Route-Block Membership Selects Packed-AWQ Arithmetic A Controlled Single-Fixture Mechanism Study Lukas Stepanek [email protected]
July 2026
arXiv:2607.26316v1 [cs.DC] 28 Jul 2026
Abstract Mixture-of-experts (MoE) inference first aligns routed tokens into padded expert blocks, then executes packed quantized matrix multiplication over those blocks. This preprocessing is often treated as bookkeeping. In one pre-specified Qwen3-Coder AWQ layer-6 fixture on a pinned vLLM/Marlin build and RTX 3090 runtime, we show that the tested route-block interventions select exact packed arithmetic trajectories. Two fixed preconstruction histories produced distinct native alignments and exact trajectories. Injecting the opposite alignment transferred W13, activation, routed-W2, and final outputs. Permuting two routes within one block preserved each native trajectory, while exchanging two prior-data-selected routes across the boundary between expert-106 blocks 40 and 41 transferred the complete opposite trajectory. Source- and binary-derived schedule geometry maps those blocks to direct/full-K and split/global-reduction classes. Forcing a single-slice 200-block grid made W13 bitwise equal. Stable canonical construction made both histories converge to a third exact trajectory. The confirmatory cohort contains 70 valid cold processes and seven required perturbation rejections. This is a causal mechanism result for one fixture, not a prevalence, allocator, portability, or serving-impact claim.
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Introduction
Packed weight-only quantization makes large-model inference practical by reducing memory traffic while retaining GPU-friendly kernels [3, 6]. In an MoE layer, however, the matrix multiplication is preceded by dynamic routing and alignment: valid routed token rows are grouped by expert and padded into fixed-size blocks. The alignment’s internal order is usually discussed as a dispatch or utilization detail. Exact floating-point output also depends on which aligned block a route enters because the downstream kernel may map neighboring block indices to different reduction schedules. This paper isolates that connection in a narrow controlled case. A fixed preconstruction treatment selected one of two native atomic alignment orders for the same inputs and packed weights. Existing evidence had already exposed the affected routes, so our study is confirmatory rather than an independent discovery cohort. Before the confirmatory runs, we pre-specified the histories, route interventions, schedule intervention, exact trajectory predictions, five cold-process replicates per cell/history, and rejection rules. Our central abstraction is route-to-eight-row-block membership. It forgets order within a padded expert block but retains which valid flattened route identifiers occupy each block. This abstraction connects dispatch to the pinned Marlin schedule: expert-106 block 40 is assigned directly with a full-K reduction, whereas block 41 is split across K and globally reduced. The contribution is evidence, not breadth: • a precise route block membership abstraction and a derivation from block index to reduction-schedule class for the pinned kernel; • a 70-process prospective mechanism matrix in which cross-order and a two-route boundary intervention transfer all four measured arithmetic surfaces, while a within-block permutation preserves them; • a schedule control in which grid 200 removes the split/global reduction and collapses the W13 distinction; and • a separately evaluated canonical construction that makes both histories converge to one third trajectory, with an auditable public recorded-evidence package. We do not estimate how often the effect occurs. We do not identify an allocator primitive, and we make no claim about model-token divergence, serving impact, portability, paging, or prefetch behavior. 1
boundary intervention
within-block control
22
28
51
expert 106, block 40
···
86
···
expert 106, block 41
split K global FP32 reduce
direct full K
Figure 1: The tested instantiation of route-block membership. Routes 22 and 28 are permuted inside block 40; routes 51 and 86 are exchanged across the 40/41 schedule boundary. Other routes are omitted from the drawing.
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Background
2.1
MoE alignment and padded blocks
Let the top-k router produce an M × k expert-ID array. Flattening in row-major order gives route IDs r ∈ [0, M k). Alignment groups valid routes by expert, pads each expert’s count to a multiple of block size b, and emits a parallel expert-block vector. The tested path uses M = 21, k = 8, 128 experts, and b = 8: 168 valid routes become 400 aligned rows in 50 active blocks. MoE systems have long used blocking to reconcile dynamic routing with GPU execution. MegaBlocks, for example, formulates sparse MoE training around block-sparse operations to avoid token dropping and padding waste [4]. Our concern differs: we hold the routed inputs and weights fixed and ask whether block membership changes exact packed arithmetic.
