The latter half of 2025 has seen a technical phenomenon widely categorized by industry analysts and cryptographers as the "zkML Singularity."
This conceptual singularity marks the transition of Zero-Knowledge Machine Learning from a theoretical research niche into a production-grade infrastructure layer capable of securing the burgeoning global artificial intelligence economy.
Following a decisive narrative shift in Q3 2025 that reprioritized end-user privacy, algorithmic accountability, and verifiable compute, the ecosystem experienced an unprecedented acceleration in technical capabilities. The period is headlined by the successful, cost-effective cryptographic proving of LLM inference and the achievement of real-time proving for Layer 1 blockchain consensus.
In this article I want to examine this 'singularity' , highlighting the convergence of three dominant operational themes:
- the maturation of Zero-Knowledge proving systems into competitive industrial engines,
- the exposure and subsequent mitigation of systemic security risks in open-source AI and
- the breakthrough performance of specialized hardware and software pipelines.
I will show that the term "Singularity" is not merely marketing hyperbole but a quantifiable technical inflection point.
The capacity to verify the execution of a 13-billion-parameter model in under 15 minutes, and the concurrent capability to prove Ethereum L1 blocks in real-time (under 12 seconds) on consumer-grade hardware, suggests that the computational overhead, historically the "impossible barrier" for Zero-Knowledge adoption has been effectively neutralized.
In addition I will examine the structural "unbundling" of the ZK stack.
Monolithic architectures have started to fracture into specialized, interoperable decentralized networks:
- Boundless for proving markets,
- zkVerify for proof aggregation and settlement, and
- Brevis and Lagrange for verifiable co-processing. This structural evolution is occurring against a backdrop of heightened cybersecurity tensions. The proliferation of unsecured, high-capability open-source AI models, exemplified by the "DeepSeek" crisis, has necessitated the adoption of verifiable compute to distinguish authenticated, safe automated agents from malicious vectors.
The following sections detail the specific technical breakthroughs of late 2025, the emerging economic models of decentralized proving markets, and the real-world integration of these technologies into sovereign defense, institutional finance, and healthcare infrastructure.
The Technical Singularity: Conquest of the Large Language Model
The defining characteristic of the zkML Singularity is the successful cryptographic conquest of the Transformer architecture.
For years, the non-arithmetic nature of neural network operations specifically non-linear activation functions like Softmax and GELU rendered the cryptographic proving of Large Language Models cost-prohibitive and computationally intractable.
Late 2025 shattered this ceiling through specific, harmonized advancements in polynomial commitment schemes, lookup arguments, and system-level engineering.
Lagrange Labs and DeepProve-1: The Production Breakthrough
The most significant operational milestone of the period was achieved by Lagrange Labs with the release of DeepProve-1.
This system represents the first production-ready zkML environment to successfully generate a cryptographic proof for a full inference of OpenAI’s GPT-2 model.
While GPT-2 is smaller than contemporary frontier models, proving its full execution trace represents the "Hello World" moment for verifiable generative AI, establishing the architectural baseline required to prove larger, modern architectures like Llama, Mistral, and Gemma.
Architectural Agnosticism: Handling Arbitrary Graphs
The primary innovation of DeepProve-1 lies in its abandonment of linear computational assumptions.
Previous iterations of zkML focused on simple Convolutional Neural Networks (CNNs) which follow relatively linear pathways. However, real-world Transformer models utilize complex, non-linear computation graphs characterized by residual connections, parallel branches, and variable-length inputs.
DeepProve-1 introduced a proving infrastructure capable of ingesting and proving these arbitrary graph structures, including the multi-input layers and branching outputs inherent to multi-head attention mechanisms.
This graph-agnostic approach is critical for interoperability.
It allows the system to ingest standard industry formats—specifically ONNX and GGUF files—directly. This capability removes the prohibitive friction of requiring data scientists to manually rewrite their PyTorch or TensorFlow models into ZK-friendly circuits, a bottleneck that had previously stifled adoption.
By supporting GGUF, a widely adopted format for quantized models, DeepProve aligned itself with the existing open-source AI supply chain.
Solving the Non-Arithmetic Challenge
Transformer architectures rely heavily on operations that are mathematically hostile to the finite fields used in ZKPs.
The Softmax function (involving exponentiation and division) and Layer Normalization are notoriously expensive to represent arithmetically.
DeepProve-1 addressed this through a novel implementation of specific layers, effectively creating "precompiles" for neural networks:
Softmax Optimization:
Utilizing refined techniques derived from the zkLLM research, Lagrange implemented a provable Softmax that manages floating-point precision sensitivity while maintaining cryptographic soundness. This ensures that the probability distribution output by the attention head is verified without requiring massive circuit overhead.
