--- license: mit task_categories: - text-generation tags: - scaling - rooflines - transformers - distributed-training - inference - code - rl-environment size_categories: - n<1K --- # scaling-tasks-v1 35 quantitative scaling tasks for the [`scaling-env`](https://app.primeintellect.ai/dashboard/environments/eltociear/scaling-env) RL environment, on the topics of Google DeepMind's free book *[How To Scale Your Model](https://jax-ml.github.io/scaling-book/)*: rooflines and arithmetic intensity, transformer FLOPs and parameter counts, KV-cache and optimizer-state memory, collective communication volume, and decode throughput. | field | meaning | |---|---| | `task_id` | `sc-000` … `sc-034` | | `category` | roofline / flops / memory / sharding / inference | | `prompt` | the question, every parameter it needs, and the exact shape of the answer | | `api_description` | the shared preamble (conventions: 6ND, bf16=2B, ring collectives, Adam state) | | `expected_output` | JSON `{"rows": [...]}`, **computed by executing a reference solution** | Categories: roofline 7, flops 8, memory 6, sharding 7, inference 7. No dependencies — every task is answered with `math`. ## Original problems, and every hardware number is stated Nothing here is copied from the book. And no task requires knowing a real chip's peak FLOPs or HBM bandwidth: the parameters are given in the task. That second point is the main design decision. An environment that required recalling a spec sheet would measure memorisation of numbers that change with each accelerator generation — and its answer keys would silently become **wrong** as hardware moves while still looking authoritative. Stating the parameters makes every problem self-contained, permanently valid, and a test of the reasoning rather than the recall. ## What the answers look like The arithmetic that decides real scaling choices, where the result is often counterintuitive: the same matmul is compute-bound at batch 1024 (intensity 683) and memory-bound at batch 1 (intensity 0.9995); attention is only 16% of a layer's FLOPs at S=8192; Adam state is 6× the weights, so a 70B model needs 11 chips of 96 GiB just to be held; a 64-way gradient all-reduce takes 6.1× longer than the step it overlaps; batch-1 decode of a 70B model is 11.4 tokens/s, fixed by bandwidth alone. ## Grading Floats at a **1e-9 relative tolerance**; strings, booleans and `None` exactly. The tolerance exists for one thing — the order of multiplications and divisions, since `6ND/(chips·peak·mfu)` and `((6N)/chips)·(D/peak)/mfu` differ in their last bits. It is orders of magnitude too tight to hide a wrong formula: a missing `(N-1)/N`, a factor of 2 and an error of one part in a million all fail, and each of those is an asserted unit check. Verify with `python environments/scaling_env/build_tasks.py --verify` (35/35). Source: