The 4x Variation: How Precise Timing Instrumentation Solved the GPU Underutilization Mystery

Introduction

In the high-stakes world of zero-knowledge proof generation, every millisecond of GPU time counts. When the cuzk proving daemon—a system designed to generate Groth16 proofs at scale—was observed running at only ~50% GPU utilization, the investigation that followed became a masterclass in systematic debugging. This article examines a single pivotal message in that investigation: message index 3040, where the assistant, armed with granular timing data from the C++ CUDA layer, definitively identified the root cause of GPU underutilization and charted the path toward a solution.

The message in question is deceptively brief—a few paragraphs of reasoning followed by a Docker build command. But within those lines lies the culmination of a multi-round investigation that spanned code reading, log analysis, nvtop visualization, and precise instrumentation. It represents the moment when scattered data points coalesced into a clear diagnosis: the bottleneck was not GPU compute, not CPU preprocessing, not mutex contention—but PCIe bandwidth contention during Host-to-Device (H2D) transfers of the a/b/c synthesis vectors.

The Investigation Context

To understand the significance of message 3040, we must first understand what preceded it. The cuzk proving pipeline operates on partitions of a circuit synthesis. Each partition goes through several phases: synthesis (CPU), preprocessing (CPU on a separate thread), and then GPU work (NTT, MSM, batch addition, tail MSM) under a mutex. The system uses two GPU workers that are supposed to interleave efficiently—while one worker holds the GPU mutex and runs kernels, the other worker's CPU preprocessing should overlap productively.

But the GPU utilization hovered around 50%, meaning the GPU was idle half the time. The initial suspects were tracker lock contention (a Rust-side mutex for status tracking) and malloc_trim overhead. The team had already ruled these out by adding Rust-side timing instrumentation (GPU_TIMING, FIN_TIMING). That left the C++ gpu_prove_start function as the primary suspect.

The assistant had been systematically working through the codebase, reading the C++ CUDA source in groth16_cuda.cu and groth16_ntt_h.cu, and examining logs from the remote deployment. By message 3040, the assistant had already added timing instrumentation around the GPU mutex acquisition and barrier wait points, and was now looking at the detailed breakdown of ntt_msm_h—the function that handles NTT and MSM operations on the h polynomial.

The Timing Data: Separating Signal from Noise

The message opens with a reasoning section that lays out the timing breakdown with remarkable clarity. The assistant had extracted CUZK_NTT_H log lines from the remote machine, which contain per-function timing for the NTT/MSM pipeline. The breakdown is presented as a table of constant versus variable costs:

Constant costs (stable across runs):

• coset_intt_sync: ~113ms (always)
• msm_invoke: ~630ms (always)
• d_b_alloc: 0ms (cached allocation)
• batch_add: ~400ms (from earlier analysis)
• tail_msm: ~197ms (from earlier analysis) Variable cost — the actual bottleneck:
• ntt_kernels: 2239ms to 8918ms — a 4x variation! This decomposition is crucial. It tells us that the actual GPU compute—the MSM operations, batch additions, and tail MSM that do the real cryptographic work—is remarkably stable at approximately 1.3 seconds per partition (630ms MSM + 400ms batch add + 197ms tail MSM + 113ms inverse NTT). If the bottleneck were GPU compute capacity, these numbers would vary with workload. They don't. The ntt_kernels measurement, however, swings wildly from 2.2 seconds to nearly 9 seconds—a 4x range. This is the anomaly that demands explanation.

The Reasoning: Connecting the Dots

The assistant's reasoning in this message is particularly valuable because it shows the process of eliminating hypotheses and converging on the true root cause. Let me quote the key passage:

This is execute_ntts_single × 3 (for a, b, c vectors). Each NTT takes the scalar data from host memory, copies it to GPU, then runs the NTT kernel.

This is the critical insight. The ntt_kernels measurement isn't just kernel execution time—it encompasses the H2D transfer of the a, b, and c vectors from host memory to GPU device memory. The assistant has read the C++ source and understands the memory transfer pattern.

The reasoning continues:

The real culprit is PCIe bandwidth contention. The H2D transfers of those large vectors are competing with other memory operations on the bus, and when synthesis workers are pinning memory with cudaHostRegister, the congestion gets worse, which explains why I'm seeing such wild swings in timing.

This is a sophisticated diagnosis. The assistant is connecting multiple observations:

1. The ntt_kernels time varies dramatically (4x)
2. The actual GPU kernel time is stable (~1.3s)
3. The variation must come from the H2D transfer component within ntt_kernels
4. PCIe bandwidth is a shared resource—when multiple synthesis threads are running concurrently, they compete for the same bus
5. cudaHostRegister (pinning host memory for DMA) can exacerbate congestion The assistant also considers an alternative hypothesis—that the timing might be deceptive due to CUDA's async execution model:

Looking at the actual kernel launch sequence with the sync events, I see that tv1→tv2 captures the launches themselves, but the real work completes later at tv3 when the synchronization happens. The timing is deceptive because these are async operations across multiple GPU streams with event-based coordination between them.

