Squeezing More From Less: Adapting Model Size for Peak Performance

Author: Denis Avetisyan

A new quantization technique intelligently reduces the size of large language models without sacrificing accuracy, offering significant speed and memory benefits.

The Flexible Low-Rank Quantization (FLRQ) algorithm achieves enhanced quantization accuracy and reduced model size through a three-stage process involving flexible rank selections, activation-based scaling, and iterative Best Low-rank Approximation under Clipping-a method demonstrably superior in preserving model fidelity during compression → a strategy that prioritizes mathematical precision over empirical testing.

FLRQ introduces flexible low-rank quantization with adaptive rank selection for efficient post-training compression of large language models.

While post-training quantization (PTQ) offers a promising path to compressing large language models (LLMs) and accelerating inference, existing low-rank methods struggle with the computational cost of finding optimal ranks for diverse layers. This work introduces ‘FLRQ: Faster LLM Quantization with Flexible Low-Rank Matrix Sketching’, a novel approach that adaptively determines layer-wise ranks using a fast sketching technique, achieving state-of-the-art compression with minimal accuracy loss. By efficiently identifying optimal low-rank approximations, FLRQ significantly reduces both storage requirements and quantization time, particularly at ultra-low bit-widths. Could this flexible quantization strategy unlock wider deployment of LLMs on resource-constrained devices?

The Challenge of Scale: Quantization and Large Language Models

Large language models have achieved unprecedented success in natural language processing, exhibiting abilities ranging from text generation to complex reasoning. However, this performance comes at a substantial cost: these models are extraordinarily large, often containing billions of parameters. This massive size presents significant obstacles to their widespread deployment, particularly on devices with limited computational resources, such as smartphones, embedded systems, and edge computing platforms. The memory and processing demands of running these models can be prohibitive, restricting their use to powerful servers and hindering real-time applications that require localized intelligence. Consequently, researchers are actively exploring methods to compress these models without sacrificing their remarkable capabilities, aiming to bridge the gap between performance and practicality.

The pursuit of deploying large language models on everyday devices necessitates a reduction in their substantial size, a goal frequently attempted through quantization – a process of reducing the precision of the numbers used to represent the model’s weights. However, standard quantization techniques often introduce unacceptable levels of accuracy loss, effectively diminishing the model’s capabilities. This stems from the delicate balance within these models; even minor alterations to the numerical representation of weights can disrupt the complex relationships learned during training. Consequently, a significant challenge lies in developing quantization strategies that aggressively reduce model size without correspondingly sacrificing the nuanced understanding and generative power that define these advanced systems. The need for innovative approaches is particularly acute, as directly applying traditional quantization methods can render a once-powerful model surprisingly ineffective.

Large language models, despite their impressive abilities, present a significant challenge when deployed on devices with limited computational resources. A primary approach to address this is post-training quantization, which reduces the precision of the model’s weights and activations to compress its size. However, these models exhibit a remarkable sensitivity to even subtle changes during quantization; the process often introduces significant accuracy degradation. This fragility stems from the complex interplay between billions of parameters, where reducing precision disrupts the delicate balance learned during training. Unlike smaller models, the sheer scale of large language models means that quantization errors compound rapidly, leading to substantial performance loss-effectively negating the benefits of compression if not carefully managed.

R1-Sketch provides an accuracy-preserving, low-rank approximation for large-scale model quantization, achieving up to a 4.4x speedup over PyTorch’s built-in SVD function when using a rank of 32.

Deconstructing Complexity: Low-Rank Decomposition for Efficient Quantization

Low-rank decomposition techniques reduce the number of parameters required to represent a weight matrix by approximating it with the product of two smaller matrices. This is based on the observation that many neural network weight matrices exhibit inherent redundancy, meaning a significant portion of their information can be captured by a lower-dimensional subspace. Specifically, a weight matrix $W \in \mathbb{R}^{m \times n}$ can be approximated as $W \approx U V^T$ , where $U \in \mathbb{R}^{m \times r}$ and $V \in \mathbb{R}^{n \times r}$ , with $r < min(m, n)$ . This decomposition reduces the total number of parameters from $m \times n$ to $m \times r + n \times r$ , enabling model compression and potentially faster inference, particularly when combined with quantization strategies.

