Zero-Knowledge Machine Learning (zkML)

• Zero-Knowledge Machine Learning (zkML) is a paradigm that applies cryptographic proofs to verify machine learning computations while keeping model details and input data private.
• It strategically uses modular slicing to tokenize ML models into subcomputations, reducing resource usage and enabling targeted, scalable verification.
• Empirical evaluations, such as in DSperse, demonstrate that slice-based zkML significantly cut memory and time costs while preserving inference accuracy.

Zero-Knowledge Machine Learning (zkML) is the paradigm in which cryptographic zero-knowledge proof (ZKP) techniques are used to provide formal, privacy-preserving and auditable guarantees about the correctness of ML computations. zkML allows a prover to convince a verifier that an ML computation (e.g., inference, evaluation, or even training) was carried out exactly as specified, without revealing private information such as the data, model parameters, or the proprietary logic of the system. By decoupling verifiability from disclosure, zkML establishes trust and accountability for the growing class of applications where model predictions affect security, privacy, regulation, or financial outcome.

1. Architectural Foundations and Concepts

zkML frameworks formalize the ML task as a statement of the form “there exists a (private) witness—such as model weights $w$ or secret data—such that the public inputs (e.g., $x$) satisfy the constraints of the model’s computation, yielding output $y$." Proof systems such as zk-SNARKs (Succinct Non-Interactive Arguments of Knowledge) or related protocols are then used to cryptographically attest to this computation.

Fundamental Formalization

Let $f(x; w) = y$ be an ML function (model $f$ with parameters $w$, input $x$, output $y$).

The prover generates: $\pi: \quad \exists w ~.~ f(x, w) = y$ and the verifier, knowing $x$, $y$, and $\pi$, can be convinced that such a $w$ exists without gaining knowledge of $w$.

Practical zkML systems require translating $f$ into an arithmetic circuit—either as a monolithic structure or via modular, optimized sub-circuits corresponding to the atomic operations (affine layers, nonlinearities, normalizations, etc.) of modern ML architectures (Peng et al., 25 Feb 2025, Ivanov et al., 9 Aug 2025, Kang et al., 2022).

2. Methodological Spectrum: Slicing, Modularity, and Strategic Proof Boundaries

One of the principal bottlenecks in classical zkML architectures is the cost associated with end-to-end circuitization of large models, which results in high memory consumption, excessive proving times, and circuit adaptation impairments. DSperse (Ivanov et al., 9 Aug 2025) introduces a modular, slice-based zkML framework that strategically enables targeted verification of selected subcomputations (“slices”) in the inference pipeline, rather than mandating full-model circuitization.

Slicing and Strategic Verification

• Slice: A contiguous, semantically meaningful sub-network, typically a layer or block (e.g., CNN block, FC layer)—must have unidirectional dataflow, parameter isolation, and independence for separate circuitization and quantization.
• Targeted Proofs: Only the selected slices are cryptographically attested using ZKPs, thereby reducing the resource footprint.

Decomposition is modeled as: $$z = F_\mathrm{pub}^{(2)} \circ F_\mathrm{priv} \circ F_\mathrm{pub}^{(1)}(x)$$ where $F_\mathrm{priv}$ comprises the segment(s) to be attested with formal zero-knowledge proofs. Non-sensitive $F_\mathrm{pub}$ blocks are left openly executed or audited. This design localizes trust boundaries, focusing formal cryptographic assurance exclusively where attack surface or proprietary value is greatest. DSperse supports this paradigm with flexible assignment, distributed execution, and orchestrator- or model-owner-determined proof boundaries.

3. Mechanisms for Distributed, Trust-Minimized, and Auditable ML Inference

A key advance of DSperse is its architecture for hybrid trust-minimization and decentralization.

Slice-Orchestrated Distributed Execution

• Assignment: Slices are distributed across (potentially untrusted) prover nodes. Each executor independently performs witness generation and proof for its assigned slice.
• Per-Slice Circuitization: By independently circuitizing each slice, memory usage and peak computational resource per prover are drastically reduced.
• Audit and Economic Incentives: For slices not attested by ZKP, correctness may be enforced through open audit, redundancy (replication across nodes and consensus), or trusted economic incentives (staking, slashing).

Enforcing Global Consistency

• Audit: Cross-slice consistency is achieved through recomputation or challenge/audit of outputs/inputs at slice boundaries for public layers.
• Redundancy/Replication: Slices may be executed by multiple independent provers, with outputs compared for mismatches or majority voted.
• Economic Mechanisms: Failures or disputes are mediated by economic stakes: dishonest behavior results in slashing or forfeiture, per established protocol logic.

This results in a pragmatic, hybrid trust-minimized zkML architecture where ZKPs are localized, and residual trust is constrained, offering a scalable trust model adaptable to heterogeneous environments, including open and regulated deployments.

