-66B, 4×T4+2×V100)	2.34× speedup, PPL held to <0.2 of FP16	Works on DRAM-scarce nodes	LLM Inference
EfficientQAT (Llama2-70B, 2b)	<3-point acc. degradation at 41h/80GB-A100	Sub-3% loss at INT2	LLM Compression
QKD (W3A3 ResNet-32)	Surpasses FP acc. (72.2% vs 70.8%), consistent improvement	Ultra–low–bit models	Vision Models
H-APQ ($N_R=8$, $m=2$)	BER matches U-APQ, saves 20 bits at relay	Significant memory savings	Relay/MIMO Systems
FAIRY2I (LLaMA-2 7B W2)	62% zero-shot accuracy, PPL=7.85 (near FP16), outperforms AQLM	Multiplication-free inference	Complex LLMs

Implementation conventions emphasize phase-aware allocation of bitwidth and quantizer parameters, grouped or block-wise minimization, and hybrid heuristic search for partition and quantization in distributed environments (Zhao et al., 2024, Wang et al., 2 Dec 2025, Chen et al., 2024).

7. Extensions, Limitations, and Future Directions

Current phase-aware quantization frameworks are being extended to cover tensor parallelism, hybrid pipeline-tensor search, and dynamic batch allocation (e.g., integration into vLLM and ORCA) (Zhao et al., 2024). Limitations remain in scaling ILPs to very large layer counts or device numbers, requiring heuristic or greedy approximations. Further directions include generalizing codebooks (AWQ, SPQR, QLoRA) in phase-aware domains, adapting schemes for online, unpredictable workloads, and merging widely-linear techniques with standard PTQ/QAT methods for broad model compatibility.

A plausible implication is continued advancement of phase-aware quantization in both training and inference pipelines, enabling ultra-low bitwidth deployment of foundation models and complex signal architectures on commodity hardware with tight accuracy bounds and substantially lowered resource requirements.