Zero-Knowledge Proofs for ML Inference

Updated 11 July 2025

Zero-knowledge proofs of ML model inference are cryptographic protocols that verify a model’s computation while concealing sensitive inputs and proprietary weights.
They convert inference processes into arithmetic circuits using polynomial constraints and specialized gadgets to securely approximate nonlinear operations.
They enable practical applications in MLaaS, federated learning, and regulatory audits by ensuring trustless verification and robust privacy preservation.

Zero-knowledge proofs (ZKPs) of ML model inference are cryptographic protocols that allow a model provider ("prover") to convince an external party ("verifier") that a specific input was processed by a prescribed ML model to produce a stated output, all without revealing sensitive model parameters, intermediate computation, or—optionally—even the input data itself. As ML is increasingly deployed in privacy-sensitive and high-stakes domains where the model weights (often considered trade secrets), user data, or even compliance behavior must be kept confidential, ZKP-based inference provides a rigorous mechanism for auditable, privacy-preserving, and trustless verification of model execution. This article presents the central methodologies, technical principles, practical engineering strategies, performance benchmarks, and open challenges in the field of zero-knowledge proofs of ML model inference.

1. Foundational Principles and Cryptographic Guarantees

Zero-knowledge proofs of ML inference leverage common cryptographic properties: completeness, soundness, and zero-knowledge. The core objective is to allow a prover holding secret weights $w$ for an ML model $f$ to generate, for any input $x$ and output $y$ , a succinct proof $\pi$ that convinces a verifier that $y = f(x; w)$ without disclosing $w$ . This is most commonly achieved by arithmetizing the entire inference process into an arithmetic (or polynomial) circuit $C$ , so that the statement $C(x, y; w) = 1$ encodes the claim " $y$ was produced by evaluating $f$ on $x$ with witness $w$ " (Kang et al., 2022, Peng et al., 25 Feb 2025).

The ZKP system (most frequently a succinct non-interactive argument of knowledge, or zkSNARK) then produces $\pi$ such that:

If $(x, y, w)$ is valid, the verifier will always accept (completeness).
If not, no adversary can efficiently produce $(x', y', \pi')$ that would be accepted (soundness).
The proof reveals nothing about $w$ or the intermediate computation beyond what is implied by $(x, y)$ (zero-knowledge) (Xing et al., 2023).

2. Circuit Construction, Arithmetization, and Model Encoding

Translating an ML model's inference computation to a ZKP-verifiable statement requires careful circuit construction and arithmetic translation:

Arithmetic Circuits: All model operations—linear (matmul, convolution), non-linear (activation functions, softmax), and control (argmax, thresholding)—are expressed as polynomial constraints over a prime field. For example, dot products are encoded as $c_i = \sum_{j=1}^N (x_{ij} - z) w_{ij}$ using a "dot product gate" (Kang et al., 2022).
Non-Linearities: Nonlinear activations are handled through lookup tables (enforcing $a_i = \text{clip}(\lfloor (c_i \cdot a)/b \rfloor, 0, 255)$ via precomputed tables), or via polynomial approximations (using Taylor expansions or Remez-based fits for activations such as sigmoid or tanh) (Xing et al., 2023, Kang et al., 2022).
Quantization and Scaling: Since field elements must be integers, floating-point weights/inputs are mapped to integer representations (using scaling factors $\alpha$ to convert $x' \to x = \lceil \alpha x' \rceil$ ), and fixed-point arithmetic is employed to balance circuit depth and accuracy (Peng et al., 25 Feb 2025, Xing et al., 2023).

The circuit's public inputs typically include $x$ , $y$ , and a cryptographic commitment (hash) of $w$ ; the secret witness is $w$ itself (Kang et al., 2022).

3. Protocols, Proof Systems, and Efficiency Engineering

Modern ZKP-based inference verification utilizes advanced SNARK systems and commit-and-prove constructions:

Proving Systems: Provers use SNARK frameworks such as Groth16, Halo2, or Spartan to produce proofs. For scalability, protocols rely on modern polynomial commitment schemes (e.g., KZG, IPA), and support batching/accumulation (Wang et al., 2022, Lycklama et al., 18 Sep 2024).
Commit-and-Prove SNARKs: To link proofs of correct inference to commitments of secret weights, efficient commit-and-prove SNARKs like Artemis aggregate the circuit's consistency checks and model commitment checks using random linear combinations, ensuring that the same weights are used as those publicly committed (Lycklama et al., 18 Sep 2024).
Efficiency Improvements: Modular design is paramount—systems such as ZKTorch decompose models into “basic blocks” (e.g., Add, MatMul, Permute), each with a specialized proof protocol, and then aggregate their proofs using parallel extensions to accumulation schemes such as Mira, yielding $3\times$ – $6\times$ improvements in size and time (Chen et al., 9 Jul 2025). Other approaches design new gadgets for frequent ML tasks (radial basis kernel exponentiation, max/min selection, etc.) (Wang et al., 2022).
Probabilistic Checking: To reduce costs—especially for federated learning—frameworks such as RiseFL deploy probabilistic integrity checks on random inner products rather than per-parameter verification, providing a tunable trade-off between soundness and runtime (Zhu et al., 2023).
Parallelization: Large models require circuit partitioning and proof parallelization; techniques split inference into smaller circuits (e.g., by layers) and accumulate results, with optimizations to minimize overall overhead (Chen et al., 9 Jul 2025, Wang et al., 2022).

