Squeezing More from Less: A New Approach to Model Compression

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Author: Denis Avetisyan

Researchers have developed a novel quantization technique that significantly improves the compression of large language models without sacrificing accuracy.

LoPRo enhances low-rank quantization via permuted block-wise rotation and Walsh-Hadamard transforms for increased efficiency and reduced model size.

Despite advances in model compression, achieving high accuracy at extremely low bitwidths-particularly below 3-bit-remains a significant challenge for post-training quantization. This work introduces LoPRo: Enhancing Low-Rank Quantization via Permuted Block-Wise Rotation, a novel fine-tuning-free quantization algorithm that enhances low-rank approximation by strategically permuting and rotating weight blocks using Walsh-Hadamard transforms. LoPRo demonstrably improves quantization accuracy on large language models like LLaMA-2, LLaMA-3, and Mixtral-8x7B, achieving state-of-the-art results with up to a 4× speedup and substantial reductions in perplexity. Could this approach unlock even greater efficiency and accessibility for deploying large language models on resource-constrained devices?

The Scaling Challenge: Quantization as a Necessary Reduction

The recent surge in large language model (LLM) capabilities, exemplified by models like LLaMA-2 and Mixtral-8x7B, has unlocked unprecedented performance across a spectrum of natural language tasks. However, this advancement comes at a substantial cost: these models require immense computational resources for both training and inference. The sheer scale of parameters-often billions-necessitates powerful hardware, including specialized accelerators and vast memory capacity, limiting accessibility and increasing operational expenses. Consequently, deploying and utilizing these state-of-the-art LLMs poses a significant challenge for many researchers and developers, hindering wider adoption and practical application despite their remarkable potential. This creates a pressing need for techniques that can reduce the computational burden without sacrificing performance.

Post-Training Quantization (PTQ) represents a crucial strategy for deploying large language models on resource-constrained hardware, aiming to diminish both model size and inference latency. This technique involves reducing the precision of the model’s weights and activations – for example, from 32-bit floating point numbers to 8-bit integers – thereby lowering computational demands and memory footprint. However, this simplification isn’t without cost; the inherent information loss during precision reduction frequently results in a discernible degradation of the model’s accuracy. While offering a pathway to faster and more efficient models, standard PTQ methods often struggle to preserve performance, especially when pushing quantization to extremely low bit-widths, creating a significant obstacle to widespread adoption and necessitating innovative approaches to mitigate these accuracy losses.

Post-Training Quantization (PTQ) represents a crucial strategy for deploying large language models on resource-constrained hardware, yet conventional PTQ methods often encounter significant performance degradation as models are compressed to extremely low bit-widths. This limitation hinders widespread adoption, as reduced precision can lead to unacceptable accuracy loss. Recent advancements, exemplified by the LoPRo technique, directly address this bottleneck by enabling substantially faster quantization without compromising model integrity; LoPRo achieves up to a 4x speedup in the process and, notably, can fully quantize the substantial Mixtral-8x7B model in a mere 2.5 hours, demonstrating a viable pathway towards efficient and accessible large language model deployment.

LoPRo: Refining Residuals for Efficient Compression

LoPRo is a Post-Training Quantization (PTQ) algorithm designed to compress Large Language Models (LLMs) without requiring any fine-tuning or retraining. Unlike methods that quantize full weight matrices, LoPRo specifically focuses on the residual matrices within the LLM architecture. These residual matrices represent the difference between successive layers and are critical for maintaining performance. By targeting these matrices for quantization, LoPRo aims to reduce model size and computational cost while minimizing accuracy loss, offering a more efficient compression strategy than full-matrix quantization techniques.

Low-Rank Approximation (LRA) functions by decomposing the original weight matrix into a product of two smaller matrices with significantly fewer parameters. This decomposition, based on the principle that weight matrices often exhibit intrinsic low-rank structure, reduces the computational complexity of the subsequent quantization process. Instead of directly quantizing the full-rank weight matrix, LRA operates on these lower-dimensional representations, decreasing both the storage requirements and the number of computations needed for quantization. The rank of the approximation is a key hyperparameter; lower ranks yield greater compression but potentially introduce more significant information loss, while higher ranks retain more information at the cost of reduced compression. By applying LRA prior to quantization, LoPRo effectively simplifies the quantization problem, allowing for more efficient and accurate model compression.

LoPRo achieves effective model compression by directly quantizing the residual matrices within a Large Language Model (LLM) architecture, circumventing the need for extensive fine-tuning or retraining. This approach is predicated on the observation that residual matrices are critical for maintaining performance during quantization. Evaluations on the Mixtral-8x7B model demonstrate an 8% improvement in accuracy compared to standard Post-Training Quantization (PTQ) techniques, indicating that targeting residual matrices specifically mitigates performance degradation typically associated with reduced precision.

Structuring the Residual Matrix for Enhanced Quantization

LoPRo utilizes a block-wise permutation strategy to reorder the columns of the residual matrix, prioritizing those with the greatest impact on model performance. This reordering is not random; it is guided by a proxy Hessian matrix, which approximates the second-order derivatives of the loss function with respect to the model weights. By analyzing the proxy Hessian, LoPRo identifies columns that, when altered, result in the most significant changes to the loss. These columns are then placed earlier in the matrix, increasing the effectiveness of subsequent quantization steps by preserving the most critical information. The block-wise approach operates on groups of columns, reducing computational overhead compared to individual column sorting while still achieving substantial reordering benefits.

