When Quantization Affects Confidence of Large Language Models?

NAACL 2024

Irina Proskurina
Luc Brun
Guillaume Metzler
Julien Velcin

Contributions

• We investigate how quantization with GPTQ influences the calibration and confidence of LLMs
• We assess the confidence alignment between compressed and full-precision LLMs at scale
• We explain the quantization loss from the initial confidence perspective

Introduction

Motivation

• Recent works on scaling laws have shown that emerging abilities come with the scale increase, which makes well-performing larger models less accessible and limits their practical usability
• Quantization may degrade the initial performance and amplify the sensitivity of an LLM to certain linguistic phenomena and stereotypes
• No attention has been paid to explaining the compression loss, particularly its variance across different texts

Post-training quantization

On the dataset $X$ we want to find a quantized version of weight $\hat{W}^{*}_{l}$ to minimize the mean squared error:

$$ \hat{W}^{*}_{l}=argmin _{\hat{W} _{l}} || \hat{W} _{l} X - W _{l} X || _{2}^2 $$

Optimal Brain Quantization (OBQ) method state that we can quantize each row independently: $ || \hat{W} _{l} X - W^{l} X || _{2}^2 = \sum _{i=0}^{d _{row}} || W _{l[i,:]} X - \hat{W}^{*} _{l[i,:]} X || _{2}^{2} $

Quantization with GPTQ

• Learn the rounding operation using a small dataset
• Split weights in groups (blocks) and quantize them group-wise, using the inverse Hessian information stored

Methodology

Zero-shot Question Answering: pipeline

Data: Six standard commonsense reasoning tasks

• question answering involving reading comprehension (BoolQ)
• natural text entailment (XStory-En, HellaSwag)
• science fact knowledge (ARC, OBQA)
• physical commonsense (PIQA)

Problem

We consider a classification problem : questions $x$ paired with candidate answers $y$:

$ \hat{y} = \underset{y \in Y}{\text{arg max }} p_{\text{LM}}(y|x), $ where: $ p _{\text{LM}}(y|x) = \prod _{i=1}^{|y|} p _{\text{LM}}(y _{[i]}|x, y _{[1:i-1]}) $

Calibration Metrics

Model calibrated : $P(\hat{Y} = Y | \hat{p} = p ) = p.$

Metrics used for estimating calibration error (CE):

• ECE for binary problems: $ECE = \sum^{M}_{m=1} \frac{|B_m|}{n}|acc(B_m) - \overline{conf}(B_m)|$
• ACE for multi-class benchmarks: $ACE = \dfrac{1}{CM} \sum_{c=1}^C\sum_{m=1}^M \vert acc(B_m,c) - \overline{conf}(B_m,c) \vert$

Results

Confidence Impact

Zero-shot accuracy scores (Acc.) and calibration error (CE) for Mistral model. The changes of the scores after GPTQ are in brackets.

Calibration Impact

Confidence and prediction entropy evaluation results on HellaSwag.

Cases of Confidence Change

The samples with lower pre-quantization confidence level are the more affected by the quantization process

Jensen-Shannon Distances

The distances between original and compressed LLMs decrease as the model size scales up

Conclusion

• In the paper, we have investigated the impact of quantization on the confidence and calibration of LLMs
• Quantization leads to an increase in calibration error and statistically significant changes in confidence levels for correct predictions
• We identify instances of confidence change occurring in data where models lack confidence before quantization
• Our findings provide insights into quantization loss and suggest a potential direction for future work, emphasizing the need to focus on calibrating LLMs, specifically on uncertain examples

Questions?

You can reach us [here]

We released the code for reproducing the experiments [here]

Project website: https://www.anr-dike.fr