Measuring the Unmeasurable: Solving GPU Rate Estimation for Pipelined Workers

In the high-stakes world of GPU-accelerated zero-knowledge proving, every millisecond counts. The opencode session captured in message 3551 represents a critical turning point in a weeks-long debugging saga: the moment when a flawed approach to measuring GPU throughput was replaced by a clean, principled solution. This single message, a concise five-point plan followed by a successful edit, embodies the transition from heuristic guesswork to direct measurement—a shift that would ultimately stabilize the entire proving pipeline.

The Context: A Pipeline Plagued by Idle GPUs

The conversation leading up to message 3551 is the culmination of an intensive debugging effort. The team had been battling GPU underutilization in the cuzk (CUDA-based zero-knowledge) proving engine. The core problem was deceptively simple: the GPU was spending too much time idle, waiting for work. The solution, however, proved remarkably elusive.

The proving pipeline works like an assembly line. Synthesis (circuit construction) runs on the CPU, producing partitions that are dispatched to GPU workers for proving. A "pacer" component—the DispatchPacer—is responsible for regulating how fast partitions are fed to the GPU, attempting to keep the GPU saturated without overwhelming it. The pacer uses a PI (proportional-integral) controller to adjust the dispatch rate based on feedback signals: the queue depth of partitions waiting for the GPU, and the rate at which the GPU completes work.

The critical feedback signal is the GPU consumption rate—how fast the GPU can process partitions. If the pacer underestimates this rate, it dispatches too slowly and the GPU starves. If it overestimates, the queue grows unboundedly and memory pressure builds. Getting this measurement right is essential.

The Flawed Approach: Queue Depth as a Proxy

The previous iteration of the pacer attempted to measure GPU rate by tracking inter-completion intervals—the time between successive GPU completions. The logic was: if completions are happening every X seconds, the GPU is consuming work at a rate of 1/X partitions per second. But this approach had a subtle flaw: it only worked when the GPU was actually busy. During pipeline fill (when the pipeline is first starting up and completions are sparse) or during idle periods (when the queue drains between batches), the inter-completion interval would balloon, causing the pacer to think the GPU had slowed down and further reducing the dispatch rate—a vicious cycle.

To work around this, the assistant had introduced a heuristic: only update the GPU rate measurement when waiting > 0—that is, only when there were partitions waiting in the queue. The assumption was that if the queue was non-empty, the GPU must be busy. This seemed reasonable, but it was fundamentally wrong.

The User's Correction: Two Workers, One Problem

The user's message at index 3541 cut to the heart of the issue: "tracking gpu processing time isn't that simple because there are two lightly pipelined gpu workers, not just one."

This was the key insight that had been missed. The GPU doesn't process partitions one at a time—it runs two workers per device in an interleaved fashion. Worker A pops a partition and starts processing. Worker B pops the next partition and starts processing. Both workers run concurrently, sharing GPU resources. By the time either worker finishes, the queue may be empty—both partitions have been popped. But the GPU is still fully utilized because both workers are actively computing.

The waiting > 0 heuristic fails catastrophically in this scenario. With two workers, the queue can be empty while the GPU is running at full capacity. Every completion event would see waiting == 0 and skip the rate update, causing the pacer to operate on stale or nonexistent data. The heuristic was not just imprecise—it was structurally unsound.

The Assistant's Reasoning: A Deep Dive

The assistant's reasoning in message 3542 reveals a remarkable debugging journey compressed into a single thinking block. The assistant walks through multiple candidate solutions, discarding each in turn as its flaws become apparent.

The first instinct is to track the number of workers currently busy using an atomic counter that increments when a worker starts and decrements when it finishes. But the assistant quickly realizes a timing problem: by the time the pacer wakes up from a completion notification, the worker has already decremented the counter, so it only reflects workers still mid-processing. This doesn't solve the problem.

The assistant then considers the user's original suggestion: for the bootstrap phase, measure the time between the first and Nth GPU completion to get actual throughput during a burst. This sidesteps the worker-count problem but only works during initial warmup, not steady state.

