The 3.6% Question: Validating Memory Scaling for the Pre-Compiled Constraint Evaluator

In the high-stakes world of Filecoin proof generation, where a single Groth16 proof for a 32 GiB sector demands hundreds of gigabytes of RAM and tens of seconds of compute, every architectural decision carries significant cost. When the assistant delivered Phase 5 Wave 1 of the cuzk proving engine — the Pre-Compiled Constraint Evaluator (PCE) — the headline numbers were impressive: a 1.42× speedup over the old synthesis path, with all 10 circuits × 130 million constraints validating bit-for-bit correct. But one number caught the user's attention: 375 GB peak RAM, up from 340 GB in the baseline. In a system destined for multi-GPU deployment, that 10% increase could compound into a serious problem — or it could be a mirage.

The user's question in [msg 1460] cut straight to the heart of the matter: "pce ram - is it static/amortised even with multiple GPUs? How much ram will an 8GPU system need with strong pipelining and maybe overprovision (2 pipelines per gpu vram permitting)." This was not a casual inquiry. It was a deployment feasibility question from someone who understands that memory is the binding constraint in GPU-accelerated proving infrastructure. The assistant's response in [msg 1462] — the subject of this article — is a masterclass in tracing through a memory model, distinguishing one-time static costs from per-pipeline working sets, and arriving at a counterintuitive conclusion: the PCE's memory overhead is effectively zero in a multi-GPU system.

The Context: Why This Question Matters

To understand the significance of this exchange, one must appreciate what the PCE actually does. The Groth16 proving pipeline for Filecoin's Proof-of-Replication (PoRep) involves synthesizing R1CS circuits with roughly 130 million constraints across 10 partitions. The old path performed full synthesis for every proof: allocating variables, enforcing constraints, and building the ProvingAssignment from scratch each time. The PCE splits this into two phases: a one-time extraction that records the circuit structure into compressed sparse row (CSR) matrices, and a fast evaluation path that reuses those matrices for every subsequent proof.

The benchmark had just shown that the PCE path completes synthesis in 35.5 seconds versus 50.4 seconds for the old path — a respectable 1.42× improvement, though below the 3–5× target because Phase 4's optimizations had already trimmed much of the enforce overhead that PCE was meant to eliminate. But the 375 GB peak memory was concerning. If that represented a genuine increase in per-pipeline memory, scaling to 8 GPUs with 2 pipelines each (16 concurrent pipelines) could push total system memory past 800 GB, potentially exceeding what was economically feasible.

The user's question revealed a sophisticated understanding of the deployment landscape. They weren't asking about single-GPU performance; they were asking about the total cost of ownership for a multi-GPU proving rig. The distinction between static and per-pipeline memory is critical in such systems because static memory is paid once regardless of scale, while per-pipeline memory multiplies with every concurrent pipeline. If the PCE's 25.7 GiB of CSR matrix data was truly shared (static), it would add only 3.6% overhead to a 712 GiB baseline. If it was somehow duplicated per pipeline, the overhead could balloon to 411 GiB — a 58% increase that would make the PCE economically unattractive for multi-GPU deployments.

Tracing the Memory Model

The assistant's response in [msg 1462] opens with an honest acknowledgment: "Right — currently we allocate a unified witness vector (4.2 GiB copy)." This admission is important because it shows the assistant is not glossing over inefficiencies. The witness copy is a genuine but unnecessary allocation: the evaluate_pce function receives separate input_assignment and aux_assignment vectors, then concatenates them into a unified witness vector for the sparse matrix-vector multiply (SpMV). The assistant immediately identifies the optimization — modifying spmv_parallel to do a split lookup with a conditional branch — but correctly defers it as a future concern.

The core of the analysis is a detailed breakdown of memory components across three categories: static PCE data, per-pipeline working set, and GPU infrastructure.

Static PCE Data (25.7 GiB)

The PreCompiledCircuit is stored in a static OnceLock — a Rust synchronization primitive that ensures exactly one initialization across all threads. This is the architectural guarantee that makes the PCE's memory static: no matter how many pipelines or GPUs are active, there is exactly one copy of the CSR matrices in process memory. The breakdown is:

Per-Pipeline Working Set (~21 GiB)

Each concurrent synthesis pipeline needs its own working set, regardless of whether it uses the PCE fast path or the old path:

GPU Infrastructure (376 GiB for 8 GPUs)

The SRS (Structured Reference String) parameters — the proving key and verification key — are stored in GPU pinned memory. At ~47 GiB per GPU, this is the largest single memory consumer in the system. It is also inherently per-GPU because each GPU needs its own copy of the parameters for kernel execution.

The Arithmetic of Scaling

The assistant's calculation for an 8-GPU system with 2 pipelines per GPU (16 concurrent pipelines) is:

| Component | Size | Count | Total | |---|---|---|---| | PCE static (CSR matrices) | 25.7 GiB | 1 | 25.7 GiB | | Per-pipeline working set | ~21 GiB | 16 | 336 GiB | | SRS params (GPU pinned memory) | ~47 GiB | 8 | 376 GiB | | Other overhead (circuit objects, etc.) | ~2 GiB | 16 | ~32 GiB | | Total | | | ~770 GiB |

Without PCE, the total would be ~712 GiB (no static 25.7 GiB, but the same per-pipeline and SRS costs). The delta is +26 GiB, or +3.6%.

