CUDA Kernel Fusion Strategies

• CUDA kernel fusion is the process of merging multiple CUDA kernels to reduce global memory transfers and launch overhead while enhancing on-chip data reuse.
• It employs vertical, horizontal, and mixed strategies to increase arithmetic intensity and expose greater parallelism for improved GPU performance.
• Compiler automation and heuristic scheduling techniques enable robust fusion across complex workloads in deep learning, scientific simulations, and other domains.

CUDA kernel fusion refers to the process of merging multiple CUDA kernels—often corresponding to consecutive stages of a computational pipeline—into a single launch so as to minimize global memory traffic, reduce kernel launch overhead, and maximize on-chip data reuse. The primary motivation is to raise arithmetic intensity, improve memory locality, and expose greater parallelism, which results in substantial speedups for memory-bound workloads, complex operator chains, and fine-grained graph computations on NVIDIA GPUs. Modern fusion strategies capture both vertical (producer–consumer) and horizontal (concurrent-task) opportunities, and are central to GPU acceleration in fields ranging from scientific simulation to deep learning and signal processing.

1. Motivations, Principles, and Roofline Analysis

The essential principle of kernel fusion is to increase arithmetic intensity—the ratio of floating-point operations to global memory transfers—by keeping intermediate results on-chip (registers, shared memory) rather than writing them repeatedly to global memory. The roofline model formalizes this:

$$P_{\text{actual}} \leq \min \left( P_{\text{peak}}, I_a \cdot B_{\text{peak}} \right),$$

where $P_{\text{peak}}$ is the hardware peak FLOP/s, $B_{\text{peak}}$ is memory bandwidth, and $I_a$ is arithmetic intensity (FLOPs/byte). For chains of low-intensity operators (BLAS-1, BLAS-2, elementwise, and reduction kernels), performance is generally memory-bound. By eliminating intermediate stores and loads, fusion boosts $I_a$, moving closer to the hardware envelope (Filipovič et al., 2013).

Other motivations include:

• Reducing the aggregate number of kernel launches, amortizing launch overhead, and improving GPU occupancy, particularly for computations with fine granularity (e.g., deep learning operator graphs, PDE elements, or high-resolution video analysis) (Long et al., 2018, Adnan et al., 2015).
• Enabling cross-kernel software optimizations, such as common subexpression elimination, loop fusion, and tiling, that require broader visibility than isolated kernels allow (Filipovič et al., 2013, Bhaskaracharya et al., 2020).
• Hiding memory latency by co-assigning multiple stages to the same threads or thread blocks, creating pipelined computation structures (Rupp et al., 2014, Trojak et al., 2021).

2. Fusion Methodologies: Vertical, Horizontal, and Mixed Strategies

CUDA kernel fusion is implemented via a variety of methodologies, distinguished by kernel dependence and resource mapping:

• Vertical Fusion (VF): Producer–consumer kernels with strict dataflow dependencies (e.g., GEMM followed by activation or pointwise maps) are merged such that all intermediates are kept on-chip. The fused kernel executes $O_1 \to O_2 \to \ldots \to O_N$ in one launch, dramatically reducing DRAM bandwidth requirements (Amoros et al., 9 Aug 2025, Chen et al., 2023, Bhaskaracharya et al., 2020).
• Horizontal Fusion (HF): Two or more independent kernels with no data dependency are invoked in parallel within the same kernel launch, increasing effective thread-level parallelism and hiding instruction/memory latencies. Each thread (or subset of threads) chooses which kernel to execute via index guards. HF is particularly effective at masking memory stalls and improving SM utilization in the mixed kernel regime (Li et al., 2020, Amoros et al., 9 Aug 2025).
• Mixed HF + VF: Combining both approaches, e.g., processing batched images (horizontal) each through chains of pointwise ops (vertical) in a single variadic template-based C++ kernel (Amoros et al., 9 Aug 2025). This achieves speedups scaling with both batch size and pipeline depth.
• Custom Pipeline and Epilogue Fusion: Specialized frameworks (e.g., CUTLASS) provide hook points (epilogues) for fusing per-element transformations directly into high-throughput routines such as GEMM, FFT, or attention (Chen et al., 2023, Bikshandi et al., 2023, Wu et al., 16 Apr 2025).