4. Practical Applications, Protocols, and Deployment Strategies

Zero-knowledge proofs of ML inference have been realized for numerous concrete applications:

ML-as-a-Service (MLaaS): In the classic MLaaS scenario, the model provider supplies a prediction and ZK proof, allowing consumers to verify outputs without ever accessing proprietary weights (Kang et al., 2022). Proofs are non-interactive and can be generated post hoc.
Certification and Auditing: Verifiable evaluation attestations aggregate proofs of inference over datasets, certifying accuracy or fairness metrics without disclosing the model or dataset (South et al., 5 Feb 2024). Audit protocols, such as ZkAudit, allow providers to prove that functions of either the dataset or the weights were computed honestly (e.g., for copyright or demographic audits) (Waiwitlikhit et al., 6 Apr 2024).
Federated and Decentralized Learning: ZKP protocols ensure clients’ local computations are correct and private in federated learning, with approaches handling both the inference and model update steps (Xing et al., 2023, Xing et al., 2023).
Fairness and Explanations: Recent works build ZKPs to prove fairness metrics (OATH, FairZK), or generate verifiable explanations (for instance, ZKP-amenable versions of LIME as in ExpProof), with all claims bound to a committed model (Franzese et al., 17 Sep 2024, Yadav et al., 6 Feb 2025, Zhang et al., 12 May 2025).
Unlearning and Edge Verification: zkSNARK-based frameworks enable verifiable unlearning (selective model editing/removal) while ensuring post-unlearning inferences remain truthful and personalized enhancements are preserved (Maheri et al., 24 Jun 2025).
Privacy-Preserving LLM Personalization: ZKPs enable privacy-preserving sharing of user traits and confidential inference for advice-generating LLM chatbots (Watanabe et al., 10 Feb 2025).

5. Performance Metrics, Resource Requirements, and Scalability

Scalability and efficiency are principal challenges:

Prover Overhead: For large-scale models (e.g., VGG, GPT-j), naive circuit-based ZKP approaches historically incurred $>10\times$ runtime overheads. State-of-the-art commit-and-prove SNARKs (Artemis) and parallel accumulators (ZKTorch) reduce this to $1.1\times$ – $1.2\times$ over baseline proving cost (Lycklama et al., 18 Sep 2024, Chen et al., 9 Jul 2025).
Verification Time and Proof Size: Verification is consistently sublinear in model size, typically requiring seconds or less; proof sizes are on the order of tens of kilobytes for large models in optimized systems (Chen et al., 9 Jul 2025).
Accuracy and Quantization: Fixed-point and circuit quantization introduce some accuracy losses (e.g., MobileNet v2 achieves 79% top-5 on ImageNet via ZKP, slightly below fp32 baselines) (Kang et al., 2022). Structured optimizations and custom gadget use mitigate quantization loss.
Comparison Table: Efficiency Benchmarks

Framework	Model	Overhead (prov.)	Proof Size	Verification
Artemis	VGG	$1.1\times$ baseline	KB-scale	Seconds
ZKTorch	GPT-j	$6\times$ faster [vs. Mira seq.]	85 KB	63 s
FairZK	47M-param DNN	343 s [fairness proof]	1.6 MB	1 ms

6. Research Challenges, Open Directions, and Limitations

Current limitations and directions include:

Generality: While recent compilers (ZKTorch, ZKML, Giza) automate translation from ONNX/TensorFlow to constraint systems, extensions to the full range of ML operations—especially for floating-point and dynamic graph models—are ongoing research themes (Chen et al., 9 Jul 2025, Peng et al., 25 Feb 2025).
Efficiency and Scalability: Despite significant progress, proving times for the largest transformer/LLMs remain in the minutes to hours per inference range; circuit depth, memory usage, and prover parallelism are active areas of improvement (Ganescu et al., 9 Feb 2024, Chen et al., 9 Jul 2025).
Security Model and Future-Proofing: Transparent setup (STARK-style proofs) and post-quantum security are desired properties, especially for compliance with regulatory frameworks such as the EU AI Act; integration of ZKPs with broader machine learning operations pipelines (ZKMLOps) is a developing trend (Scaramuzza et al., 26 May 2025).
Privacy-Utility Tradeoff: Trade-offs between strict privacy (no leakage via model/architecture commits) and practical deployment (some architectural metadata must be revealed for verification) are unresolved in certain real-world applications (Waiwitlikhit et al., 6 Apr 2024).
Verification of Non-Inference Tasks: Extending ZKP systems from inference to include verifiable preprocessing, online monitoring, training, and even unlearning presents unique challenges in both circuit design and cryptographic guarantees (Scaramuzza et al., 26 May 2025, Maheri et al., 24 Jun 2025).

7. Societal, Regulatory, and Commercial Impact

The adoption of ZKPs for ML inference is rapidly emerging in regulated, adversarial, and privacy-sensitive environments:

Trustless MLaaS: Service providers can issue cryptographic “receipts” for model executions, enabling non-repudiable, audit-friendly MLaaS models (Kang et al., 2022).
Regulatory Compliance: Protocols support robust, public auditing (including verification of fairness and responsible AI claims) without trade secret leakage, aligning with legal requirements such as the EU AI Act (Franzese et al., 17 Sep 2024, Scaramuzza et al., 26 May 2025).
Commercialization: Commercial applications include privacy-preserving trading bots, risk assessment, on-chain CAPTCHAs, and privacy-first LLM deployment (Peng et al., 25 Feb 2025).
Foundations for Trustworthy AI: ZKP-based inference enables the construction of ML systems whose results are not only reproducible in principle, but cryptographically guaranteed to be computed as publicly claimed, paving the way for transparent, auditable, and fair AI deployments.

By encapsulating the inference logic of ML models within cryptographically sound, efficiently verifiable zero-knowledge proofs, the field provides a roadmap towards scalable and trustworthy deployment of complex, private models in high-assurance settings. Continued advancements in protocol efficiency, automated arithmetization, and integration into the broader ML lifecycle will determine the future landscape of verifiable machine learning inference.