Quantization Strategy:
The system applies a post-operation quantization strategy within the Add Layer. By maintaining shared lookup tables to handle precision, DeepProve manages to handle the quantization complexities without exploding the constraint count of the proof.
ConcatMatMul:
To handle Multi-Head Attention (MHA), DeepProve introduced a ConcatMatMul layer. This enables matrix multiplication across concatenated tensors, a prerequisite for the higher-dimensional operations required in modern transformers where multiple attention heads process data in parallel.
zkLLM and the "tlookup" Protocol: The Theoretical Foundation
Underpinning many of these practical breakthroughs is the theoretical framework established by the zkLLM paper (Sun et al., CCS 2024/2025). This research was pivotal in identifying that the true bottleneck in zkML was not matrix multiplication—which, being linear algebra, is relatively arithmetically friendly to SNARKs—but rather the non-linear operations that punctuate the linear layers.
The tlookup Protocol
The research introduced tlookup, a parallelized lookup argument designed specifically for deep learning workloads. In traditional ZK circuits, operations like ReLU (Rectified Linear Unit) or Softmax might require complex bit-decomposition to prove, consuming vast amounts of constraints and proving time. tlookup maps these non-arithmetic tensor operations to precomputed lookup tables with no asymptotic overhead.
This innovation allows for the efficient verification of activations without executing the expensive algebra within the circuit itself. It exploits the fact that while the function itself is complex, the range of valid inputs and outputs in a quantized model is finite and can be tabulated. The prover merely needs to prove that the input-output pair exists in the trusted table, a much cheaper operation than re-computing the function.
zkAttn: Verifying Attention
Building on tlookup, the protocol introduced zkAttn, a specialized proof protocol for the Transformer attention mechanism. Attention is the "brain" of the LLM, determining which parts of the input sequence are relevant to the current token. zkAttn decomposes the attention block into three verifiable components:
Verifiable Matrix-Multiplication: Checks the integrity of the Query, Key, and Value projections.
Softmax Reformulation: Uses tlookup on factorized terms to verify the attention weights.
Row-Sum Consistency: Checks that the probability distributions sum to one, ensuring the model isn't "hallucinating" attention scores.
The impact of this specialized architecture is quantifiable and dramatic. Benchmarks indicate that zkLLM can verify the inference of a 13-billion-parameter model in under 15 minutes, producing a proof smaller than 200 kB. While 15 minutes is not yet "real-time" for a conversational chatbot, it is sufficiently fast for asynchronous verification of high-value decisions, such as financial auditing, medical diagnosis, or asynchronous agent settlement.
Comparative Analysis of zkML Approaches (Late 2025)
The market has adopted distinct technical approaches to solving the scalability problem, creating a diverse ecosystem of proving engines. The following table summarizes the leading methodologies as of Q4 2025.
| Framework | Core Architecture | Key Innovation | Performance/Throughput | Primary Use Case |
|---|---|---|---|---|
| DeepProve (Lagrange) | GKR-based / Graph-agnostic | Proving arbitrary graphs & GGUF support; Specialised layers for Transformers | 50x-150x faster proof generation than EZKL | Verifiable Inference for LLMs (GPT-2, Llama); Defence & Enterprise |
| zkLLM (Sun et al.) | Specialised Circuits | tlookup & zkAttn protocols for non-arithmetic ops | 13B params in <15 mins; Proof size <200kB | Academic/Foundational Architecture; Basis for custom implementations |
| JOLT (Atlas) | Lookup-Centric zkVM | "Lasso" lookups replacing arithmetic circuits; RISC-V based | Proves models in seconds; <5% overhead for some queries | General purpose compute; AI Memory (Kinic) |
| SP1 Hypercube | RISC-V zkVM | Precompiles + "Jagged PCS"; Formally verified | 99.6% ETH blocks in <12s (Brevis implementation) | Real-time L1 Consensus; Rollup bridging; Fault Proofs |
The Prover Performance Wars: The Race to Real-Time
While Lagrange and the zkML sector focused on the complexity of AI models, a parallel race emerged regarding the speed of proving blockchain consensus. This sector, referred to as "Operational Maturation" in industry newsletters, shifted focus from the theoretical "can it be built?" to the logistical "how efficiently can it run at scale?". The goal was Real-Time Proving (RTP): generating a ZK Proof of an Ethereum block within the 12-second slot time of the network itself.
