Experimental layer-wise + pruned (layers 26 and 29) quantization of google/gemma-3-12b-it

Using LLaMA C++ release b5540 for quantization.

Original model: google/gemma-3-12b-it

From the original model creators:

Terms of Use: Terms

Authors: Google DeepMind

Model Information Summary description and brief definition of inputs and outputs.

Description Gemma is a family of lightweight, state-of-the-art open models from Google, built from the same research and technology used to create the Gemini models. Gemma 3 models are multimodal, handling text and image input and generating text output, with open weights for both pre-trained variants and instruction-tuned variants. Gemma 3 has a large, 128K context window, multilingual support in over 140 languages, and is available in more sizes than previous versions. Gemma 3 models are well-suited for a variety of text generation and image understanding tasks, including question answering, summarization, and reasoning. Their relatively small size makes it possible to deploy them in environments with limited resources such as laptops, desktops or your own cloud infrastructure, democratizing access to state of the art AI models and helping foster innovation for everyone.

Inputs and outputs Input:

Text string, such as a question, a prompt, or a document to be summarized Images, normalized to 896 x 896 resolution and encoded to 256 tokens each Total input context of 128K tokens for the 4B, 12B, and 27B sizes, and 32K tokens for the 1B size Output:

Generated text in response to the input, such as an answer to a question, analysis of image content, or a summary of a document Total output context of 8192 tokens Usage

PLEASE READ THIS BEFORE USING THESE EXPERIMENTAL VERSIONS!

An area of personal interest is finding ways to optimize the inference performance of LLMs when deployed in resource-constrained environments like commodity hardware, desktops, laptops, mobiles, edge devices, etc. There are many approaches to accomplish this, including architecture simplification and knowledge distillation, but my focus has been primarily on quantization and pruning.

The method used to produce these experimental versions is covered in Squeezing Tensor Bits: the quest for smaller LLMs, but at a high level it involves using a custom version of llama-imatrix and llama-quantize to identify influential tensors, quantize the most important layers to higher bit precision and the less important to lower bits, and remove (prune) one or more layers. This process was partly inspired by Dumitru's et al Layer-Wise Quantization: A Pragmatic and Effective Method for Quantizing LLMs Beyond Integer Bit-Levels, and Xin Men's et al ShortGPT: Layers in Large Language Models are More Redundant Than You Expect

As of version b5125, llama-quantize can now perform tensor-wide quantization (TWQ), whereby user-defined tensors are quantized at a specific level, or perform layer-wise quantization (LWQ) by selecting different quantization types per tensor/layer. For example, --tensor-type attn_v=q6_k will quantize all Attention Value tensors at q6_k (TWQ), and --tensor-type "\.([0-9]|1[01257]|31)\.attn_k=q4_k" will quantize Attention Key tensors on layers 0 to 9, 10, 11, 12, 15, 17 and 31 at q4_k, leaving the remaining layers at their default value (LWQ).

A custom version of llama-quantize is used to prune the model by providing a comma-separated list in the --prune-layers command line option. The pruning operation will renumber remaining layers to avoid gaps in the sequence, update the relevant model metadata and, if an imatrix is available, it will use the correct importance score vector. This option can be used alongside --tensor-type to perform tensor/layer-wise quantization on selected tensor types, whilst at the same time pruning others. For example:

llama-quantize --tensor-type attn=q6_k --prune-layers 3,7,11 --imatrix imatrix.dat model-f32.gguf model-q4_k_m.gguf q4_k_m

An enhanced version of llama-imatrix generates useful statistics to guide the tensor and layer selection process. --show-statistics will display:

Tensor statistics:

  • ฮฃ(Bias): the sum of all activations over the tensor (i.e. the Importance Scores)
  • Min & Max: minimum and maximum activation values
  • ฮผ & ฯƒ: activations' mean and standard deviation
  • % Active: proportion of elements whose average activation exceeds a very small threshold (1e-6). Helpful to determine how alive/dormant the tensor is during inference
  • N: number of activations in the tensor
  • Entropy: entropy of the activation distribution, in bits (standard Shannon entropy measurement)
  • E (norm): Normalized entropy.
  • ZD Score: z-score distribution as described in 3.1 Layer Importance Scores in the Layer-Wise Quantization paper
  • CosSim: cosine similarity between same type tensors with respect to the previous layer (i.e. blk.7.attn_k and blk.6.attn_k)

Layer statistics:

  • ฮฃ(Bias): weighted average of the sum of all activations over the tensor (i.e. the Importance Scores)
  • ZD Score: weighted average of the z-score distribution as described in 3.1 Layer Importance Scores in the Layer-Wise Quantization paper
  • CosSim: weighted average of the cosine similarity of whole layer with respect to the previous layer (i.e. Layer 3 and 2)

Please note that tensor statistics are calculated for each individual tensor and should be used to compare between tensors of the same type only. For example, assuming that attn_k in layer 10 has a higher influence during inference than attn_k in layer 7 because its ฮฃ(Bias) is larger makes sense, whilst concluding the same between attn_k and ffn_down does not.