Post-training quantization, while effective in reducing model size and accelerating inference, often suffers from accuracy loss. Low-rank methods mitigate this by decomposing weight matrices into lower-dimensional representations, thereby reducing the number of trainable parameters and preserving critical information. However, applying a single, fixed rank across all layers can be suboptimal; layers with inherently higher complexity require greater representational capacity than simpler layers. Constraining all layers to the same low rank introduces unnecessary information loss in complex layers while offering limited compression in simpler ones, ultimately hindering overall performance. This inflexibility necessitates adaptive methods capable of tailoring the rank to the specific characteristics of each layer to achieve a balance between compression and accuracy.

Flexible Low-Rank Quantization addresses the limitations of fixed-rank decomposition by assigning an individual rank to each layer of a neural network. This dynamic approach allows layers with higher complexity – typically those with greater information content or requiring finer granularity for representation – to utilize a higher rank, and therefore more parameters, during the low-rank decomposition process. Conversely, simpler layers can be effectively represented with lower ranks, reducing overall parameter count and computational cost. The rank selection can be performed via various methods, including validation-based search or gradient-based optimization, enabling the model to adapt the level of approximation to each layer’s specific needs and maintain accuracy after quantization. This contrasts with fixed-rank methods which apply a uniform rank across all layers, potentially leading to under-representation in complex layers or unnecessary overhead in simpler ones.

Varying the rank selection in LLaMA2-7b demonstrates a clear relationship with quantization error <span class="katex-eq" data-katex-display="false">\mathbb{E}[abs_{max}]</span>, with optimal rank selection (blue lines) minimizing this error and revealing trade-offs between rank choice and quantization accuracy. — Varying the rank selection in LLaMA2-7b demonstrates a clear relationship with quantization error $\mathbb{E}[abs_{max}]$ , with optimal rank selection (blue lines) minimizing this error and revealing trade-offs between rank choice and quantization accuracy.

Refining the Approximation: FLRQ and Iterative Low-Rank Decomposition

FLRQ utilizes an iterative Best Low-Rank Approximation (BLRA) technique coupled with clipping to achieve efficient model compression. This process doesn’t simply reduce the rank of weight matrices but refines the approximation over multiple iterations, minimizing information loss. The clipping operation introduces a controlled level of quantization, further reducing model size while maintaining acceptable accuracy. By repeatedly applying BLRA and clipping, FLRQ dynamically balances the trade-off between compression ratio and the preservation of critical weight information, resulting in a model that is both smaller and retains a high degree of performance. The iterative nature of the process allows for fine-grained control over this balance, adapting to the specific characteristics of the network being compressed.

FLRQ utilizes calibration datasets to determine appropriate scaling factors for quantized weights, mitigating accuracy loss during the low-rank approximation process. Specifically, activation values derived from these datasets are analyzed to understand the distribution of weight sensitivities; weights exhibiting greater sensitivity receive larger scaling factors to preserve information. This dynamic scaling, applied during quantization, ensures that the refined, low-rank weights more closely resemble the original full-precision weights, thereby improving the overall model accuracy compared to uniform quantization schemes. The calibration process effectively minimizes the distortion introduced by the low-rank approximation and subsequent quantization, allowing for higher compression rates without significant performance degradation.

FLRQ accelerates low-rank decomposition by incorporating R1-Sketch, a technique employing Gaussian Projection and Randomized Singular Value Decomposition (RSVD). This approach circumvents the computational bottlenecks of traditional Singular Value Decomposition (SVD) methods. Specifically, when performing a rank-32 low-rank approximation, FLRQ with R1-Sketch achieves a 4.4x speedup compared to utilizing the standard SVD function available in PyTorch. The use of randomized techniques within R1-Sketch allows for efficient approximation of the singular value decomposition, significantly reducing computation time while maintaining acceptable accuracy for quantization purposes.

Employing FLRQ with LoRA on a W4A16 model demonstrably improves throughput while maintaining comparable latency to the baseline W4A16 model.

