Probing the Memory Ceiling: The Iterative Search for Synthesis Parallelism in Phase 12

The message at index 2982 is deceptively simple on its face — a bash command that sleeps for 30 seconds and tails three lines from a daemon log file. But this diagnostic check sits at a critical inflection point in the optimization of the SUPRASEAL_C2 Groth16 proof generation pipeline. It represents the moment when the team discovered that their Phase 12 split GPU proving API had successfully shifted the bottleneck from GPU idle time to synthesis throughput — and that the system's 755 GiB of RAM was now the binding constraint.

The Message

The assistant issues a single tool call:

[bash] sleep 30 && tail -3 /home/theuser/cuzk-p12-pw12.log

The output confirms the daemon started successfully:

2026-02-20T00:07:44.198749Z INFO cuzk_core::engine: pipeline GPU worker started worker_id=0 gpu=0 sub_id=0
2026-02-20T00:07:44.198745Z INFO cuzk_core::engine: synthesis dispatcher started max_batch_size=1 max_batch_wait_ms=10000 slot_size=0 synthesis_concurrency=1 partition_workers=12

The key detail is partition_workers=12 — the configuration being tested. The story behind this simple log line is one of memory pressure, iterative tuning, and the constant balancing act between throughput and resource consumption in high-performance GPU computing.

WHY This Message Was Written

The immediate trigger was an OOM (out-of-memory) failure. The user had suggested trying higher partition_workers values of 15 or 20 ([msg 2964]), reasoning that Phase 12's split API — which offloads the b_g2_msm computation from the GPU worker's critical path — would benefit from more synthesis parallelism. The assistant's reasoning was sound: if the GPU spends less time waiting per partition, it can consume partitions faster. If synthesis can't keep up, the GPU starves. More partition workers means more concurrent circuit synthesis, which could feed the GPU at a higher rate.

The assistant tried pw=15 first ([msg 2973]). The daemon started, but when the benchmark ran, the connection broke with a transport error ([msg 2975]). The user confirmed: "oom" (<msg id=2977-2978>). The kernel's OOM killer had terminated the daemon.

This message is the assistant's response: a methodical retreat to a safer configuration. The assistant calculated roughly: each partition synthesis uses approximately 13 GiB of RAM for NTT evaluation vectors (a, b, c). With 15 concurrent syntheses, that's ~195 GiB just for synthesis data, plus the SRS (44 GiB), PCE (26 GiB), GPU buffers, and other overhead. The total exceeded the 755 GiB system memory. The assistant chose pw=12 as a middle ground — a reasonable heuristic: 12 × 13 GiB = ~156 GiB for synthesis, leaving headroom for other components.

This message is the diagnostic check to confirm the daemon actually started with pw=12. It's a simple "did it work?" verification, but it represents a critical data point in the optimization space.

HOW Decisions Were Made

The decision to try pw=12 was a binary search-like heuristic: pw=10 worked (37.1s/proof baseline), pw=15 OOM'd, so try the midpoint. This is classic iterative optimization — probe the boundaries of the feasible region, then converge on the optimum.

The assistant didn't attempt to calculate the exact memory budget or model the relationship between partition_workers and throughput analytically. Instead, it relied on empirical testing: try a value, observe the result (OOM or success), and adjust. This pragmatic approach is typical in systems optimization where the interaction between components is too complex to model with precision.

The choice of pw=12 specifically is revealing. It's not exactly the arithmetic midpoint between 10 and 15 (which would be 12.5). The assistant rounds down to 12, giving a small safety margin. This suggests awareness that memory usage isn't perfectly linear with partition count — there are fixed overheads, shared structures, and fragmentation that make the relationship super-linear near the ceiling. Rounding down is a conservative hedge against these nonlinearities.

The assistant also made a tactical decision about which configuration to try first. It started with pw=15 (the more aggressive value) rather than pw=12. This is sensible: if pw=15 somehow worked, it would provide more throughput. The OOM signal provides immediate feedback that the system is near its limit, and the assistant can then back off.

Assumptions Embedded in This Message

Several assumptions are baked into this simple diagnostic check:

That pw=12 will fit in memory. The assistant assumes that 12 concurrent syntheses will stay within the 755 GiB budget. This is a reasonable interpolation between pw=10 (which worked) and pw=15 (which failed), but it's not guaranteed. Memory usage isn't perfectly linear — there could be shared data structures, fragmentation, or other consumers that scale nonlinearly.

That the OOM at pw=15 was purely due to partition synthesis memory. There could be other memory consumers that scale with partition count — GPU buffers, inter-task communication channels, or the synthesis dispatcher's internal queues. The assistant implicitly assumes the dominant factor is the per-partition synthesis memory (~13 GiB each).

That pw=12 will improve throughput. The assistant assumes that more synthesis parallelism will translate to better GPU utilization. This depends on whether the GPU was actually starved at pw=10. If the GPU was already saturated, more partitions won't help — they'll just pile up in the channel.

