Keyword-enhanced Hierarchical Quantization Encoding

• KHQE is a multi-stage encoding framework that structures high-dimensional data into hierarchical layers using keyword enhancement for efficient similarity search.
• It combines keyword-enhanced embeddings with coarse-to-fine hierarchical quantization and residual attribute quantization to preserve both semantic structure and distinctive attributes.
• KHQE optimizes retrieval and ranking through minimum-cost flow optimization and supports hardware-efficient deployments with sub-8-bit quantization and mixed-precision strategies.

Keyword-enhanced Hierarchical Quantization Encoding (KHQE) is a multi-stage encoding framework designed to preserve both hierarchical semantics and key attribute signals in high-dimensional data representations for similarity search, efficient retrieval, federated optimization, and generative ranking systems. By emphasizing critical keywords in input content and applying structured quantization strategies, KHQE enables fast, scalable, and highly relevant matching between queries and items, while also supporting hardware-efficient deployment scenarios and resource constraints.

1. Conceptual Foundations and Motivations

KHQE draws on advances from hierarchical quantization methods (Jeong et al., 2019), keyword-centric embedding strategies, and mixed-precision quantization schemes for model compression and computational efficiency (Zeng et al., 2022, Hariri et al., 20 Feb 2025). In the context of industrial search systems, especially those with large and noisy textual corpora, KHQE directly addresses the challenge of representing heterogeneous item attributes and maintaining query-item relevance. By structuring the encoded representation into hierarchical levels, KHQE achieves exponential granularity: semantic buckets are formed in coarse layers, while distinctive attributes are preserved in finer levels.

Such representations find broad application in recall and ranking for e-commerce (Chen et al., 3 Sep 2025), streaming keyword spotting for edge hardware (Zeng et al., 2022), adaptive quantization in federated learning (Azimi-Abarghouyi et al., 13 May 2025), and mixed-precision caching for LLM inference (Hariri et al., 20 Feb 2025).

2. Hierarchical Quantization Methodology

The core encoding workflow proceeds in multiple steps:

1. Keyword Enhancement: Initial embeddings $e_{(q)}$ (for queries) and $e_{(i)}$ (for items) are averaged with respective core keyword embeddings, extracted via discriminant models (e.g., Qwen-VL) and pattern-matchers (e.g., Aho-Corasick). This yields:

$$e_{(q)}^o = \frac{1}{2}\left[e_{(q)} + \frac{1}{m} \sum_{i=1}^m e_{k}^i\right] \quad e_{(i)}^o = \frac{1}{2}\left[e_{(i)} + \frac{1}{n} \sum_{j=1}^n e_{k}^j\right]$$

where $m,n$ are the numbers of core keywords for query and item, respectively.

1. Hierarchical Quantization: The enhanced embeddings undergo coarse-to-fine quantization. RQ-Kmeans constructs the hierarchical semantic ID (SID), capturing prominent shared features at upper layers and finer item-specific uniqueness at lower layers.
2. Residual Attribute Quantization: Standard quantization can over-aggregate, losing fine-grained distinctions. Thus, Optimized Product Quantization (OPQ) is applied to the residual portion (the difference between the original and quantized global embedding) to recover unique attributes missed by hierarchical tokenization.

This dual strategy reliably preserves semantic structure and item-specific detail. Quantized codebooks enable exponential bucketization, supporting large-scale similarity search and efficient inference with bucket lookup.

3. Optimization via Minimum-Cost Flow and Layered Quantizer Design

Hierarchical hash code assignment is formulated as a combinatorial optimization, solvable in polynomial time via minimum-cost flow (MCF):

• Vertices in the flow network represent average class embeddings and candidate indices.
• Multi-level bipartite graphs connect class nodes to bucket nodes at each level, with flows subject to sparsity and capacity constraints.
• The cost function minimized by MCF includes both unary terms $-c_p^T z_p$ and pairwise penalties ($\alpha$ for siblings, $\beta$ for non-siblings), enforcing semantic clustering and separation.

This guarantees optimal discrete code assignment per mini-batch. For federated and distributed layered systems (Azimi-Abarghouyi et al., 13 May 2025), the quantization function at each layer $Q_n(\cdot)$ is chosen to satisfy unbiasedness and variance scaling:

$$E\{ Q_n(x) | x\} = x, \quad E\{ \|Q_n(x) - x\|^2 | x\} \leq q_n \|x\|^2$$

Parameters $(s_n)$ control each layer’s quantization granularity, supporting adaptive communication cost management under bandwidth constraints.

