Swizzling Patterns in GPU Optimization

• Swizzling patterns are systematic remappings of data and thread assignments designed to eliminate memory bank conflicts and improve cache locality in GPU computations.
• They use explicit mathematical formulas to tailor memory layouts and scheduling for both intratile and intertile optimizations, crucial for efficient fused kernel execution.
• LLM-driven automation of swizzling pattern generation accelerates tuning compared to manual heuristics, achieving significant performance gains in high-throughput machine learning workloads.

Swizzling patterns are systematic remappings of data access or compute schedules in high-performance computing, with the principal aim of optimizing utilization of underlying hardware memory banks, caches, or execution resources. In modern GPU-accelerated machine learning workloads, swizzling patterns are essential for alleviating memory bank conflicts, maximizing data locality, and enabling high-throughput fused-kernel designs. These patterns, both at the shared memory level (intratile) and across accelerator dies (intertile), are mathematically constructed to tailor data layout or thread scheduling specifically to the memory and interconnect topology of the target device.

1. Definition and Purpose of Swizzling Patterns

Swizzling patterns, in GPU contexts, refer to the deliberate remapping of thread or program identifiers, or the computation of logical (shared) memory addresses, such that the resulting memory accesses are either bank-conflict free or optimally co-located for cache reuse. The need for swizzling arises from the mismatch between the natural order in which data is produced or consumed by different pipeline stages (e.g., FFT, GEMM, iFFT) and the requirements of the hardware, such as evenly distributing memory accesses across shared memory banks or localizing them within the same accelerator complex die (XCD) to maximize L2 cache reuse. Swizzling can be applied intra-block within shared memory or inter-block for device-level scheduling.

2. Swizzling in Shared Memory: Eliminating Bank Conflicts

Memory bank conflicts in shared memory are a significant performance bottleneck on modern GPUs, where the physical shared memory is organized into a fixed number of banks (e.g., 32 in NVIDIA GPUs). When multiple threads in a warp access the same bank, serialization occurs, degrading throughput. Swizzling patterns are devised to remap either the data layout or the thread-wise accesses such that each thread's memory access targets a distinct bank.

TurboFNO (Wu et al., 16 Apr 2025) exemplifies this approach with two principal swizzling schemes:

• FFT-to-GEMM Swizzling: Threads producing FFT output add an offset proportional to their thread ID:

$\text{addr}[i] = \text{base} + i + \Delta(i)$

where $\Delta(i)$ is selected (e.g., $0$ for 16-point, $i/2$ for 8-point FFTs) to ensure bank alignment and avoid conflict. This results in 100% bank utilization for subsequent GEMM stages, which expect a column-major, non-interleaved memory layout.

• GEMM-to-iFFT Swizzling: After GEMM, threads write their computed tiles to shared memory with an offset:

$$\text{addr}[i] = \text{base} + i + \left\lfloor i/\beta \right\rfloor$$

where $\beta$ is associated with tile width (e.g., 4), ensuring even distribution of accesses and enabling the iFFT to read from shared memory without conflict.

These patterns are explicitly constructed based on the size of the FFT and the expected memory layout of subsequent compute stages.

3. Swizzling Across Accelerator Dies: Cache Locality and XCD Co-location

On advanced, disaggregated GPU architectures, memory hierarchy is hierarchical, with L2 caches partitioned across physical dies or accelerator complexes (XCDs), and the scheduling of workgroups (program IDs, PIDs) can significantly affect data reuse and cross-die communication. SwizzlePerf (Tschand et al., 27 Aug 2025) abstracts swizzling to the process of remapping workgroup PIDs such that blocks which share data are co-located on the same XCD, thereby maximizing L2 cache hit rate and reducing inter-die bandwidth utilization.

The swizzling mapping is

$$\text{new\_pid} = (\text{pid} \bmod \text{num\_xcds}) \times \left\lceil \frac{\text{num\_blocks}}{\text{num\_xcds}} \right\rceil + \left\lfloor \frac{\text{pid}}{\text{num\_xcds}} \right\rfloor$$

where $\text{num\_blocks}$ is the number of workgroups and $\text{num\_xcds}$ is the number of accelerator dies. This schedule aligns blocks with shared data (e.g., adjacent output tiles or those sharing input matrix rows) onto the same XCD, increasing L2 hit rates by up to 70% and accelerating kernels by up to 2.06$\times$ for certain workloads.