Brevis and the "Pico Prism" Breakthrough
In October 2025, Brevis Network announced a seminal achievement with its Pico Prism technology.
Historically, verifying Ethereum's consensus via ZK (a "zkEVM" type operation for Layer 1) required massive server clusters and minutes of computation, rendering it useful for historical verification but useless for real-time interaction. Pico Prism altered the economic and temporal calculus of this operation.
Benchmarks released in late 2025 demonstrated the system's capability to prove Ethereum blocks (specifically those with a 45M gas limit) with 99.6% coverage in under 12 seconds. The average proving time was reported at approximately 6.9 seconds. This implies that a ZK proof of the entire Ethereum state transition can be generated faster than the network finalizes the block.
Crucially, this performance was achieved using consumer-grade hardware. The benchmarks utilized 64 NVIDIA RTX 5090 GPUs. While still a significant hardware footprint, this represents a 50% reduction in hardware costs compared to previous generations, which required clusters of ~160 RTX 4090s, while delivering 3.4x better performance. By proving blocks within the slot time, Brevis enables "Real-Time Proving," allowing light clients, bridges, and other chains to verify Ethereum's state instantly without trusting a centralized RPC or waiting for a long finality window.
Succinct Labs and SP1 Hypercube: The Formal Verification Advantage
Competing directly with Brevis is Succinct Labs, developers of the SP1 zkVM. In 2025, Succinct launched SP1 Hypercube, a system designed to optimize the proving of the RISC-V instruction set. SP1 Hypercube distinguishes itself not just by speed, but by rigor.
In collaboration with the Nethermind Security Formal Verification team, Succinct Labs formally verified the correctness of the core RISC-V chips within SP1 Hypercube using the Lean proof assistant. This formal verification covers 62 opcodes, providing a mathematical guarantee of correctness that is essential for high-value financial applications. In a landscape rife with potential circuit bugs, the ability to mathematically prove that the zkVM adheres strictly to the RISC-V Sail specification is a significant competitive moat.
Technically, SP1 utilizes a "Jagged Polynomial Commitment Scheme" (Jagged PCS). This allows for more efficient handling of uneven computational workloads, a common feature in general-purpose programs where different execution paths have vastly different complexities. This "write once, prove anywhere" approach, combined with the security of formal verification, has made SP1 the preferred engine for projects like OP Kailua, Optimism's fault-proof system, which relies on the zkVM to secure its rollup infrastructure.
JOLT Atlas: The Lookup Singularity
A third vector of innovation comes from the JOLT framework, specifically the "Atlas" implementation. JOLT rejects the traditional reliance on complex arithmetic circuits in favor of a lookup-centric approach, often referred to as the "Lookup Singularity".
JOLT compiles programs to RISC-V and uses the "Lasso" lookup argument to verify execution. This bypasses the heavy algebraic constraints typically required for each operation. By late 2025, JOLT Atlas reported the ability to prove certain models in seconds, often without requiring the massive GPU clusters needed by other systems. This efficiency is particularly well-suited for memory-intensive tasks, leading projects like Kinic to leverage JOLT for creating "Plaid for AI"—verifiable AI memory and retrieval systems that allow agents to recall information with cryptographic certainty.
Infrastructure Unbundling: The Rise of the Modular Stack
The 2025 ecosystem is defined by the "unbundling" of the Zero-Knowledge stack. In the early 2020s, a ZK project was typically a monolith, building its own prover, verifier, and application layer. By 2025, these functions have separated into distinct, interoperable layers, creating a specialized supply chain for verifiable computation.
The Proving Marketplaces: Boundless (ZKC)
As the demand for proofs skyrocketed due to the proliferation of zkRollups and zkML applications, a bottleneck emerged: the availability of specialized hardware and the coordination of proving tasks. Boundless (associated with the ZKC token) emerged as the dominant decentralized marketplace for off-chain computation, facilitating a liquid market for ZK proofs.
The "Proof of Verifiable Work" Model
Boundless operates as a "universal layer" where applications request proofs and independent provers compete to generate them. The network utilizes a consensus mechanism termed Proof of Verifiable Work (PoVW). In this model, provers stake ZKC tokens to bid on jobs. They earn rewards (in ZKC and the requester's native token) by generating valid proofs. Unlike Bitcoin's Proof of Work, which utilizes energy for probabilistic hashing, PoVW directs computational energy toward useful verification, transforming the proving market into a commodity layer.
Market Dynamics and Security
To prevent "griefing" attacks where a prover claims a job but fails to deliver, delaying the network, provers must post collateral, typically in USDC or ZKC. If they fail to prove within the agreed deadline or submit an invalid proof, they are slashed. This economic security model ensures reliability even in a permissionless network.
