{"id":"047c0f11-6614-4392-b76a-121144c85ca6","arxiv_id":"2607.02097","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"WBMM replaces gather-based large-kernel depthwise convolution with windowed batched matrix multiplication, yielding higher throughput for larger windows and 1.31-1.88x training speedups on ImageNet, COCO and ADE20K while preserving accuracy.","lead":"WBMM splits input feature maps into windows and builds weight matrices from a compact bias table so that large-kernel convolutions run as fast batched matrix multiplies instead of irregular gathers. If the speed and accuracy claims hold, it lets vision models use much larger receptive fields without the usual slowdown penalty.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Whether WBMM weight-matrix construction from relative-position bias exactly replicates full large-kernel depthwise convolution (receptive field + numerics) is unverified","rationale":"Reader's weakest assumption matches the load-bearing point exactly; full-text review does not supply the missing direct equivalence verification, so the UNVERDICTED status and LOW confidence remain appropriate.","tokens_in":1758,"tokens_out":304,"duration_ms":12763,"concrete_test":"Run a 224x224 feature map through both a reference depthwise conv (kernel size matching the claimed receptive field) and WBMM (14x14 windows) using identical weights and bias table; report max absolute and relative element-wise difference. If any output differs by >1e-6, equivalence fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The operator benchmarks and end-to-end results rest on the claim that partitioning into windows, indexing a compact relative-position bias table, and performing batched matmul produces identical per-layer receptive-field coverage and numerical behavior to a standard gather-based large-kernel depthwise convolution. The paper adds inter-block cross-window communication and hierarchical reparameterization, but provides no direct element-wise or kernel-equivalence check between WBMM and a reference large-kernel implementation at the 14x14 scale used in the speed claims. Without that, hidden discrepancies in boundary handling, effective kernel support, or floating-point accumulation order could exist even if final accuracies match after training.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript proposes Windowed Batch Matrix Multiplication (WBMM) to implement large receptive-field depthwise convolutions by partitioning feature maps into contiguous windows, indexing a compact relative-position bias table to build weight matrices, and performing batched matrix multiplication for regular memory access. It claims this yields throughput that improves with window size (opposite to standard depthwise conv), operator-level speedups with 14x14 windows versus 5x5 baselines while delivering 7.8x larger per-layer receptive field, and, when augmented with inter-block cross-window communication plus hierarchical reparameterization, 1.31-1.88x training speedups with comparable or higher accuracy on ImageNet-1K, COCO, and ADE20K across GPU/CPU/edge devices; code is released.","tokens_in":1904,"tokens_out":578,"duration_ms":15200,"significance":"If the equivalence between WBMM and reference large-kernel depthwise convolution holds exactly (receptive-field coverage and numerics) and the reported speedups prove reproducible without hidden accuracy loss, the approach could provide a practical route to scale receptive fields in convolutional backbones without custom kernels or specialized hardware, with potential impact on efficient vision model design.","major_comments":[{"comment":"§3 (WBMM construction): the central claim that indexing the compact relative-position bias table and performing windowed batched matmul exactly replicates the receptive-field coverage and numerical behavior of a gather-based large-kernel depthwise convolution is asserted but unsupported by any direct element-wise output comparison, kernel-equivalence test, or boundary-handling verification at the 14x14 scale used for the speed claims; without this check, discrepancies in effective kernel support or accumulation order remain possible even if downstream accuracies match.","section":"§3"},{"comment":"§4 (operator benchmarks) and §5 (end-to-end results): the reported 1.31-1.88x training speedups and accuracy numbers on ImageNet-1K/COCO/ADE20K lack accompanying experimental protocol details, hardware specifications, error bars, or full ablation tables isolating the contribution of WBMM versus the added cross-window and reparameterization components; this makes it impossible to assess whether the performance advantage is load-bearing or reproducible.","section":"§4, §5"}],"minor_comments":[{"comment":"The abstract states concrete speed/accuracy numbers but the main text should explicitly cross-reference the corresponding tables/figures for each claim.","section":null},{"comment":"Notation for window partitioning and bias-table indexing could be clarified with a small diagram or pseudocode snippet to aid reproducibility.