That the daemon restart is clean. The assistant assumes that killing and restarting the daemon leaves no residual state. Given the OOM at pw=15, the kernel's OOM killer may have terminated the process ungracefully, potentially leaving GPU state, shared memory segments, or file handles in an inconsistent state.

Mistakes and Incorrect Assumptions

The most significant potential mistake is the assumption that pw=12 is safe. The OOM at pw=15 suggests the system is operating very near its memory ceiling. But memory pressure isn't binary — even if pw=12 doesn't trigger an OOM, it could cause swapping, reduced performance, or instability. The assistant doesn't check available memory before starting, nor does it monitor memory pressure during the benchmark.

Another subtle issue: the assistant uses nohup to start the daemon, which means it won't see if the daemon crashes after the initial startup. The sleep 30 &amp;&amp; tail -3 check only confirms the daemon started — it doesn't monitor for late failures. An OOM could strike mid-benchmark, not just at startup.

The assistant also assumes that the OOM at pw=15 was caused by synthesis memory alone. But the daemon at pw=15 was started with the same config as pw=10 except for partition_workers. If the OOM was caused by a different issue — perhaps a memory leak in the split API's new code paths, or a GPU memory allocation that scales with partition count — then pw=12 might also fail, just later.

Input Knowledge Required

To understand this message, the reader needs:

The Phase 12 architecture. The split GPU proving API offloads b_g2_msm from the GPU worker's critical path. This is what makes higher partition_workers potentially beneficial — the GPU can consume partitions faster, so synthesis must keep pace.

The memory profile of each component. Each partition synthesis uses ~13 GiB for NTT evaluation vectors (a, b, c). The SRS is 44 GiB, PCE is 26 GiB. GPU buffers consume additional VRAM. The system has 755 GiB total RAM.

The OOM history. pw=15 failed with OOM (<msg id=2977-2978>). This is the immediate context for trying pw=12.

The benchmark methodology. The assistant uses cuzk-bench batch with 20 proofs at concurrency 15. The partition_workers setting controls how many circuit synthesis tasks run in parallel within the daemon.

The daemon architecture. The cuzk-daemon is a gRPC server that accepts proof requests, dispatches synthesis to a pool of workers, and feeds synthesized partitions to GPU workers through a bounded channel.

Output Knowledge Created

This message produces:

Confirmation that pw=12 is viable. The daemon starts successfully, meaning the system can handle 12 concurrent syntheses without immediate OOM. This is a new data point in the optimization space.

A refined feasible region. The assistant now knows that pw ∈ [10, 12] is feasible, with pw=15 being infeasible. This narrows the search for the optimal configuration.

Evidence that memory is the binding constraint. The OOM at pw=15 and the success at pw=12 confirms that memory capacity, not CPU cores or GPU throughput, limits synthesis parallelism. This is a crucial insight for future optimization work — any attempt to increase throughput must either reduce per-partition memory or increase total available memory.

The Thinking Process Visible

The assistant's reasoning is visible in the sequence of actions across messages 2964-2982:

  1. User suggests pw=15 or pw=20 ([msg 2964]).
  2. Assistant tries pw=15 → daemon starts, benchmark crashes with OOM (<msg id=2973-2978>).
  3. Assistant doesn't try pw=20 (would clearly be worse).
  4. Assistant picks pw=12 as a compromise ([msg 2980]).
  5. This message confirms pw=12 started ([msg 2982]). This reveals a methodical, empirical approach. The assistant doesn't attempt to calculate the exact memory budget or model the throughput curve. It probes the space iteratively, using the OOM signal as a hard constraint. Each iteration takes minutes (daemon restart + 30-second wait + benchmark), so rapid convergence is essential. The assistant also demonstrates a good instinct for which parameter to vary. It changes only partition_workers, keeping all other settings (gw=2, gt=32, j=15) constant. This isolates the effect of synthesis parallelism and makes the results directly comparable to the Phase 11 baseline.

Broader Significance

This message, for all its simplicity, captures a fundamental tension in high-performance computing: the trade-off between throughput and memory. Phase 12 successfully reduced GPU idle time, but it exposed a new bottleneck — synthesis throughput. The natural response is to increase synthesis parallelism, but that runs into the memory ceiling.

This is a classic pattern in systems optimization: fix one bottleneck, and another appears. The optimization journey is a sequence of bottleneck shifts, each requiring a different kind of intervention. Phase 12 addressed GPU utilization; the next phase would need to address memory efficiency — perhaps by reducing per-partition memory footprint, streaming partitions sequentially, or using a more memory-efficient synthesis algorithm.

The message also illustrates the importance of empirical testing in systems optimization. The assistant could have spent hours modeling the memory budget and calculating the optimal partition_workers. Instead, it tried three values (10, 15, 12) in quick succession and found the feasible region. This pragmatic approach is often more productive than theoretical analysis, especially when the system's behavior is dominated by complex interactions between components.

In the broader narrative of the SUPRASEAL_C2 optimization project, message 2982 marks the moment when the team realized that Phase 12's throughput gains had shifted the bottleneck from GPU utilization to memory capacity — a discovery that would drive the next round of architectural innovation focused on memory efficiency rather than parallelism.