It is crucial to distinguish between Boundless (ZKC), the compute marketplace founded by RISC Zero veterans, and Boundless Network (BUN), a separate Web3 wallet ecosystem. The market cap and utility of ZKC (circulating supply ~200M, valued around $30M-$40M) reflect its role as critical infrastructure for the ZK economy, whereas BUN operates in a different vertical.
The Verification Layer: zkVerify
Once a proof is generated by the Boundless network, it must be verified on-chain. This verification step is historically expensive; verifying a SNARK on Ethereum Mainnet can cost hundreds of thousands of gas units, limiting throughput. zkVerify (developed by Horizen Labs) launched to solve this aggregation problem through a modular blockchain architecture.
zkVerify acts as a specialized settlement layer solely for proof verification. It aggregates multiple proofs from different sources—such as various rollups, zkML applications, and bridges—and submits a single, compressed attestation to Ethereum or Bitcoin. This aggregation reduces verification costs by over 90%. For context, zkRollups spent over $42.8 million on verification gas in 2023 alone; zkVerify's model effectively recaptures this value. The protocol is proving-scheme agnostic, supporting SNARKs, STARKs, and emerging standards like Binius, positioning it as a neutral "Switzerland" for the ZK ecosystem.
The Coprocessor Layer: Brevis and Lagrange
The "ZK Coprocessor" model represents the third pillar of the unbundled stack. It allows smart contracts to offload heavy data processing that would be impossible to execute in the Ethereum Virtual Machine (EVM).
Brevis:
Focuses on historical data access. It enables contracts to query historical blockchain states (e.g., "Did this user hold an NFT 3 years ago?") trustlessly. Its Steel module allows EVM chains to process millions of state queries in a single call, writing only the verified result back to the chain.
Lagrange:
Focuses on "Verifiable SQL" and heavy computation on top of blockchain data. Its integration into EigenLayer as an AVS (Actively Validated Service) allows it to leverage Ethereum's economic security for these off-chain tasks, creating a "Hyper-Parallel" coprocessor for complex data crunching.
The Hardware Race: ASICs vs. Consumer GPUs
The physical layer of the zkML Singularity is witnessing a divergence between commoditization and specialization. This hardware race will determine the future centralization profile of the proving network.
The Consumer GPU Boom and Democratization
The breakthrough of Pico Prism utilizing NVIDIA RTX 5090s proved that consumer-grade gaming hardware is sufficient for high-performance ZK proving. This is a vital development for decentralization; it implies that one does not need enterprise-grade H100 clusters, which are often restricted by supply chain bottlenecks and sanctions, to participate in the proving network. This democratization aligns with the goals of networks like Boundless, allowing a broader range of participants to mine ZKC and provide redundancy to the network. The cost efficiency—$128k for a cluster capable of real-time proving versus nearly double that for previous generations—lowers the barrier to entry for independent node operators.
The Rise of ZK SoCs: ZPN Chain
Conversely, ZPN Chain represents the push for extreme specialization. In late 2025, ZPN claimed to deploy the first ZKP System-on-Chip (SoC), a dedicated silicon chip optimized solely for Zero-Knowledge operations.
ZPN asserts its custom silicon can reduce proof verification time from 75 minutes (on a standard GPU) to just 13 seconds. While such speed is transformative, industry observers note that this trend risks re-creating the centralization vectors seen in Bitcoin ASIC mining. If only a few manufacturers control the production and distribution of efficient ZK SoCs, the decentralized proving market could become an oligopoly, undermining the censorship resistance of the network. ZPN is positioning itself as a privacy-focused Layer 1, utilizing these chips to support Real-World Asset (RWA) trading and data traceability with instant privacy, backed by foundations in the US, UK, and Singapore.
The Geopolitics of Trust: The "DeepSeek" Crisis
The shift in 2025 was not just about supply (better provers) but demand. The "zkML Singularity" was catalyzed by a crisis in AI trust, specifically triggered by the "DeepSeek" event.
The "DeepSeek" Catalyst and Security Risks
The release of DeepSeek, a powerful open-source model from China, without the safety guardrails common in Western models, acted as a forcing function for the industry. DeepSeek’s capabilities allowed for the automated generation of sophisticated phishing campaigns, ransomware, and malware, bypassing the ethical filters present in models like GPT-4 or Claude.