Algorithmic fusion decisions are guided by dependency analysis, scheduling heuristics, resource estimation (register/shared usage, occupancy), and domain-specific legality constraints (Long et al., 2018, Zheng et al., 2020, Niu et al., 2021).

3. Compiler and Automation Techniques

To automate robust kernel fusion in complex computation graphs:

• Source-to-source compilers transform high-level scripts (or intermediate representations) into fused CUDA kernels. Examples include compilers for BLAS map/reduce sequences and BLAS-2/BLAS-3 tile-level fusion (Filipovič et al., 2013).
• Fusion planners and heuristic search: Frameworks such as FusionStitching (TensorFlow/XLA, Alibaba) enumerate fusion candidates by combining schedule consistency checks, cost-model-guided search, and greedy/beam search to select performant fusion patterns (Long et al., 2018, Zheng et al., 2020, Long et al., 2019).
• Polyhedral compilation: Loop nests for GEMM + pointwise epilogues are lifted into the integer set polyhedral model, enabling automatic tiling, dependency resolution, and vertical fusion for matrix multiplications, bias, activation, etc., with tensor core code emission (Bhaskaracharya et al., 2020).
• DAG-based memory minimization: MCFuser applies directed acyclic graph (DAG) analysis to minimize redundant memory traffic by optimally placing loads/stores and fusing operator tiles, combined with evolutionary search in the fusion/schedule parameter space (Zhang et al., 27 Jun 2025).
• Component-based meta-programming: C++17 metaprogramming and variadic templates generate a unique fused kernel based on the user-specified sequence of (possibly hundreds of) library function calls, abstracting both HF/VF (Amoros et al., 9 Aug 2025).

4. Practical Fusion Patterns: Case Studies

4.1 GEMM + Epilogue Fusion (CUTLASS, Tensor Core)

• In atomistic spin dynamics, the most intensive calculation—spin–spin correlation—is refactored as a GEMM, with Q-matrix elementwise weightings fused directly as a custom epilogue via CUTLASS, avoiding redundant global memory round-trips and increasing arithmetic intensity. On NVIDIA A100, fused CUTLASS kernels yield 26–33% speedup over cuBLAS+Thrust and up to 25× over CPU baselines (Chen et al., 2023).
• FlashAttention-2 on Hopper is realized as a single pipeline—Q·K^T (GEMM), fused online row-wise softmax, P·V (GEMM)—all in one kernel using the WGMMA and TMA instructions, with custom CUTLASS kernel layouts and asynchronous copy. Speedups up to 3× over previous fused-scan designs on earlier hardware (Bikshandi et al., 2023).

4.2 Map/Reduce and Pointwise Chains

• Compiler-generated fusions for BLAS-1/BLAS-2 (map-reduce) kernels achieve up to 2.61× speedup over CUBLAS for sequences such as AXPY+DOT and SGEMV/GEMVT pairs. Tiling, shared memory register allocation, and partial reductions are used to eliminate intermediate loads and stores (Filipovič et al., 2013).
• DNNFusion expands the operator-level fusion space for ONNX graphs using a mapping-type (one-to-one, many-to-one, reshuffle) classification, aggressive graph rewriting, profiling-guided legality checks, and a greedy/seed-and-grow block planner to multiplex operators into single fused kernels, delivering up to 9.3× speedup on embedded/mobile GPUs (Niu et al., 2021).

4.3 Advanced Scientific and PDE Workloads

• Hyperbolic diffusion in flux reconstruction enables the fusion of multiple stages (flux computation, divergence, source) into a single kernel; up to 4× speedup is observed in 3D flow, with careful register/shared/global memory balancing and per-block codegen-time memory management (Trojak et al., 2021).
• Pipelined iterative solvers (CG, BiCGStab, GMRES) fuse vector AXPYs and SpMV + reductions in a minimal kernel set, greatly reducing launches and global memory traffic for small to medium system sizes (Rupp et al., 2014).

4.4 Deep Learning Quantization Pipelines

• Quantization-aware training for Visual SLAM workloads implemented four-step fake-quantization as one fused kernel, cutting per-layer kernel count by 4× and reducing median inference latency by 23–29% in production deployments (Liao, 16 Nov 2025).