4. Empirical Evaluation: Resource Efficiency and Fidelity

The DSperse framework is empirically benchmarked on LeNet-5 segmented into five logical slices, evaluated with two zkML proving systems (EZKL and JSTProve). Both raw resource metrics and fidelity are reported, enabling rigorous assessment.

Metric	Unsliced Total	Sliced (Sum over Slices)
Peak proof mem (MB)	32,262.7	20,105.9
Peak witness mem (MB)	1,048.6	51.6
Proof gen time (s)	478.7	163.2
Verif. time (s)	0.99	0.61
Fidelity (D1 mean)	0.0076	0.0075

Salient Observations

• Memory Usage: Sliced configuration reduces proof generation memory by ∼38% and verification by ∼45% (EZKL).
• Runtime: Witness generation time cut by ∼77%, proof generation by ∼66%, verification by ∼38% (EZKL). JSTProve yields similar directional improvements; some increase in witness time is observed due to orchestration overhead.
• Fidelity: Output logits (as measured by $D_1$ distance) are as close or closer to original floating-point outputs in the sliced setting ($D_1$ mean: 0.0075 vs 0.0076); predicted classes remain invariant.
• Circuit Complexity: Sliced models exhibit less aggressive quantization/approximation, allowing for higher-fidelity conversions and more efficient circuit constraint encoding.

Empirical conclusion: Slicing in DSperse yields substantial gains in practical deployability—enabling models and infrastructures that are infeasible under full-monolithic circuitization, while maintaining full inference correctness and negligible impact on output fidelity.

5. Prover and Verification Backend Agnosticism

DSperse is explicitly designed to be backend-agnostic, supporting plug-and-play with multiple ZKP backends (EZKL, JSTProve, with potential for others). This modularity decouples architectural choices from commitment to a particular proof system, ensuring portability and extensibility as proving systems evolve.

• Slice-level ZKP: Each slice can be circuitized and proven using different backends or parameters, facilitating heterogeneous resource utilization and incremental upgrades.

This architectural modularity increases the resilience of deployment and underpins the claim that observed efficiency/flexibility arises from the slicing paradigm and not backend-specific optimizations.

6. Implications for Scalability, Hybrid Trust, and Future ZKML Research

The DSperse approach fundamentally aligns proof boundaries to trust and risk boundaries, a property required for scalable zkML in practical, distributed, or hybrid-trust settings. It offers the following architectural and research advantages:

• Scalability: By permitting resource tailoring and flexible placement of ZKP modules, large and complex pipeline models become tractable for cryptographic attestation where necessary.
• Extensibility: Underpins future research into recursive ZKP composition for full, end-to-end soundness as cryptographic recursion and proof aggregation advances mature.
• Hybrid Trust: Provides a robust pathway for integrating economic or social trust models with formal cryptographic guarantees, scaling from purely cryptographic to pragmatic trust minimization.
• Interoperability: Supports migration between different proving technologies and adapts to evolving regulatory or infrastructure requirements.

A plausible implication is that DSperse's slice-based modularity generalizes well to both proprietary/regulated pipelines (where some blocks must be formally attested), and high-throughput, decentralized environments (where resource allocation and trust trade-offs are paramount).

7. Concrete Example: Applying Slicing in Practice

To implement DSperse in a production pipeline:

1. Slice selection: Identify logical model boundaries (e.g., all fully connected blocks, specific activation sequences) where cryptographic assurance is most critical.
2. Per-slice deployment: Allocate slices to dedicated prover infrastructure with resource profiles matching their complexity.
3. Open execution: Leave standard or non-sensitive slices open to audit, replicate, or test in plain.
4. Composition: Use orchestration to enforce global consistency—plug in audits, redundancy, or incentive mechanisms as needed.
5. Proof aggregation and submission: Collect proofs at the slice boundary; submit to the orchestrator or, where relevant, on-chain smart contracts or verification endpoints.
6. End-to-end soundness: As recursive proof composition and efficient ZKP aggregation techniques become available, replace trust/minimized boundaries with formal cryptographic chaining to extend security coverage.

References Table: Key DSperse Empirical Metrics

Metric	Unsliced	Sliced
Peak proof mem (MB)	32,262.7	20,105.9
Peak witness mem (MB)	1,048.6	51.6
Proof gen time (s)	478.7	163.2
Verif. time (s)	0.99	0.61
Fidelity (D1 mean)	0.0076	0.0075

Conclusion

DSperse advances the field of zero-knowledge machine learning by implementing a scalable, slice-based verification framework that drastically reduces prover resource requirements while preserving end-to-end accuracy and modularity. Its architectural choices localize cryptographic assurance, enabling tailored trust minimization and supporting distributed deployments. Empirical evaluation demonstrates the practical impact of slicing on resource consumption, fidelity, and throughput. DSperse’s design is sufficiently flexible to serve as the basis for hybrid cryptographic-trust infrastructures and future recursive or fully end-to-end zkML solutions (Ivanov et al., 9 Aug 2025).