Visioning: Homomorphic Encryption

Homomorphic Encryption (HE) stands at the frontier of secure data processing, offering the strong capability to perform computations on encrypted data, denoted as $Enc(data)$, without decryption. This form of encryption, defined through operations $\oplus$ and $\otimes$ that correspond to addition and multiplication on encrypted data, ensures that $Enc(a) \oplus Enc(b) = Enc(a+b)$ and $Enc(a) \otimes Enc(b) = Enc(a \times b)$, for any data $a$ and $b$. The appeal of HE lies in its ability to maintain data in a secure, encrypted state, $Enc(data)$, throughout the computation process, thus safeguarding the confidentiality of sensitive information.

Applying HE within the context of LLMs in decentralized inference systems paints a visionary landscape. In such a setting, HE could enable the privacy and security of data inputs and outputs, represented as $Enc(x)$ for inputs and $Enc(y)$ for outputs, facilitating complex computations by LLMs without revealing the underlying user data. This capability is particularly crucial in decentralized systems, where ensuring data privacy and security is the key, yet the collaborative nature of training and utilizing LLMs necessitates secure, distributed computation.

However, integrating HE with LLMs for decentralized inference is embryonic and challenging. The foremost obstacle is the computational overhead introduced by HE operations, which, given the voluminous size and computational requisites of LLMs, renders real-time or near-real-time inference an infeasible task. The operations on encrypted data, especially when considering the iterative and complex nature of LLMs, encapsulated by functions $f_{\theta}(Enc(x)) = Enc(y)$, demand significant computational resources. Moreover, adapting HE to accommodate the dynamic, iterative processes inherent in LLM training and inference within decentralized frameworks adds complexity.

Despite these obstacles, the aspiration to leverage HE for ensuring SP in LLM applications within decentralized systems remains a potent driver of innovation. Acknowledging the current practical challenges of implementing HE for LLMs in decentralized settings, the narrative evolves towards exploring pragmatic methodologies for secure data processing. This journey leads to adopting Split Learning as a tangible approach to achieving data privacy and security in decentralized inference systems.