Overview

Lagrange is a leader in zero-knowledge proof generation for safe and private AI. Its flagship product, DeepProve, is the fastest zkML system available, enabling AI verification through zero-knowledge proofs. Lagrange also builds a decentralized ZK Prover Network and an SQL-based ZK Coprocessor. The Prover Network enables secure, low-cost proof generation for ZK rollups, operated by major validators like Coinbase Cloud and Kraken. The ZK Coprocessor allows smart contracts to offload complex, data-heavy computations and verify them onchain.

Lagrange’s partnerships with industry leaders like Nvidia, Intel, Matter Labs (ZKsync), Mira Network, Lit Protocol, Caldera, AltLayer, Arbitrum, OpenGradient, Polygon, LayerZero, and EigenLayer underscore its cutting edge leadership at the intersection of zero-knowledge technology and AI verification.

Lagrange builds three core products: DeepProve (a zkML system), a decentralized Prover Network and a ZK Coprocessor.

• DeepProve—a zero-knowledge machine learning (zkML) inference framework built—proves neural network inferences with cryptographic proofs. The system allows someone to prove that “the output Y came from running the model on input X,” all the while keeping the model’s weights protected, bringing verifiability and privacy to AI models everywhere.

• Lagrange ZK Prover Network powers proof generation for ZK rollups and for Lagrange’s ZK Coprocessor. Lagrange launched the first production-ready ZK prover network in the industry, operated by top operators including Coinbase, Kraken, OKX and more. Now, Lagrange’s ZK Prover Network is expanding to address key challenges faced by rollups and advance ZK adoption and utility. Decentralized proving enables rollup ecosystem to operate with higher liveness guarantees, more security and lower cost.

• Lagrange’s SQL-based ZK Coprocessor, an infrastructure that enables DeFi protocols to verifiably compute over historical onchain storage, receipt and transaction state. Rather than being constrained by gas limits, smart contracts can directly request proofs of complex data-heavy computations and then verify the results asynchronously back onchain. Examples of use cases built with Lagrange’s ZK Coprocessor include, complex liquidity-mining incentive program, volume-based trading discounts on DEXs and funding rate calculations for options or perps protocols.

LA Token Utility

$LA is the fuel for Lagrange’s cryptographic engine. It is a utility token that aligns the interests of clients, provers, and token holders for decentralized proving activities in the Lagrange Prover Network that are essential for use cases like DeepProve. The $LA token is primarily used by clients to pay for proof generation fees, but also plays a role in subsidizing the costs of provers while allowing token holders to stake and delegate. Lagrange’s tokenomics are built around a simple principle: proof demand = token demand.

The $LA token can be staked into the Lagrange Prover Network to determine the eligibility of provers to generate proofs. Provers within the network independently bid in an auction to produce proofs within a specified timeframe and stake $LA tokens as collateral to guarantee liveness. If a Prover fails to deliver a proof on time, they face penalties, incentivizing them to meet their commitments and ensuring the network’s reliability.

Therefore, each Prover maintains an incentive to behave honestly and faces penalties if it behaves maliciously or fails to guarantee liveness. The fees associated with the generation of those proofs accrue back to Provers and $LA token stakers. Therefore, as more proofs are generated on the network, the rewards for staking $LA increase.