Following block-wise permutation, a Walsh-Hadamard Transform (WHT) is applied to the columns of the residual matrix. This transform, based on a matrix of +1 and -1 values, rotates the columns. Columns identified as having similar importance-as determined by the preceding permutation stage-are rotated in a correlated manner. This rotation concentrates the energy of the matrix into fewer dimensions, thereby improving the effectiveness of subsequent quantization by reducing the variance within each quantized group and increasing the signal-to-noise ratio. The WHT’s inherent properties facilitate this energy compaction without introducing significant computational overhead.

The application of block-wise permutation and the Walsh-Hadamard transform, in conjunction with Rank-1 Sketch-based Singular Value Decomposition (R1SVD), significantly improves the performance of low-bit quantization techniques. Evaluations demonstrate a 0.4 perplexity reduction on the Mixtral-8x7B model and a 0.36 perplexity reduction on the LLaMA-2 7B model when compared to the performance of GPTVQ. This indicates that the combined transformations effectively restructure the residual matrix, enabling more efficient representation with reduced precision and minimizing information loss during the quantization process.

Expanding the Horizon: Complementary Techniques and Future Potential

Beyond traditional quantization methods, a suite of techniques – including GPTQ, LQER, QUIP, and Vector Quantization – are actively being explored to enhance the accuracy of reduced-precision models. GPTQ, for instance, leverages an optimal brain surgeon approach to minimize quantization error, while LQER focuses on minimizing the error through a least-squares optimization process. QUIP introduces a learnable quantization scheme, adapting the quantization levels during training for improved performance. Vector Quantization, conversely, represents weights as indices into a learned codebook, offering a different perspective on compression. These diverse strategies each address the challenges of information loss inherent in quantization, aiming to preserve model performance while significantly reducing memory footprint and computational demands – a crucial step towards broader accessibility and deployment of large language models.

The quantization process, while reducing model size and accelerating inference, can introduce performance degradation due to the limited precision of reduced bit-width representations. To counteract this, techniques like Outlier Truncation and Rotation are employed as refinement strategies. Outlier Truncation specifically addresses the impact of extreme weight values – often present in large language models – by limiting their magnitude, preventing them from disproportionately influencing the quantized representation. Rotation, on the other hand, transforms the weight matrix to improve its suitability for quantization, effectively redistributing the values to minimize information loss. By strategically managing these outliers and optimizing weight distributions, these techniques significantly mitigate the accuracy drop often associated with low-bit quantization, preserving model performance and enabling successful deployment on devices with limited computational resources.

Recent advancements in quantization are rapidly redefining the possibilities for large language model deployment. The synergistic combination of techniques – notably including LoPRo alongside methods like GPTQ and vector quantization – is demonstrably expanding the boundaries of low-bit precision. This convergence isn’t merely theoretical; studies reveal a significant 10% accuracy improvement on Mixture-of-Experts (MoE) models when compared to standalone GPTQ implementations. Such gains are critical, as they directly translate to the ability to run increasingly complex LLMs on devices with limited computational resources – opening doors for on-device AI, edge computing applications, and broader accessibility to powerful language technologies.

The pursuit of LoPRo exemplifies a dedication to reductive design. It meticulously pares away redundancy within large language models, achieving compression through a novel application of Walsh-Hadamard transforms and block-wise permutation. This echoes John von Neumann’s sentiment: “It is possible to carry out any operation which can be done by a Turing machine.” LoPRo doesn’t simply approximate function; it distills it, retaining essential performance while minimizing computational cost. The method’s success stems from an understanding that true elegance isn’t about adding complexity, but about achieving maximum impact with minimal components – a lossless compression of model parameters, mirroring the beauty of fundamental principles.

What Lies Ahead?

The pursuit of efficient large language models invariably leads to quantization. LoPRo offers a refinement-a block-wise permutation coupled with the Walsh-Hadamard transform-but elegance should not be mistaken for a solution. The core problem remains: information, once discarded, is not easily recovered. Future work must address the fundamental tension between aggressive compression and the preservation of nuanced semantic understanding. The current emphasis on post-training quantization, while pragmatic, skirts the more difficult question of how to design models inherently robust to reduced precision.

Mixed-precision approaches, hinted at by this work, represent a logical progression. However, the automated discovery of optimal bit-width assignments remains a challenge. Intuition suggests a correlation between layer sensitivity and representational complexity, but translating this into a self-evident algorithm is proving elusive. The field needs less emphasis on novel transformations and more on principled methods for identifying and protecting critical information within these models.

Ultimately, the true measure of success will not be the size of the compressed model, but its continued ability to mean something. The simplicity of gravity should be the guiding principle. Any further complication must be justified by a demonstrable, and substantial, improvement in both efficiency and fidelity – not merely a shuffling of the bits.

Original article: https://arxiv.org/pdf/2601.19675.pdf

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

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2026-01-28 14:04