From 80x to 385x: A Best-Matching-Unit Search at the L2 Roof, Measured Against a Symmetrically Tuned Baseline

GPU-accelerated Self-Organizing Map (SOM) implementations are among the most competitive options for large-scale SOM analysis, but growing dataset sizes increasingly challenge their practical use because workloads no longer fit cleanly within device-memory limits. We introduce FloatSOM, a SOM framework for scalable training and deployment that supports multi-GPU execution, out-of-memory disk-backed streaming, and novel topologies beyond regular lattices. We evaluate FloatSOM on 14 synthetic and real benchmark datasets together with controlled speed scaling benchmarks, and show that these improved topologies, combined with topology-aware hyperparameter fine-tuning, yield lower quantization error than current state-of-the-art SOM baselines. FloatSOM also sustains this performance at large scale with high-throughput distributed execution; in the largest benchmark, it trains a 1024-node SOM network on 1,000,000,000 samples with 50 features in 6.16 minutes on 8 GPUs across two separate high-performance-computing nodes.

Sparse matrix computation performance on GPU depends on how representation and execution schedule match the input structure and target hardware. No single implementation consistently dominates across sparsity patterns, operators, and hardwares. Existing sparse compilers and specialized systems cannot cover all of them simultaneously. We present SparseDitto, an agentic sparse compilation framework for sparse matrix computation on GPUs. It jointly synthesizes representation, execution schedule, and hardware mapping in a unified compilation plan. Structural analysis and a learned template-ranking prior guide architecture-aware synthesis. LLM-guided lowering realizes each plan as CUDA code, while target-GPU profiling drives plan refinement. SparseDitto covers multiple operators, e.g., SpMV, SpMM, and SpGEMM, and various representations within one framework. It can also automatically adapt to different hardwares. Across various SuiteSparse matrices, SparseDitto achieves geometric-mean speedups over cuSPARSE of $2.68\times$ on an NVIDIA RTX PRO 6000 and $2.79\times$ on an NVIDIA H200 (up to 146.61$\times$). Its generated SpMM kernels accelerate full-batch GCN training by up to $3.39\times$.

Selecting the top-$k$ elements is a fundamental operation for inducing sparsity in large-scale models and optimization problems, enabling robust expert activation, token routing or attention pruning. However, hard top-$k$ is non-differentiable, while existing differentiable alternatives become increasingly expensive as the number of coordinates grows. We introduce Fast LapSum, a scalable solver for the LapSum soft top-$k$ formulation that preserves an exact selection mass of $k$, while supporting end-to-end differentiation. In Fast LapSum, we reduce sorting cost using probabilistic bracketing, which restricts sorting to a narrow band of scores around the threshold using a binomial order-statistic from kernel-noised samples. A certification pass upgrades the probabilistic localization to a verified one at the cost of one additional linear pass, with a full-sort fallback that covers the worst-case scenario. Our certified GPU implementation processes $10^6$, $10^7$, and $10^8$ scores in median times of $0.92$, $1.39$, and $7.24$ ms, respectively, making exact-budget soft top-$k$ practical within million-scale optimization loops. We demonstrate this capability in two applications: megapixel sparse adversarial examples with a small fraction of initial image pixels, where Fast LapSum achieves an order-of-magnitude speedup over state-of-the-art methods, and 3D Gaussian splatting. In the latter, we use Fast LapSum to reduce the number of Gaussians produced by Adaptive Density Control to a substantially smaller number while retaining nearly the same rendering quality and massively reducing computation. These results demonstrate that exact-budget differentiable top-$k$ can be incorporated into practical million-scale optimization pipelines.