There are two Pull Request (prune and imatrix) to merge these changes back into the core llama.cpp project. This may or may not ever happen so, until then, the modified version will be available on GitHub (prune and imatrix).

For testing and comparison I use models produced by Unsloth (Daniel and Michael Han do some really advanced level stuff!) and Bartowski (see credits below) but when they don't provide versions of the required model, all tests and comparisons are done against naive quantizations obtained by simply running llama-quantize with no further optimization. In this case however, whilst both have versions of this model, Unsloth's uses a different vocabulary size on their quants (262144 vs 262208) which does not allow for a valid like-for-like comparison.

All experimental versions were generated using an appropriate imatrix created from calibration datasets available at eaddario/imatrix-calibration. At its core, an Importance Matrix (imatrix) is a table or, more broadly, a structured representation that scores the relative importance of different features or parameters in a machine learning model. It essentially quantifies the "impact" each feature has on a specific outcome, prediction, or relationship being modelled, and it helps to counterbalance the negative effects of quantization and pruning.

The process to generate these models is roughly as follows:

  1. Convert the original model's tensors to GGUF F16*
  2. Estimate the Perplexity score for the F16 model (baseline) using the wikitext-2-raw-v1 dataset, and save the logits
  3. Generate an imatrix from selected calibration datasets
  4. Determine tensor and layer Importance Score contribution using the modified version of llama-imatrix
  5. Select an appropriate quant level for each tensor and quantize/prune the model using llama-quantize. In this model's case, layers 26 and 29 have been pruned
  6. Calculate Perplexity, KL Divergence, ARC (Easy+Challenge), HellaSwag, MMLU, Truthful QA and WinoGrande scores for each quantized model
  7. Keep versions with the best scores
  8. Repeat until all desired quants are created. I find that quantizations below Q3/IQ3 are not fit for my purposes and therefore do not usually generate them, but happy to provide other quants on request.

*BF16 would be preferred, but Apple's GPUs don't support it yet, and therefore any operations are executed in the CPU, making it unacceptably slow. This is expected to change in the near term but until then, if you are using Apple kit avoid using any models tagged BF16

Models

Sizes (in GB)

Model Bartowski Repo Shrinkage
gemma-3-12b-it-pruned-IQ3_M 5.66 5.21 8.0%
gemma-3-12b-it-pruned-IQ3_S 5.21 5.04 3.3%
gemma-3-12b-it-pruned-IQ4_NL 6.89 6.16 10.6%
gemma-3-12b-it-pruned-Q3_K_L 6.48 5.33 17.7%
gemma-3-12b-it-pruned-Q3_K_M 6.01 5.04 16.1%
gemma-3-12b-it-pruned-Q3_K_S 5.46 4.81 11.9%
gemma-3-12b-it-pruned-Q4_K_M 7.30 6.20 15.1%
gemma-3-12b-it-pruned-Q4_K_S 6.94 6.17 11.1%
gemma-3-12b-it-pruned-Q5_K_M 8.44 7.32 13.3%
gemma-3-12b-it-pruned-Q5_K_S 8.23 7.26 11.8%
gemma-3-12b-it-pruned-Q6_K 9.66 9.01 6.7%
gemma-3-12b-it-pruned-Q8_0 12.50 10.98 12.2%

