The Critical Benchmark: Finding the Optimal Partition Worker Count for Phase 12 Memory Backpressure

At first glance, message [msg 3224] appears to be nothing more than a routine benchmark invocation — a single bash command launching a 20-proof batch run of the cuzk Groth16 proving engine. But in the context of the Phase 12 optimization campaign, this message represents a pivotal moment of empirical validation. It is the moment where the assistant tests whether the carefully engineered memory backpressure mechanism scales to higher partition worker counts, and whether the DDR5 bandwidth wall hypothesis — established during Phase 11 — holds true under increased parallelism.

The Message in Full

The assistant executed the following command:

FIL_PROOFS_PARAMETER_CACHE=/data/zk/params /home/theuser/curio/extern/cuzk/target/release/cuzk-bench batch --type porep --c1 /data/32gbench/c1.json --count 20 --concurrency 20 2>&1

The output, truncated in the conversation, shows the first five completions of a twenty-proof batch benchmark for the Filecoin Proof-of-Replication (PoRep) circuit with a 32 GiB sector size:

[1/20] COMPLETED — 92.7s (prove=73844 ms, queue=300 ms)
[2/20] COMPLETED — 143.2s (prove=67298 ms, queue=780 ms)
[3/20] COMPLETED — 178.1s (prove=74521 ms, queue=1236 ms)
[4/20] COMPLETED — 755.1s (prove=62956 ms, queue=8379 ms)
[5/20] COMPLETED — 193.0s (prove=7...

This run uses partition_workers=14 (pw=14), with gpu_workers_per_device=2 (gw=2) and gpu_threads=32 (gt=32) — the same GPU configuration that proved optimal in earlier phases. The daemon was configured with a freshly created configuration file (/tmp/cuzk-p12-pw14.toml) that set these parameters, and the assistant had just verified that the effective channel lookahead matched the partition worker count at 14.

Why This Message Was Written: The Optimization Sweep

To understand why this particular benchmark was run, one must trace the reasoning chain that led to it. The assistant had just completed implementing three critical memory backpressure mechanisms on top of the Phase 12 split GPU proving API:

Early a/b/c free: Clearing approximately 12 GiB per partition of evaluation vectors immediately after prove_start returns, since the GPU kernels (NTT + MSM) had finished with them and only density bitvecs and assignment data were needed for the background b_g2_msm finalization.
Channel capacity auto-scaling: Sizing the synthesis-to-GPU channel to max(synthesis_lookahead, partition_workers) instead of the previously hardcoded value of 1. This prevented completed synthesis outputs from blocking on send() while holding large allocations.
Partition permit held through send: The semaphore permit — which bounds the total number of partitions in flight — was now released only after the channel send succeeded, rather than immediately after synthesis completion. Since the channel capacity matched the worker count, sends were non-blocking, adding zero latency while bounding total in-flight outputs. These changes had already produced dramatic results. The assistant had benchmarked pw=10 at 38.5 seconds per proof with 321 GiB peak RSS, and — most importantly — pw=12 at 37.7 seconds per proof with 400 GiB peak RSS. Previously, pw=12 had caused an out-of-memory (OOM) crash at 668 GiB. The memory backpressure fix had reduced peak memory by 40% and turned an OOM failure into a successful run with better throughput than pw=10. The natural next question was: can we push further? If pw=12 improved throughput over pw=10 (37.7s vs 38.5s), perhaps pw=14 would improve it further. Or perhaps the system had already hit the DDR5 memory bandwidth wall identified during Phase 11, where additional parallelism merely increases memory contention without improving throughput. The pw=14 benchmark was designed to answer this question.

The Reasoning Behind the Configuration

The assistant's choice of pw=14 as the next test point reveals a systematic experimental methodology. Having established a baseline at pw=10 and found improvement at pw=12, the natural increment was to pw=14. The assistant was not guessing randomly — it was conducting a parameter sweep, holding all other variables constant (gw=2, gt=32, 20 proofs at concurrency 20) while varying only the partition worker count.

The configuration file was generated inline:

[daemon]
listen = "0.0.0.0:9820"
[srs]
param_cache = "/data/zk/params"
preload = ["porep-32g"]
[synthesis]
partition_workers = 14
[gpus]
gpu_workers_per_device = 2
gpu_threads = 32

This was created in message [msg 3215], immediately after the assistant finished analyzing the pw=12 results. The assistant then killed the previous daemon, started a new one with the pw=14 configuration, verified it was ready, and launched the RSS monitor before running the benchmark seen in the subject message.

