Memory Under the Microscope: Tracing the PCE's Multi-GPU Scaling Model in cuzk's Proving Engine

Introduction

In the high-stakes world of Filecoin proof generation, memory is not just a resource—it is the architecture. The SUPRASEAL_C2 Groth16 pipeline, responsible for producing Proof-of-Replication (PoRep) proofs for Filecoin storage providers, is notorious for its ~200 GiB peak memory footprint. After implementing the Pre-Compiled Constraint Evaluator (PCE) in Phase 5 of the cuzk proving engine optimization effort, the assistant had just demonstrated a 1.42× synthesis speedup (35.5s vs 50.4s baseline) and validated correctness across all 10 circuits × 130 million constraints. But a new question loomed: would the PCE's memory overhead scale gracefully in a multi-GPU deployment?

Message 1461 is the assistant's response to the user's pointed query: "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 question is not merely academic—it goes to the heart of whether the PCE architecture is viable for production deployment in heterogeneous cloud rental markets where GPU instances are rented by the hour and memory efficiency directly translates to cost.

This article dissects message 1461, examining its reasoning, assumptions, methodology, and the knowledge it creates. We will see how the assistant transitions from performance optimization to memory modeling, how it verifies its own assumptions by reading source code mid-response, and how it constructs a precise accounting that will inform critical deployment decisions.

The Subject Message: A Memory Model Under Construction

The message begins with the assistant acknowledging the question and proposing to trace through the memory model. This is characteristic of the assistant's approach throughout the session: rather than speculating, it grounds its analysis in the actual code and data structures.

The message is structured in three parts:

1. Static memory analysis — what is allocated once and shared across all pipelines
2. Per-pipeline memory analysis — what is allocated for each concurrent synthesis
3. A source code verification — reading eval.rs to check whether the unified witness vector is a copy or can be optimized away Let us quote the message in full (with no secrets to redact):

Great question. Let me trace through the memory model to give you precise numbers.

>

## PCE Memory Analysis

>

### What's static (allocated once, shared by all pipelines)

>

The PreCompiledCircuit is stored in a static OnceLock — one copy in process memory:

>

| Component | Size | |---|---| | CSR A matrix (309M nnz × 36B + 130M row_ptrs × 4B) | ~11.6 GiB | | CSR B matrix (130M nnz × 36B + 130M row_ptrs × 4B) | ~5.2 GiB | | CSR C matrix (283M nnz × 36B + 130M row_ptrs × 4B) | ~10.7 GiB | | Density bitmaps | ~50 MiB | | Total PCE static | ~25.7 GiB |

>

This is paid once per process, regardless of GPU count or pipeline depth. All pipelines read from the same &'static PreCompiledCircuit via the OnceLock.

>

### What's per-pipeline (allocated per in-flight synthesis)

>

Each concurrent synthesis needs:

>

| Component | Size | Notes | |---|---|---| | WitnessCS witness (input + aux) | ~4.2 GiB | 130M × 32B | | Unified witness vector for MatVec | ~4.2 GiB | Copy of above, contiguous | | Output a vector | ~4.2 GiB | 130M × 32B | | Output b vector | ~4.2 GiB | | | Output c vector | ~4.2 GiB | | | ProvingAssignment (receives a/b/c) | ~0 | Moves ownership, no copy | | Total per pipeline | ~21 GiB |

>

Actually, I should check whether the unified witness vector is a copy or if we could optimize it away. Let me verify:

>

[read] /home/theuser/curio/extern/cuzk/cuzk-pce/src/eval.rs

The message then issues a read tool call to inspect eval.rs at line 95, specifically the evaluate_pce function signature.

Why This Message Was Written: The Reasoning and Context

The User's Concern

The user's question arrives at a critical juncture. The assistant has just completed Phase 5 Wave 1 of the PCE implementation, achieving a 1.42× speedup and committing 13 files with 1,423 insertions. The benchmark reported a peak RAM of 375 GB—a number that would alarm any deployment engineer. The user, who has been deeply engaged throughout the optimization effort, immediately zeroes in on the memory implications for multi-GPU systems.

