The processing of gigapixel whole slide images within vision language models faces a major difficulty due to an excessive number of visual tokens. Existing solutions typically rely on spatial downsampling or heuristic pruning strategies that operate without training, and these methods often discard subtle but clinically meaningful patterns because pathological evidence is scattered irregularly across the tissue. To overcome this limitation, we reformulate token reduction in whole slide images as a trainable sparsification problem, allowing the model to learn an optimal selection strategy instead of following fixed heuristics. We propose a decoupled routing architecture. To enable gradient propagation through the nondifferentiable pruning operation during training, we introduce a component called SparseLearn. This component uses a variance-preserving noise gate that regulates the information flow of each patch via a differentiable Soft Top-K operator, together with a diagonal attention denoiser that recovers perturbed representations without leaking spatial information. At inference time, the SparseLearn module is entirely discarded, and the trained scorer applies a deterministic Hard Top-K operator to keep only the highest scoring 32 tokens, incurring no extra computation. By compressing the visual sequence down to a sparse set of just 32 tokens, which represents as little as 0.78% of the original length, our framework achieves 73.32% overall accuracy on SlideBench (TCGA), consistently surpassing sampling-based baselines and general-purpose vision language models. It also demonstrates strong zero shot generalization on SlideBench (BCNB) and WSI VQA*. By resolving the visual context bottleneck and preventing the dilution of sparse diagnostic evidence, this work provides a highly efficient paradigm for end to end gigapixel whole slide image reasoning.