This is the punchline: the PCE's memory overhead is amortized to insignificance in a multi-GPU system. The 25.7 GiB of CSR matrices is paid once, regardless of whether the system has 1 GPU or 8 GPUs. The per-pipeline working set — which dominates at 336 GiB for 16 pipelines — is unchanged from the old path. The GPU SRS parameters — the largest single cost at 376 GiB — are also unchanged.

The assistant's conclusion is emphatic: "So yes, the PCE is effectively free in a multi-GPU system — 25.7 GiB static, amortized across all pipelines."

The Optimization That Wasn't Needed

The assistant identifies one potential optimization: eliminating the 4.2 GiB unified witness copy per pipeline by modifying the SpMV kernel to do a split lookup. This would save 67 GiB system-wide (4.2 GiB × 16 pipelines), bringing per-pipeline working set from ~21 GiB to ~17 GiB. The cost would be a conditional branch per SpMV entry — a branch that the assistant notes would be "probably negligible at 0.5% branch mispredict rate" based on the perf stat data from [msg 1458] showing a 0.50% branch misprediction rate across the entire benchmark run.

But the assistant frames this as an optional optimization, not a necessity. The question at the end of the message — "Want me to investigate eliminating that witness copy as part of memory optimization, or does the 26 GiB static overhead seem acceptable for an 8-GPU system that needs ~740 GiB total anyway?" — is a deliberate handoff to the user. The assistant has done the analysis, presented the numbers, and identified the trade-offs. The decision now rests with the user, who understands their deployment constraints better than the assistant can.

Assumptions and Potential Pitfalls

The analysis rests on several assumptions that deserve scrutiny:

  1. The per-pipeline working set is identical with and without PCE. The assistant asserts this based on the observation that the old path's ProvingAssignment grows to the same size organically. This is likely correct for the steady state, but the old path may have different peak memory patterns due to its allocation/deallocation behavior. The benchmark showed 340 GB peak for the old path and 375 GB for the PCE path — a 35 GB difference that the assistant attributes to holding both paths' results simultaneously for validation comparison (as confirmed in [msg 1461] by reading the benchmark source). In production, only one path would be active at a time, so the 375 GB peak is a benchmark artifact.
  2. The OnceLock truly prevents duplication. The Rust OnceLock (or the more common OnceCell/Once) guarantees single initialization, but only within a single process. If the proving system uses multiple processes (e.g., one per GPU), each process would have its own 25.7 GiB copy. The assistant implicitly assumes a single-process architecture, which is the design of the cuzk daemon.
  3. The SRS parameters are 47 GiB per GPU. This number comes from the existing system and may vary with parameter sizes. The assistant does not verify this number in the message, instead treating it as a known constant from the deployment environment.
  4. The witness copy optimization is safe. The split lookup (if col < num_inputs { input[col] } else { aux[col - num_inputs] }) introduces a branch that, while predicted to be negligible, could interact poorly with GPU warp execution if the SpMV were ever ported to GPU. For the CPU-based MatVec, the 0.5% branch misprediction rate suggests the impact would be minimal.

The Thinking Process: A Window into Systems Analysis

What makes this message particularly instructive is the visible reasoning process. The assistant does not simply answer "yes, it's amortized" — it traces through the entire memory model, component by component, building up from first principles. The structure reveals a systematic approach:

  1. Acknowledge the current limitation (the witness copy) rather than hiding it.
  2. Define the deployment scenario (8 GPUs, 2 pipelines each) to make the analysis concrete.
  3. Break down memory into categories (static, per-pipeline, GPU infrastructure) that map to different scaling behaviors.
  4. Calculate each category independently, then sum for the total.
  5. Compare with and without PCE to isolate the delta.
  6. Identify a potential optimization and evaluate its cost-benefit.
  7. Present the decision to the user with clear framing. This is the hallmark of a mature systems analysis: it does not stop at answering the question but provides the framework for understanding why the answer is correct and what the remaining trade-offs are.

Output Knowledge Created

This message creates several pieces of durable knowledge:

Conclusion

The assistant's response to the user's memory scaling question is a textbook example of how to evaluate architectural decisions in resource-constrained systems. By tracing through the memory model component by component, distinguishing static from per-pipeline costs, and comparing with and without the PCE, the assistant arrives at a conclusion that is both precise and counterintuitive: the feature that appears to add 10% peak memory in a single-GPU benchmark adds only 3.6% in a realistic multi-GPU deployment. The 375 GB peak was a benchmark artifact, not a fundamental cost of the PCE architecture.

The message also demonstrates intellectual honesty — acknowledging the witness copy inefficiency rather than sweeping it under the rug — and good judgment in framing the optimization decision as a user choice rather than prescribing a solution. The result is a piece of analysis that not only answers the immediate question but equips the user with the understanding needed to make informed deployment decisions.