2.2
Packed-AWQ Marlin arithmetic
AWQ is an activation-aware weight-only quantization method [6]. Marlin provides mixed-precision kernels with tiled scheduling, pipelining, and parallel reduction [3]. The tested vLLM path applies Marlin-style packed-AWQ MoE GEMMs to the aligned rows. Floating-point addition is non-associative, so a route that moves between a direct/full-K tile and a split-K tile with global reduction can follow a different exact rounding trajectory even though its mathematical dot product and packed weights are unchanged.
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The route-block abstraction
3.1
Definition
For expert e, let Ae be its aligned sequence after padding. Consecutive groups of eight positions form expert-local blocks. We define B(e, j) = {r : r is valid for expert e and occupies Ae [8j : 8j + 8]}. (1) Padding sentinels are excluded and order inside B(e, j) is ignored. The complete mode identity is the ordered sequence of (e, j, sort(B(e, j))). Consequently, swapping two valid routes inside the same B(e, j) preserves the abstraction, while moving a route across an eight-row boundary changes it.
3.2
Mapping block index to schedule class
The captured public call has N = 1536 and K = 2048. The pinned auto-selector chooses thread k = 64, thread n = 128, 128 threads, and three resident blocks per SM. Each of the 50 MoE blocks therefore has 12 N -tiles and 32 K-tiles, for 600 global (MoE block, N -tile) tiles. With the native grid of 246 CUDA blocks, the first 2 · 246 = 492 global tiles receive direct/full-K assignments. The remainder begins at MoE block 492 = 41 (2) 12
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Cell
Intervention
Frozen exact prediction
Native Own order Cross order Canonical Within block Boundary Single slice
untreated H0/H1 inject each history’s own plan inject the opposite plan stable (e, r) construction permute routes 22/28 exchange routes 51/86 own plan, grid 200
distinct H0 and H1 trajectories reproduce its native trajectory transfer all four opposite surfaces both histories equal one third trajectory preserve each native trajectory transfer the complete opposite trajectory identical W13; no final-collapse prediction
Table 1: Pre-specified cells. Each cell/history has five independent cold processes. Qualification contains 20 processes, causal transfer 20, and ablation 30. and is split into two 16-K-tile slices followed by global FP32 reduction. Thus block 40 is direct/full-K and block 41 is split/reduced. Membership in B(106, 40) versus B(106, 41) selects a reduction-schedule class (Figure 1). At grid 200, the direct region covers 400 global tiles. The remainder begins at block ⌊400/12⌋ = 33 but receives one 32-K-tile slice. All column tiles are therefore single-slice and the global reduction is bypassed. This derivation was frozen before the grid-200 outcome. It corrects an earlier transposition of thread k and thread n; the superseded grid-240 prediction was rejected before arithmetic execution.
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Prospective study
4.1
Fixture, software build, and histories
The fixture is layer 6 of the QuantTrio/Qwen3-Coder-30B-A3B-Instruct-AWQ checkpoint at Hugging Face revision c58857a7f41c0920f73d1b56678640f9c02017d7 [7]. Its 17-file manifest has SHA-256 bf498217bf4da3d43864150212 b630f08340d05e6922696dd7562539b11798e8; the derived model identity is 94ab8051a1bfbb6671aebade458b55760ca2 ab3432da057e385c4327ce4a286c. The layer has hidden size 2048 and uses 4-bit AWQ with group size 128. The checkpoint-derived fixture has SHA-256 4f4c0812377ab927727a726ee94aafa453dc02933ebd6913c740a6d335d431a8. The software build pins vLLM commit 752a3a504485790a2e8491cacbb35c137339ad34 [8]; its tracked diff has SHA-256 1c366352593f896113785cb6a5e137ee2b646c267eb185a6decb3033f7239744 and its final native extension has SHA-256 b941455ec4fcf8b4b567f51575271a7f7928922a2a8291d41abb9ed78b5165b5. The runtime is an RTX 3090 (compute capability 8.6), driver 580.159.03, CUDA 13.0, and PyTorch 2.11.0+cu130. Every arm uses identical input, top-k IDs, top-k weights, and resident packed weights. H0 performs no extra allocation/prewarm prelude. Before model construction, H1 allocates and retains three persistent CUDA tensors shaped like the fixture’s input, top-k weights, and top-k IDs; it copies the immutable fixture into them and synchronizes once. They are never used as operator inputs or outputs. H1 is a composite treatment: it may select a different native alignment, but it cannot identify allocation, fragmentation, address residue, prewarming, or a named allocator behavior as the cause.