The question reveals several layers of concern:

1. Is the PCE memory static or duplicated? If each GPU pipeline requires its own copy of the 25.7 GiB CSR matrix, an 8-GPU system with 2 pipelines per GPU would need 16 × 25.7 = 411 GiB just for the PCE data, which would be prohibitive.
2. Can the system be overprovisioned? The user mentions "2 pipelines per gpu vram permitting," indicating a sophisticated understanding of GPU pipeline economics. In a proving system where GPU time is the bottleneck, running multiple pipelines per GPU (time-slicing the GPU) can improve throughput, but only if host memory allows.
3. What is the total system memory requirement? The user wants a concrete number for an 8-GPU deployment, which would inform hardware purchasing decisions (how many DIMMs, what capacity, what channel configuration).

The Assistant's Motivation

The assistant's response is motivated by several factors:

First, the 375 GB peak from the benchmark is misleading. The benchmark ran both the old path and the PCE path sequentially within the same process for validation purposes. The 375 GB peak likely represents holding both paths' allocations simultaneously. The assistant needs to disentangle benchmark artifacts from real production memory usage.

Second, the PCE's architectural promise depends on memory amortization. The entire premise of the PCE is that the one-time extraction cost (46.9s) is amortized across all future proofs. If the memory cost is also amortized (static, shared), that strengthens the case. If it's duplicated per pipeline, that weakens it.

Third, the assistant needs to verify its own understanding. The message shows the assistant reading eval.rs mid-response to check whether the unified witness vector is a copy. This is a moment of intellectual honesty: rather than assuming, the assistant goes to the source to confirm.

How Decisions Were Made

The Decision to Separate Static vs. Per-Pipeline Memory

The assistant makes a crucial analytical decision: to decompose memory into two categories—static (shared) and per-pipeline (working set). This is not an arbitrary choice but a reflection of the PCE's architectural design.

The static category captures the PreCompiledCircuit stored in a static OnceLock. This is a Rust concurrency primitive that ensures the value is initialized exactly once and then shared immutably across all threads. The assistant correctly identifies that this memory is "paid once per process, regardless of GPU count or pipeline depth."

The per-pipeline category captures the working set needed for a single concurrent synthesis. This includes the witness vectors, output a/b/c vectors, and the unified witness vector used for the MatVec multiplication.

This binary decomposition is powerful because it allows the user to compute total memory for any deployment configuration:

Total Memory = 25.7 GiB (static) + N × 21 GiB (per pipeline)

Where N is the number of concurrent pipelines. For an 8-GPU system with 2 pipelines per GPU (16 concurrent pipelines):

Total = 25.7 + 16 × 21 = 25.7 + 336 = 361.7 GiB

This is substantially less than the 375 GB benchmark peak, and importantly, the 25.7 GiB is not multiplied by the number of GPUs.

The Decision to Verify the Witness Copy

The assistant's note—"Actually, I should check whether the unified witness vector is a copy or if we could optimize it away"—is a real-time methodological decision. The assistant realizes that the 4.2 GiB "unified witness vector for MatVec" entry in the per-pipeline table might be an unnecessary copy. If the WitnessCS witness data is already contiguous, the MatVec could potentially operate on it directly, saving 4.2 GiB per pipeline.

This decision to verify mid-response demonstrates a commitment to accuracy over speed. The assistant could have simply presented the table and moved on, but it chose to validate the assumption by reading the source code.

Assumptions Made by the Assistant

Explicit Assumptions

1. The OnceLock ensures single initialization. The assistant assumes that the static OnceLock mechanism works as documented—that all pipelines share the same PreCompiledCircuit reference without duplication. This is a safe assumption given Rust's guarantees about OnceLock (or OnceCell/OnceLock in standard library).
2. The CSR matrix sizes are correct. The assistant presents precise numbers: 309M nnz for A, 130M nnz for B, 283M nnz for C. These come from the PCE extraction process and are assumed to be accurate.
3. The per-pipeline working set is ~21 GiB. This assumes that the witness, unified witness, and output vectors are all 130M × 32B = 4.2 GiB each, and that no additional hidden allocations exist.
4. ProvingAssignment takes ownership without copying. The assistant notes "~0" for ProvingAssignment size, assuming move semantics avoid duplication.

Implicit Assumptions

1. The memory model is additive. The assistant assumes that static and per-pipeline memory can be summed linearly without unexpected interactions (e.g., allocator fragmentation, page table overhead, or Rust's capacity doubling for Vec growth).
2. The benchmark's 375 GB peak is an artifact. The assistant implicitly assumes that the 375 GB peak from the benchmark is due to holding both old-path and PCE-path data simultaneously, not due to some deeper issue like per-partition PCE copying. This assumption is reasonable but will be explicitly tested in subsequent messages (the user later asks about this very point).
3. GPU VRAM is not a constraint for host memory. The user's question mentions "vram permitting," but the assistant's analysis focuses entirely on host (system) RAM. The assumption is that GPU VRAM is a separate concern and that the host memory model is the primary scaling factor.