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful review and constructive comments on the WBMM manuscript. We address the two major comments below and will incorporate revisions to strengthen the claims on equivalence and experimental reproducibility.","responses":[{"response":"We agree that an explicit numerical verification would make the equivalence claim more robust. By construction, WBMM partitions the feature map into contiguous windows and uses the compact relative-position bias table to assemble the exact weight matrix for each window before batched matrix multiplication; this is mathematically identical to the gather-based depthwise convolution (same kernel weights, same receptive-field support per output position, and identical accumulation). Window boundaries are handled by the partitioning scheme to preserve the original convolution semantics without padding artifacts inside windows. Nevertheless, we will add a direct element-wise output comparison (including L2 difference and boundary cases) between WBMM and a reference large-kernel depthwise convolution implementation at the 14×14 scale in the revised §3.","revision_made":"yes","referee_comment":"[§3] §3 (WBMM construction): the central claim that indexing the compact relative-position bias table and performing windowed batched matmul exactly replicates the receptive-field coverage and numerical behavior of a gather-based large-kernel depthwise convolution is asserted but unsupported by any direct element-wise output comparison, kernel-equivalence test, or boundary-handling verification at the 14x14 scale used for the speed claims; without this check, discrepancies in effective kernel support or accumulation order remain possible even if downstream accuracies match."},{"response":"We acknowledge that the current manuscript provides insufficient protocol transparency. The released code (http://github.com/wansong-s/WBMM) already contains the full training and benchmarking scripts, but we will expand §§4–5 with: (i) complete experimental protocols (optimizer, learning-rate schedule, data augmentation, batch size, number of epochs), (ii) hardware specifications (GPU/CPU/edge device models and software versions), (iii) error bars computed over at least three independent runs, and (iv) expanded ablation tables that isolate the WBMM operator from the inter-block cross-window communication and hierarchical reparameterization modules. These additions will allow readers to assess the contribution and reproducibility of each component.","revision_made":"yes","referee_comment":"[§4, §5] §4 (operator benchmarks) and §5 (end-to-end results): the reported 1.31-1.88x training speedups and accuracy numbers on ImageNet-1K/COCO/ADE20K lack accompanying experimental protocol details, hardware specifications, error bars, or full ablation tables isolating the contribution of WBMM versus the added cross-window and reparameterization components; this makes it impossible to assess whether the performance advantage is load-bearing or reproducible."}],"tokens_in":1509,"tokens_out":593,"duration_ms":20884,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's main contribution is the WBMM operator. It partitions the input into windows, pulls weights from a compact relative-position bias table, and runs the work as regular batched matrix multiplication. This produces the unusual behavior that throughput improves as window size grows, which is the opposite of standard gather-based depthwise convolution.\n\nThey combine it with inter-block cross-window communication and hierarchical reparameterization, then report operator-level speedups and end-to-end training gains of 1.31-1.88x on ImageNet-1K, COCO, and ADE20K while keeping accuracy comparable or higher. The code is public and the method runs on GPU, CPU, and edge hardware without custom kernels.\n\nThe soft spot is the unverified equivalence claim. The approach assumes that indexing the bias table inside each window exactly reproduces the receptive field and floating-point behavior of a full large-kernel depthwise convolution. The abstract gives no element-wise or kernel-level check at the 14x14 size used for the speed numbers, so differences in boundary handling or accumulation order could exist even if final accuracies match after training. Experimental details such as hardware specs, error bars, and ablation tables are also missing from the summary.\n\nThis work is aimed at people optimizing CNN backbones for large receptive fields on current hardware. A reader who needs practical convolution speedups rather than a new architecture would find the operator and scaling results useful.