4.2
Pre-specified cells and analysis
Routes 51/86 and 22/28 were selected from prior H0/H1 data. The former were the only routes differing at the captured W13 boundary; the latter remained together in block 40. We disclosed this prior-data selection before the new cross-order and surgical-intervention outcomes. The study executed replicate-major with history order alternated by replicate. A separate scorer reloaded raw tensors, recomputed hashes and route block membership, enforced intervention and grid consumption, and required five exact outcomes per cell/history. Seven mutations—route, expert block, treatment marker, grid marker, stage hash, raw tensor, and source/binary identity—were each rejected for the predeclared reason. Timing in this cohort was operational telemetry and was not analyzed as performance.
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5
Results
5.1
Route-block membership transfers exact arithmetic
All 70 prospective processes were valid. Table 2 gives the exact trajectory relation rather than an averaged metric. Native H0 and H1 were distinct at every captured surface. Injecting each native plan under its own history reproduced its native trajectory, excluding intervention machinery as the source of the difference. Cross-order injection transferred all four surfaces to the opposite exact trajectory. Cell
H0 result
H1 result
Replicates
Native Own order Cross order Canonical Within block Boundary Grid 200
H0 H0 H1 C H0 H1 S at W13
H1 H1 H0 C H1 H0 S at W13
5+5 5+5 5+5 5+5 5+5 5+5 5+5
Interpretation distinct intervention-neutral complete transfer history collapse membership-preserving two-route sufficiency single-slice W13 collapse
Table 2: Exact results. H0, H1, and C are three distinct four-surface trajectories. S is the shared grid-200 W13 trajectory; activation, W2, and final grid-200 values were recorded but were not pass criteria. Changing only the order of routes 22 and 28 within block 40 preserved each history’s native trajectory. Exchanging routes 51 and 86 across blocks 40 and 41 transferred the complete opposite trajectory, although the other 18 H0/H1 membership changes remained untouched. In this fixture, those two prior-data-selected membership changes were sufficient for the observed transfer. The native difference was sparse: seven FP16 W13 elements on routes 51 and 86 (maximum absolute difference 7.62939453125 × 10−6 ), three activation elements on rows 17 and 86 (9.5367431640625 × 10−7 ), ten routed-W2 elements on route 51 (7.62939453125 × 10−6 ), and one final element on row 6 (9.5367431640625 × 10−7 ). These counts describe this fixture; they are not prevalence or practical-impact estimates.
5.2
The schedule control
Under the native 246-block grid, block 40 and block 41 occupy the two derived schedule classes. At grid 200, H0 and H1 W13 tensors became bitwise equal with shared SHA-256 prefix 44118553b1d46f3f. This confirms the pre-specified schedule-class explanation at W13. It does not isolate one instruction or one FP32 addition, and it does not imply final output collapse.