This shows the assistant grappling with the complexity of CUDA timing. CUDA operations are asynchronous by default—kernel launches return immediately, and the actual execution happens later. The timing measurements must account for synchronization points to be meaningful. The assistant verifies that the synchronization is captured correctly and concludes that the 2-9s range is real, not an artifact of measurement.

The nvtop Correlation

The assistant references an nvtop screenshot that was shared by the user in a previous message. The nvtop visualization shows GPU utilization over time at 0.1-second resolution:

The nvtop fits: those ~1-2s GPU compute spikes are the MSM/batch_add/tail_msm kernels, and the gaps are H2D transfers + barrier waits happening while the GPU mutex is held.

This correlation between the timing logs and the visual data is powerful. The nvtop shows:

• Short bursts at 75-100% GPU utilization (the actual CUDA kernels)
• Gaps of 1-5 seconds at 0-25% utilization (the H2D transfers and idle periods)
• PCIe RX bandwidth dropping to 1-4 GB/s during gaps and bursting to 50 GB/s during compute phases The assistant had earlier noted that the PCIe RX bandwidth was only 1.015 GiB/s during the gaps—far below the PCIe Gen5 x16 theoretical maximum of ~50 GB/s. This is the signature of memory bandwidth contention: when multiple threads are simultaneously accessing host memory for H2D transfers, the effective bandwidth per thread collapses.

The Decision to Add More Instrumentation

Despite having identified the likely root cause, the assistant doesn't jump to a fix. Instead, it decides to add more precise instrumentation to confirm the diagnosis:

I should instrument the code with detailed timing around mutex waits, barrier waits, and lock hold times to get the full picture of what's happening.

This is a mature engineering decision. The assistant has a strong hypothesis, but wants to verify it before committing to a solution. The new instrumentation will measure:

1. Mutex wait time: How long does a worker wait to acquire the GPU mutex?
2. Barrier wait time: How long does the GPU thread wait for CPU preprocessing to finish?
3. Total mutex hold time: How long does each worker hold the GPU mutex? These measurements will confirm whether the GPU is truly idle during the H2D transfer gaps (as the nvtop suggests) or whether there's another factor at play. The message concludes with a Docker build command to compile and deploy the instrumented binary:

cd /tmp/czk && DOCKER_BUILDKIT=1 docker build --no-cache -f Dockerfile.cuzk-rebuild -t cuzk-rebuild:timing2 . 2>&1 | tail -15

This is the practical execution step—building a new Docker image with the additional timing instrumentation and preparing to deploy it to the remote machine for live workload analysis.

Assumptions and Their Validity

The assistant makes several assumptions in this message, most of which are well-supported by the evidence:

Assumption 1: The ntt_kernels timing includes H2D transfer. This is correct based on reading the C++ source. The execute_ntts_single function performs a synchronous or stream-synchronized cudaMemcpy of the a/b/c vectors before launching the NTT kernels.

Assumption 2: PCIe bandwidth contention is the primary cause of variation. This is strongly supported by the 4x variation in ntt_kernels while GPU compute remains stable. However, the assistant acknowledges this needs confirmation via the new mutex/barrier timing.

Assumption 3: The actual GPU compute is ~1.3s. This is calculated from the stable components: msm_invoke (630ms) + batch_add (400ms) + tail_msm (197ms) + coset_intt_sync (113ms) = ~1.34s. This is well-supported by the log data showing these values as stable across runs.

Assumption 4: The nvtop gaps correspond to H2D transfers. This is a reasonable correlation but could also include barrier wait time (GPU waiting for CPU preprocessing). The new instrumentation will distinguish these cases.

One potential blind spot: the assistant assumes that the H2D transfer is the bottleneck within ntt_kernels, but the NTT kernel itself could also vary if the GPU's memory subsystem is under pressure. However, the stable msm_invoke time (which also uses GPU memory) suggests the GPU's compute and memory subsystems are not the bottleneck—only the PCIe transfer is.