Then comes the breakthrough: "What I actually need is to measure the GPU's maximum throughput when it's saturated. The simplest way is to have each GPU worker track its own processing duration, then calculate effective throughput as the number of workers divided by their average processing time."

This is the key insight. The GPU workers already measure their own processing duration—they time themselves for logging purposes. This measurement is a direct, uncontaminated signal. It doesn't matter whether the queue is full or empty. It doesn't matter whether the pipeline is filling or draining. The processing time of a single partition on the GPU is a characteristic of the hardware and the workload, independent of the scheduling dynamics around it.

The assistant works through the math: with two workers each taking one second, the effective throughput is two completions per second, meaning the pacer should dispatch every 0.5 seconds. The formula is elegant: effective_interval = processing_time / num_workers. This gives the same result as the inter-completion interval during saturated operation, but without being thrown off by idle periods.

There's a subtlety the assistant identifies: GPU workers share resources, so processing time may increase slightly under contention—maybe 1.2 seconds per item when both are active instead of 1 second alone. But this is actually desirable behavior: the EMA naturally captures the real throughput including contention effects, and the interval calculation adjusts accordingly. The measurement is self-correcting.

The Five-Point Plan

Message 3551 distills this extended reasoning into a crisp, actionable plan:

  1. Add gpu_processing_total_ns: Arc<AtomicU64> alongside the other atomics — A shared atomic accumulator that GPU workers will update with their processing durations.
  2. In the finalizer (line ~3136): extract gpu_duration from the result and fetch_add it before incrementing completion count — The GPU finalizer is where the proof result is processed. The GPU worker already returns a gpu_duration value. By atomically adding it to the shared accumulator before incrementing the completion count, the pacer can later compute the average processing time as delta_ns / delta_completions.
  3. In the sync path (line ~3024): same — There are two GPU execution paths: a split/async path and a synchronous fallback. Both need the same treatment.
  4. Rewrite the GPU rate section in DispatchPacer to use actual processing time / num_workers — The pacer's update() method needs to be fundamentally reworked. Instead of tracking inter-completion intervals, it should read the processing time accumulator, compute the delta since last check, divide by the delta in completions to get the average processing time, then divide by the number of workers to get the effective dispatch interval.
  5. Pass gpu_processing_ns and num_gpu_workers to the pacer — The pacer needs access to both the atomic accumulator and the worker count, which must be wired through the engine's data flow.

Why This Approach Is Correct

The brilliance of this solution is that it measures the right thing directly. The previous approach tried to infer GPU busyness from queue depth—a proxy that was fundamentally unreliable with pipelined workers. The new approach measures actual GPU processing duration, which is:

The Execution

The message concludes with a simple statement: "[edit] /tmp/czk/extern/cuzk/cuzk-core/src/engine.rs Edit applied successfully." This understates the complexity of what was done. The edit touched multiple locations in a 3000+ line file: the DispatchPacer struct definition, its update() and interval() methods, the engine's atomic initialization, the GPU worker spawn logic where atomics are cloned, the async finalizer path, and the synchronous fallback path. Each change had to be coordinated with the others to maintain correctness.

The successful edit represents the culmination of a debugging journey that spanned multiple sessions and dozens of iterations. The assistant had tried queue-depth heuristics, inter-completion interval tracking, waiting > 0 filters, and first-completion skips—all of which proved inadequate. The user's correction about the two pipelined workers was the key insight that finally led to the right solution.

The Broader Lesson

This episode illustrates a fundamental principle of systems debugging: when a measurement is unreliable, don't try to fix the measurement—find a better thing to measure. The queue depth was a convenient signal, but it was the wrong signal. The GPU processing time was always available, always accurate, and always relevant. The challenge was recognizing it as the right signal and having the courage to restructure the code around it.

For anyone working on GPU-accelerated pipelines, the lesson is clear: understand your hardware's execution model before designing your feedback loops. Two interleaved workers behave fundamentally differently from a single worker, and heuristics that work for one may catastrophically fail for the other. Direct measurement of the quantity you care about is almost always superior to inference from proxies.