Input Knowledge Required

To fully understand this message, one needs substantial context from the preceding optimization campaign:

The Phase 12 split API architecture: The GPU proving pipeline was restructured so that prove_start (GPU work: NTT + MSM) is decoupled from prove_finalize (CPU post-processing: b_g2_msm). This allows the GPU to begin work on the next partition while the CPU finalizes the previous one, but it also means synthesized partitions can pile up in memory if synthesis outpaces GPU consumption.
The memory backpressure problem: Without the three fixes described above, synthesized partitions accumulated in the synthesis→GPU channel, causing unbounded memory growth. At pw=12, this led to OOM at 668 GiB — exceeding the system's 755 GiB memory budget.
The DDR5 bandwidth wall: Phase 11 analysis identified that DDR5 memory bandwidth contention was the primary bottleneck. Multiple CPU cores competing for the same memory bus caused slowdowns as worker counts increased beyond a certain point.
The benchmark methodology: The assistant uses 20 proofs at concurrency 20 (j=20) as a standard benchmark workload. The prove time shown in each completion line represents the time from when the proof started GPU work to when it finished, while queue time represents how long the proof waited before a GPU worker became available.
The system configuration: Two GPUs, 755 GiB total memory, with SRS parameters preloaded from /data/zk/params.

Output Knowledge Created

The pw=14 benchmark produced several critical data points. From the subsequent message ([msg 3225]), we learn the aggregate result: pw=14 achieved 37.8 seconds per proof with 456.9 GiB peak RSS. This is essentially identical throughput to pw=12 (37.7s) but with 57 GiB more peak memory (457 GiB vs 400 GiB).

The individual completion lines in the truncated output reveal interesting behavior. The fourth completion shows a wall time of 755.1 seconds with only 62.9 seconds of prove time and 8.4 seconds of queue time. The enormous gap between wall time and (prove + queue) suggests this proof spent over 680 seconds waiting for something — likely blocked on the semaphore or channel while all GPU workers were busy with other proofs. This is a natural consequence of running 20 proofs concurrently with only 2 GPU workers per device (4 total GPU workers): proofs spend most of their time waiting in line.

More subtly, the prove times show variation: 73.8s, 67.3s, 74.5s, 62.9s... This variation reflects the complex interaction between CPU synthesis, GPU compute, and memory bandwidth contention. When multiple proofs compete for the same DDR5 bandwidth, individual proof times can vary significantly.

The Thinking Process Visible in the Reasoning

The assistant's reasoning is revealed through the sequence of actions surrounding this message. After the benchmark completes, the assistant immediately evaluates the result in [msg 3225]:

pw=14: 37.8s/proof! Let me check RSS

The exclamation mark conveys genuine satisfaction — the result is positive. But then the assistant immediately checks RSS, revealing the dual objective: not just throughput, but memory efficiency. The peak RSS of 456.9 GiB is higher than pw=12's 400 GiB, and the throughput is essentially identical (37.8s vs 37.7s). This tells the assistant that pw=14 offers no advantage.

The assistant then pushes further to pw=16 ([msg 3226]), which yields 38.4 seconds per proof with 510 GiB peak RSS — strictly worse on both metrics. This confirms the DDR5 bandwidth wall hypothesis: beyond pw=12, additional partition workers consume more memory without improving throughput, because they all compete for the same memory bus.

The final synthesis in the commit message ([msg 3240]) crystallizes the conclusion:

Optimal config: pw=12 — best throughput with bounded memory.

Assumptions and Potential Pitfalls

The assistant made several assumptions in this benchmark run. First, it assumed that 20 proofs at concurrency 20 provides a representative sample. While 20 is reasonable for throughput measurement, it may not capture long-tail memory behavior. A 100-proof run might reveal different peak memory patterns.

Second, the assistant assumed that the system's 755 GiB memory budget is the relevant constraint. In production, the daemon may share the machine with other services, reducing the available budget. The 457 GiB peak at pw=14 might be acceptable in isolation but problematic in a shared environment.

Third, the assistant assumed that the DDR5 bandwidth wall is the limiting factor for pw>12. While the evidence supports this — pw=14 and pw=16 both show worse throughput-per-worker — there could be other factors at play, such as lock contention in the channel implementation or NUMA effects on the dual-socket system.

Fourth, the assistant implicitly assumed that the optimal pw value is independent of the GPU configuration. But pw=12 might only be optimal with gw=2, gt=32. With different GPU settings, the optimal synthesis parallelism might shift.

The Deeper Significance

This message, for all its apparent simplicity, represents a crucial moment in the optimization campaign. It is the point where the assistant confirms that the memory backpressure fix works correctly at scale — pw=14 runs without OOM, proving the fix is robust — while simultaneously discovering that further parallelism yields diminishing returns. The DDR5 bandwidth wall, first identified as a hypothesis in Phase 11, is now empirically validated across four data points (pw=10, 12, 14, 16).

The result is a clear optimal configuration: pw=12 at 37.7 seconds per proof with 400 GiB peak RSS. This is a remarkable achievement considering that the same configuration previously crashed with an OOM at 668 GiB. The 40% memory reduction, combined with successful execution, validates the entire Phase 12 memory backpressure design.

In the broader narrative of the cuzk optimization project, this message marks the transition from implementation and debugging to systematic benchmarking and tuning. The hard problems — the split API design, the channel capacity logic, the semaphore fix — are solved. What remains is the engineering work of finding the optimal operating point within the newly stable system.