According to God of Prompt on X, citing a new Columbia University paper, independent frontier models like GPT, Gemini, Qwen, Mistral, and Cohere exhibit high cross-model CKA similarity (0.595–0.881), enabling a single affine map to align internal representations for private inference (as reported by the Columbia study via the X thread). According to the thread, the HELIX system replaces full-transformer encrypted inference—previously 25–281GB per query and 20–60s latency—with a linear alignment plus homomorphic encrypted classification, achieving sub-second latency and under 1MB communication with 128-bit CKKS security. As reported by the same source, HELIX trains the alignment map using encrypted client embeddings on public data, then runs inference by locally applying the alignment, encrypting the transformed features, and letting the provider perform a single linear operation; the provider never sees plaintext inputs or model weights. According to the X post, tokenizer compatibility strongly predicts cross-model generation quality (r=0.898), and models over 4B parameters with tokenizer match rate above 0.7 can generate coherent text across families using only a linear transform. Business impact: according to the Columbia results as relayed by God of Prompt, enterprises in regulated sectors could cut private LLM inference costs and latency by orders of magnitude, unlocking viable deployments for hospitals, banks, and legal firms that cannot share raw data with third-party providers.