Input Knowledge Required

To fully understand this message, one needs:

1. CUDA programming model: Understanding of async kernel launches, streams, events, and the distinction between cudaMemcpy (synchronous) and cudaMemcpyAsync (asynchronous). The assistant's reasoning about timing accuracy depends on knowing when synchronization actually occurs.
2. PCIe architecture: Knowledge that PCIe is a shared bus where multiple DMA transfers compete for bandwidth. The concept of pinned memory (cudaHostAlloc) and its interaction with DMA engines.
3. Zero-knowledge proof pipeline: Understanding of the Groth16 proving system, including the role of NTT (Number Theoretic Transform) and MSM (Multi-Scalar Multiplication) as the dominant computational phases. Knowledge that a/b/c vectors are the wire assignments from circuit synthesis.
4. The cuzk architecture: Understanding of the partitioned proving pipeline, the two-worker interleaving model, the GPU mutex, and the separation of CPU preprocessing (prep_msm_thread) from GPU kernel execution.
5. Previous investigation steps: The earlier rounds that ruled out tracker lock contention and malloc_trim, and the existing CUZK_TIMING and CUZK_NTT_H instrumentation.

Output Knowledge Created

This message creates several important pieces of knowledge:

1. Definitive bottleneck identification: The ntt_kernels phase (H2D transfer + NTT kernel) is the primary variable cost, ranging from 2.2s to 8.9s per partition.
2. Stability of GPU compute: The actual GPU kernel execution time is stable at ~1.3s per partition, proving the GPU itself is not the bottleneck.
3. PCIe bandwidth contention hypothesis: The 4x variation in H2D transfer time is most likely caused by memory bandwidth contention from concurrent synthesis threads.
4. Instrumentation gap identification: The existing timing doesn't capture mutex wait time, barrier wait time, or total mutex hold time—these need to be added for confirmation.
5. Action plan: Build and deploy a new binary with the missing instrumentation to confirm the hypothesis before implementing a fix.

The Thinking Process: A Window into Debugging Methodology

The assistant's reasoning in this message exemplifies several key debugging principles:

Principle 1: Decompose the problem into constant and variable components. By separating the stable costs (MSM, batch add, tail MSM, iNTT) from the variable cost (NTT kernels), the assistant narrows the search space dramatically. The bottleneck must be in the variable component.

Principle 2: Correlate multiple data sources. The assistant doesn't rely solely on timing logs. It cross-references nvtop visualization (GPU utilization patterns), PCIe bandwidth measurements (RX/TX rates), and code analysis (understanding what execute_ntts_single does). The convergence of evidence from independent sources strengthens the diagnosis.

Principle 3: Verify timing accuracy. The assistant explicitly considers whether CUDA's async execution model could produce misleading timings. It reasons through the stream/event synchronization to confirm that the measurements are real.

Principle 4: Resist premature action. Despite having a strong hypothesis, the assistant doesn't immediately implement a fix. It adds more instrumentation to confirm the diagnosis. This prevents wasted effort if the hypothesis is wrong and provides quantitative data to guide the solution.

Principle 5: Understand the hardware bottleneck. The assistant doesn't stop at "the H2D transfer is slow." It identifies the root cause as PCIe bandwidth contention—a hardware-level resource conflict. This understanding is essential for designing the right fix.

The Broader Implications

The diagnosis in this message has significant implications for the cuzk architecture. If H2D transfer is the bottleneck, several solution paths become viable:

1. Pinned memory pool: Allocate a/b/c vectors directly in pinned (DMA-able) memory using cudaHostAlloc, eliminating the staged copy through a bounce buffer. This is the "zero-copy" approach.
2. Asynchronous transfer overlap: Use CUDA streams to overlap H2D transfers of one partition with GPU computation of another partition.
3. Synthesis throttling: Limit the number of concurrent synthesis threads to reduce memory bandwidth contention.
4. Partition size tuning: Adjust partition sizes to balance H2D transfer time against GPU compute time. The assistant would go on to implement Option B (the pinned memory pool) in subsequent messages, as described in the chunk summaries. But at this moment in message 3040, the focus is still on confirmation—building the instrumented binary to verify the hypothesis before committing to a solution.

Conclusion

Message 3040 represents the turning point in a complex debugging investigation. What began as a vague observation of "GPU underutilization" was systematically narrowed down through Rust-side instrumentation, C++ code reading, log analysis, and nvtop visualization to a specific hardware-level bottleneck: PCIe bandwidth contention during H2D transfers.

The assistant's reasoning demonstrates the power of precise instrumentation combined with deep understanding of the system architecture. By decomposing the timing data into constant and variable components, correlating multiple data sources, and reasoning through the CUDA execution model, the assistant arrived at a diagnosis that was both specific and actionable.

The message also exemplifies good engineering judgment: the decision to add more instrumentation rather than jumping to a fix, the careful consideration of alternative explanations, and the practical step of building and deploying the instrumented binary. These are the hallmarks of a systematic debugging process.

For anyone debugging performance issues in GPU-accelerated systems, this message offers a valuable lesson: when you see variable performance, look for shared resources. In this case, the shared resource was the PCIe bus, and the contention came from concurrent memory operations that were invisible at the application level. Only by drilling down into the hardware-level interactions—through precise timing, visualization, and code analysis—could the true bottleneck be identified.