Perplexity and KL Divergence scores

Model ฮผPPL ๐œŒPPL ฮผKLD RMS ฮ”p
gemma-3-12b-it-pruned-IQ3_M 35.478449 ยฑ0.411747 80.18% 1.229937 ยฑ0.004277 30.166 ยฑ0.089
gemma-3-12b-it-pruned-IQ3_S 32.557804 ยฑ0.369351 80.53% 1.196823 ยฑ0.004146 29.810 ยฑ0.088
gemma-3-12b-it-pruned-IQ4_NL 36.879518 ยฑ0.436763 80.79% 1.190922 ยฑ0.004215 29.578 ยฑ0.088
gemma-3-12b-it-pruned-Q3_K_L 33.537202 ยฑ0.371564 79.10% 1.263077 ยฑ0.004253 31.084 ยฑ0.088
gemma-3-12b-it-pruned-Q3_K_M 34.029948 ยฑ0.376082 78.62% 1.300974 ยฑ0.004321 31.537 ยฑ0.088
gemma-3-12b-it-pruned-Q3_K_S 36.103787 ยฑ0.402250 77.13% 1.395578 ยฑ0.004559 32.089 ยฑ0.088
gemma-3-12b-it-pruned-Q4_K_M 31.219358 ยฑ0.342580 80.83% 1.106608 ยฑ0.003932 29.739 ยฑ0.088
gemma-3-12b-it-pruned-Q4_K_M-bartowski 9.197963 ยฑ0.073909 98.63% 0.045560 ยฑ0.000416 6.400 ยฑ0.054
gemma-3-12b-it-pruned-Q4_K_S 31.245217 ยฑ0.343080 80.86% 1.105266 ยฑ0.003926 29.698 ยฑ0.088
gemma-3-12b-it-pruned-Q5_K_M 30.668770 ยฑ0.335889 81.60% 1.039101 ยฑ0.003848 29.177 ยฑ0.088
gemma-3-12b-it-pruned-Q5_K_S 30.644285 ยฑ0.335716 81.62% 1.038541 ยฑ0.003836 29.119 ยฑ0.088
gemma-3-12b-it-pruned-Q6_K 30.107026 ยฑ0.329175 81.96% 1.009233 ยฑ0.003785 28.800 ยฑ0.088
gemma-3-12b-it-pruned-Q8_0 30.014168 ยฑ0.327772 82.04% 1.004325 ยฑ0.003776 28.772 ยฑ0.088
gemma-3-12b-it-pruned-F16 9.042786 ยฑ0.071503 100% N/A N/A

ARC, HellaSwag, MMLU, Truthful QA and WinoGrande scores

Scores generated using llama-perplexity with 750 tasks per test, and a context size of 768 tokens.

For the test data used in the generation of these scores, follow the appropriate links: HellaSwag, ARC, MMLU, Truthful QA and WinoGrande

Model ARC HellaSwag MMLU Truthful QA WinoGrande Avg Score
gemma-3-12b-it-pruned-IQ3_M 66.9333 ยฑ1.7190 74.67 42.0000 ยฑ1.8034 39.4667 ยฑ1.7860 67.4667 ยฑ1.7119 58.11
gemma-3-12b-it-pruned-IQ3_S 65.0667 ยฑ1.7420 74.80 42.8000 ยฑ1.8079 40.4000 ยฑ1.7930 66.1333 ยฑ1.7292 57.84
gemma-3-12b-it-pruned-IQ4_NL 68.2667 ยฑ1.7007 75.47 42.6667 ยฑ1.8072 40.1333 ยฑ1.7910 68.5333 ยฑ1.6968 59.01
gemma-3-12b-it-pruned-Q3_K_L 67.8667 ยฑ1.7063 75.73 42.5333 ยฑ1.8065 40.2667 ยฑ1.7920 67.0667 ยฑ1.7172 58.69
gemma-3-12b-it-pruned-Q3_K_M 68.6667 ยฑ1.6949 75.20 44.4000 ยฑ1.8155 40.0000 ยฑ1.7900 65.8667 ยฑ1.7325 58.83
gemma-3-12b-it-pruned-Q3_K_S 67.6000 ยฑ1.7100 75.20 43.7333 ยฑ1.8126 39.8667 ยฑ1.7890 66.5333 ยฑ1.7242 58.59
gemma-3-12b-it-pruned-Q4_K_M 69.8667 ยฑ1.6766 77.47 43.6000 ยฑ1.8119 40.8000 ยฑ1.7958 68.4000 ยฑ1.6988 60.03
gemma-3-12b-it-pruned-Q4_K_M-bartowski 69.6000 ยฑ1.6807 81.07 43.6000 ยฑ1.8119 41.0667 ยฑ1.7976 75.7333 ยฑ1.5664 62.21
gemma-3-12b-it-pruned-Q4_K_S 69.8667 ยฑ1.6766 77.33 43.4667 ยฑ1.8113 40.8000 ยฑ1.7958 69.6000 ยฑ1.6807 60.21
gemma-3-12b-it-pruned-Q5_K_M 68.8000 ยฑ1.6929 77.87 45.3333 ยฑ1.8190 41.2000 ยฑ1.7984 68.8000 ยฑ1.6929 60.40
gemma-3-12b-it-pruned-Q5_K_S 68.9333 ยฑ1.6909 77.73 45.0667 ยฑ1.8180 41.3333 ยฑ1.7993 68.6667 ยฑ1.6949 60.35
gemma-3-12b-it-pruned-Q6_K 68.9333 ยฑ1.6909 78.66 45.4667 ยฑ1.8194 40.8000 ยฑ1.7958 68.6667 ยฑ1.6949 60.51
gemma-3-12b-it-pruned-Q8_0 68.8000 ยฑ1.6929 78.40 45.4667 ยฑ1.8194 41.7333 ยฑ1.8018 68.8000 ยฑ1.6929 60.64
gemma-3-12b-it-pruned-F16 69.2000 ยฑ1.6869 81.20 45.3333 ยฑ1.8190 41.4667 ยฑ1.8002 74.8000 ยฑ1.5864 62.40

