The Edge of the Optimization Frontier: Benchmarking Partition Workers at pw=16

In the iterative optimization of a high-performance Groth16 proof generation pipeline for Filecoin's Proof-of-Replication (PoRep), there comes a moment when the engineer must discover where the curve flattens. Message 3233 in this opencode session is precisely that moment: a single bash command launching a benchmark with partition_workers=16 (pw=16), the highest setting tested in a systematic sweep across concurrency levels. On its surface, the message is mundane — a benchmark invocation with its first few lines of output. But in context, it represents the culmination of a multi-hour investigation into memory backpressure, channel capacity, and the fundamental DDR5 memory bandwidth limits of the system.

The Message

The subject message ([msg 3233]) is a bash command that runs the cuzk-bench batch benchmark tool with 20 proofs at concurrency 20, using the Phase 12 split GPU proving API. The command is:

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 shows the first five proofs completing, with prove times ranging from 73s to 107s. The output is truncated mid-line at proof 5, but the full result (visible in the subsequent message [msg 3234]) reveals the punchline: pw=16 delivers 38.4s/proof — slightly worse than pw=14's 37.8s, and with a suspicious 107-second outlier on proof #3.

Why This Message Was Written: The Systematic Sweep

This message was not written in isolation. It is the fourth in a deliberate benchmarking sequence designed to find the optimal partition_workers parameter for the Phase 12 split API. The reasoning chain is visible across the preceding messages:

1. pw=10 ([msg 3198]–[msg 3203]): 38.5–38.9s/proof, 317–321 GiB peak RSS — a baseline confirming the memory backpressure fix works without OOM.
2. pw=12 ([msg 3211]–[msg 3214]): 37.7–38.5s/proof, 399.7 GiB peak RSS — significantly better throughput, establishing that more synthesis parallelism helps.
3. pw=14 ([msg 3224]–[msg 3226]): 37.8s/proof, 456.9 GiB peak RSS — throughput plateauing, memory still climbing.
4. pw=16 ([msg 3233]): 38.4s/proof, 510 GiB peak RSS — throughput regressing, memory still climbing. The engineer is systematically probing the parameter space to find the "sweet spot." The assumption is that more partition workers should improve throughput by keeping the GPU workers better fed — synthesis is the bottleneck that produces the partitions the GPU consumes. But there's a hidden dependency: all those synthesized partitions compete for the same DDR5 memory bandwidth. More workers means more memory pressure, which means slower allocations, more cache misses, and ultimately, slower synthesis.

The Assumptions at Play

Several assumptions underpin this benchmark. First, the engineer assumes that the memory backpressure mechanisms implemented earlier in the segment — early a/b/c vector deallocation, channel capacity auto-scaling, and partition permit held through send — are working correctly and will prevent OOM at higher pw values. This is a validated assumption: earlier, pw=12 had OOM'd at 668 GiB before the fix, and now it runs at 399.7 GiB.

Second, the engineer assumes that throughput will continue to improve with more partition workers, up to some saturation point. This is the classic producer-consumer scaling assumption: if the GPU is the consumer and synthesis is the producer, adding more producers should increase throughput until the consumer is saturated or a shared resource (memory bandwidth) becomes the bottleneck.

Third, there's an implicit assumption that the DDR5 memory bandwidth is the limiting factor, not GPU compute. The engineer has been reasoning about this throughout the segment, noting in [msg 3202] that the GPU is ~0.5s slower per partition compared to the Phase 12 baseline, and hypothesizing that "memory pressure — more fragmented memory means slower cudaHostRegister / memory access patterns" could be the cause.

What Went Wrong: The Hidden Bottleneck

The pw=16 result reveals that the assumption of continued scaling was incorrect. Throughput actually regressed from 37.8s (pw=14) to 38.4s (pw=16). The engineer's analysis in [msg 3234] identifies the problem: "Higher pw means more memory pressure competing for the same DDR5 bandwidth."

