Comment by hansvm

Batching order, as you mentioned, matters a lot, and for any heavily optimized kernels it will change from one machine to the next. You also have the choice of backend numerical library from, e.g., different OS versions. There are floating-point bugs from time to time, especially in GPUs. Many operations (like transcendentals) are usually given a couple bits of wiggle room in the result. Another program executing could have changed the floating-point rounding mode on one device. More aggressive ML optimizers might automatically apply various forms of reduced precision to the requested high-level operation. If you have enough optimizations enabled, you might non-deterministically get compiled instructions like fmadd so that any one build of your library is deterministic (excluding other ideas mentioned above) but different machines with different builds (because of a staged rollout, different architectures, engineering mistakes, etc) can have different outputs. And so on.