Predictive systems increasingly span heterogeneous modalities such as graphs, language, and tabular records, but sparsity and efficiency remain modality-specific (graph edge or neighborhood sparsification, Transformer head or layer pruning, and separate tabular feature-selection pipelines). This fragmentation makes results hard to compare, complicates deployment, and weakens reliability analysis across end-to-end KDD pipelines. A unified sparsification primitive would make accuracy-efficiency trade-offs comparable across modalities and enable controlled reliability analysis under representation compression. We ask whether a single representation-level mechanism can yield comparable accuracy-efficiency trade-offs across modalities while preserving or improving probability calibration. We propose L0-Gated Cross-Modality Learning (L0GM), a modality-agnostic, feature-wise hard-concrete gating framework that enforces L0-style sparsity directly on learned representations. L0GM attaches hard-concrete stochastic gates to each modality's classifier-facing interface: node embeddings (GNNs), pooled sequence embeddings such as CLS (Transformers), and learned tabular embedding vectors (tabular models). This yields end-to-end trainable sparsification with an explicit control knob for the active feature fraction. To stabilize optimization and make trade-offs interpretable, we introduce an L0-annealing schedule that induces clear accuracy-sparsity Pareto frontiers. Across three public benchmarks (ogbn-products, Adult, IMDB), L0GM achieves competitive predictive performance while activating fewer representation dimensions, and it reduces Expected Calibration Error (ECE) in our evaluation. Overall, L0GM establishes a modality-agnostic, reproducible sparsification primitive that supports comparable accuracy, efficiency, and calibration trade-off analysis across heterogeneous modalities.