zkAttn: ZK Proofs for Transformer Attention

• zkAttn is a zero-knowledge proof protocol that validates the correctness of Transformer attention mechanisms without revealing model parameters.
• It employs interactive proofs with multilinear sumchecks and tlookup techniques to verify both arithmetic and non-arithmetic operations within the attention circuit.
• The protocol achieves scalable performance with O(√D) proof sizes and sub-15-minute proof generation for models like OPT-13B and LLaMa-2-13B, enabling practical deployment.

zkAttn is a specialized zero-knowledge proof protocol for verifying the correctness of the attention mechanism in Transformer architectures, designed for practical deployment at the scale of contemporary LLMs. Introduced as a component within zkLLM, zkAttn addresses the cryptographic challenge of attesting to the validity of attention computations—including both their arithmetic and non-arithmetic aspects—without revealing proprietary model parameters. zkAttn is engineered to balance proof size, computation time, and accuracy, achieving O(√D) proof sizes for D-dimensional tensors, sub-15-minute proof generation for 13 billion-parameter models, and sub-200 kB final proofs, while maintaining statistical soundness and privacy guarantees through rigorous algebraic commitments and interactive proofs (Sun et al., 24 Apr 2024).

1. Foundations of Zero-Knowledge Proofs for Deep Learning

zkAttn leverages an interactive proof system grounded in multilinear extensions and polynomial commitments within a prime field $\mathbb{F}$ ($|\mathbb{F}| \approx 2^{254}$, specifically the scalar field of BLS12-381) (Sun et al., 24 Apr 2024). The construction inherits security from the discrete logarithm hardness assumption and achieves 128-bit security with negligible soundness/completeness error under the Schwartz–Zippel lemma. Tensor operations corresponding to matrix multiplications and summations are enforced via zero-knowledge sumchecks, while polynomial commitments (Hyrax, a Pedersen variant) provide succinct, binding, and hiding properties with $O(\sqrt{D})$ communication for D-dimensional tensors. Arithmetic and non-arithmetic operations are handled separately—sumcheck enforces arithmetic constraints, while non-arithmetic functions (e.g., exponentiation, Softmax) require specialized techniques.

2. The tlookup Primitive for Non-Arithmetic Operations

At the core of zkAttn’s ability to attest to attention mechanisms is tlookup (“tensor lookup”), an argument for verifying non-arithmetic tensor operations which reduces to set-lookup via rational function identities [Haböck 2022, as cited in (Sun et al., 24 Apr 2024)]. Concretely, to prove that a secret tensor $S \subseteq T$ (where $T$ is a public table), zkAttn encodes the containment as:

$$\sum_{i=0}^{D-1} (X + S_i)^{-1} = \sum_{j=0}^{N-1} m_j (X + T_j)^{-1}$$

for all $X$ over $\mathbb{F}$, with $m_j$ denoting multiplicity counts. zkAttn applies tlookup within the attention circuit to verify each segment of the Softmax and the normalization constraint. Instead of verifying the Softmax directly, zkAttn decomposes the operation using digitized exponent computation over base-$b$ segments, enabling efficient enforcement via table lookups and algebraic sumchecks in zero knowledge. This mechanism enables non-arithmetic operations to be incorporated into the proof system with negligible asymptotic overhead, preserving both efficiency and accuracy.

3. Circuit Design for Transformer Attention

The protocol fully attests to the standard attention head computation:

• $Z = QK^\top$ (matrix multiplication, with queries $Q \in \mathbb{F}^{m \times d}$, keys $K \in \mathbb{F}^{n \times d}$)
• $Y = \operatorname{Softmax}(Z / \sqrt{d})$ (rowwise, fixed-point encoded)
• $O = YV$ (aggregation over values $V \in \mathbb{F}^{n \times d_v}$)

Matrix multiplication is proven via multilinear sumchecks, with random linear combinations over tensor indices ensuring binding to committed values. For Softmax, zkAttn constructs a fixed-point encoding using scale parameter $\gamma = 2^{16}$ and deconstructs the exponentials into $K = 5$ segments, each looked up in a table $T^{(k)}$ of $b \approx 2^{16}$ entries. The protocol proves, for each row, that the normalized values sum to a pre-specified tolerance and reconstructs Softmax via products of lookup-segmented exponentials, ensuring compositional correctness. The final aggregation $O = YV$ is enforced via a sumcheck constraint over the committed tensors.