Security researchers at Palo Alto Networks (Unit 42) discovered that DeepSeek could be easily "jailbroken" using techniques like "Deceptive Delight" and "Bad Likert Judge," allowing it to generate instructions for incendiary devices or keyloggers. The digital ecosystem was subsequently flooded with AI agents that were indistinguishable from humans or trusted bots but were executing malicious logic.
zkML as "Proof of Inference"
This crisis necessitated the adoption of "Proof of Inference." Applications began using zkML to cryptographically prove that a specific response came from a specific, safe model (e.g., a verified, safety-aligned Llama-3 instance) and not a malicious DeepSeek fork. zkML became the "digital passport" for safe AI interaction.
In this paradigm, an AI agent must present a ZK proof alongside its output, certifying that the output was generated by a specific model weights hash. If the proof is valid, the user knows the model adheres to known safety standards; if the proof is missing or invalid, the agent is treated as potentially hostile.
Applications: From Novelty to Necessity
As the technology matured, applications moved from experimental "toys" to critical infrastructure in defense, finance, and healthcare.
Defense and Autonomous Systems: Auditable Warfare
Lagrange Labs announced a landmark integration with Anduril, a defense technology company. By embedding DeepProve into the Lattice SDK, Anduril enabled autonomous defense systems (such as drones and surveillance towers) to generate cryptographic proofs of their decision-making processes.
This capability introduces "Tactical Auditing." A drone can now prove,
"I engaged this target because the visual data matched Threat Profile X with 99% confidence,"
without transmitting the raw, bandwidth-heavy video feed or revealing the classified neural network weights to the open network. This allows for real-time accountability in Lethal Autonomous Weapons Systems (LAWS), a critical requirement for military compliance and international humanitarian law. The proof ensures that the AI functioned within its Rules of Engagement (ROE) without requiring a human to manually review every frame of video.
Financial Compliance and "Trustless Agents"
In the financial sector, zkML is enabling the concept of "Trustless Agents" capable of programmable money. Standards like ERC-8004 are facilitating agent-to-agent payments, where an AI agent can buy data, run an inference, and settle payment without human intervention.
Furthermore, zkML allows for privacy-preserving compliance. Financial institutions are using the technology to prove they have performed Anti-Money Laundering (AML) checks on a user's transaction history without revealing the user's identity or the specific transaction details to the public chain. This solves the "privacy vs. compliance" deadlock that has plagued institutional DeFi adoption.
Healthcare and Diagnostics
The ability to run ML inference on private data without exposing that data is unlocking healthcare applications. zkML allows a model to process patient data (e.g., an MRI scan) locally and return a diagnosis along with a proof of correctness. This ensures the patient's data never leaves their local enclave (preserving HIPAA/GDPR compliance) while proving that the diagnosis was generated by a certified medical AI model, not a random number generator.
Regulatory and Future Outlook
Regulatory Engagement and Sandbox Testing
The regulatory landscape is adapting rapidly. The SEC has begun engaging with these technologies, with Lagrange Labs participating in an SEC sandbox to demonstrate how DeepProve can be used for investor protection. The objective is to prove that a financial advisor (whether AI or human) acted within specific risk limits and fiduciary mandates without requiring the SEC to constantly inspect the firm's proprietary trading data. This points toward a future where "Algorithmic Auditing" becomes a standard regulatory requirement for any AI deployed in finance.
The Road to 2026: Bridging the Gap
Despite the singularity, challenges remain.
Cost vs. Value: While proof costs have dropped to ~$0.02 for some tasks , proving a massive LLM token-by-token is still more expensive than standard inference. The industry is likely to move toward "Optimistic zkML," where proofs are only generated when a result is challenged, or "High-Value Inference," where only critical decisions (like authorizing a payment) are proven.
Hardware Centralization: The tension between the decentralized ethos of Boundless (relying on consumer GPUs) and the raw speed of ZPN's ASICs will define the market dynamics of 2026. If ASICs dominate, the proving layer may become centralized around a few fabrication foundries.
Conclusion
The zkML Singularity of late 2025 was not a single invention but a convergence of cryptographic optimization, hardware acceleration, and geopolitical necessity. The ability to compress the intelligence of a Neural Network into a succinct cryptographic proof (DeepProve), combined with the ability to verify that proof instantly on a blockchain (Pico Prism/zkVerify), has created the substrate for a new digital economy. We have moved from the era of "Trust, but verify" to "Verify, then trust." As AI agents begin to manage significant capital and make critical decisions in defense and healthcare, the cryptographic guarantees provided by this new infrastructure are no longer optional—they are the prerequisite for the continued scaling of artificial intelligence.
Originally published on: academy.extropy.io
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