Floating-point arithmetic is not associative. (A+B)+C does not necessarily equal A+(B+C), but you can get a performance improvement by calculating A, B, and C in parallel, then adding together whichever two finish first. So, in theory, transformers can be deterministic, but in a real system they almost always aren't.
Similarly you could not allow re-ordering of operations and similar - so the results are guaranteed to be deterministic (even if still "not correct" compared to infinite precision arithmetic) - but that would also have a big performance cost.
Technically possible, but I think unlikely to happen in practice.
On the higher level, these large models are sequential and there’s nothing to parallelize. The inference is a continuous chain of data dependencies between temporary tensors which makes it impossible to compute different steps in parallel.
On the lower level, each step is a computationally expensive operation on a large tensor/matrix. These tensors are often millions of numbers, the problem is very parallelizable, and the tactics to do that efficiently are well researched because matrix linear algebra is in wide use for decades. However, it’s both complicated and slow to implement fine grained parallelism like “adding together whichever two finish first” on modern GPUs. Just too much synchronization, when total count of active threads is many thousands, too expensive. Instead, operations like matrix multiplications are often assigning 1 thread per output element or fixed count of output elements, and reduction like softmax or vector dot product are using a series of exponentially decreasing reduction steps, i.e. order is deterministic.
However, that order may change with even minor update of any parts of the software, including opaque pieces at the low level like GPU drivers and firmware. Library developers are updating GPU kernels, drivers, firmware and OS kernels collectively implementing scheduler which assigns work to cores, both may affect order of these arithmetic operations.
I don’t think the issue is determinism per se but chaotic predictions that are difficult to rely on.
[1] https://docs.nvidia.com/cuda/cublas/index.html#results-repro...
https://news.ycombinator.com/item?id=37006224
https://news.ycombinator.com/item?id=45200925
The TL;DR is that LLMs are often not deterministic because GPUs compute submatrices in parallel and sum them up in different orders, depending on which finish first. This is maybe a few percent faster than always using the same order, but it absolutely could be made deterministic if people cared enough. CUDA even provides deterministic primitives if desired. Of course also use the same random seed for samplers, but that is trivial.