Mistakes or Incorrect Assumptions

The Unified Witness Vector Copy

The most significant potential mistake is the assumption that the unified witness vector is a copy. The assistant reads eval.rs to verify this:

pub fn evaluate_pce<Scalar: PrimeField>(
    pce: &PreCompiledCircuit<Scalar>,
    input_assignment: Vec<Scalar>,
    aux_assignment: Vec<Scalar>,
) -> PceEvalResult<Scalar> {

The function takes input_assignment and aux_assignment as owned Vec<Scalar>. Inside, it likely concatenates them into a unified witness vector. If this concatenation creates a new allocation (which it almost certainly does, since Vec::extend may reallocate), then the 4.2 GiB entry is correct. However, if the function could be refactored to operate on the two vectors in-place without concatenation, that 4.2 GiB could be saved.

The assistant does not complete this verification in message 1461—the read tool call is issued but its result is not yet available (this is a single message, and tool calls are dispatched together). The verification happens in the next message (msg 1462, which is in the next chunk). This is a structural limitation of the conversation format: the assistant can issue tool calls but cannot act on their results within the same message.

The Missing GPU VRAM Analysis

The user specifically asks about "2 pipelines per gpu vram permitting," but the assistant's analysis focuses entirely on host RAM. GPU VRAM is a separate constraint: each GPU needs to hold the SRS parameters (~several GiB), the proving key, and the working buffers for NTT and MSM operations. The assistant does not address whether 2 pipelines per GPU is feasible given VRAM constraints. This is a gap, though it may be intentional—the assistant may be deferring GPU-specific analysis to a later discussion.

The Absence of Memory Fragmentation

The assistant's additive model assumes perfect memory utilization. In practice, Rust's allocator (jemalloc or glibc malloc) may introduce fragmentation, especially with the large allocations (4.2 GiB each) involved. The 21 GiB per-pipeline figure is a lower bound; actual usage may be higher due to allocator overhead, alignment padding, and Vec capacity rounding.

Input Knowledge Required to Understand This Message

To fully grasp the assistant's analysis, the reader needs:

1. Understanding of CSR (Compressed Sparse Row) Format

The assistant references "CSR A matrix (309M nnz × 36B + 130M row_ptrs × 4B)." CSR is a standard sparse matrix format where:

• nnz = number of non-zero entries
• Each entry stores a column index (4B) and a value (32B for a field element in Fr)
• row_ptrs is an array of length (num_rows + 1) storing offsets into the nnz array The 36B per entry = 4B (column index) + 32B (field element value).

2. Knowledge of R1CS (Rank-1 Constraint System)

The PCE captures the R1CS structure of the PoRep circuit. The A, B, C matrices correspond to the three linear combinations in each constraint: A·w * B·w = C·w, where w is the witness vector. The MatVec (sparse matrix-vector multiplication) computes these products.

3. Understanding of Rust's OnceLock and Static Memory

The static OnceLock<PreCompiledCircuit> pattern ensures that the PCE data is initialized once (on first access) and then shared immutably across all threads. This is critical for the memory amortization argument.

4. Familiarity with the Proving Pipeline

The reader needs to know that the proving pipeline has distinct phases: witness generation (computing the witness vector), synthesis (building the R1CS constraints), and proving (GPU-based NTT/MSM). The PCE replaces the synthesis phase with a pre-computed matrix-vector multiplication.

5. Context from Previous Messages

The reader should know that:

• The benchmark used 10 circuits (one per partition of the PoRep proof)
• Each circuit has ~130M constraints
• The old path achieved 50.4s, the PCE path 35.5s
• Peak RAM was 375 GB (old + PCE combined)
• The PCE extraction (one-time) took 46.9s

Output Knowledge Created by This Message

1. A Precise Memory Accounting Model

The message creates a clear, actionable memory model:

| Category | Size | Scaling | |---|---|---| | Static PCE (shared) | 25.7 GiB | Once per process | | Per-pipeline working set | ~21 GiB | Per concurrent synthesis | | Total for 8 GPU × 2 pipelines | ~362 GiB | 25.7 + 16 × 21 |

This model allows the user to compute memory requirements for any deployment configuration.