5.3
Canonical third trajectory
Stable construction orders valid routes by (expert ID, flattened route ID). Under both histories it produced the same route block fingerprint and the same four surface hashes. Its final hash begins 717d4f34, whereas native H0 and H1 begin bdfadfc9 and 1c317016; canonical construction is a third exact trajectory, not recovery of either historical native trajectory. opposite order or 51/86 boundary swap
native H0
stable construction
native H1 opposite order or 51/86 boundary swap
stable construction
canonical C
Figure 2: Exact trajectory relations. The canonical result is a third trajectory shared by both histories; it is not restoration of H0 or H1. 4
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Separate evaluation of canonical construction
The canonical implementation was evaluated in a separate, pre-specified cohort on a minimal eight-file vLLM patch. It uses one CUDA thread per expert to scan flattened routes in ascending route ID, is disabled by default, and is scoped to AutoAWQ-Marlin. The evaluation recorded 104 randomized alignment cases against an exact CPU reference, 1,024 fixed-vector packed-AWQ replays, all 48 MoE layers (480 observations in 10 processes), and 30 hook-free cold processes across code, chat, and long-context prompts. Unsupported configurations failed closed. The mechanism-study and implementation-evaluation builds share the exact vLLM base, model identity, model manifest, layer-6 fixture, GPU/runtime anchors, and seven byte-identical deterministic operator files. They have different complete diffs and native extension hashes and were executed as different populations. The separate cohort therefore corroborates the implementation solution; its processes are not added to the prospective 70.
6.1
Exact single-operating-point measurements
A separate pre-specified performance protocol fixed the software build, operating points, warmups, timing boundaries, statistics, and non-inferiority margins. Its independent validator recomputed the medians and ratios, so we report them once and without a general performance label. Operating point
Canonical
Stock
Canonical/stock
0.2412 28.401
0.2416 28.362
0.9986 1.0014
Layer-6 call (ms) Batch-1 fixed prompt (tokens/s)
Table 3: Two single-operating-point medians from the separate pre-specified implementation evaluation; full-precision values remain in the artifact. Layer timing used seven alternating 50-call CUDA-event blocks after 20 warmups per mode. End-to-end timing used five alternating requests, one warmup per mode, and 64 forced greedy tokens. These data do not establish negligible overhead, speedup, serving-scale throughput, or portability.
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Historical corroboration
A prior stock-versus-4-MiB-candidate comparison showed bidirectional order transfer, canonical collapse to the same 717d4f34... output, and grid-200 W13 collapse. That contrast was construction-confounded: 36 routes changed block membership and its highlighted routes were 22, 28, 109, and 126. It is corroborating evidence only. We neither relabel its arms as H0/H1 nor count its runs in the 70-process cohort. Separate historical controls tested whether initialized/preallocated state alone restored the historical stock trajectory. It did not: H0 matched the current-candidate result in five of five runs, while H1 matched the historical candidate in four of five and stock in one of five. This rules out reliable restoration of the stock trajectory but does not establish broad allocator causality.
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Related work
Table 4 contrasts our route-block mechanism with AWQ quantization [6], Marlin scheduling [3], MegaBlocks block-sparse MoE training [4], UniEP deterministic token ordering [10], and Bit-Exact inference invariance [2]. WiSP reports output-preserving vLLM expert paging but leaves GPTQ/AWQ to future work and does not study alignment-induced packed arithmetic [9]. Two contemporaneous, open vLLM software records are especially adjacent. PR 46639 proposes full-K Marlin execution to remove batch-size-dependent split-reduction effects [5]; PR 48032 proposes stable route alignment after tracing Marlin output differences to atomic alignment order [1]. Neither record reports the selected eight-row boundary intervention, within-block control, schedule-collapse control, and canonical third trajectory tested here. Both were unmerged when accessed and are cited as public engineering records, not peer-reviewed results.