4. Mathematical Construction and Automated Generation of Swizzling Patterns

Swizzling patterns are synthetically derived through explicit mathematical formulas based on the properties of the memory subsystem (e.g., bank count, die topology), tensor tiling, and workload-specific communication patterns. In both TurboFNO and SwizzlePerf, these patterns take the form of address arithmetic or thread/block-ID remapping formulas.

SwizzlePerf uniquely automates swizzling pattern generation by using LLMs that are provided with detailed architectural context: device memory maps, block-scheduling policies, performance logs, and historical tuning data. The LLM produces candidate swizzling code, which is iteratively refined in a feedback loop driven by hardware profiling metrics such as the L2 hit rate. This process reproduces human expert-level remapping strategies, but at vastly accelerated timescales (minutes, versus weeks for human engineers in the provided case of GEMM). A plausible implication is that this LLM-based automation can systematically explore non-intuitive or architecture-specific swizzling strategies which may not be readily apparent through manual tuning.

5. Impact on Fused Pipelines and Overall Performance

The application of swizzling patterns is central to achieving high efficiency in fully fused compute pipelines. In TurboFNO, FFT, GEMM, and iFFT are fused into a single monolithic GPU kernel in which intermediate results never leave shared memory, circumventing the cost of global memory transactions and kernel launch overheads. Properly swizzled shared memory layouts ensure that each kernel stage can achieve full memory bandwidth, as required for sustained throughput. Experimental results demonstrate that these optimizations provide up to 150% speedup relative to implementations using sequential cuFFT and cuBLAS invocations, attributable primarily to the reduction in bank conflicts and improved pipe-lining of compute stages (Wu et al., 16 Apr 2025).

In the inter-tile context, SwizzlePerf demonstrates on a suite of 10 kernels that swizzling can yield a mean speedup of 1.29$\times$, with certain kernels achieving up to 2.06$\times$, and L2 hit rate improvements averaging 23.9% and reaching up to 70% (Tschand et al., 27 Aug 2025). These results highlight the broad applicability of swizzling beyond a specific fused pipeline, extending to diverse ML and scientific workloads.

6. Methodological Distinctions and Limitations

Traditional swizzling methods rely on manual, heuristic-driven engineering that can be time and labor intensive, lacking explicit feedback from device-level metrics. SwizzlePerf contrasts with these approaches by integrating an automated, hardware-aware LLM with a feedback loop based on profiling metrics. Hardware-unaware baselines, or those overwhelmed by unfiltered documentation, are unable to generalize effective swizzling patterns, demonstrating that targeted hardware-context is a critical enabler of this methodology (Tschand et al., 27 Aug 2025).

While swizzling is highly effective at reducing bank conflicts and improving cache locality, its optimality is inherently hardware-dependent. Patterns designed for one architecture cannot be naïvely transferred to another without profiling and adaptation. This suggests continued need for tools or frameworks capable of per-architecture swizzling synthesis as hardware evolves.

7. Connections to Broader Research Themes

Swizzling patterns intersect with ongoing research in architecture-aware optimization, automated kernel synthesis, and memory-centric performance engineering. Their adoption in contexts such as Fourier Neural Operators, GEMM, softmax, and stencil computations demonstrates their versatility. The rise of LLM-driven autotuning frameworks marks a shift toward systematic, automated capture of domain expertise for hardware optimization, indicating a broader trend in performance engineering for heterogeneous and disaggregated architectures.

Swizzling Level	Example System	Principal Optimization Objective
Shared Memory (Intra-tile)	TurboFNO	Bank conflict elimination, kernel fusion
XCD (Inter-tile)	SwizzlePerf	L2 locality, cross-die communication

In summary, swizzling patterns are a fundamental, platform-adaptive technique for organizing data and scheduling computation to maximally exploit the hardware's memory and execution resources. Their formal mathematical construction, and more recently their LLM-driven automated generation, have established them as a cornerstone optimization for high-performance, architecture-aware GPU kernel design (Wu et al., 16 Apr 2025, Tschand et al., 27 Aug 2025).