While Post-Training Quantization (PTQ) offers a compelling path to smaller and faster models without retraining, it's important to understand its inherent limitations, especially when using simpler or "basic" PTQ algorithms like straightforward MinMax quantization. These limitations often manifest as a drop in model accuracy, which can sometimes be significant enough to render the quantized model unsuitable for its intended task.

The Primary Challenge: Accuracy Degradation

The core trade-off in quantization is between computational efficiency (lower precision) and representational fidelity (accuracy). Mapping continuous floating-point values to a discrete set of integers inevitably introduces error, known as quantization error. For a value $x$ , its quantized representation $x_q$ involves a mapping function $Q(\cdot)$ and a de-quantization function $D(\cdot)$ :

$x_q = D(Q(x))$

The quantization error for this value is $e = x - x_q$ . Basic PTQ methods aim to minimize this error statistically across the model's weights and activations, but they don't always succeed, particularly under aggressive quantization (e.g., using fewer bits like INT4).

Several factors contribute to accuracy degradation in basic PTQ:

Sensitivity to Outliers: Weights and activations in LLMs often exhibit non-uniform distributions with long tails or distinct outliers. Basic range-setting algorithms, like MinMax, determine the quantization scale based on the absolute minimum and maximum values observed during calibration. If significant outliers exist, they stretch this range considerably. This forces the majority of the values, which lie within a much narrower band, to be quantized into only a few available integer levels, leading to substantial precision loss for the bulk of the data. While techniques exist to handle outliers (as discussed previously), basic PTQ implementations might not incorporate sophisticated clipping or range-tuning methods, making them vulnerable.
Uniform Quantization vs. Non-Uniform Data: Most basic PTQ schemes employ uniform quantization. This means the gap (step size) between consecutive integer levels represents the same change in the original floating-point scale. However, model parameters and activations are rarely uniformly distributed; they often follow bell-shaped or Laplacian distributions. Uniform quantization is suboptimal for representing these distributions, as it assigns the same precision to densely populated areas near the mean as it does to sparsely populated tail regions.
Layer Sensitivity Variation: Different layers within an LLM can have vastly different sensitivities to quantization noise. For instance, attention mechanisms or later layers responsible for fine-grained predictions might be more susceptible to precision loss than earlier layers. Basic PTQ often applies a uniform quantization strategy (e.g., quantizing all linear layers to INT8) without accounting for this varying sensitivity. This can disproportionately affect critical parts of the model, leading to a noticeable drop in overall performance.
Aggressive Low-Precision Quantization: While quantizing to INT8 often yields good results with basic PTQ, pushing to lower bit-widths like INT4 dramatically increases the quantization error. Each integer level must represent a much larger range of floating-point values. Basic PTQ methods often struggle to maintain acceptable accuracy at these lower bit levels without more advanced techniques that specifically address the increased error. The plot below illustrates a typical (hypothetical) trend where accuracy degradation accelerates as bit precision decreases.

Accuracy often drops non-linearly as bit precision decreases, with significant degradation common below INT8 using basic PTQ methods.
Calibration Data Dependence: The effectiveness of PTQ heavily relies on the calibration dataset used to determine quantization parameters (scale and zero-point). If the calibration data is small, unrepresentative of the actual inference data distribution, or lacks diversity, the resulting quantization parameters will be suboptimal. This leads to increased quantization error when the model processes real-world inputs. While this affects all PTQ, basic methods might be less robust to imperfections in calibration compared to techniques that adjust weights or use more sophisticated range analysis.

These limitations highlight that while basic PTQ is a valuable tool for model optimization, it's not a silver bullet. When accuracy preservation is paramount, or when targeting very low bit-widths, the degradation caused by these factors may be unacceptable. This motivates the need for the more advanced PTQ techniques (like GPTQ, AWQ) discussed in the next chapter, or the use of Quantization-Aware Training (QAT), which allows the model to adapt to quantization noise during the training or fine-tuning process. Understanding these limitations helps in choosing the right quantization strategy for your specific model and application requirements.