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Master GPU kernel optimization with 91+ comprehensive guides. Each guide includes performance benchmarks, code examples, and step-by-step optimization techniques.
Optimize CUDA max pooling, average pooling, and global pooling with efficient memory access and reduction patterns.
Optimize CUDA activation functions: ReLU, GELU, SiLU/Swish, and fused implementations for transformers.
Optimize CUDA image resizing with bilinear, bicubic interpolation, and efficient batch processing for data augmentation.
Optimize CUDA SAXPY (a*x + y) with memory coalescing, vectorized loads, and grid-stride loops. Learn bandwidth optimization techniques for memory-bound kernels.
Master CUDA vector addition - the foundational GPU operation. Learn memory coalescing, grid-stride loops, and achieve maximum memory bandwidth.
Optimize CUDA MSE loss for regression tasks. Learn fused forward-backward computation, vectorized operations, and reduction strategies.
Optimize CUDA L2 normalization for unit vectors. Learn fused norm computation and division, batched row-wise normalization.
Optimize CUDA ReLU activation for neural networks. Learn vectorized max operation, fused kernels, and in-place computation.
Optimize CUDA Leaky ReLU for neural networks. Learn efficient negative slope handling, vectorization, and parametric variants.
Optimize CUDA sigmoid activation. Learn numerically stable implementation, fast approximations, and fusion strategies.
Optimize CUDA tanh activation for RNNs and normalization. Learn CUDA intrinsics and fusion with gates.
Optimize CUDA softplus for smooth ReLU approximation. Learn stable log(1+exp(x)) computation.
Optimize CUDA ELU for self-normalizing networks. Learn efficient negative exponential computation.
Optimize CUDA tensor concatenation along any axis. Learn memory-efficient views vs copies.
Optimize CUDA tensor stacking to create new dimensions. Learn efficient batching of same-size tensors.
Optimize CUDA tensor reshaping. Learn when reshape is free (view) vs requires copy.
Optimize CUDA tensor flattening to 1D. Learn zero-copy views for contiguous tensors.
Optimize CUDA tensor splitting into chunks. Learn view-based splitting for contiguous tensors.
Compute matrix trace (sum of diagonal elements) efficiently on GPU using parallel reduction. Simple but essential for many linear algebra algorithms.
Compute Frobenius norm (matrix L2 norm) efficiently on GPU. Essential for regularization, convergence checking, and numerical analysis.
Solve triangular systems Lx=b or Ux=b efficiently on GPU using cuBLAS trsv/trsm. Building block for LU, QR, and Cholesky solvers.
Implement Jacobi iterative method on GPU for simple parallel solving. Good for preconditioning and smoothing in multigrid.
Compute inverse Fast Fourier Transform on GPU using cuFFT. Essential for frequency domain processing and signal reconstruction.
Master CUDA matrix multiplication (GEMM) with shared memory tiling, memory coalescing, and warp-level optimizations. Learn how to achieve near-cuBLAS performance.
Master CUDA memory coalescing to maximize GPU memory bandwidth. Learn access patterns, alignment requirements, and techniques to achieve peak memory throughput.
Master CUDA parallel reduction for computing sums efficiently. Learn tree-based reduction, warp-level primitives, and techniques to achieve maximum throughput.
Learn to find maximum values in large arrays using CUDA parallel reduction. Master argmax, multi-array max, and fused max-reduction patterns.
Master CUDA matrix transpose with coalesced memory access. Learn shared memory techniques, bank conflict avoidance, and in-place transpose optimizations.
Master CUDA histogram computation with atomic operations, privatization, and sorting-based approaches. Learn to optimize for different bin counts and data distributions.
Optimize CUDA softmax with online computation, warp reductions, and numerical stability. Essential for transformer and classification models.
Optimize CUDA layer normalization with fused kernels, warp reductions, and Welford algorithm. Essential for transformer inference.
Optimize CUDA batched matrix multiplication for multi-head attention, grouped convolutions, and parallel linear layers.
Optimize CUDA embedding table lookups with coalesced access, shared memory caching, and sparse gradient updates.
Optimize CUDA Fast Fourier Transform with cuFFT, batched transforms, and memory-efficient plans for signal processing.
Optimize CUDA scatter and gather operations for sparse updates, embedding gradients, and graph neural networks.
Master CUDA memory management: pools, unified memory, pinned memory, and allocation strategies for high performance.
Master asynchronous memory transfers with cudaMemcpyAsync to overlap data movement with kernel execution. Learn stream synchronization, pinned memory, and multi-stream patterns.
Optimize CUDA dot product with warp-level primitives, shared memory reduction, and atomic operations. Learn reduction patterns that achieve 100+ GFLOPS.
Optimize CUDA matrix-vector multiplication (SGEMV). Learn row-wise parallelism, shared memory reduction, and cuBLAS integration.
Optimize CUDA group normalization for CNNs and transformers. Learn channel grouping, fused kernels, and batch-independent normalization.
Optimize CUDA instance normalization for style transfer and image generation. Learn per-sample per-channel normalization with fused kernels.
Optimize CUDA dropout for neural network regularization. Learn efficient random number generation, fused operations, and inverted dropout.
Optimize CUDA cross-entropy loss for classification. Learn numerically stable log-softmax, fused loss computation, and gradient calculation.
Optimize CUDA binary cross-entropy for binary classification and multi-label tasks. Learn numerically stable sigmoid-BCE fusion.
