Cerberus Squeezing: FHE Inference Optimization

• Cerberus Squeezing is a quantization and circuit-fusion technique that reduces FHE gate count and noise in transformer models.
• It employs dynamic quantization, multi-head attention fusion, and adversarial alignment to enable efficient inference with minimal accuracy loss (<1% perplexity increase).
• The technique integrates zero-knowledge proofs within a decentralized mining protocol to verify encrypted computations without exposing sensitive data.

Cerberus Squeezing is the principal quantization and circuit-fusion technique in the BasedAI protocol, designed to enable practical, privacy-preserving inference with fully homomorphic encryption (FHE) on large-scale transformer LLMs. It addresses key bottlenecks associated with FHE-compliant quantization, particularly when deploying attention-heavy architectures, by optimizing both computational efficiency and cryptographic noise growth. Cerberus Squeezing uniquely integrates dynamic quantization, multi-head attention fusion, and adversarial alignment principles, forming the backbone of BasedAI’s zero-knowledge LLM (ZK-LLM) inference pipeline (Wellington, 2024).

1. Motivation and Background

Fully Homomorphic Encryption (FHE), since Gentry (2009), permits computation directly on encrypted data, but every arithmetic operation on ciphertext incurs significant computation overhead and noise accumulation in the ciphertext space. Standard, bitwise quantization for transformer layers results in a polynomial explosion in the number of required FHE gates, causing prohibitive latency and energy consumption. For multi-head attention mechanisms, naïve FHE deployment exacerbates gate bloat and frequent noise-resetting steps (relinearization and bootstrapping), further reducing model throughput.

Cerberus Squeezing addresses these issues by:

• Clustering multi-head attention (MHA) sub-operations into fused FHE circuits, sharply reducing gate count and the need for noise-resetting.
• Employing adversarial alignment, following insights from Goodfellow et al. (2014), to ensure that quantization-induced distortions are statistically imperceptible to downstream model layers.

2. Algorithmic Structure and Methodology

Cerberus Squeezing is embedded in the decentralized User–Miner–Validator workflow characteristic of BasedAI. The following outlines the core computational process:

1. Encryption: A user encrypts their input $q$, yielding $c_q = H_{\mathrm{Enc}}(q)$ with an FHE transform $H$.
2. Squeezing and Model Preparation: The miner applies the Cerberus Squeezing operator $S$ to the encrypted input, $c_x = S(c_q)$, and generates squeezed model weights, $W_{\mathrm{squeezed}} = S(W) = Q(\Phi(W))$, where $Q$ is a quantization map and $\Phi$ is a circuit that fuses MHA sub-operations.
3. Encrypted Inference: Miners use $f_{\mathrm{FHE}}$ to compute the encrypted response with squeezed weights: $$\widehat{c}_y = f_{\mathrm{FHE}}(c_x;W_{\mathrm{squeezed}})$$.
4. Zero-Knowledge Proof: The miner submits a succinct zk-SNARK proof $\pi$ demonstrating correct application of $S$ and $f_{\mathrm{FHE}}$ without revealing sensitive data.
5. Validation and Decryption: Validators verify $\pi$ before users decrypt output $y = H_{\mathrm{Dec}}(c_y)$.

This design ensures that at no point do miners or validators access plaintext queries or responses; all data on-chain remains encrypted.

3. Mathematical Formulation

3.1. Dynamic Quantization and Squeezing Operator

The squeezing operator encompasses both quantization and MHA fusion:

• Quantization: $$Q:\mathbb{R}^n \rightarrow \{k\Delta+z \mid k\in\mathbb{Z}\}$$, with zero-point $z$ and scale $\Delta$. Uniform quantization error is bounded as $\|W-Q(W)\|_{\infty} \le \frac{\Delta}{2}$.
• Adaptive scaling: For input tensor $X \in \mathbb{R}^{N \times M}$, per-sample standard deviations $\sigma_i$ and adaptive scales $S_i$ (dependent on threshold $T$) determine quantization levels $L$.
• MHA Fusion: Instead of $k$ FHE circuits for $k$ heads, Cerberus Squeezing merges these into a single homomorphic circuit $\Phi$:

$$\Phi(X; \{W^Q_i, W^K_i, W^V_i\}, W_O) \approx [\mathrm{MHA}(X)]$$

yielding a substantial reduction in gate complexity: if $$\mathrm{Cost}_{\text{naïve}} \approx k C_{\text{head}}$$, then $$\mathrm{Cost}_{\text{squeezed}} \approx C_\Phi \ll k C_{\text{head}}$$.

3.2. Adversarial Alignment

The SqueezingModule $S$ is aligned with a lightweight discriminator $D$ so that quantized embeddings remain indistinguishable from full-precision ones, minimizing perceived errors through an adversarial loss: $$\mathcal{L}_{\mathrm{adv}} = \mathbb{E}_{x\sim p_{\mathrm{orig}}}[\log D(x)] + \mathbb{E}_{x\sim p_{\mathrm{orig}}}[\log(1 - D(S(x)))]$$ This structure restricts squeezing-induced distortions, preserving transformer performance after quantization.

3.3. Zero-Knowledge Guarantees

Each inference is corroborated by a zk-SNARK proof: $$\pi\!:\! \text{``I know }W, S(c_q)\text{ such that }c_x = S(c_q) \text{ and } \widehat{c}_y = f_{\mathrm{FHE}}(c_x; S(W))\text{.''}$$ Validators confirm the correctness of computation without revealing $q$ or $y$, ensuring zero-knowledge throughout the workflow.

4. Integration in Decentralized P2P Mining Protocols

BasedAI employs a stake-weighted design in its P2P mining/validation network:

• Miners and validators stake $BASED$ tokens and register to either propose encrypted inference (miners) or verify zk-proofs (validators).
• All on-chain data remains encrypted, with only end users possessing decryption privileges.
• Validators execute proof verifications and cross-checks, imposing penalties (slashing staked $BASED$) for detected invalid proofs.

The user–miner–validator–user loop forms a robust, cryptographically enforced privacy pipeline, with Cerberus Squeezing essential to making such a pipeline performant at scale.

5. Empirical Performance and Evaluation

Cerberus Squeezing demonstrates marked efficiency improvements relative to naïve FHE quantization. On toy expressions, it reduces bitwise encryption operations from 11 to 5. Internal tests with GPT-2–level ZK-LLMs show:

• Gate count reduction in MHA layers: ≈60–70%
• End-to-end inference latency reduction: ≈55%
• Loss in LLM accuracy: <1% perplexity increase

A summary of key metrics is provided below:

Method	Gate Count	Latency	Accuracy Loss
FHE naïve	100%	100%	0%
FHE + Cerberus Squeezing (est.)	30–40%	45–50%	<1%

This improvement is achieved without requiring decryption for model inference at any stage.

6. Significance and Future Directions

Cerberus Squeezing constitutes the technical linchpin for scalable, private, and decentralized transformer inference in the BasedAI framework. It merges dynamic quantization, adversarial alignment, and multi-head attention fusion, dramatically reducing FHE overhead while maintaining faithful model outputs and cryptographic privacy for all parties. The technique enables practical deployment of ZK-LLMs in adversarial, decentralized settings, with miners and validators collaborating without access to private data.

Future work includes benchmarking on GPT-3–scale models and further adversarial tuning of the SqueezingModule to minimize quantization error and further optimize the balance between model fidelity, privacy, and computational performance (Wellington, 2024).