On the compute side there's the issue of scalability. CPUs are designed to perform a handful of operations at one time. They typically have a small number of dedicated integer, float, and other ALU configurations. Having dedicated matrix multiplication instructions would still lock that to how many matrix-capable ALUs there are in the CPU.

GPUs are designed to process a large number of calculations at once (so they can process triangles in 3D graphics). This makes them good at ML applications as they can process many of the matrix calculations at once. A 4090 has 16,384 CUDA cores (general compute ALUs) and 512 Tensor cores (dedicated matrix compute ALUs); a 5090 has 21,760 CUDA and 680 Tensor cores.

The other issue when training models (and running larger models) is the amount of VRAM (or RAM for CPUs) available. GPUs are limited in this aspect, whereas CPUs can have a lot higher memory. This affects things like batch size and the size of model that can be trained or fine-tuned.

https://unsloth.ai has guides for how to fine-tune existing models like Qwen 3.8 27B, memory requirements, etc.

https://medium.com/@kailaspsudheer/the-transformers-arithmet... has some information on training a base model. A 7B llama model is estimated at taking ~34GB memory for inference at F32, but was observed requiring 96GB memory when training (for the model weights, gradients, activations, and optimizer states).

Note: you can reduce the memory required for training by recomputing the gradients, at a cost of performance/time. You can also do other tricks like performing a QLoRA/LoRA pass on the model then merging that into the model to create a checkpoint.

I don't know what sized model you could train on 64GB/128GB RAM via a CPU.