Yes — with 31.0 GB to spare
Gemma 4 31B at Q4_K_M fits your CPU only · DDR5 dual-channel entirely on the GPU at 8K context, at an estimated 2.1 tokens per second. Past 206K the KV cache pushes it over — quantise the cache to q8_0, or step down a quantisation, to go longer.
The dense flagship: strongest maths of the 24–32 GB class (89% AIME), clean prose, vision. Q4 is a tight 24 GB fit.
The VRAM budget
Quantisation ladder
| Quant | Weights | Total @ 8K | Max context | Tok/s | Quality | Fit |
|---|---|---|---|---|---|---|
| Q8_0 | 31.0 GB | 33.6 GB | 120K | 1.2 | −0.1% ppl | Long context |
| Q6_K | 23.9 GB | 26.5 GB | 165K | 1.6 | −0.4% ppl | Long context |
| Q5_K_M | 20.7 GB | 23.3 GB | 186K | 1.8 | −0.8% ppl | Long context |
| Q4_K_M | 17.6 GB | 20.2 GB | 206K | 2.1 | −1.9% ppl | Recommended |
| Q3_K_M | 14.2 GB | 16.9 GB | 227K | 2.6 | −5.4% ppl | Long context |
| Q2_K | 12.2 GB | 14.8 GB | 240K | 3.1 | −15% ppl | Long context |
Quality is the published perplexity delta against f16 weights. Max context assumes an f16 KV cache; q8_0 roughly doubles it. This model interleaves sliding-window layers (1024 tokens, 10 of 60 layers global), which is why its cache barely grows with context.
How to run it
$ llama-server \
-hf google/gemma-4-31B-it:Q4_K_M \
-c 8192 -ngl 99
The engine underneath most of the others. Every knob is exposed. More on llama.cpp.