Optimize CUDA cosine similarity for embeddings and retrieval. Learn fused dot product and normalization, batched computation.
Optimize CUDA Swish (SiLU) activation for modern networks. Learn efficient x*sigmoid(x) implementation and fusion.
Optimize CUDA Mish activation. Learn efficient x*tanh(softplus(x)) computation and numerical stability.
Optimize CUDA SELU for self-normalizing neural networks. Learn fixed-point scaling parameters.
Optimize CUDA GELU for transformers. Learn tanh approximation and exact erf-based computation.
Optimize CUDA log-softmax for numerical stability. Learn log-sum-exp trick and fusion with cross-entropy.
Optimize CUDA argsort for index sorting. Learn radix sort with keys and parallel merge sort.
Optimize CUDA cumulative sum with scan algorithms. Learn Blelloch scan and work-efficient parallel prefix.
Optimize CUDA cumulative product for running products. Learn scan with multiplication and numerical stability.
Optimize CUDA tensor dimension permutation. Learn stride manipulation and efficient transpose.
Optimize CUDA broadcasting for element-wise operations on different-shaped tensors.
Optimize CUDA unique element finding. Learn sort-based and hash-based approaches.
Compute matrix determinants efficiently on GPU using LU decomposition and parallel reduction. Essential for linear algebra and machine learning applications.
Compute spectral norm (operator norm, largest singular value) efficiently using power iteration on GPU. Essential for Lipschitz constraints and GAN training.
Compute matrix condition number on GPU for numerical stability analysis. Essential for understanding when linear systems are ill-conditioned.
Solve overdetermined linear systems on GPU using QR decomposition and normal equations. Essential for regression and data fitting.
NumPy-compatible least squares solver on GPU returning solution, residuals, rank, and singular values. Full-featured replacement for numpy.linalg.lstsq.
Solve linear systems via QR decomposition on GPU. Numerically stable method for square and overdetermined systems.
Solve banded linear systems on GPU exploiting band structure for O(n·bandwidth²) complexity. Essential for finite difference and spline applications.
Solve symmetric positive definite systems using conjugate gradient method on GPU. The gold standard for large SPD sparse systems.
Implement Gauss-Seidel iteration on GPU using graph coloring for parallelism. Faster convergence than Jacobi with careful parallelization.
Implement Successive Over-Relaxation for accelerated iterative solving on GPU. Optimal relaxation can dramatically speed convergence.
Compute 2D Fast Fourier Transform on GPU using cuFFT. Essential for image processing, convolution, and spectral analysis.
Master CUDA 2D convolution for deep learning CNNs. Learn direct convolution, im2col, Winograd algorithm, and cuDNN integration techniques.
Master CUDA prefix scan (parallel scan) for cumulative sums. Learn Blelloch algorithm, work-efficient scan, and applications in stream compaction.
Master CUDA bitonic sort for GPU sorting. Learn sorting networks, key-value sorting, and when to use bitonic vs radix sort.
Master CUDA stencil computations for PDEs, image filtering, and simulations. Learn halo exchange, temporal blocking, and multi-GPU stencil patterns.
Optimize CUDA attention with FlashAttention, memory-efficient backprop, and multi-head parallelism. Critical for transformer performance.
Optimize CUDA sparse matrix operations with cuSPARSE, efficient formats (CSR, COO, BSR), and sparse-dense products.
Master CUDA warp-level primitives: shuffle, vote, match, and cooperative operations for maximum GPU efficiency.
Master CUDA cooperative groups for flexible thread synchronization, grid-wide barriers, and modular kernels.
Program CUDA Tensor Cores directly with WMMA API for matrix operations at 10x+ the speed of CUDA cores.
Master CUDA asynchronous memory copies with memcpy_async, pipeline barriers, and overlap compute with data transfer.
Optimize CUDA graph algorithms: BFS, PageRank, connected components with load balancing and irregular memory access.
Implement CUDA quantization for INT8/INT4 inference with calibration, packed formats, and dequantization fusion.
Optimize CUDA 1D FFT with Cooley-Tukey algorithm, shared memory butterflies, and bank conflict avoidance. Learn frequency domain processing for signals up to 10x faster.
Optimize CUDA batch normalization with welford online algorithm, warp reductions, and fused activations. Learn training and inference patterns for 5-10x speedups.
Optimize CUDA top-k selection for beam search and sampling. Learn radix select and heap-based algorithms.
Compute nuclear norm (trace norm, sum of singular values) on GPU using SVD. Essential for low-rank matrix approximation and matrix completion.
Compute Moore-Penrose pseudo-inverse on GPU using SVD. Essential for solving least-squares problems and handling rank-deficient systems.
Solve linear systems using SVD decomposition on GPU. Most stable method for ill-conditioned and rank-deficient systems.
Solve sparse linear systems on GPU using cuSPARSE direct and iterative methods. Essential for large-scale scientific computing and graph problems.
Solve large linear systems using iterative Krylov methods on GPU. Essential for systems too large for direct factorization.
Solve general non-symmetric linear systems using GMRES (Generalized Minimal Residual) on GPU. Most robust Krylov method.
Solve non-symmetric linear systems using BiCGSTAB on GPU. Fixed memory cost alternative to GMRES for general systems.
Implement geometric and algebraic multigrid on GPU for O(n) complexity solving. The fastest method for elliptic PDEs.
Compute 3D Fast Fourier Transform on GPU using cuFFT. Essential for volumetric data, physics simulations, and medical imaging.
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