The Pivot Point: How One Benchmark Data Point Revealed the Memory-Performance Scaling Law of a Groth16 Proving Engine

Introduction

In the course of a systematic low-memory benchmark sweep for the SUPRASEAL_C2 Groth16 proof generation pipeline, a single assistant message at index 3305 served as the pivot point between two phases of investigation. This brief message — consisting of just two sentences and a file write — reported the results of a pw=10 gw=1 configuration and initiated the next benchmark run at pw=10 gw=2. On its surface, the message appears unremarkable: a data point, a decision, a file creation. But in the context of the broader investigation, this message crystallized the entire memory-versus-throughput scaling relationship that the sweep was designed to uncover, and it set the stage for the deployment guidance that would become the final deliverable of the session.

The Message

The subject message reads in full:

[assistant] pw=10 gw=1: 310 GiB peak, 45.4s/proof, 39.5s avg prove. Now for reference, let me also run pw=10 gw=2 (the Phase 12 known-good config) to get comparable numbers: [write] /tmp/cuzk-lowmem-pw10-gw2.toml Wrote file successfully.

This is the entirety of the assistant's contribution in this round. It reports a single benchmark result, announces the intent to run the next configuration, and writes a configuration file to disk.

Context and Motivation

To understand why this message was written, one must understand the arc of the preceding 60+ messages. The user had asked ([msg 3272]): "Run cuzk with lower parallelsms to see how low we can get RSS requirements on smaller systems and the timings. Try 1/2/5/7, also lower queues/gpu workers that would also hold a lot of memory." This request came immediately after the assistant had completed Phase 12 — a major engineering effort to add memory backpressure to the split GPU proving API, culminating in a working configuration at pw=12 gw=2 that achieved 37.7 seconds per proof but consumed approximately 400 GiB of peak RSS.

The user's question was fundamentally about deployability. The Phase 12 configuration, while performant, required a machine with roughly 768 GiB of RAM to operate safely. This is a substantial machine — expensive to rent in cloud markets and potentially overkill for smaller storage operations. The user wanted to know: what does the engine look like when you scale it down? What configurations are viable on 128 GiB, 256 GiB, or 512 GiB systems?

The assistant responded by designing a systematic benchmark sweep across partition_workers (pw) values of 1, 2, 5, 7, and (as an extension) 10 and 12, crossed with gpu_workers_per_device (gw) values of 1 and 2. Each configuration was run through a standardized benchmark: 5 proofs at concurrency 5, with peak RSS measured via /proc/pid/status (VmHWM). A custom shell script (/tmp/cuzk-lowmem-bench.sh) was written to automate the cycle of starting the daemon, monitoring RSS, running the benchmark, and collecting results.

By the time the assistant reached message 3305, it had already collected data for pw=1 gw=1 (104 GiB peak, ~290s/proof), pw=2 gw=1 (110 GiB, 152s/proof), pw=5 gw=1 (170 GiB, 68.4s/proof), pw=7 gw=1 (208 GiB, 53.3s/proof), and pw=5 gw=2 (170 GiB, 68.6s/proof — nearly identical to gw=1, confirming that the second GPU worker added no value at low pw). The pw=7 gw=2 run was also complete (results not yet reported but visible in the next message).

The Significance of the pw=10 gw=1 Data Point

The pw=10 gw=1 result — 310 GiB peak, 45.4s/proof — was the most informative single data point in the entire sweep. Here's why.

First, it confirmed the linear memory scaling relationship that the earlier points had only hinted at. The baseline RSS (daemon idle with SRS loaded) was consistently 69 GiB across all configurations. Each additional partition worker added approximately 20 GiB of memory. The formula 69 + pw × 20 predicted 269 GiB for pw=10, but the actual was 310 GiB — slightly higher, suggesting either a non-linear component or additional memory from the GPU worker's in-flight buffers at higher throughput. This was a critical finding for deployment guidance: system integrators could now estimate memory requirements with a simple linear formula.

Second, the throughput of 45.4s/proof at pw=10 gw=1 was remarkably close to the Phase 12 reference of 37.7s/proof at pw=12 gw=2, but at 310 GiB instead of 400 GiB. This meant that a single-GPU-worker configuration at pw=10 achieved 84% of the throughput of the dual-worker configuration while consuming 22% less memory. For cost-sensitive deployments, this was arguably the better trade-off.

Third, the prove time of 39.5s (the GPU computation portion) versus the wall-clock throughput of 45.4s revealed that only about 6 seconds per proof were spent on CPU-side synthesis and queueing overhead. The GPU was the bottleneck, not the CPU — which was exactly the design goal of the split API.

The Decision to Run pw=10 gw=2

The second sentence of the message — "Now for reference, let me also run pw=10 gw=2 (the Phase 12 known-good config) to get comparable numbers" — reveals the assistant's methodological thinking. Having established the gw=1 baseline, the assistant needed the gw=2 comparison to complete the picture. The Phase 12 reference had been pw=12 gw=2, but that was run at concurrency 20 (j=20), which inflated memory due to more in-flight proofs. Running pw=10 gw=2 at j=5 would provide a clean comparison: same partition worker count, same concurrency, just the GPU worker count varied.

This decision was not trivial. Each benchmark run took 5-8 minutes of wall time (daemon startup + SRS loading + 5 proofs), and the assistant was being careful to collect comparable data. Running pw=10 gw=2 would answer the question: does the second GPU worker help at pw=10, or is synthesis still the bottleneck? The earlier pw=5 comparison had shown no benefit from gw=2 — synthesis couldn't feed two GPU workers fast enough. At pw=10, with twice as many synthesis threads, perhaps the GPU could be kept busier.

The Broader Achievement

This message, though brief, represents the culmination of the assistant's shift from optimization engineering to production characterization. The Phase 12 engineering work (messages 3245-3271) had been about making the engine work correctly under memory pressure — fixing use-after-free bugs, implementing early deallocation, adding channel capacity auto-scaling, and holding partition permits through sends. That was the "make it work" phase.

The benchmark sweep, of which this message is a key milestone, was the "characterize it for deployment" phase. The assistant was no longer asking "can we make it faster?" but rather "what configurations make sense for different hardware budgets?" This is a fundamentally different engineering mindset — one that recognizes that raw performance is only valuable if it can be deployed cost-effectively.

The data from this sweep would eventually be synthesized into a deployment guidance table in the project documentation, showing concrete recommendations: 128 GiB systems should use pw=2 gw=1 (152s/proof), 256 GiB systems should use pw=5 gw=1 (68s/proof), 512 GiB systems should use pw=10 gw=1 (45s/proof), and 768 GiB systems could use pw=12 gw=2 (42s/proof). This guidance, committed as 9bb657e5, was the practical deliverable that answered the user's original question.

Conclusion

Message 3305 is a study in how the most consequential moments in a technical investigation can appear mundane. A single benchmark result, a config file write, a decision about what to run next — these are the building blocks of systematic engineering. But within this message lies the confirmation of a linear memory scaling law, the identification of the optimal memory-throughput trade-off point, and the methodological rigor that would produce actionable deployment guidance. It is the message where the assistant stopped optimizing and started measuring — and in doing so, transformed a complex engineering artifact into a well-characterized, deployable system.