2. Identification of Optimization Opportunities

By separating the unified witness vector as a distinct 4.2 GiB entry, the assistant implicitly identifies a potential optimization: if the MatVec could operate directly on the WitnessCS data without concatenation, 4.2 GiB per pipeline could be saved. For 16 concurrent pipelines, that's 67 GiB of potential savings.

3. A Verification Methodology

The assistant demonstrates a methodology for validating memory assumptions: read the source code. The mid-response read of eval.rs shows how to ground memory analysis in actual data structures rather than relying on mental models.

4. A Framework for Deployment Decisions

The message provides the user with the information needed to make hardware decisions. For an 8-GPU system with 2 pipelines per GPU, the user now knows they need at least ~362 GiB of host RAM, plus GPU VRAM for each GPU's proving buffers. This is a concrete, actionable number.

The Thinking Process Visible in the Reasoning

The Structure of the Analysis

The assistant's thinking is visible in the way it structures the response:

1. Acknowledge the question — "Great question. Let me trace through the memory model to give you precise numbers."
2. Decompose the problem — Separate static from per-pipeline memory. This is a classic systems analysis technique: identify what is shared and what is per-instance.
3. Quantify each component — For each matrix (A, B, C), compute size from nnz count and row pointer count. For each per-pipeline vector, compute size from witness length and field element size.
4. Verify assumptions — The mid-response read of eval.rs shows the assistant thinking: "I think the unified witness is a copy, but let me check the actual function signature to be sure."
5. Present the model — The assistant presents the results in tabular form, making them easy to reference and discuss.

The Moment of Self-Correction

The most revealing part of the thinking process is the sentence: "Actually, I should check whether the unified witness vector is a copy or if we could optimize it away. Let me verify:"

This is a moment of self-awareness. The assistant realizes that it is making an assumption (that the unified witness vector requires a copy) and decides to verify it before committing to the analysis. This is not a mistake—it's a methodological strength. The assistant recognizes the limits of its knowledge and takes steps to fill the gap.

However, as noted earlier, the verification is incomplete within this message. The read tool call is issued, but its result will only be available in the next message. This creates a slight tension: the assistant presents the per-pipeline table as if the unified witness vector entry is confirmed, but the confirmation hasn't arrived yet. In practice, the assistant's intuition is correct—the concatenation does create a new allocation—but the verification happens off-screen.

The Implicit Dialogue with the User

The assistant's response also shows an awareness of the user's expertise. The user asks about "strong pipelining" and "overprovision," terms that indicate deep familiarity with GPU deployment patterns. The assistant matches this level of discourse, providing precise byte-level accounting rather than vague estimates. The response assumes the user can interpret CSR matrix sizes, understand OnceLock semantics, and extrapolate from per-pipeline numbers to total system requirements.

Conclusion

Message 1461 is a masterclass in systems-level memory analysis under uncertainty. Faced with a pointed question about multi-GPU scaling, the assistant constructs a precise, verifiable memory model that separates static (shared) from per-pipeline (working set) memory, quantifies each component, and provides a framework for deployment decisions.

The message's greatest strength is its intellectual honesty: the assistant recognizes when it needs to verify an assumption and takes immediate action to do so. The mid-response read of eval.rs is not just a verification step—it is a demonstration of methodology, showing how to ground abstract analysis in concrete source code.

The gaps in the analysis—the incomplete verification of the witness copy, the absence of GPU VRAM analysis, the lack of fragmentation modeling—are not failures but invitations for further investigation. They set the stage for the next phase of the conversation, where the assistant will empirically validate the memory model with a custom benchmark and confirm that the 375 GB peak was indeed a benchmark artifact.

For the user, the message provides exactly what was requested: a clear answer about whether PCE memory is amortized across multiple GPUs. The answer is yes—the 25.7 GiB static cost is paid once per process, and the per-pipeline working set of ~21 GiB is essentially unchanged from the old path. This validates the PCE architecture for multi-GPU deployment and gives the user confidence to proceed with hardware planning.

In the broader narrative of the cuzk optimization effort, this message marks a transition from performance optimization to deployment readiness. The PCE has been proven correct and faster; now it must be proven practical. Memory analysis is the first step toward that goal, and message 1461 lays the foundation with clarity and precision.