Post-training LLM compression often relies on low-rank approximations, which force all columns of a projection matrix to share a single low-dimensional subspace. We propose *CoSpaDi*, a training-free compression framework that replaces this single-subspace assumption with a union-of-subspaces model via sparse dictionary learning. *CoSpaDi* factorizes each weight matrix into a dense dictionary and column-sparse coefficients, allowing different columns to select different subsets of dictionary atoms at the same storage budget. To preserve model behavior, we use calibration activations to transform functional reconstruction into a standard dictionary learning problem. Across Llama and Qwen models, CoSpaDi improves accuracy-compression and perplexity-compression trade-offs over SVD-based and structured pruning baselines at 20-40% compression ratios, while naturally supporting sparse-dense computation and post-training quantization of sparse coefficients.

Expanding the vocabulary of conditional text-to-speech (TTS) models typically requires extensive fine-tuning with paired audio, creating a major bottleneck for low-resource and cross-lingual adaptation. To address this, we introduce SEAM, a zero-audio initialization method that constructs embeddings for unseen tokens from known subtokens. Unlike standard pooling strategies that ignore sequential structure, SEAM applies a spectral filter to preserve temporal phonetic order and uses closed-form ridge regression to align the new embeddings with the pretrained conditioning manifold. Across three languages and two TTS architectures, SEAM matches baseline performance using up to four times less training data, reducing sample complexity by 75% compared to random initialization and mean pooling. Our approach provides a lightweight, reproducible, and theoretically grounded solution for vocabulary expansion in low-resource speech synthesis.