All steps are compiled into a rank-1 constraint system (R1CS) with proof size and verifier workload running in $O(\sqrt{D})$, where $D = m \cdot n$ is the per-head attention size. Throughout, all commitments to tensors are cryptographically hiding, preventing extraction of model parameters.

4. Proof Complexity and Resource Trade-offs

zkAttn’s performance and resource requirements are summarized as follows (Sun et al., 24 Apr 2024):

Operation	Prover Time	Proof Size	Verifier Time
tlookup (size $D$)	$O(D)$	$O(\sqrt{D})$	$O(\log D)$
Single attention head (K segments)	$O(Kmn)$	$O(K\sqrt{mn})$	$O(K\log(mn))$
Matrix multiply	$O(dmn)$	$O(d)$	$O(d)$
Softmax ($K$ segments)	$O(Kmn)$	$O(K\sqrt{mn})$	$O(K\log(mn))$

Softmax approximations exhibit $\ell_1$ error $\epsilon_{\text{attn}} < 10^{-2}$, matching float16 quantization noise. Over an L-layer, H-head architecture, total resource consumption grows as $O(LH[(d + d_v + K)mn])$ for proofs, and $O(LHK\sqrt{mn})$ in communication. Empirical results on sequence length 2048 indicate no more than 0.01 perplexity degradation attributable to quantization.

5. GPU-Parallelized Implementation

zkAttn’s reference implementation is CUDA-parallelized and uses Filecoin’s ec-gpu library for BLS12-381 operations, with supporting CPU code utilizing mcl (Sun et al., 24 Apr 2024). Sumcheck kernels split summation domains across CUDA threads; vectorized batch-inversion is used for field inverses in tlookup. Lookup tables for segment-wise exponentials reside in device memory, accessed through parallelized index computation. Commitment generation and evaluation proofs exploit multi-scalar multiplication on the GPU, and per-layer proof generation is pipelined with CPU-based Fiat–Shamir challenge derivation and verification precomputation. With a 40 GB A100 GPU, memory is fully saturated via batching over attention heads and sequence positions, maintaining communication efficiency via CUDA streams when transmitting to the CPU verifier.

6. Empirical Performance and Deployment

zkAttn enables end-to-end zero-knowledge attestation of full 13B-parameter LLMs, including OPT-13B and LLaMa-2-13B, with measured performance:

Model	Commit Time	Prover Time	Proof Size	Verify Time	GPU Mem
OPT-13B	1270 s	713 s	160 kB	3.71 s	22.9 GB
LLaMa-2-13B	986 s	803 s	188 kB	3.95 s	23.1 GB

The zkLLM system built around zkAttn achieves approximately 50× speedup and 10× scale-up versus previous systems (e.g., zkML), while maintaining compact proofs (<200 kB) and inference-proof times under 15 minutes for large-model, long-sequence settings.

A notable outcome is that model privacy is cryptographically protected; the proof reveals only the validity of the computation and no information about model parameters, thereby enabling verifiable inference even in the presence of proprietary weights. The system is suitable for LLM inference scenarios where regulatory, legal, or user-driven demands require cryptographically sound output authenticity without intellectual property leakage. The approach generalizes to arbitrary LLM deployments, as long as standard attention mechanisms are used (Sun et al., 24 Apr 2024).

7. Context and Implications

zkAttn marks a significant advance in the practical deployment of zero-knowledge proofs for deep learning, particularly in high-throughput multi-head attention circuits. By handling both field arithmetic and the fixed-point, exponential Softmax via algebraic and lookup-based arguments, zkAttn demonstrates that large-scale privacy-preserving inference attestation is not only theoretically feasible but attainable with current hardware and cryptographic techniques. While some additional memory and fixed-point imprecision are introduced, the empirical impact on accuracy and verification remains negligibly small in deployments targeting LLMs with billions of parameters. A plausible implication is that zkAttn opens the door to regulatory-compliant, third-party verifiable AI-as-a-service without sacrificing proprietary model confidentiality (Sun et al., 24 Apr 2024).