4. Implementation Strategies for Efficiency

KHQE is engineered for practical deployment in both software and hardware settings:

• Sub-8-Bit Quantization: In embedded and ARM NEON hardware environments (Zeng et al., 2022), a two-stage quantization aware training (QAT) is effective. Dense weights are squashed using a nonlinear $\tanh()$ transformation (remapping a roughly Gaussian distribution to near-uniform), enabling efficient subsequent linear quantization. All additional parameters—gains, biases, batch normalization terms, activations—are quantized linearly, with careful scaling and activation clipping.
• Mixed-Precision Strategies: For hierarchical caches (e.g., LLM KV cache), optimal bit-allocation is informed by norm disparity (Hariri et al., 20 Feb 2025): keys, which have higher spectral and Frobenius norms, are quantized at higher precision, while values tolerate more aggressive quantization. This reduces error amplification through transformer layers and improves memory efficiency.
• Quantum Resource Efficiency: In quantum-enabled neural architectures (Bosco et al., 8 Oct 2024), flexible quantization (with memoization) and integrated encoding decouple the number of quantum resources (qubits, circuit depth) from input patch size, supporting scalable inference on NISQ devices.

5. Performance Analysis and Empirical Outcomes

KHQE delivers strong performance in both accuracy and efficiency metrics across domains:

Scenario	Relative Improvement (KHQE vs. Baseline)	Metric
E-commerce Search (Chen et al., 3 Sep 2025)	CUR @ L2: +24.8%, CUR @ L3: +26.2%	Codebook Utilization Rate
E-commerce Search (Chen et al., 3 Sep 2025)	Recall@10: +5.25 (abs.), MRR@10: +1.56	Ranking Precision
Online A/B Test (Chen et al., 3 Sep 2025)	CTR: +1.67%, Buyer: +2.40%, Orders: +3.22%	User Engagement
Embedded KWS (Zeng et al., 2022)	CPU: up to –3×, Memory: up to –4×	Hardware Efficiency
Similarity Search (Jeong et al., 2019)	SUF: up to 1298×	Search Speedup

In e-commerce (Chen et al., 3 Sep 2025), KHQE’s dual quantization increases codebook utilization and independent coding rates, contributing to improved recall and ranking. Offline studies show clear gains over traditional tokenizers. Online deployment demonstrates statistically significant lift in key business metrics while reducing operational cost by more than 75% and improving model FLOPs utilization.

In hardware scenarios (Zeng et al., 2022), QAT-based KHQE maintains detection quality (DET curves) at parity with floating-point models (low single-digit FDR degradation) despite aggressive bit-width reductions. Quantum implementations (Bosco et al., 8 Oct 2024) provide accuracy improvements over both classical and rotationally encoded quanvolutional models.

6. Practical Applications and Broader Implications

KHQE is suitable for:

• Large-scale similarity search: Enables exponential bucket space for fast retrieval with discriminative capacity, as demonstrated for image datasets (CIFAR-100, ImageNet) (Jeong et al., 2019), product retrieval, and video search.
• E-commerce item ranking: Robustly represents items’ searchable attributes for relevance matching with short, intent-driven queries amid noisy and redundant descriptions (Chen et al., 3 Sep 2025).
• Federated learning: Layer-specific quantization supports scalable communication and compresses updates with provable error bounds (Azimi-Abarghouyi et al., 13 May 2025).
• Streaming keyword spotting: Permits resource-efficient deployment on commodity ARM and neural network accelerators with sub-8-bit quantization (Zeng et al., 2022).
• LLM cache compression: Mixed-precision schemes guided by spectral gap analysis of key/value matrices yield memory savings with minimal performance loss in long-context generative models (Hariri et al., 20 Feb 2025).
• Quantum neural architectures: Decoupled quantization and encoding strategies improve expressibility and circuit resource efficiency (Bosco et al., 8 Oct 2024).

A plausible implication is the emergence of importance-based and adaptive quantization policies, whereby key attributes, identified contextually (keywords), are allocated higher resolution within the hierarchy, further mitigating quantization-induced degradation.

7. Future Directions

Continued research is invited in several domains:

• Adaptive Quantization: Integrating data-dependent quantizer selection and bit allocation (potentially tensioned by spectral norm estimators) for even greater encoding fidelity, especially under resource constraints or heterogeneous data distributions (Azimi-Abarghouyi et al., 13 May 2025, Hariri et al., 20 Feb 2025).
• Joint Optimization Frameworks: Blending combinatorial algorithms (e.g., minimum-cost flow) with gradient-based meta-optimization for robust end-to-end learning and faster convergence despite non-differentiable latent codes (Jeong et al., 2019).
• Enhanced Retrieval Precision: Adding domain-specific discriminant models for more accurate keyword extraction—increasing both collaborative and semantic alignment, potentially improving industrial search and recommendation metrics (Chen et al., 3 Sep 2025).
• Quantum-Enhanced Encoding: Exploring further integration of hierarchical and flexible quantization for scalable quantum neural networks in computer vision, with cross-comparison to classical and hybrid hardware settings (Bosco et al., 8 Oct 2024).
• Open Tooling: Wider dissemination of source code and parameter studies for adaptive KV cache quantization (Hariri et al., 20 Feb 2025), facilitating rapid experimentation and deployment.

Incorporating these advances will further refine the balance between memory efficiency, computational speed, and retrieval/model accuracy in next-generation ranking, search, federated optimization, and resource-constrained inference systems.