Tokens per Second - Benchmarks

Scores generated using llama-bench. Naive (llama-quantize with no optimization) Q4_K_M quantization included for comparison.

model size params backend threads test t/s
gemma-3-12b-it-pruned-Q4_K_M 5.77 GiB 11.32 B Metal,BLAS 12 pp512 523.27 ยฑ3.74
gemma-3-12b-it-pruned-Q4_K_M 5.77 GiB 11.32 B Metal,BLAS 12 tg128 46.92 ยฑ0.60
gemma-3-12b-it-pruned-Q4_K_M 5.77 GiB 11.32 B Metal,BLAS 12 pp1024+tg1024 75.45 ยฑ0.35
gemma-3-12b-it-pruned-Q4_K_M-bartowski 6.79 GiB 11.77 B Metal,BLAS 12 pp512 482.36 ยฑ23.04
gemma-3-12b-it-pruned-Q4_K_M-bartowski 6.79 GiB 11.77 B Metal,BLAS 12 tg128 45.54 ยฑ1.21
gemma-3-12b-it-pruned-Q4_K_M-bartowski 6.79 GiB 11.77 B Metal,BLAS 12 pp1024+tg1024 74.27 ยฑ0.19

Metrics used

Perplexity: one of the key metrics used in NLP evaluation. It measures the quality of a language model by evaluating how well it predicts the next token given a particular sequence of words. A PPL of 1 indicates an exact match between predicted and actual, whereas values greater than one indicate a degree of "surprise" the generated token differs from the expected.

Kullbackโ€“Leibler (KL) Divergence: a statistical measure of how much a probability distribution differs from another. When quantizing models (or altering the original tensors in any way for that matter), the closest we can preserve the weights' probability distribution to the original model the better, thus the closest to 0 the better.

AI2 Reasoning Challenge (ARC): a benchmark to evaluate the ability of AI models to answer complex science questions that require logical reasoning beyond pattern matching.

HellaSwag: the Harder Endings, Longer contexts, and Low-shot Activities for Situations With Adversarial Generations (bit of a mouthful!) is a benchmark designed to test commonsense natural language inference. It requires the model to predict the most likely ending of a sentence.

MMLU: the Massive Multitask Language Understanding evaluates LLMsโ€™ general knowledge and problem-solving abilities across 57 subjects, including elementary mathematics, US history, computer science, and law.

Truthful QA: evaluates how well LLMs generate truthful responses to questions. It identifies whether AI models can avoid generating false or misleading information, particularly in areas where human knowledge is prone to misconceptions.

Winogrande: based on the Winograd Schema Challenge, is a natural language understanding task requiring models to resolve ambiguities in sentences involving pronoun references.

Credits

LLaMa C++ has a large and vibrant community of contributors (~1,200 last time I checked) that actively maintain and extend its functionality, adding new models and architectures almost as fast as they appear (considering the breakneck speed at which the AI/ML field is advancing, this alone is a remarkable feat!), and whilst I'm grateful to each and everyone of them, I want to recognise three people in particular: Thank You! Colin Kealty for the many contributions and for being one of the best sources of high quality quantized models available on Hugging Face, and a really big Thank You! to Georgi Gerganov for his amazing work with llama.cpp and the ggml/gguf libraries, and Iwan Kawrakow for being one of the key authors behind the many quantisation algorithms and the imatrix functionality.

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