5. Performance and Resource Trade-offs

The practical effectiveness of kernel fusion depends on balancing several architectural and algorithmic considerations:

• Occupancy vs. On-Chip Pressure: Fusion increases register/shmem use per thread/block; over-fusion can lead to register spilling or decreased blocks/SM occupancy, necessitating per-architecture parameter tuning (Chen et al., 2023, Bikshandi et al., 2023, Trojak et al., 2021).
• Synchronization and Parallelism: Fine-grained fusion may require synchronization barriers (e.g., __syncthreads); misaligned thread/block mapping can reduce the benefits or create correctness issues. Multi-stage block-level and per-warp compositions are employed to maximize safety and utilization (Long et al., 2018, Niu et al., 2021, Zheng et al., 2020).
• Bank Conflicts and Memory Layouts: Fused pipelines must ensure conflict-free shared-memory access. Data layout transformations (e.g., swizzling) and register/shared-memory anchoring of key tiles are central for FFT–GEMM–iFFT (TurboFNO) and attention pipelines (Wu et al., 16 Apr 2025, Bikshandi et al., 2023).
• Legality and Generality: Fusion is constrained by inter-operator dependencies—e.g., cross-block communication or global reductions limit kernel boundaries—and by features such as data-dependent control flow, irregular index patterns, or resource limits for very deep fusions (Filipovič et al., 2013, Niu et al., 2021).

6. Impact, Benchmarks, and Generalization

Empirical speedups across domains are substantial:

Application	Speedup vs. Baseline	Notable Feature	Reference
Atomistic spin dynamics	26–33% over cuBLAS+Thrust, 25× over CPU	Fused CUTLASS GEMM + epilogue	(Chen et al., 2023)
BLAS-1/2 sequences	up to 2.6× over CUBLAS	Compiler-generated map/reduce fusion	(Filipovič et al., 2013)
TurboFNO (FFT–GEMM–iFFT)	up to 1.5× over PyTorch/cuBLAS+cuFFT	Architecture-aware multi-stage fusion	(Wu et al., 16 Apr 2025)
FlashAttention-2 (Hopper)	20–50% over previous gen	Fused online-softmax+GEMM via CUTLASS	(Bikshandi et al., 2023)
DNN inference (mobile)	up to 9.3×	Mapping-type-guided plan expansion	(Niu et al., 2021)
PDE / FR (ACM)	2.3×–4× in 3D	Hyperbolic reformulation, planar+lines fusion	(Trojak et al., 2021)
Visual SLAM QAT	23–29% latency reduction	Fused fake-quantization pipeline	(Liao, 16 Nov 2025)
Pipelined CG/GMRES	2–3× (small), 1.5× (medium)	Iterative fusion, pipelined reductions	(Rupp et al., 2014)

These studies establish that, across scientific and ML domains, CUDA kernel fusion is pivotal for achieving both memory- and launch-bound efficiency. Recent C++ metaprogramming strategies further democratize fusion for scientific libraries and application users (Amoros et al., 9 Aug 2025).

7. Limitations and Current Research Frontiers

• Fusion with deep or irregular data-dependencies (stencils, dynamic sparsity, graph irregularity) remains challenging, requiring richer models of legality and synchronization (Filipovič et al., 2013, Niu et al., 2021).
• Excessive on-chip resource use can negate gains from fusion; tuning tile/block sizes and fusion depth must account for specific GPU microarchitectures.
• Cross-GPU fusion and distributed variants (e.g., partitioned fusion for NVLink clusters) are actively explored, especially for large-scale DNN and scientific workflows (Chen et al., 2023).
• While domain-specific code generators (e.g., auto-tuned polyhedral or DSL-based emitters) provide automation, general-purpose compilers remain less reliable at producing fusion plans that match hand-optimized or CAD-generated kernels (Zhang et al., 27 Jun 2025, Bhaskaracharya et al., 2020).
• Extending fusion methodologies to handle persistent/pipelined kernels, adaptive tiling, or dynamic graphs remains a priority for both hardware and software frameworks.

Kernel fusion, in sum, is an established and rapidly developing pillar of GPU high-performance computing, delivering order-of-magnitude speedups when properly engineered and coupled with resource- and dependency-aware algorithms. Its continued evolution underpins both the scalability of deep learning and the feasibility of large-scale scientific simulations on modern accelerator hardware.