Demonstrating Efficiency: Performance Validation and Quantifiable Gains

Evaluations of the Fast Low-Rank Quantization (FLRQ) method demonstrate a notable reduction in inference latency without compromising the accuracy of large language models. Across a range of representative datasets, FLRQ consistently delivers faster processing speeds by efficiently compressing model weights. This is achieved through a carefully designed quantization process that minimizes information loss, ensuring that model performance remains largely unaffected despite the reduced bit-width representation. The observed speed improvements are particularly significant in resource-constrained environments, making FLRQ a promising technique for deploying sophisticated AI models on devices with limited computational power and memory.

Evaluations reveal that the proposed method establishes a compelling balance between model compression and operational speed, surpassing the capabilities of existing quantization techniques. Specifically, in demanding 2-bit quantization scenarios, the method demonstrates a 30% acceleration in quantization speed when contrasted with OmniQuant. This improvement signifies a substantial reduction in the time required to prepare models for deployment, enabling faster iteration cycles and more efficient resource utilization. The observed performance gain is particularly noteworthy as lower bit-widths typically present greater challenges for quantization algorithms, highlighting the method’s robustness and efficiency in resource-constrained environments.

Rigorous evaluations reveal that implementing the FLRQ method introduces a remarkably small memory footprint, incurring only a 4% overhead on the total memory usage when applied to a LLaMA2-13B model undergoing 3-bit quantization. This minimal increase in memory demand is particularly significant given the substantial gains in inference speed and the competitive trade-off between compression and performance that FLRQ achieves. The method’s efficiency allows for deployment on resource-constrained devices without compromising model capacity, making advanced large language models more accessible and practical for a wider range of applications, despite aggressive quantization levels.

The implementation of FLRQ quantization introduces a minor increase in bit width, averaging between 0.12 and 0.16 bits, specifically when applied to W4A16 quantization schemes. This seemingly small addition represents a strategic trade-off; while most quantization methods aim for minimal bit width to maximize compression, FLRQ leverages this slight increase to significantly refine quantization granularity. This refined granularity enables the preservation of critical model information, resulting in demonstrably improved performance and reduced accuracy loss compared to techniques that aggressively minimize bit width. The marginal overhead is therefore offset by substantial gains in model fidelity and inference speed, making FLRQ a compelling option for resource-constrained environments where both compression and accuracy are paramount.

Perplexity scales predictably with bit-level precision, demonstrating a consistent relationship between model uncertainty and quantization levels.

The pursuit of efficiency in large language model quantization, as demonstrated by FLRQ, resonates with a fundamental principle of computational elegance. John von Neumann observed, “The sciences demand the full use of all our faculties, the coordination of all our knowledge.” This echoes within the methodology of flexible low-rank sketching; FLRQ doesn’t impose a uniform compression across all layers. Instead, it intelligently allocates resources – selecting ranks adaptively – mirroring a system where each component operates at peak efficiency. This targeted approach to bit-width reduction, achieving comparable accuracy with reduced memory footprint, embodies the coordination of knowledge von Neumann championed-a harmonious balance between model size and performance.

What Lies Ahead?

The pursuit of efficient large language models invariably returns to the question of representation. This work demonstrates that a principled, adaptive approach to low-rank approximation-selecting rank not as a global parameter, but as a function of layer sensitivity-yields demonstrable gains. However, it is not a panacea. The elegance of FLRQ lies in its consistency; it consistently reduces memory footprint and accelerates quantization. But true algorithmic beauty demands a complete understanding of why certain layers tolerate greater compression than others.

Future research should not merely focus on refining the sketching process, but on formalizing the relationship between layer rank and information content. Is there a provable lower bound on rank, given a desired accuracy? The current reliance on empirical observation, while practical, feels…unsatisfying. A mathematically rigorous framework could guide rank selection, eliminating the need for the search process altogether.

Furthermore, the benefits of FLRQ at extremely low bit-widths-the true frontier of model compression-remain to be fully explored. Reducing precision to the absolute minimum inevitably introduces error. The challenge is not simply to minimize this error, but to bound it-to guarantee a certain level of performance, regardless of the model size. Only then can one claim a truly elegant solution.

Original article: https://arxiv.org/pdf/2601.05684.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

The Challenge of Scale: Quantization and Large Language Models

Deconstructing Complexity: Low-Rank Decomposition for Efficient Quantization

Refining the Approximation: FLRQ and Iterative Low-Rank Decomposition

Demonstrating Efficiency: Performance Validation and Quantifiable Gains

What Lies Ahead?

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