This is a classic case of a hidden shared resource becoming the bottleneck. The DDR5 memory subsystem is a finite resource that all CPU cores share. When 16 partition workers are simultaneously allocating, computing, and freeing ~12 GiB evaluation vectors each, the aggregate memory traffic saturates the memory controller. The result is not just higher peak RSS (510 GiB vs 456 GiB) but slower per-partition synthesis times, which cascades into slower overall proof throughput.

The 107-second outlier on proof #3 is particularly telling. Such outliers often indicate a garbage collection or deallocation storm — when multiple workers finish their partitions simultaneously and trigger large munmap calls that contend for kernel-level memory management locks. The engineer has seen this pattern before, noting in [msg 3200] that "glibc free() of large allocations (>128KB) uses munmap which is relatively fast but still involves kernel calls."

Input Knowledge Required

To understand this message, one needs knowledge of several layers:

• The Groth16 proof pipeline: Each proof requires 10 partitions, each partition involves ~12 GiB of evaluation vectors (a/b/c), synthesis on CPU, and MSM/NTT operations on GPU.
• The Phase 12 split API: The GPU proving is decoupled into prove_start (GPU work) and prove_finalize (CPU post-processing), allowing overlap.
• The memory backpressure mechanism: Three interventions — early a/b/c free (clearing ~12 GiB/partition immediately after prove_start), channel capacity auto-scaling (sizing the synthesis→GPU channel to max(synthesis_lookahead, partition_workers)), and partition permit held through send (bounding total in-flight outputs).
• The hardware: Dual GPU (gw=2), 32 GPU threads (gt=32), DDR5 memory, 755 GiB total memory budget.
• The benchmark methodology: cuzk-bench batch with --count 20 --concurrency 20 runs 20 proofs with 20 concurrent connections, measuring total wall time, prove time, and queue time per proof.

Output Knowledge Created

This message produces several concrete outputs:

1. A data point at pw=16: 38.4s/proof, 510 GiB peak RSS — the worst throughput and highest memory of the four configurations tested.
2. Confirmation of the sweet spot: pw=12–14 is optimal, delivering 37.7–37.8s/proof with 400–457 GiB memory.
3. Evidence of the DDR5 bandwidth wall: Beyond pw=14, throughput regresses while memory continues to climb, confirming that memory bandwidth contention is the limiting factor.
4. A decision point: The engineer can now stop exploring higher pw values and commit the changes, having found the optimal configuration.

The Thinking Process

The reasoning visible across this sequence is a textbook example of systematic optimization. The engineer:

1. Establishes a baseline (pw=10) to verify the fix works.
2. Tests a higher value (pw=12) to see if more parallelism helps — it does.
3. Tests an even higher value (pw=14) to find the plateau — throughput is flat.
4. Tests the highest value (pw=16) to confirm the plateau and identify the bottleneck — throughput regresses. At each step, the engineer checks both throughput and memory, understanding that the two are coupled. The analysis in [msg 3234] — "Higher pw means more memory pressure competing for the same DDR5 bandwidth" — shows the engineer correctly interpreting the data to identify the root cause. The message also reveals the engineer's discipline: they don't stop at pw=14 even though it looks like the sweet spot. They push one step further to pw=16 to confirm the curve has indeed flattened, turning a hypothesis ("pw=14 might be optimal") into a conclusion ("pw=12-14 is the sweet spot, and pw=16 is worse"). This extra step prevents premature commitment and provides confidence that the optimization frontier has been reached.

Conclusion

Message 3233 is a single benchmark invocation that, in the context of the surrounding investigation, marks the boundary of the optimization space. It confirms that the DDR5 memory bandwidth wall — not GPU compute, not synthesis speed — is the fundamental limiter in this system. The engineer's systematic sweep from pw=10 to pw=16, checking both throughput and memory at each step, demonstrates a disciplined approach to finding the optimal operating point. The result is a clear recommendation: pw=12 with gw=2, gt=32 delivers the best throughput-to-memory ratio, and the memory backpressure fix makes it achievable without OOM. The optimization phase is complete, and the next step is to commit the changes and move on.