\n\nIt deserves a serious referee because the core construction is concrete, the code is available, and the performance bottleneck it targets is real.","headline":"WBMM turns large-kernel depthwise conv into batched matmul over windows with a bias table, and the reported scaling where bigger windows run faster is the part that stands out.","tokens_in":2400,"tokens_out":398,"would_cite":false,"duration_ms":20317,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Windowed batch matrix multiplication enables efficient computation of large receptive field convolutions by converting irregular memory access into regular batched matrix operations.","keywords":["large kernel convolution","depthwise convolution","batch matrix multiplication","receptive field","efficient convolution","window partitioning","relative position bias","computer vision"],"falsifier":"A direct numerical comparison showing whether the output of WBMM matches that of a standard large-kernel depthwise convolution within floating point tolerance on the same input, or an accuracy difference exceeding 0.5% on ImageNet-1K when replacing one with the other in a model.","tokens_in":2665,"feed_emoji":"⚡","tokens_out":694,"duration_ms":31304,"temperature":0.7,"pith_summary":"The paper aims to show that large kernel depthwise convolutions can be made faster and more scalable by partitioning the input into windows and using a compact relative position bias table to build weight matrices for batched matrix multiplication. This approach reverses the usual trend where larger kernels slow down computation, instead improving throughput as windows grow larger. A sympathetic reader would care because it allows vision models to use bigger receptive fields without the typical speed penalty, leading to training speedups of 1.31 to 1.88 times on ImageNet, COCO, and ADE20K with no loss in accuracy.","feed_headline":"Windowed batch multiplication speeds large-kernel convolutions","feed_subtitle":"By partitioning inputs into windows and using bias tables for weights, it turns irregular memory access into regular batched matrix multipli","key_machinery":"Windowed Batch Matrix Multiplication (WBMM) that partitions input into windows and uses a compact relative position bias table to construct weight matrices for batched matrix multiplication, enabling regular memory access.","core_discovery":"WBMM partitions the input feature map into contiguous windows and indexes a compact relative-position bias table to construct the weight matrices, allowing the large receptive field depthwise convolution to be performed as a batched matrix multiplication with regular memory access patterns.","pith_inferences":["This method may allow vision transformers or CNNs to incorporate much larger kernels than previously practical.","Similar windowing and bias table techniques could be applied to other operations suffering from irregular memory access in deep learning.","By avoiding the need for custom acceleration kernels, it lowers the barrier for deploying large receptive field models on diverse hardware."],"forward_implications":["WBMM with 14x14 windows runs faster than 5x5 depthwise convolution while providing a 7.8 times larger per-layer receptive field.","Combined with inter-block cross-window communication and hierarchical window reparameterization, it achieves 1.31-1.88x training speedup with comparable or higher accuracy on ImageNet-1K, COCO, and ADE20K.","Throughput improves as window size increases, opposite to standard depthwise convolutions.","Advantages hold across GPU, CPU, and edge devices without needing specialized kernels."],"fun_headline_variants":["Windowed batches enable regular memory access for large-kernel convolutions","WBMM uses window partitioning for batched matrix multiplication in convolutions","Partitioning into windows indexes bias tables for regular batched convolution computation","WBMM converts irregular memory access to regular via windowed batch multiplication"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"Constructing the weight matrices from the compact relative-position bias table inside each window exactly preserves the receptive field coverage and numerical behavior of a full large-kernel depthwise convolution.","fun_headline_variants_meta":{"raw":{"variants":["Windowed batches enable regular memory access for large-kernel convolutions","WBMM uses window partitioning for batched matrix multiplication in convolutions","Partitioning into windows indexes bias tables for regular batched convolution computation","WBMM converts irregular memory access to regular via windowed batch multiplication"]},"model":"grok-4.3","cost_usd":0.010985,"raw_usage":{"total_tokens":4823,"prompt_tokens":643,"num_sources_used":0,"completion_tokens":72,"cost_in_usd_ticks":109849500,"prompt_tokens_details":{"text_tokens":643,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":4108,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":643,"tokens_out":72,"duration_ms":26081,"temperature":1.0,"reasoning_tokens":4108,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T15:36:00.166501+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct numerical comparison showing whether the output of WBMM matches that of a standard large-kernel depthwise convolution within floating point tolerance on the same input, or an accuracy difference exceeding 0.5% on ImageNet-1K when replacing one with the other in a model.","supporting_citations":[],"review_version":1}