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Limitations and threats to validity
One selected fixture. The study has one independent problem instance: one checkpoint, layer, prompt-derived fixture, GPU, runtime, and kernel build. Five cold processes per cell establish repeatability, not external validity. 5
Work
Primary focus
Ordering/determinism
AWQ Marlin
weight-only quantization packed mixed-precision kernels block-sparse MoE training expert-parallel training megakernel inference verification
not the focus complex tiled scheduling block organization for efficiency deterministic token order determinism versus invariance full-K versus split-K
MegaBlocks UniEP Bit-Exact vLLM PR 46639 vLLM PR 48032 This work
Relation to this study
supplies the quantized model form supplies the pinned schedule whose classes we derive related blocking, not exact packed-arithmetic causality related canonical ordering under a different system and workload related exact-output framing, not the route-block intervention WNA16 batch adjacent schedule control; no selected invariance boundary-transfer study Marlin route alignment stable route ordering adjacent order control; no schedule-class causal matrix single-fixture mechanism route-block membership causal boundary, within-block, and stable construction schedule, and canonical controls
Table 4: Compact comparison with the closest conceptual lines of work. The focal routes were selected from prior data. We do not estimate a denominator or prevalence. Composite treatment. H1 is a fixed preconstruction-state treatment. It establishes association between that composite treatment and native alignment, followed by causal control of alignment and arithmetic. It does not identify allocator, fragmentation, address, or prewarm primitives. Pinned arithmetic explanation. The source/binary derivation and grid control establish direct/full-K versus split/global-reduction schedule classes for one pinned Marlin geometry. They do not identify a single responsible instruction or generalize across GPU architectures, compiler versions, shapes, or kernels. Exact differences are not practical impact. The final native difference is one FP16 element. We did not test token divergence, task quality, or serving impact. Sparse exact differences can be scientifically diagnostic without being operationally important. Separate implementation evidence. The canonical-implementation evaluation shares exact anchors but uses a different full diff, binary, and process population. Its single-point timings cannot support general performance, serving-scale, or portability claims. Software-build linkage. The corrected schedule geometry was derived with a qualified precursor extension, whereas the 70-process cohort used the final extension identified above. The binaries differ. The pinned ops.cu and marlin template.h schedule sources are byte-identical across the two builds; the artifact records both source hashes and both extension identities. This source join supports the schedule derivation but does not combine the two process populations. Recorded versus native reproducibility. The public artifact includes the exact pre-specified plans, capture/scorer sources, software-build diff, pre-execution study record, and execution records. It omits checkpoint-derived tensors, private prompt, binary extensions, and raw tensor captures. Its verifier checks recorded evidence and exact relations. Exact independent reproduction of the reported bit patterns is unavailable from the public package because the omitted prompt and fixture tensors are required to reconstruct the reported fixture; rebuilding the pinned environment with a new fixture is a methodological replication, not confirmation of those bit patterns. Publication chronology. The contracts and outcomes were first published together after execution. The companion artifact exposes byte-level cross-linkage and recorded execution chronology, not an independent thirdparty preregistration timestamp.
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Artifact and evidence discipline
The companion artifact is hosted at https://github.com/gustavgauge/route-block-arithmetic; the immutable arxiv-v1-submission-r2 release is the paper’s submission package and links to the unchanged recorded-evidence snapshot. The exact evidence snapshot is Git commit f17755bf90dbca97ddee78ad70d1bfc58ad282e2. Its sole
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claim/evidence/provenance ledger separates five classes: the prospective cohort, schedule derivation, historical corroboration and controls, the canonical-implementation evaluation, and unsupported claims. Frozen contracts, stage summaries and independent scores, perturbation record, schedule geometry, implementation verdict, exact timing record, historical inventory, and checkpoint manifest are SHA-256 pinned. The CPU-only verifier recounts the 20/20/30 stage populations and all cell/history replicates; verifies trajectory equalities and transfers; checks the schedule arithmetic; confirms all seven rejection records; validates the historical/cohort separation and checkpoint identity; verifies the pre-execution study record, software-build identities, plans, execution records, and scorer sources; and recomputes the separate timing medians and ratios. It is intentionally not a GPU tensor re-execution. Use of AI tools. The author used OpenAI Codex for code execution, evidence cross-checking, and drafting and editing assistance. The author reviewed the analyses, verified the cited artifacts, and assumes responsibility for the paper’s contents.
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Conclusion
In this controlled fixture, MoE alignment acted as arithmetic control flow. The tested route-block boundary intervention changed which packed reduction schedule the selected routed rows entered and transferred their exact trajectory. The within-block permutation preserved each native trajectory, removing split reduction collapsed W13, and stable construction removed the observed history dependence by selecting a third exact trajectory. The evidence supports that mechanism at the stated boundary—no broader claim is required for the result to be useful or falsifiable.
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